Risk management and market efficiency on the Midwest …/67531/metadc103339/... · Jones, Kevin. Risk management and market efficiency on the Midwest Independent System Operator electricity

APPROVED: Imre Karafiáth, Major Professor Rusty. MacDonald, Committee Member Steven Cole, Committee Member Margie Tieslau, Committee Member Marcia Staff, Chair of the Department of

Finance, Insurance, Real Estate and Law

James D. Meernik, Acting Dean of the Toulouse Graduate School

RISK MANAGEMENT AND MARKET EFFICIENCY ON THE MIDWEST INDEPENDENT SYSTEM

OPERATOR ELECTRICITY EXCHANGE

Kevin Jones, B.S., M.B.A

Dissertation Prepared for the Degree of

DOCTOR OF PHILOSOPHY

UNIVERSITY OF NORTH TEXAS

December 2011

Jones, Kevin. Risk management and market efficiency on the Midwest Independent

System Operator electricity exchange. Doctor of Philosophy (Finance), December 2011, 350 pp.,

235 tables, 1 figure, references, 70 titles.

Midwest Independent Transmission System Operator, Inc. (MISO) is a non-profit

regional transmission organization (RTO) that oversees electricity production and transmission

across thirteen states and one Canadian province. MISO also operates an electronic exchange

for buying and selling electricity for each of its five regional hubs.

MISO oversees two types of markets. The forward market, which is referred to as the

day-ahead (DA) market, allows market participants to place demand bids and supply offers on

electricity to be delivered at a specified hour the following day. The equilibrium price, known

as the locational marginal price (LMP), is determined by MISO after receiving sale offers and

purchase bids from market participants. MISO also coordinates a spot market, which is known

as the real-time (RT) market. Traders in the real-time market must submit bids and offers by

thirty minutes prior to the hour for which the trade will be executed. After receiving purchase

and sale offers for a given hour in the real time market, MISO then determines the LMP for that

particular hour.

The existence of the DA and RT markets allows producers and retailers to hedge against

the large fluctuations that are common in electricity prices. Hedge ratios on the MISO

exchange are estimated using various techniques. No hedge ratio technique examined

consistently outperforms the unhedged portfolio in terms of variance reduction. Consequently,

none of the hedge ratio methods in this study meet the general interpretation of FASB

guidelines for a highly effective hedge.

One of the major goals of deregulation is to bring about competition and increased

efficiency in electricity markets. Previous research suggests that electricity exchanges may not

be weak-form market efficient. A simple moving average trading rule is found to produce

statistically and economically significant profits on the MISO exchange. This could call the long-

term survivability of the MISO exchange into question.

ii

Copyright 2011

by

Kevin Jones

iii

ACKNOWLEDGEMENTS

I would like to take this opportunity to thank my committee chair, Dr. Imre Karafiath, for

his insight and dedication. His assistance has been invaluable during this endeavor. I am also

extremely grateful for Dr. Rusty MacDonald’s efforts. Dr. MacDonald’s guidance made this

dissertation possible. I also want to express my appreciation for the assistance I received from

Dr. Steve Cole and Dr. Margie Tieslau. I would also like to thank my wife for her patience and

understanding throughout this process.

iv

TABLE OF CONTENTS

Page ACKNOWLEDGEMENT ..................................................................................................................... iii Chapters 1. INTRODUCTION ........................................................................................................................... 1

2. LITERATURE REVIEW ................................................................................................................... 7

Unique Characteristics of Electricity Prices

Hedge Ratio Estimation

Relationship between Spot and Forward Electricity Prices

Inefficiencies in Deregulated Electricity Markets

Prior Research on the MISO Exchange

Hypotheses

3. DATA AND METHODOLOGY ...................................................................................................... 26

Sample

Stationarity

Forward Premia/Discounts

Hedge Ratio Methodology

Hedge Ratio Effectiveness

Tests of Market Efficiency

4. RESULTS ..................................................................................................................................... 35

Summary Statistics

Forward Premia

v

MV and GARCH(1,1) Hedge Ratio Estimates

ARDL(1,1) and MGA Hedge Ratio Estimates


Trading Rule Results

5. CONCLUSION ............................................................................................................................. 43

APPENDIX: DATA TABLES .............................................................................................................. 45

REFERENCES ................................................................................................................................ 345

1

CHAPTER 1

INTRODUCTION

Historically, US electricity markets were dominated by vertically integrated

organizations that generated and transmitted electricity to local retailers and end-users. These

organizations were essentially treated as natural monopolies by the government. As such,

several laws were passed to limit the geographical scope and financial structure of these

companies.

Electricity markets in the United States have undergone major changes in the past

twenty years. In particular, the federal government shifted toward a policy of less regulation in

the US electricity industry. To this end, several laws were passed in the 1990s that were

designed to increase competition in electricity markets.

The Energy Policy Act of 1992 gave the Federal Energy Regulatory Committee (FERC)

authority to force transmissions owners to provide service to generator owners on a case by

case basis (H.R.776.ENR). FERC order 888 attempted to make the country’s transmission

systems more accessible to electricity suppliers by establishing what is known as the open

access rule. FERC order 888 (1996) stipulates that “all public utilities that own, control, or

operate facilities used for transmitting electric energy in interstate commerce to have on file

open access non-discriminatory transmission tariffs that contain minimum terms and conditions

of non-discriminatory service.” FERC order 889 (1996) created the Open Access Same-Time

Information System (OASIS). OASIS is an electronic system that provides information about

transmission capacity and transmission price for wholesale electricity.

2

The federal government, through FERC orders 888 and 889, has increased competition

in the wholesale electricity by making transmission lines accessible to all electricity producers.

As Banjeree and Noe (2006) point out, retail prices for electricity are still highly regulated.

Because of this, the US electricity industry may best be described as partially deregulated.

FERC orders 888 and 889 led to the establishment of several regional transmission

organizations (RTOs). RTOs are responsible for coordinating the flow of electricity across state

lines. In December 2001, Midwest Independent Transmission System Operator, Inc. (MISO)

became the first nation’s first RTO. Midwest ISO is a non-profit, member based organization

that manages electricity transmission across thirteen states and one Canadian province. Figure

1 shows the geographical footprint of the two major RTOs in America; MISO and the

Pennsylvania, New Jersey, and Maryland (PJM) Interconnection.

Figure 1. MISO and PJM Coverage Areas. Reprinted from Midwest ISO Fact Sheet (2009).

3

The MISO coverage area is broken into five regional hubs: Cinergy, First Energy (FE), Illinois (IL),

Michigan (MI), and Minnesota (MN). Collectively, these five hubs have a generating capacity of

over 138,000 megawatts and serve over 40 million people (MISO 2009C).

MISO created an electronic marketplace for trading electricity contracts after obtaining

approval from FERC in April 2005. Midwest ISO matches buyers and sellers of electricity and

determines market clearing prices for each of its five regional hubs. The market clearing price is

referred to as the locational marginal price (LMP). Locational marginal prices are quoted in

terms of dollars per megawatt hour ($/MWh) and represent the cost of supplying the last

incremental amount of energy at a particular node on the MISO grid (Midwest ISO 2009B). Each

hub is treated as its own, independent exchange, since location, congestion, and transmission

losses vary across regions and have a large impact on the equilibrium price for electricity.

Those who wish to place sale offers or purchase bids on the MISO exchange must be a

registered market participant (MP). Market participants are classified into at least one of the

following four categories (Midwest ISO 2009B). Transmission owners (TOs) are entities that

either own or lease facilities used in the interstate transmission of electricity. Generation

owners (GOs) own or lease generation facilities located within the MISO coverage area. Load

serving entities (LSEs) are parties that take transmission service on behalf of wholesale or retail

power customers and are obligated to provide energy for end-use customers. The final

category, known as other marketing entities (OMEs), consists of parties that do not have

ownership rights to transmission nor generating facilities within the MISO footprint. MISO

reports that there are 300 market participants on the MISO exchange (Midwest ISO 2009C).

4

MISO oversees both a spot and forward market for electricity that operates 24 hours a

day, 7 days a week. The spot market is known as the real-time (RT) market. Market

participants that trade in the real-time market must submit bids and offers by thirty minutes

prior to the hour for which the trade will be executed (Midwest ISO 2009B). After receiving

purchase and sale offers for a given hour in the real time market, MISO then determines the

equilibrium price (LMP) for that particular hour. Each of the five regional hubs has 24 distinct

real-time LMPs, one for each hour of the day. Thus, MISO announces 120 RT locational

marginal prices each day.

The forward market for electricity is referred to as the day-ahead (DA) market. Market

participants place demand bids and supply offers on electricity to be delivered at a specified

hour the following day. Bids and offers must be received by 1100 EST on the day prior to

delivery (Midwest ISO 2009B). Day-ahead prices are posted for all five hubs by 1600 EST on the

day prior to delivery. Demand in excess of the megawatt hours contracted for in the day-ahead

market is filled at the real-time LMP for any given hour. In other words, market participants

that underestimate demand when placing a bid in the day-ahead market for a specified hour

must purchase electricity in the real-time market the next day at that given hour. Conversely,

market participants who overestimate demand for electricity for a specific hour in the day-

ahead market will become sellers at the real-time LMP on that specific hour the following day.

Midwest ISO has a minimum of four settlement dates for daily transactions on both the

real-time and day-ahead markets. The first settlement date occurs 7 days (S7) after the given

operating day. Subsequent settlement dates occur 14 (S14), 55 (S55), and 105 (S105) days after

a particular operating day (Midwest ISO 2009B). The S55 and S105 settlement dates are

5

primarily used to account for updated meter information that becomes available after the S14

settlement date. MISO utilizes additional settlement dates for DA and RT transactions if

necessary. According to MISO (Midwest ISO 2009B), differences in settlement data typically

consist of updated meter information. Market participants are required to review the S7

statement and notify MISO of any discrepancies prior to the S14 statement issuance. Invoices

for daily transactions on the real-time and day-ahead markets are not sent to market

participants until S7 and S14 statements have been issued. Invoices are sent out on a weekly

basis. Market participants have seven days from the invoice date to make payments with

immediately available funds. MISO makes payments to market participants with a positive

balance within 48 hours of the invoice date.

Trading on the MISO exchange began in the fall of 2005. Since the exchange is relatively

new, there is little research that examines the efficiency of locational marginal prices used on

the MISO exchange. Borenstein, Bushnell, Knittel, and Wolfram (2001) find that using past

information led to statistically and economically significant profits on a California electricity

exchange similar to MISO. The authors conclude that an inefficient pricing mechanism

contributed to the demise of that exchange. Basic weak-form tests of the locational marginal

prices generated by MISO may provide insight into the long-term viability of the exchange.

Large seasonal and intra-day price fluctuations are characteristic of electricity prices.

Organized electricity exchanges may provide a means for electricity producers and wholesalers

to mitigate their price risk. The ability to construct a hedge that is deemed highly effective by

FASB standards may have an impact on the variability of earnings statements of MISO market

6

participants. This study examines the effectiveness of several different hedge ratio estimation

techniques.

The dissertation is structured as follows. A review of the relevant literature and

hypotheses are discussed in Chapter 2. Methodology and data are discussed in Chapter 3.

Chapter 4 explains the results and Chapter 5 provides a summary.

7

CHAPTER 2

LITERATURE REVIEW and HYPOTHESES

Unique Characteristics of Electricity Prices

Electricity prices possess several unique characteristics that are discussed in previous

research. Perhaps the most notable aspect of electricity markets is that prices often fall well

below zero. Several theories exist as to why this occurs. Knittel and Roberts (2005), De Jong

and Sewalt (2007) and Genoese, Genoese and Wietschel (2010), believe excess supply of

electricity is the main cause for this phenomenon. Government regulations, coupled with large

start-up costs, make it difficult for power companies to shut down production when demand is

low (Knittel and Roberts 2005). Since this excess supply is essentially non-storable1, electricity

must be passed to wholesalers at a loss. These negative prices actually represent power

suppliers paying wholesalers to take energy off the grid.

Negative electricity prices are also linked to the use of wind power to generate

electricity. Government subsidies of wind farms increase the probability of grounding the grid

at certain hours. Negative prices therefore may represent a disposal fee. Giberson (2008)

attributes the prevalence of negative prices in the western region of the Electricity Reliability

Council of Texas (ERCOT) in part to government subsidies given to West Texas wind farms.

Although wind turbines are more common in Texas and California, several wind farms are

present in the MISO footprint. It is difficult to measure the impact that wind power has on

locational marginal prices, as MISO does not provide information on how electricity is

1 Methods to store large amounts of electricity, such as geographical storage and hydroelectricity storage, have been in existence for several years. These storage techniques, however, are rarely used due to their high start-up and maintenance costs.

8

generated within its regional hubs. Huisman, Huurman and Mahieu (2007), as well as many

others, attribute all of these characteristics to the non-storability and short term price

inelasticity of electricity. Since electricity is not easily stored, market participants cannot use an

inventory system to meet supply and demand when prices rise. Both demand and supply in

electricity markets may be inelastic. Demand for electricity is often inelastic in winter and

summer months. The amount of electricity that can be transmitted through a system such as

MISO’s is limited to the generating capacity of its market participants. When demand is high

(as in the summer and winter months), the equilibrium price will also rise, but electricity

production is limited to the generating capacity on the grid. While production capabilities can

be increased in the long run by building more generators, the supply of electricity is inelastic in

the short term. The skewness and high variance of electricity prices poses problems for both

electricity retailers and producers as these characteristics can make earnings for both groups

volatile. Bessembinder and Lemmon (2002) develop a model for forward premiums and

discounts based on the expected variance and skewness of spot electricity prices.

Hedge Ratio Estimation

One of the most basic methods to mitigate price risk in the spot market for a commodity

is to construct a naïve hedge. The naïve hedge ratio assumes that the hedger offsets their long

(short) position in the spot market by shorting (buying) an equal position in the forward market.

Thus, the naïve hedge (number of units held long divided by the units in the short position) is

one. The naïve hedging strategy is a perfect hedge against price risk only if the spot and

forward price movements are identical. Since this is typically not the case, more advanced

hedging strategies should also be analyzed.

9

Johnson (1960) and Ederington (1979) propose one of the most widely used hedging

strategies to date.

The one-period, percentage returns to a hedged portfolio ( ) may be described as follows:

(1.) - .

and represent one-period percentage changes in spot and forward prices, respectively.

The hedge ratio, h, is the number of forward contracts sold to hedge against the price risk of

one unit of the spot asset. Setting h equal to one represents the naïve hedging strategy. The

variance of the hedged portfolio is:

(2.)

-

and

denote the variance of the spot and futures returns, respectively. The optimal

hedging strategy, according to Johnson, is to minimize (2). The minimum variance hedge ratio,

h*, is the covariance of spot and futures prices divided by the variance of the futures price:

(3.)

One of the reasons that the minimum variance (MV) hedge ratio remains popular over

fifty years after its publication is that it can be estimated rather easily. The minimum variance

hedge can be obtained via the OLS regression of spot market returns on forward market

returns.

(4.)

Equation (4) is a linear model that may be estimated by ordinary least squares (OLS) regression

to obtain a minimum variance hedge ratio based on price changes. and represent one-

period price changes in spot and forward prices, while is the estimate for the minimum

variance hedge ratio. MV hedge ratios are also estimated using price levels in this study.

10

Several authors (Cecchetti, Cumby & Figlewski 1988, Hsin, Kuo & Lee 1994) estimate

hedge ratios based on expected utility maximization. These measures rely on the assumptions

that the joint distribution of spot and futures returns is normal and investor utility functions are

known. A certainty equivalent method is then used to measure the effectiveness of the hedge.

Although this hedging procedure incorporates risk and return as well as utility of wealth

maximization, the joint distribution of spot and forward electricity returns in other electricity

markets have been shown to not be bivariate normal (Knittel & Roberts 2005). This makes it

difficult to justify using hedge ratio estimation techniques that maximize expected utility in

electricity markets.

Other mean-variance hedge ratios created by Howard and D’Antonio (1984) and Chang

and Shanker (1986) rely on maximizing the Sharpe index. Chen, Lee and Shrestha (2001) state

that these hedge ratios and their effectiveness measures are seldom used due to the fact that

the Sharpe index is a non-linear function of the hedge ratio. Chen, Lee and Shrestha (2001)

provide an example of a hedge that minimizes instead of maximizes the Sharpe ratio.

Mean-variance and minimum variance hedge ratios assume that investors have a

symmetric attitude toward risk. Several studies (Kahneman & Tversky 1979, Adams & Montesi

1995, Benartzi & Thaler 1995) suggest that investors are more sensitive to losses than gains. If

investors assign more weight to potential losses in their decision making, hedge ratios should

be constructed and evaluated based on asymmetric risk measures.

One common risk measure in the loss aversion literature is the lower partial moment

(LPM). Following Fishburn (1977) and Lien and Tse (2002), let R denote a random return for a

11

given portfolio and C represent the target rate of return. If F is the distribution function of R,

then the nth order lower partial moment of R is (Fishburn 1977, Lien & Tse 2002):

(5.) ∫ ( - )

- ( )

Some important caveats should be mentioned about this risk measure. Calculating LPM

requires the practitioner to estimate the joint distribution of returns and assign an attitude

toward risk (n) associated with falling below C (Fishburn 1977, Lien & Tse 2002). Large n values

are associated with investors placing great importance on the size of the shortfall (Fishburn

1977, Lien & Tse 2002).

Even if the distribution of returns can be estimated and risk tolerances can be

quantified, there is no analytic expression for minimizing LPM subject to C (Fishburn 1977, Lien

& Tse 2002). Other asymmetric risk estimates (Gul 1991, Kang, Brorsen & Adam 1996, Grant &

Kajii 1998) also rely on the ability to identify utility functions and risk tolerances, which limits

the practical use of these measures.

The naïve and minimum variance hedging strategies assume that the variance of

equation (4), and thus the optimal hedge ratio, is time-invariant. If the OLS regression of spot

prices on forward prices displays heteroskedasticity, the resulting hedge ratio estimates will be

inefficient. OLS estimates of MISO hedge ratios may be inefficient and biased given the price

spikes and seasonality of electricity prices. Dynamic hedging strategies allow for hedge ratios

to change over time to incorporate new information that occurs during the hedging period.

If the relationship between spot and forward returns changes over time, investors will

be concerned with minimizing risk conditional on currently available information. The

generalized autoregressive conditional heteroskedasticity (GARCH) methodology developed by

12

Bollerslev (1986) provides a way to model conditional variance and estimate optimal hedge

ratios that are allowed to fluctuate with newly available information.

GARCH (p,q) models are widely used to forecast variance conditional on past

information. These models parameterize past information about volatility and forecast

variance so that their weights can be estimated. GARCH models comprise two equations: one

for the mean of the variable under investigation and one for the conditional variance. The

ARCH term “p” indicates the number of lagged squared error terms to include in the conditional

variance equation, and the GARCH term “q” indicates the number of lagged conditional

variance terms to include in the conditional variance equation.

The simplest GARCH model to employ is GARCH (1,1). Bollerslev (1986) notes that

GARCH models are only conditionally heteroskedastic, unconditional variance is constant and

the model is mean-reverting. The mean equation of interest here is the relationship between

spot and forward returns:

(6.) Bollerslev (1986) assumes the error term of equation (6) fluctuates based on information

obtained in the previous period. Specifically, Bollerslev (1986) describes the error term of (6)

as follows:

(7.) - ( )

(8.) -

- .

Bollerslev (1986) assumes the conditional variance, t t-1, is normally distributed and

may be modeled as an autoregressive moving average (ARMA) process. reflects the long run

13

average variance. t-1 (GARCH term) represents the previous period’s forecast variance and

t-1 (ARCH term) reflects information regarding volatility obtained in the previous period. The

optimal hedge ratio, t, minimizes the conditional variance of the hedge portfolio. The iterative

process described by Bollerslev (1986), which uses maximum likelihood estimation (MLE), may

be utilized to estimate this model in both levels and in first differences. This study will

estimate GARCH(1,1) hedge ratios using price differences.

The autoregressive distributed lag (ARDL) model described by Pesaran (1997) and Chen,

Lee and Shrestha (2004) may also be used to estimate hedge ratios. Unlike the naïve, minimum

variance, or GARCH approach, ARDL(p,r) models provide estimates of both the long-run and

short-run relationship between spot and forward prices. While the error correction model

(ECM), as described by Engle and Granger (1987), can also provide long-term and short-term

relationships between spot and futures prices, it rests on the assumption that spot and forward

prices are non-stationary (a discussion on stationarity is provided in chapter 3). Christensen,

Hurn, and Lindsay (2009) among others, find that both spot and forward prices in electricity

markets are stationary. The ARDL model, however, can still be estimated if both price series

fluctuate about a long-term mean. The p term represents the order of the autoregressive

component of the model, while the r term is the distributed lag component. The ARDL(1,1)

model can be written as follows:

(9.) - -

The short-run hedge ratio is represented by and -

is the long-run hedge ratio

estimate. As with the minimum variance hedge ratio, the ARDL model may be estimated with

14

OLS. The assumption of constant variance can be relaxed by using MLE to fit the ARDL model

with a GARCH error process.

Dimson (1979), Cohen, Hawawini, Mayer, Schwartz, and Whitcomb (1983) and Luoma,

Martikainen, and Perttunen (1993), note that OLS beta coefficients will be biased downward if

the spot security is thinly traded. This bias, known as temporal aggregation bias, occurs

because the information that heavily traded and thinly traded securities reveals is different.

Finance theory suggests that the current price of a security should be the present value

of all its future cash flows. In order for this theory to hold, any new information about future

cash flows must be quickly incorporated into current prices. For heavily traded securities, this is

typically a reasonable assumption. If a security is thinly traded, there may be a delay between

when information is gathered and when prices in the market are set. In other words, the price

of a thinly traded security may reflect current expectations about future cash flows and

aggregated information that occurred since the last trade. This discrepancy between

information sets reflected in thinly and heavily traded security prices will tend to underestimate

the covariance of the thinly traded security with the more heavily traded asset (Dimson 1979).

Since OLS hedge ratio estimates are the ratio of covariance between spot and forward prices to

the variance of the forward prices, hedge ratios for thinly traded securities will be biased

downward due to temporal aggregation bias.

Luoma et al (1993) use the ARDL model to estimate the systematic risk of thinly traded

securities in Finland. They find that the beta coefficients obtained using the ARDL model are

robust to temporal aggregation bias. As Pesaran (1997) notes, the ARDL model is more general

than the error correction model since the ARDL model does not rely on the assumption that a

15

cointegration relationship exists between the independent and dependent variables. Chen, Lee

and Shrestha (2004) utilize the ARDL model to estimate hedge ratios in the futures market of

several commodities.2 The ARDL model will be used in this study to estimate hedge ratios since

electricity spot and forward prices have been reported not to be cointegrated (Christensen,

Hurn, & Lindsay 2009) and to account for the possibility of temporal aggregation bias.

The method of group averages (MGA), as described by Greene (2000), is robust to both

thin trading, outliers, and temporal aggregation bias. Large price spikes are typical in electricity

markets. As such, hedge ratios estimated via OLS may be biased. The method of group

averages overcomes this problem by essentially fitting a line between two subsamples: one

consisting of independent variable values (forward prices) that fall below the median and

another consisting of independent variable values that fall above the median. OLS slope

coefficients will be similar to those obtained from the method of grouped averages if the OLS

betas are not greatly influenced by outliers. MGA hedge ratio estimates are calculated using

price levels and differences in this study.

The Relationship between Spot and Forward Electricity Prices

Understanding the relationship between spot prices and forward prices on the MISO

exchange is complicated by the fact that electricity is not easily stored. Therefore, the cost-of-

carry models proposed by several authors (Kaldor 1939, Working 1948, Brennan 1958) that rely

on the ability of an investor to create a synthetic forward contract by taking a long position in

the spot market and selling the asset at the desired expiration date do not apply to electricity

contracts (Bessembinder & Lemmon 2002, Longstaff & Wang 2004). Instead of using cost-of-

2 Equation (11) in Chen, Lee and Shrestha (2004) is the ARDL(1,1) model.

16

carry models, the relationship between electricity day-ahead and real-time prices may be

evaluated by examining equilibrium compensation for risk. From this perspective, the

difference between forward prices and expected future spot prices (the forward premium)

represents the price risk of the underlying asset (Longstaff and Wang 2004).

Keynes (1930) popularizes the theory that hedging pressure from suppliers will cause

the forward price to typically be below the expected future spot price. Suppliers of

commodities are naturally long in the spot price of the commodity that they produce. Keynes

theorizes that most suppliers desire to reduce price risk. In Keynes’ view, suppliers, all of whom

have the same expectations about future spot prices, must trade forward contracts with

speculators in order to reduce price risk. Keynes’ theory suggests that the forward rate will

then be bid down to a point that is below the expected future spot rate in order to entice

speculators to buy them. Normal backwardation is the term used to describe a situation where

the forward price is below the expected future spot price. A normal contango relationship

exists when the forward price is above the expected future spot price.

If Keynes’ theory of normal backwardation is correct, speculators should, on average,

earn positive returns at the expense of hedgers. Empirical tests of normal backwardation have

produced mixed results. Hartzmark (1987) examines whether the theory of normal

backwardation holds for large traders in commodity futures. Hartzmark (1987) defines large

non-commercial traders of commodity futures as speculators and large commercial traders of

commodity futures as hedgers. The author finds that hedgers, not speculators, typically earn

positive returns. This finding contradicts the theory of normal backwardation. Kolb (1992) also

finds little evidence of normal backwardation in commodity futures. However, Hakkio and Rush

17

(1989) and Krehbiel and Adkins (1993) have found evidence of normal backwardation in

currency and precious metal futures.

Bessembinder and Lemmon (2002) published one of the first comprehensive models for

deregulated electricity prices. The authors focus on the determinants of forward premiums and

forward discounts in electricity. They suggest that forward premiums and discounts are a

function of expected variance and skewness of wholesale electricity spot prices. Wholesale

spot price skewness increases the chance that electricity retailers will experience spikes in their

production costs. This increase in the probability of production cost spikes entices retailers to

buy day-ahead forward contracts, which in turn, would increase day-ahead prices and forward

premiums. Large variances in spot prices represent price risk in delivering energy to electricity

retailers. In order to hedge against this price risk, electricity producers would sell forward

contracts. This selling pressure may cause the forward price to fall below the expected future

spot price. The authors find that their model is consistent with forward premiums and

discounts observed on the PJM market.

Shawky, Marathe, and Barrett (2003) estimate hedge ratios and forward premiums for

wholesale electricity futures for delivery on the California-Oregon border. The authors find that

risk premiums are typically positive and much higher than those reported in other

commodities. Hedge ratios are estimated via exponential GARCH and also found to be higher

than other commodities. Unlike most studies of electricity markets, the authors report low

levels of autocorrelation in both the futures and spot prices. The authors use this finding as

support for the efficiency of this particular market.

18

Bystrom (2003) examines the Nordic Power Exchange (Nord Pool), one of the oldest and

largest electricity exchanges in the world. Nord Pool is similar to the MISO exchange in terms of

structure, but covers a larger geographic area, and has more market participants. Bystrom

estimates short-term static and dynamic hedge ratios and evaluates their performance. The

two dynamic hedge ratios Bystrom uses are bivariate GARCH, and orthogonal GARCH. These

dynamic hedging strategies are compared to minimum variance and naïve hedge ratio

estimates. The author finds that although electricity prices are heteroskedastic, the minimum

variance hedge ratio outperforms both GARCH hedge ratio estimates in terms of variance

reduction.

Bessembinder and Lemmon (2002) define the forward premium for the PJM

Interconnection and California Power Exchange as:

(10.) - .

represents the forward price for delivery of electricity for month t in market i. is the

cost-based estimate of the spot price for electricity for month t in market i. The authors obtain

by developing a theoretical model for spot electricity prices. Longstaff and Wang (2004)

also define the theoretical forward premium as equation (10). Longstaff and Wang (2004)

examine forward premiums on the PJM exchange by calculating average realized forward

premia, which they define as:

(11.)

∑ -

represents the average one day forward premium (discount) for hour i on the PJM eastern

hub. Equation (11) is an unbiased estimate of the theoretical forward premium if expectations

19

are unbiased. Shawky et al (2003) estimate daily futures premiums on the New York Mercantile

Exchange using the following equation:

(12.) - .

Ft and St represent the futures price and spot price for day t, respectively. Shawky et al (2003)

then synchronize the start and end dates of each futures contract in their study in order to

track the average futures premium over time. Bessembinder and Lemmon (2002), Shawky at el

(2003) as well as Longstaff and Wang (2004) find that positive forward premiums exist in

electricity markets, which is incongruent with the Keynesian theory of normal backwardation.

Inefficiencies in Deregulated Electricity Markets

In theory, the prices of fuel oil, natural gas, and electricity should be related for a couple

of reasons. The power generated from fuel oil, electricity, and natural gas can be measured in

the same basis, British thermal units (BTUs). Since all three forms of energy produce the same

output (BTUs), a long-term relationship should exist between the prices for all three.

Furthermore, oil and gas are often used as substitutes in the production of energy and

electricity is often generated using natural gas.

Serletis and Herbert (1999) examine the price relationship between natural gas, fuel oil,

and electricity in the eastern United States. The authors first examine the correlations between

the three price series and find that natural gas and fuel oil are highly correlated, but neither

have a high correlation with electricity prices. Serletis and Herbert also report that electricity

prices are mean-reverting, while fuel oil and natural gas are not. This implies that price shocks

have a long impact on fuel oil and natural gas prices as compared to electricity prices. The

20

authors suggest that the disconnect between electricity prices and prices from the other two

forms of energy may allow for arbitrage profits.

Banerjee and Noe (2006) argue that many of the inefficiencies and unique pricing

characteristics found in electricity prices are due to the fact that electricity markets are only

partially deregulated. The authors note that while electricity exchanges themselves may be

deregulated, utility companies that trade on these markets are not. Utility companies act as

intermediates between power generation companies and end-use customers. The price that

utility companies may charge to end-users is still highly regulated. This puts the average utility

company in a serious bind, as they have little control of their cost or revenue structure. As a

result, the authors state that no optimal hedging position for utility companies can be obtained

by only using forward contracts.

Borenstein, Bushnell, Knittel, and Wolfram (2001) examine an electricity exchange in

California after its collapse. The authors report that a sustained decoupling of forward and spot

prices is the main reason that the market failed. Borenstein et al (2001) state that the learning

curve on the part of market participants, along with intense selling pressure from hedgers in

the market and changes in the price generating process caused the forward market of the

exchange to file for bankruptcy in 2001.

Borenstein et al (2001) note that in the months prior to its collapse, spot prices were

much higher than forward prices. The authors construct a test of weak-form efficiency of the

market in the months prior to the collapse. The trading rule they utilize is based on the

unbiased expectations hypothesis. The rule assumes that a market participant buys or sells

electricity in the spot or forward market in a given week based on the relationship between

21

real-time and day-ahead prices for the previous week. They find that this rule provides

statistically and economically significant profits.

Borenstein, Bushnell, and Wolak (2002) model the determinants of electricity price

changes over a two year period in California after deregulation. They determine that price

spikes in the summer months were mainly due to electricity suppliers exerting market power.

The authors argue that price inelasticity of supply and demand for electricity in the short run

allows generation owners to exert a significant amount of market power with a relatively small

market share.

The ability of generation owners to exercise market power, according to the authors, is

primarily a function of their production capacity. Essentially, GOs with sizable capacity become

price makers during times of high demand. Large capacity GOs reduce costs by decreasing

production during times of high demand, while the electricity that they choose to produce

becomes more valuable since there is less energy on the grid. Borenstein et al (2002) note that

this type of withholding strategy will result in Pareto inefficient prices and a significant

deadweight loss for the entire market. This would tend to suggest that electricity pricing, even

after deregulation, may not be competitive in times when demand is predictably high.

The impact of virtual bidding on electricity markets has been examined across several

exchanges. The failure of the California Power Exchange and the California ISO is partly

attributed to the fact that these markets were designed to be used only by electricity providers

and purchasers (Borenstein, Bushnell, Knittel, & Wolfram, 2001). Hadsell and Shawky (2007)

examine the impact that the introduction of virtual bidding had on forward premiums on the

New York Independent System Operator (NYISO) market. They find that forward premiums

22

decreased in off-peak hours and increased during peak hours after virtual bidding was allowed

on the NYISO exchange. Virtual bidding is also associated with lower volatility in real-time and

day-ahead NYISO markets (Hadsell 2007). These results suggest that allowing the trade of

financially settled electricity contracts provides efficiency to the market.

Prior Research on the MISO Exchange

Perhaps due to the newness of the market, only a few papers have been published

covering the MISO exchange. Bowden and Payne (2008) utilize various ARIMA and GARCH

procedures to forecast prices on the MISO exchange. While their models perform well in both

in-sample and out-of-sample testing, it is important to note that the scope of their research was

extremely limited. The authors focused on only one month’s data (July to August 2007). It is

possible that the forecasting performance would be greatly reduced if a longer sample was

used, especially across multiple seasons.

Bowden, Hu, and Payne (2009) evaluate day-ahead premiums on the MISO exchange.

Consistent with prior research covering other electricity markets, positive forward premiums

are found on each hub. Bowden et al (2009) take this as a sign that the pricing mechanism on

the MISO exchange is inefficient. This is in contrast with previous research that asserts that

positive forward premiums can exist in an efficient market (Bessembinder & Lemmon 2002,

Shawky et al 2003, Longstaff & Wang 2004).

Hypotheses

Both the real-time and day-ahead markets are open to physical delivery and virtual

bidding (financially settled contracts). Other marketing entities are restricted to making virtual

bids, while other market participants may make both virtual and physical bids. The ability to

23

enter into energy contracts without taking physical delivery of electricity was instituted as a

means to open the market to speculators which, in turn, should increase liquidity and the

efficiency of electricity prices.

Unlike other power exchanges, virtual bidding has been a fixture on the MISO market

since its inception in 2005. In the absence of hedging pressure and non-competitive behavior

of generating owners, simple trading rules such as the ones used by Borenstein et al (2001)

should not be profitable on the MISO exchange. Every market participant can take part in

virtual bidding to eliminate arbitrage opportunities. This has not been tested before on the

MISO exchange and may shed light on the efficiency of the market.

Even though it is possible for speculators to place trades on the MISO exchange, most

market participants are either producers or retailers of energy. If generation owners can exert

market power over the MISO exchange, as was found in California (Borenstein et al 2002), it

may be the case that simple trading rules will be profitable, especially during peak demand

hours. It is likely that the 300 MPs on the MISO exchange vary in terms of production capacity.

As noted earlier, differences in capacity can cause electricity to be inefficiently priced during

peak demand times. Therefore, trading based on prior information will be profitable during

peak hours.

Hypothesis 1: Trading rules based on prior information will be profitable during peak hours

(08:00-17:00) on the MISO exchange.

Electricity prices follow several known seasonal and intraday patterns. If GOs on the

MISO exchange vary in capacity, large capacity firms may withhold production in order to

24

decrease costs and increase revenues. If this is the case, simple trading rules based on prior

information may be both economically and statistically significant.

Choosing a hedge ratio estimation technique may have an impact on the earnings

statements of MISO market participants. The Statement of Financial Accounting Standards

(SFAS) No. 133 and its amendment, SFAS No. 138, mandates that forwards and other derivative

contracts be reported on the balance sheet and assessed at fair value. Prior to SFAS 133,

derivatives were reported at historical cost. This provided a means for companies to shield

their true exposure to risk since many derivative contracts, including forward contracts, have no

initial cost.

SFAS 133 differentiates how gains and losses from hedges are treated based on the

effectiveness of the hedge. A hedging relationship is deemed highly effective if “changes in the

fair value of the derivative are significantly offset by changes in fair value attributed to the

hedged risk” (FASB 1998). If a hedge is shown to be highly effective, SFAS 133 allows for gains

and losses from the derivative to be recorded at the same time as gains and losses that occur

from the underlying hedged position. If the hedge is not highly effective, gains and losses from

the derivative must be reported in current earnings. Therefore, hedges that are deemed not to

be highly effective can increase earnings volatility.

The Financial Accounting Standards Board (FASB) does not explicitly specify what

constitutes a highly effective hedge. Finnerty and Grant ( ) contend that “highly effective”

should be interpreted as meaning that ”changes in the value of the derivative are offset by 8

to 125 percent of the cash flows of the hedged item or that regression of changes in the spot

position on changes in the forward position should produce an R2 of at least .8.”

25

The MISO exchange has far fewer participants than most commodity futures markets.

This, coupled with the unique characteristic of electricity prices (non-storability, extremely high

variance, mean-reversion, negative prices) can cause hedge ratios on the MISO exchange to be

less effective than those found in other commodity markets. Even though the MPs may use

day-ahead contracts to reduce price risk, it is not certain that these contracts can be used to

create a portfolio that has 80% less variance than the underlying, unhedged spot position.

Hypothesis 2: Hedge ratios estimated for the MISO market will not be highly effective by FASB

standards.

This study also is the first to estimate two broad categories of hedge ratios on the MISO

exchange; those that are robust to temporal aggregation and those that are subject to temporal

aggregation bias. As previously discussed, a market such as MISO may be dominated by

hedgers who are more likely to buy and sell electricity in the day-ahead rather than trade on

the more volatile real-time market. If this is the case, hedge ratio techniques that do not

account for temporal aggregation will be biased and would also result in a less effective hedge.

MGA and ARDL models are robust to temporal aggregation, while naïve, MV, and GARCH based

hedge ratios are not.

Hypothesis 3: Hedge ratios that account for the temporal aggregation of real-time prices will be

more effective (in terms of variance reduction) than those that do not.

26

CHAPTER 3

DATA AND METHODOLOGY

Sample

All analysis in this study uses hourly day-ahead and real-time locational marginal prices

(LMPs) from June 1, 2006 to April 11, 2009 obtained from the Midwest Independent System

Operator (MISO) website (www.midwestiso.org). Each hour of the day is treated as its own

time series for each hub in both the real-time and day-ahead markets. Weekly price series are

used in this study. Weekly price series are examined because of the weekly settlement feature

of the MISO exchange. Patterns in prices may be attributed to the implicit credit involved in the

settlement process. Furthermore, weekly settlements may create an incentive for market

participants not to reveal their true demand for electricity on non-settlement days. This would

tend to put downward pressure on the LMP for non-settlement days. The weekly settlement

feature of the MISO exchange has not been taken into account in previous research. The

weekly sample consists of 149 spot and forward observations for each hour of the day and each

hub.

Stationarity

One of the more important statistical concepts when dealing with time series data is

stationarity. A series is stationary if it displays a constant mean and variance over time and the

probability density function of any segment of the series is the same as the probability density

function for any other segment. Most statistical analysis relies on the assumption that the

sample is stationary. If price data follows a random walk, however, variance will not be

constant and the price series will be non-stationary. Although prior research on electricity

http://www.midwestiso.org/

27

markets has shown prices are stationary (Knittel and Roberts 2005), it is still important to test

the stationarity of day-ahead (DA) and real-time (RT) prices in order to avoid spurious

regression results and biased test statistics.

Often times, non-stationary data can be made stationary by differencing the series. If a

time series is stationary in levels, then it is said to be intergrated of order zero, or I(0). A time

series is I(1) if it is non-stationary in levels, but the first difference of the series is stationary.

I(1) series are also referred to as having a unit root. Thus, I(p) represents the number of

differences that must be applied to the series to obtain a stationary process.

The augmented Dickey-Fuller (ADF) test is a statistical measure used to detect the

presence of a unit root in time series data (Dickey and Fuller 1979). The ADF test equation is

(13.) - - - -

Traditional Dickey-Fuller tests assume that the error term in (10) is white noise;

t N( , ) and Cov( t s)=0. ADF tests relax this assumption by using lagged values of the

dependent variable as regressors to adjust for serial correlation in the error structure. The

Akaike information criteria (AIC) or Schwartz information criteria (SIC) may be used to

determine the amount of lags to be included in (13). represents a time trend coefficient.

Equation (13) allows for a test of three possible models. A random walk model can be

tested by restricting and to zero. Setting only to zero allows for a test of a random walk

model with drift. Placing no restrictions on or results in testing a random walk model with

drift and time trend. The null hypothesis for all three specifications of (13) is that equals zero,

which means that the model has a unit root. A conventional t-test statistic with revised critical

28

values is used for ADF tests. The critical values for ADF tests are larger than those of

conventional t-tests.

Forward Premia/Discounts

The existence of forward premiums and discounts on the MISO market is examined in

this study. Following the methodology of Longstaff and Wang (2004), average one week

forward premia and discounts are calculated using the following equation:

(14.)

∑ -

represents the average one week forward premium (discount) for hour i on a given MISO

hub.

The test statistic for (14.) is:

(15.) t=

.

Average one week forward premiums (discounts) will be calculated for each of the twenty-four

hourly time series on every MISO hub.

Hedge Ratio Methodology

Two groups of hedge ratios are used for this analysis. Naïve, minimum variance (MV),

and generalized autoregressive conditional heteroskedasticity (GARCH) hedge ratio estimation

techniques are used extensively in the literature. While these hedging methods may be

common, they will result in downward biased hedge estimates if there is a discrepancy in the

frequency of trading between the spot and forward markets. Although less popular in the

derivatives literature, autoregressive distributed lag (ARDL) and method of group averages

(MGA) estimators do not suffer from temporal aggregation bias. All five hedge ratios are

evaluated for each hour of the day, across each hub, with the weekly price series. Hedge ratios

29

are estimated for a hedging horizon of one to four weeks for each method. Price levels and

price differences are used in the analysis of naïve, MV and MGA hedge ratios. GARCH(1,1) and

ARDL(1,1) hedge ratios are estimated with price differences.

MV, GARCH, and ARDL hedge ratios are calculated using a rolling windows estimation

technique. The first twenty day-ahead and real-time price observations for each hedging

horizon is used to estimate an initial hedge ratio. These estimates are then updated

throughout the hedging horizon by removing the oldest day-ahead and real-time price in the

estimation window and replacing it with the most current day-ahead and real-time price. This

procedure provides a means to update the hedging strategy based on new information

throughout the hedging horizon.

While the procedure estimating each hedge ratio is discussed in the previous chapter, it

is worthwhile to discuss the method of group averages in more detail. For the method of group

averages estimation, real-time and day-ahead prices will be broken into three groups. Each pair

of DA and RT prices for a given hour will be sorted from highest to lowest based on day-ahead

prices. The observations are then divided into three equal subsamples. The observations in the

middle group are then discarded; the estimation deals only with the RT and DA prices that fall

in the highest and lowest group. The beta estimate is:

(16.)

.

represents the average real-time price observed in the group with the highest day-ahead

prices, while is the average real-time price from the group with the lowest day-ahead prices.

and represent the average day-ahead price in the highest and lowest group, respectively.

The first twenty real-time and day-ahead prices in the hedging horizon are used to estimate a

30

static hedge ratio for the remainder of the hedging horizon. If ordinary least squares (OLS)

estimation represents the best linear unbiased estimate of beta, hedge ratios estimated with

OLS will be similar to those obtained via MGA.


Hedge ratio effectiveness has garnered much attention in derivatives research over the

past fifty years. Johnson (1960) proposes that investors should evaluate the following

relationship for hedging performance:

(17.) e = 1-[Var(Rh)/Var(Rs)].

Var(Rs) represents the variance of returns for a portfolio consisting of only spot holdings, while

Var(Rh) is the variance of returns from the hedged portfolio. Equation (17) measures the

percentage reduction in variance that an investor realizes from instituting the hedge. This

effectiveness measure has been utilized extensively in the hedge ratio literature (Ederington

1979, Malliaris & Urrutia 1991, De Jong, De Roon & Veld 1997). This technique is often

extended to compare the variance of portfolio returns using an OLS hedge to portfolios

consisting of other based hedges (Baillie & Myers 1991, Kroner & Sultan 1993, Hsu, Tseng &

Wang 2008).

It is important to note that comparing hedge ratios based on variance reduction as

specified in equation (17) may be biased. In a series of essays, Lien (2005a, 2005b, 2008) points

out that comparing the variance reduction of the minimum variance hedge ratio with other

hedging models is biased. Johnson’s (196 ) hedge ratio estimate is designed to minimize

unconditional variance. Equation (17) favors OLS hedge ratios since it analyzes the

31

effectiveness of the hedge based on unconditional variance. Using this measure to evaluate the

performance of variance hedge ratios, according to Lien, is therefore biased in favor of OLS.

This study uses Morgan’s test for differences between variances as a means to evaluate

the effectiveness of each hedging methodology. Morgan’s (19 9) test statistic for differences in

variance is expressed as:

(18.) ( - )

( - ) , where

-

[(

) -

] .

The out-of-sample variance of each hedging technique is compared to the variance of

the unhedged portfolio using Morgan’s test. Pairwise comparisons of the out-of-sample

variance of each hedging strategy based on Morgan’s test are also made for a hedging horizon

of one to four weeks.

Tests of Market Efficiency

Fama (1970) operationalizes the concept of an efficient market. Fama states that a

market is weak-form efficient if past information is fully reflected in current prices. If the MISO

exchange meets this level of efficiency, simple trading rules based on prior relationships

between spot and forward prices should not generate excess returns. A market is deemed

semi-strong form efficient if prices incorporate all publicly available information; past and

present. Finally, a market is considered strong-form efficient if all public and inside information

is incorporated in prices. It is important to note that each successive level of efficiency includes

the one prior to it. In other words, a market that is semi-strong form efficient must, by

definition, be weak-form efficient. Therefore, it is important to test weak-form efficiency on

the MISO exchange before tests of semi-strong form efficiency can be performed.

32

The first test of market efficiency that will be examined is the one presented in

Borenstein et al (2001). This rule is based on the unbiased expectations hypothesis. The

unbiased (or pure) expectations hypothesis states that the current forward price is an unbiased

estimator of the future spot price. This relationship can be expressed as follows:

(19.) -

denotes the current day-ahead LMP for electricity to be delivered in hour i on day t+1 and

denotes the real-time LMP for electricity for hour i on day t+1.

If the unbiased expectation hypothesis holds, the intercept of (19) will be zero. The rule,

based on the work of Borenstein et al (2001), assumes that a market participant uses prior

information about the relationship between forward and futures prices to make buy and sell

decisions. For example, if the 17:00 day-ahead LMP was above the day’s 17: real-time price

for a given week, the speculator will sell the 17:00 day-ahead contract and buy electricity at the

17:00 real-time price the following week.

In order to test the profitability of this rule, (19) will be re-specified as follows

(Borenstein et al 2001):

(20.) -

TR is an indicator variable that equals one if the real-time price for a given hour in the previous

period is higher than the day-ahead price in the previous period. If TR equals one, market

participants who use this rule will sell at the real-time price and buy at the day-ahead price the

following period. If the real-time price was below the day-ahead price in the previous period,

TR equals negative one. The coefficient associated with TR indicates the dollar amount per

megawatt hour that could be earned by implementing this rule. This will be tested for each

33

hour of the day, across all five hubs. If this model produces statistically and economically

significant results, as it did on the California market studied by Borenstein et al (2001), it could

be a sign that the market is not weak-form efficient.

One of the more popular tests of weak-form market efficiency is the simple moving

average trading rule. As Brock, Lakonishok, and LeBaron (1992) note, moving average trading

rules consist of creating both a long-run and short-run moving average of the price series in

question. A moving average (MA) price series can be expressed as

(21.) (

)∑ -

-

The moving average process creates a series of averages for various subsets within the sample.

Moving averages are often used in technical analysis to smooth out price fluctuations. This can

be especially useful in electricity data given the price spikes that have been documented in

prior research.

A short-run moving average (typically one day) is compared to a longer term moving

average (usually 50, 100 or 200 days). As Brock et al (1992) describe, a buy signal is created

when the short run moving average rises above its long term trend. This is because a short-run

moving average that rises above its long-run moving average counterpart is seen as the

initiation of an upward trend. A sell sign is initiated when the short-run moving average falls

below the long-run moving average.

Unlike most financial assets, electricity prices are mean-reverting (Knittel and Roberts

2005). This means that a technical analyst who observes a short-run moving average that is

above its long-run counterpart would initiate a sell order. This is because the price of the spot

or forward contract is likely to decrease back to its long term average. Following similar logic, a

34

buy order would be initiated when the short-term moving average series is below the long-term

moving average series.

Since this study focuses on weekly instead of daily data, a (1,25) trading rule is used.

Whenever the short-run (1 week) MA return series is above the long-run (25 week) MA dollar

return series, a sell order is initiated. The profitability of the rule is examined by the following

relationship:

(22.) .

Equation (22) expresses the dollar return on day-ahead and real-time prices ( ) as a function of

the moving-average trading rule established in the previous period. The indicator variable Rule

equals one if the short-term moving average is below the long-run moving average in the

previous period and negative one if the opposite is true. Equation (22) is estimated via OLS.

The coefficient estimated would represent the average dollar return received from

implementing the rule. LeBaron (1999) uses (22) to estimate trading rule profits in the foreign

exchange market. Although the rule is easily implemented, LeBaron reports that positive and

statistically significant profits are achieved by implementing the rule.

LeBaron (1999) notes that the profitability of the simple moving average rule may be

due to the fact that many market participants, particularly central banks, are not strict profit

maximizers. As Banjeree and Noe (2006) discuss, the profit maximizing function for many

market participants on electricity exchanges is skewed due to government regulation. It seems

reasonable that this type of trading rule could be profitable in peak hours, when the wealth

maximization function is perhaps skewed the most.

35

CHAPTER 4

RESULTS

Summary Statistics

Tables3 A1-A5 show the descriptive statistics of the weekly day-ahead (DA) price series

for all five Midwest Independent System Operator (MISO) hubs. Prices are stated in terms of

dollars per megawatt hour ($/MWh). Three of the five hubs exhibit negative prices for DA

electricity. This is not uncommon in electricity markets, since electricity is virtually non-storable

and shut-down costs can be extremely large. Variability is quite high in the forward market,

which is consistent with previous research in electricity markets. Skewness and kurtosis figures

suggest that DA prices are not normally distributed. The autocorrelation coefficients associated

with DA prices are also high, which may result in inefficient ordinary least squares (OLS) hedge

ratio estimates.

Real-time (RT) summary statistics for the weekly price series in each hub are provided in

Tables A6-A10. Not surprisingly, RT prices on each hub display higher variation than their day-

ahead counterparts. Maximum prices are higher and minimum prices are lower on the real-

time market as compared to the day-ahead market. While skewness and kurtosis figures in the

weekly real-time data are generally higher than the weekly day-ahead data, AR(1) coefficients

are lower in the weekly real-time price series.

As previously discussed, the weekly settlement of the MISO exchange may place

downward pressure on real-time and day-ahead prices on non-settlement days. The MISO

market settles each Wednesday. In the intervening days, market participants may underbid

3 All tables appear in the appendix.

36

their true demand for electricity. Should this occur, day-ahead and real-time prices would tend

to peak on Wednesday and then gradually decrease until reaching a minimum on the following

Tuesday.

Tables A11-A15 display the percentage of times that the lowest locational marginal price

(LMP) occurred on each day of the week, for each of the 24 hourly series DA time series on

each hub. For example, Table A11 reveals the lowest price for DA electricity to be delivered at

0:00 hours on the IL hub occurs on Saturday 28% of the time. Minimum DA prices most

frequently occur during the weekend across all five hubs. This is most likely due to a decrease

in industrial demand during the weekend. Similar results for the RT market are displayed in

Tables A16-A20. It seems that any effect that weekly settlements may have on depressing

prices is overshadowed by the lack of demand for electricity during the weekend.

The random walk with drift model is used to test for a unit root in MISO electricity

prices. Tables A21-A22 display the weekly DA and RT augmented Dickey-Fuller (ADF) test

statistics for each hour of the day across all five MISO hubs. The null of a unit root is rejected

for all 24 RT price series on each of the five hubs. The null of a unit root cannot be rejected for

about 16% (19/120) of the time series on the DA market. Non-stationarity in the weekly DA

data seems to be a concern between 13:00 and 17:00 hours.

Forward Premia

Average weekly forward premia and discounts in terms of dollars per megawatt hour

are shown in Table A23. Positive, statistically significant forward premiums are typically found

between the hours of 09:00-12:00 and 19:00-22:00. Statistically significant forward discounts

are found between 04:00 and 06:00. Four of the five hubs have both statistically significant

37

average forward premiums and discounts. These findings tend to support Bessembinder and

Lemmon’s ( ) theory that both forward premiums and discounts may exist throughout the

day on electricity exchanges.

MV and GARCH(1,1) Hedge Ratio Estimates

As mentioned previously, minimum variance (MV) and generalized autoregressive

conditional heteroskedasticity (GARCH) hedge ratio estimates may suffer from temporal

aggregation bias. Because of this, analysis of rolling MV and GARCH(1,1) hedge ratios will be

discussed together. Tables A24-A43 present summary statistics for minimum variance hedge

ratio estimates using price levels over a hedging period of 1-4 weeks. The average MV hedge

ratio estimate tends to be below one for each hub, which could be evidence of the temporal

aggregation bias. The averages of the two week and four week hedge ratio estimates for each

hub tends to be higher than the one week and three week hedge ratio averages. The minimum

and maximum columns show that there is a large degree of variation for hedge ratio estimates

for each hour of the day, across all hedging horizons. The lowest MV hedge ratio estimate is

generally negative for each hub using a one week hedging horizon, but is typically positive for a

hedging period of 2-4 weeks.

Summary statistics for MV hedge ratio estimates using price differences are shown in

Tables A44-A63. MV hedge ratio estimates obtained from price differences exhibit high

variation across hours and hubs. The average of MV hedge ratio estimates utilizing price

differences is negative more often than those estimated with price levels. In general, using

price differences to estimate MV hedge ratios results in lower averages and higher standard

deviations for each hedging horizon. As with price levels, the averages of the two week and

38

four week hedge ratio estimates using price differences are usually higher than the averages for

the one week and three week hedge ratios estimates.

GARCH(1,1) summary statistics are shown in Tables A64-A83. Rolling GARCH(1,1) hedge

ratio estimates appear to share similar characteristics with rolling MV hedge ratios. As with the

MV hedge ratio estimates, the average GARCH(1,1) hedge ratio is usually less than one. The

standard deviation of the GARCH(1,1) hedge ratio estimates is high relative to their mean,

which is also true with the MV hedge ratio estimates. The average of the rolling GARCH(1,1)

hedge ratios also tend to be higher for the two and four week hedging horizon as compared to

the one and three week hedging intervals.

ARDL(1,1) and MGA Hedge Ratio Estimates

Summary statistics for short-run and long-run autoregressive distributed lag (ARDL)

hedge ratio estimates are presented in Tables A84-A123. As with MV and GARCH(1,1) hedge

ratios, the average of short-run and long-run ARDL(1,1) hedge ratio estimates is typically below

one. Both long-run and short-run ARDL(1,1) hedge ratio estimates have a high standard

deviation relative to their respective means over each hedging horizon. The average of both

short-run and long-run estimates varies greatly between each hourly time series and across

hubs. The average of the long-run ARDL(1,1) hedge ratios are generally higher than their short-

run counterparts for each hub for the one week and three week hedging period. The average

of short-run ARDL(1,1) hedge ratio estimates tends to be higher than the average of long-run

hedge ratio estimates when using a two and four week hedging horizon.

Method of group average (MGA) hedge ratios estimated with price levels and price

differences are presented in Tables A124-A131. Since the MGA hedge ratios are static,

39

descriptive statistics are not available. MGA hedge ratio estimates vary greatly between hours

and across hubs for all hedging horizons. The frequency of negative MGA hedge ratio estimates

is higher when using price differences. Unlike MV and GARCH(1,1) hedge ratios, there does not

seem to be a pattern between the magnitude of the MGA hedge ratio estimate and the amount

of time that the hedge is in place.


Standard deviations of out-of-sample dollar returns for naïve, MV and MGA hedged

portfolios are shown in Tables A132-A151. Each of these hedged portfolios is constructed using

RT and DA price levels. The standard deviations shown in each table are in terms of dollars per

megawatt hour ($/MWh). On the basis of risk reduction, the naïve and MGA hedge typically

outperform the MV hedge for each hub and each hedging horizon. The MV hedge often

produces a higher standard deviation than the unhedged position. In fact, the standard

deviation of the unhedged position for each hub is similar to that of the portfolios hedged using

the naïve and MGA techniques. None of these hedging techniques meet the generally accepted

definition for a highly effective hedge when using price levels.

Tables A152-A171 show the out-of-sample standard deviation of dollar returns for each

hedging technique using price differences. When price differences are used, each hedging

method generally produces similar volatility. The unhedged position typically outperforms all

hedging techniques for each hub and hedging period when using price differences. There is no

instance where the variance of the hedged position is 80% less than the unhedged position

using either price levels or price differences. The standard deviation of dollar returns using

both price levels and differences lend support to hypothesis 2.

40

Tables A172-A191 show the t-statistics for Morgan’s test of differences between

variances for hedged portfolios constructed with price levels. Each column represents a

comparison of the variance of out-of-sample returns for two hedging strategies. A positive,

statistically significant t-statistic indicates that the first hedging strategy listed in the column

produces a higher variance than the second. A negative, statistically significant t-statistic

means that the first hedging strategy listed in the column has a lower variance than the second.

The last row in each table is a tally of the number of negative, statistically significant

coefficients found in each column.

These tables provide further evidence that the naïve and MGA strategies are similar to

each other and superior to the MV hedge in terms of risk reduction. The unhedged position

often times provides a significantly lower variance than the MV hedge. Of all the hedging

strategies examined using price levels, the MGA strategy generally performs the best when

compared to the unhedged portfolio. When price levels are used, it appears that the MGA

strategy may be the best of the techniques examined in terms of risk reduction. This can be

seen as evidence in support of hypothesis 3. While the MGA hedge seems superior to the naïve

and MV hedging strategies when using price levels, it is important to reiterate that the MGA

strategy does not meet the standard for a highly effective hedge.

Tables A192-A231 show t-statistics for Morgan’s test of differences between variances

for hedged portfolios constructed with price differences. The difficulty of managing risk on the

MISO exchange is also apparent when price differences are used to construct hedged

portfolios. Morgan’s test for differences in variance provides evidence in support of hypothesis

2 in both levels and differences. None of hedging technique utilized in this study consistently

41

provides a variance that is significantly lower than the variance of the unhedged position. No

hedging strategy clearly dominates the others when price differences are used, which may be

seen as evidence against hypothesis 3

Trading Rule Results

Tables A232-A235 show the profits ($/MWh), along with t-statistics (in italics) obtained

from implementing a (1,25) weekly moving average trading rule on day-ahead and real-time

prices on the MISO exchange. Since day-ahead and real-time prices are mean-reverting, a buy

signal is created if the short-run moving average falls below the long-run moving average. A sell

signal occurs if the opposite is true. This rule produces economically and statistically significant

profits in both the day-ahead and real-time price series. When used in the day-ahead market,

the moving average trading rule results in significant profits (at 5% level or better) between 9

and 20 hours of the day, depending on the hub.

The simple moving average trading rule is more successful when applied to the RT price

series. The magnitude and frequency of significant profits is higher in the real-time market.

Many of the returns in the real-time markets are greater than $10, which is large compared to

the mean electricity price for any hour on any hub. The (1,25) rule results in significant profits

in the real-time market between 18 and 21 hours of the day, depending on the hub. Trading

rule profits in both the real-time and day-ahead market occur the least on the Minnesota hub

and are most common on the First Energy hub.

The profits obtained from the (1,25) moving average rule tend to support the idea that

the MISO exchange is not weak-form efficient. But it should be noted that the Borenstein et al

(2001) trading rule, as described by equation 17, did not produce statistically significant profits

42

for any hour of the day, on any hub. Taking both of these findings into account, there seems to

be evidence that the relationship between spot and forward prices is efficient, but the pricing

mechanism that determines real-time and day-ahead LMPs may not be weak-form efficient.

43

CHAPTER 5

CONCLUSION

The purpose of this study is to examine the effectiveness of hedging instruments

available to market participants on the Midwest Independent System Operator (MISO)

exchange and to examine the efficiency of the pricing mechanism used on the exchange.

Electricity markets are primarily utilized by participants that would like to reduce price risk.

This makes hedge ratios constructed with MISO prices susceptible to temporal aggregation bias.

Because of this, two types of hedge ratios were estimated; those robust to the effects of thin

trading and those that are prone to temporal aggregation bias. In total, five hedge ratio

estimation procedures were evaluated on the basis of risk reduction: naïve, minimum variance

(MV), generalized autoregressive conditional heteroskedasticity (GARCH), autoreressive

distributed lag (ARDL) and method of group averages (MGA).

In terms of portfolio variance reduction, the naïve and MGA approach tends to

outperform the other hedging techniques employed in this study. While this is the case, no

hedge ratio method examined here meets the Financial Accounting Standards Board (FASB)

guidelines for a highly efficient hedge. In fact, the variance of the unhedged position is

frequently less than the variance of the hedged portfolios constructed in this study. This means

that gains and losses based on any of these hedging strategies would have to be reported in

current earnings, instead of being matched with the gains and losses from the underlying

position. Given the nature of the market, this may not be a huge disadvantage if most market

participants use the day-ahead contract for short-term hedging.

44

There is an abundance of research that suggests that electricity markets, even after

deregulation, may not be efficient in the Fama (1970) sense. Two rather simple trading rules

are employed on the MISO exchange as tests of weak-form market efficiency. The first rule is

used by Borenstein et al (2001) in their evaluation of the California energy market. This rule

creates a buy signal in the real-time (RT) market if last period’s RT price was below last period’s

day-ahead (DA) price and a sell signal in the RT market if the opposite is true. The Borenstein

(2001) rule produces statistically and economically significant results in the weekly price series

of any hub. This would tend to suggest that profits cannot be earned by trading based on the

past relationship between day-ahead and real-time prices.

A simple moving average trading rule is also used to determine the efficiency of the

MISO exchange. Unlike traditional moving average (MA) trading rules, a buy signal is created

when the short-run moving average falls below the long-run moving average, and a sell signal is

created when the opposite occurs. The reason for this may be that MISO electricity prices are

mean-reverting. This rule generally provides economically and statistically significant returns in

the weekly DA and RT price series for each hub. This suggests that the proprietary co-

optimization formula that MISO uses to calculate DA and RT prices is not weak-form efficient.

45

APPENDIX

DATA TABLES

Table A1 Descriptive Statistics for Day-Ahead Forward Prices on the Illinois Hub

This table represents the summary statistics of twenty-four price series for day-ahead electricity traded on the Illinois hub. Each of the twenty-four price series are generated using weekly (settlement day) locational marginal prices (LMPs) obtained from June 6, 2006 to April 11, 2009. LMPs are expressed in terms of dollars per megawatt hour ($/MWh).

Hour Mean Median Std. Dev. Kurtosis Skewness Minimum Maximum AR (1)

0:00 27.84 23.95 11.43 2.48 1.62 11.91 72.90 0.41

1:00 22.69 20.86 8.11 3.24 1.44 1.66 57.78 0.41

2:00 21.29 19.65 7.87 3.53 1.37 -2.43 52.81 0.38

3:00 20.13 19.14 7.50 2.97 0.95 -4.55 50.56 0.44

4:00 20.12 18.81 7.49 3.74 1.05 -5.72 52.90 0.45

5:00 21.97 20.51 7.85 2.99 1.07 -2.40 55.29 0.47

6:00 28.33 25.15 13.13 3.18 1.61 4.70 76.01 0.62

7:00 39.35 34.86 19.78 0.93 1.11 10.01 104.77 0.70

8:00 48.04 41.08 22.44 -0.29 0.76 13.77 108.87 0.62

9:00 51.61 48.51 19.64 -0.11 0.60 15.77 104.88 0.48

10:00 57.55 55.33 19.58 -0.13 0.38 16.54 108.05 0.43

11:00 60.71 59.78 21.15 0.21 0.37 17.23 132.75 0.42

12:00 62.47 62.16 23.43 1.45 0.71 17.57 159.32 0.48

13:00 62.88 60.83 26.31 1.56 0.92 17.47 163.61 0.53

14:00 62.54 58.04 28.99 1.02 0.98 16.37 161.94 0.56

15:00 61.22 53.34 33.25 1.31 1.23 15.79 180.00 0.62

16:00 62.19 48.80 37.84 1.08 1.27 15.60 180.00 0.66

17:00 60.41 49.70 34.90 2.45 1.51 15.69 202.62 0.59

18:00 62.31 55.55 27.13 2.30 1.28 20.76 168.61 0.49

19:00 70.10 66.35 26.87 0.42 0.64 19.39 159.06 0.44

20:00 67.57 64.79 22.26 0.95 0.58 19.76 144.48 0.37

21:00 62.08 59.50 21.50 0.67 0.67 19.53 135.00 0.46

22:00 47.93 43.09 19.55 1.75 1.17 19.16 125.29 0.37

23:00 34.64 31.02 14.42 3.03 1.49 16.85 103.11 0.29

46

Table A2 Descriptive Statistics for Day-Ahead Forward Prices on the Cinergy Hub

This table represents the summary statistics of twenty-four price series for day-ahead electricity traded on the Cinergy hub. Each of the twenty-four price series are generated using weekly (settlement day) locational marginal prices (LMPs) obtained from June 6, 2006 to April 11, 2009. LMPs are expressed in terms of dollars per megawatt hour ($/MWh).


0:00 30.29 25.95 11.77 2.68 1.71 17.62 74.79 0.34

1:00 24.91 22.10 8.03 4.10 1.85 15.23 59.57 0.31

2:00 23.34 21.07 7.31 3.73 1.76 12.75 54.50 0.33

3:00 22.40 20.37 6.92 3.57 1.63 11.30 52.31 0.36

4:00 22.67 20.98 6.96 4.27 1.75 11.80 54.71 0.36

5:00 24.99 23.15 7.75 3.98 1.68 12.49 57.77 0.38

6:00 32.65 27.98 14.39 2.87 1.63 12.49 86.01 0.56

7:00 43.56 38.03 21.13 0.65 1.02 14.24 107.80 0.60

8:00 51.67 44.83 23.46 0.59 0.93 15.77 139.76 0.52

9:00 55.03 51.24 21.80 4.77 1.43 16.29 172.16 0.37

10:00 60.83 57.92 21.54 5.39 1.33 17.10 179.85 0.36

11:00 63.49 61.80 21.50 3.88 0.96 17.82 175.53 0.42

12:00 64.97 63.50 24.01 6.01 1.42 18.18 200.00 0.44

13:00 65.04 62.62 25.80 6.15 1.50 17.79 211.01 0.54

14:00 64.11 59.00 28.06 3.45 1.28 16.65 203.66 0.59

15:00 62.88 54.82 32.38 2.54 1.38 16.06 210.37 0.63

16:00 64.25 50.15 38.56 3.39 1.61 15.87 249.00 0.63

17:00 62.10 52.70 34.45 4.40 1.76 15.96 234.31 0.57

18:00 64.60 58.60 28.10 9.06 2.10 21.12 236.24 0.43

19:00 72.21 70.00 26.88 2.07 0.81 19.75 196.99 0.40

20:00 69.84 65.99 21.92 0.73 0.48 20.11 153.35 0.33

21:00 64.37 61.05 22.04 2.81 1.03 19.87 168.33 0.40

22:00 49.60 45.39 19.13 1.28 1.07 19.49 125.03 0.30

23:00 37.13 33.37 15.05 3.45 1.64 18.82 106.34 0.21

47

Table A3 Descriptive Statistics for Day-Ahead Forward Prices on the Michigan Hub

This table represents the summary statistics of twenty-four price series for day-ahead electricity traded on the Michigan hub. Each of the twenty-four price series are generated using weekly (settlement day) locational marginal prices (LMPs) obtained from June 6, 2006 to April 11, 2009. LMPs are expressed in terms of dollars per megawatt hour ($/MWh).


0:00 31.41 26.76 12.53 2.70 1.69 17.21 80.07 0.34

1:00 25.73 23.33 8.51 4.33 1.87 14.88 63.05 0.28

2:00 24.14 22.01 7.92 4.16 1.81 12.28 56.96 0.28

3:00 23.10 21.48 7.31 3.12 1.51 11.12 54.67 0.33

4:00 23.68 21.99 7.56 4.14 1.74 11.65 57.18 0.29

5:00 26.16 24.19 8.11 4.10 1.69 12.71 62.21 0.32

6:00 34.57 30.75 14.77 2.86 1.56 12.82 87.25 0.52

7:00 46.11 40.72 21.46 0.76 0.97 14.10 114.20 0.55

8:00 54.17 47.25 24.12 1.32 1.00 16.36 155.95 0.48

9:00 57.63 53.58 22.98 5.51 1.48 16.89 185.62 0.32

10:00 63.93 60.80 22.83 4.19 1.18 17.69 183.41 0.34

11:00 66.77 64.24 22.77 0.97 0.65 18.44 149.99 0.40

12:00 68.36 66.27 25.33 3.03 1.15 18.83 182.70 0.43

13:00 68.59 65.00 27.51 2.61 1.19 18.39 184.30 0.53

14:00 67.74 62.87 29.81 1.81 1.16 17.22 182.74 0.60

15:00 66.25 56.53 34.60 1.92 1.39 16.60 199.14 0.64

16:00 67.47 52.08 40.25 1.74 1.43 16.41 205.06 0.68

17:00 64.60 54.50 34.99 2.44 1.52 16.50 198.70 0.64

18:00 67.04 61.19 27.52 2.02 1.22 21.84 167.11 0.53

19:00 75.21 72.62 27.69 -0.06 0.47 20.46 166.75 0.48

20:00 72.76 69.50 22.68 0.30 0.39 20.80 148.72 0.37

21:00 67.26 63.53 23.86 2.88 1.11 20.54 178.80 0.40

22:00 52.18 47.34 21.20 2.27 1.32 20.15 138.39 0.31

23:00 38.69 34.36 15.84 3.22 1.62 19.38 109.20 0.22

48

Table A4 Descriptive Statistics for Day-Ahead Forward Prices on the Minnesota Hub

This table represents the summary statistics of twenty-four price series for day-ahead electricity traded on the Minnesota hub. Each of the twenty-four price series are generated using weekly (settlement day) locational marginal prices (LMPs) obtained from June 6, 2006 to April 11, 2009. LMPs are expressed in terms of dollars per megawatt hour ($/MWh).


0:00 32.11 24.66 18.88 3.10 1.54 8.44 123.15 0.59

1:00 22.75 18.43 13.49 2.52 1.56 1.89 72.23 0.50

2:00 20.16 16.10 11.80 2.43 1.46 -1.51 69.82 0.54

3:00 18.49 15.19 10.61 2.76 1.38 -3.66 65.75 0.54

4:00 18.35 15.00 10.41 3.17 1.44 -4.87 64.46 0.54

5:00 20.03 17.85 10.98 2.42 1.35 -1.51 64.40 0.54

6:00 26.11 20.83 15.06 1.91 1.37 5.41 79.48 0.66

7:00 41.93 35.73 22.86 0.69 1.01 7.58 114.96 0.71

8:00 56.08 47.78 29.09 1.48 0.94 8.74 187.72 0.62

9:00 64.13 58.83 29.18 1.86 1.03 15.76 190.32 0.55

10:00 68.23 67.01 26.14 1.43 0.68 17.31 181.90 0.48

11:00 71.72 69.82 33.89 29.37 3.88 18.04 347.26 0.28

12:00 73.27 71.28 34.86 26.33 3.67 18.67 347.46 0.31

13:00 72.07 67.79 40.28 52.12 5.70 18.30 450.00 0.28

14:00 70.65 65.21 41.83 45.30 5.24 17.16 450.00 0.35

15:00 69.13 59.81 44.11 36.82 4.61 16.55 450.00 0.42

16:00 69.55 56.26 47.20 27.67 3.91 16.35 450.00 0.51

17:00 67.72 58.90 41.52 21.51 3.38 16.44 382.27 0.48

18:00 69.54 65.76 33.04 9.23 2.04 19.94 273.49 0.44

19:00 80.65 75.43 38.38 3.78 1.36 18.11 264.89 0.58

20:00 80.83 77.01 35.48 5.50 1.60 14.52 255.25 0.46

21:00 72.28 70.18 27.84 5.35 1.42 17.80 217.39 0.44

22:00 57.92 54.31 28.47 11.18 2.42 15.88 233.26 0.38

23:00 40.97 35.76 24.72 13.00 2.75 10.36 191.61 0.40

49

Table A5 Descriptive Statistics for Day-Ahead Forward Prices on the First Energy Hub

This table represents the summary statistics of twenty-four price series for day-ahead electricity traded on the First Energy hub. Each of the twenty-four price series are generated using weekly (settlement day) locational marginal prices (LMPs) obtained from June 6, 2006 to April 11, 2009. LMPs are expressed in terms of dollars per megawatt hour ($/MWh).


0:00 29.33 25.52 13.02 3.15 1.01 -18.56 76.20 0.35

1:00 24.34 22.36 8.91 2.89 1.26 1.26 60.00 0.35

2:00 22.81 21.33 8.12 2.76 1.26 8.22 55.36 0.33

3:00 21.94 20.68 7.89 2.20 0.91 1.13 53.13 0.35

4:00 22.29 21.03 7.89 3.02 0.92 -4.23 55.58 0.38

5:00 24.96 22.97 8.41 3.83 1.51 8.41 60.96 0.40

6:00 31.73 28.19 14.73 3.24 1.35 -11.31 83.05 0.52

7:00 43.06 38.22 21.99 1.18 0.90 -19.42 111.07 0.56

8:00 51.39 45.07 24.09 0.84 0.96 11.39 144.93 0.52

9:00 54.40 49.98 23.39 5.11 1.41 8.12 181.83 0.37

10:00 60.32 56.56 22.66 4.52 1.29 17.46 180.95 0.36

11:00 63.18 60.69 22.41 0.77 0.67 18.20 148.61 0.42

12:00 64.87 61.94 25.00 3.04 1.16 18.58 178.68 0.41

13:00 64.95 61.57 26.73 3.00 1.29 18.08 185.29 0.51

14:00 63.76 58.88 29.00 2.13 1.12 -3.52 181.81 0.56

15:00 62.18 54.45 33.40 2.44 1.42 -3.69 196.75 0.63

16:00 62.65 49.61 37.41 1.96 1.41 0.24 201.82 0.67

17:00 60.38 48.95 33.27 2.83 1.55 0.00 194.34 0.62

18:00 62.14 57.40 25.11 3.19 1.43 21.46 164.39 0.45

19:00 69.80 66.06 26.11 0.24 0.58 20.08 161.16 0.36

20:00 68.58 65.88 22.75 0.07 0.43 20.44 142.40 0.30

21:00 63.20 58.86 23.37 3.42 1.20 20.20 178.46 0.37

22:00 48.84 44.66 20.39 2.67 1.37 19.81 134.03 0.26

23:00 35.97 32.00 15.47 2.40 1.32 1.30 94.92 0.24

50

Table A6 Descriptive Statistics for Real-Time Prices on the Illinois Hub

This table represents the summary statistics of twenty-four price series for real-time electricity traded on the Illinois hub. Each of the twenty-four price series are generated using weekly (settlement day) locational marginal prices (LMPs) obtained from June 6, 2006 to April 11, 2009. LMPs are expressed in terms of dollars per megawatt hour ($/MWh).


0:00 27.16 22.34 18.23 19.66 3.64 -1.79 158.95 0.17

1:00 21.29 20.11 17.81 27.89 -2.94 -120.64 70.32 0.05

2:00 19.16 18.77 15.13 14.92 -1.98 -74.32 82.55 0.11

3:00 17.67 18.23 11.90 7.04 -1.21 -38.74 58.91 0.05

4:00 18.37 18.62 18.74 22.18 -0.69 -93.35 137.02 0.01

5:00 21.33 21.13 15.86 7.90 -1.31 -56.88 74.25 0.12

6:00 31.64 25.77 27.45 7.30 1.43 -68.43 159.68 0.19

7:00 41.30 33.40 28.24 1.15 1.19 -19.64 142.21 0.29

8:00 50.47 39.63 36.63 3.67 1.47 -47.62 189.18 0.21

9:00 43.69 38.39 21.54 3.11 1.43 -2.95 135.12 0.09

10:00 52.10 42.74 29.56 5.21 1.85 -3.79 202.01 0.01

11:00 55.38 47.95 29.17 1.90 1.08 -30.67 155.70 0.22

12:00 56.28 47.94 33.42 2.43 1.12 -52.17 178.02 0.17

13:00 61.00 56.32 35.23 1.78 1.12 -19.15 205.95 0.27

14:00 61.22 50.55 39.75 4.23 1.77 4.95 239.75 0.31

15:00 57.78 41.83 42.87 4.24 1.90 0.18 234.28 0.43

16:00 61.41 40.86 51.02 5.78 2.11 -11.21 325.73 0.40

17:00 56.63 41.80 43.60 6.48 2.15 -20.36 270.86 0.34

18:00 59.61 49.12 40.84 5.31 1.71 -59.03 266.42 0.20

19:00 62.45 58.14 31.49 1.88 1.24 14.20 181.57 0.25

20:00 61.99 51.70 33.45 0.74 1.09 15.78 167.63 0.13

21:00 60.02 56.69 33.22 1.77 1.24 6.29 184.75 0.24

22:00 43.21 34.71 23.48 2.13 1.27 3.18 143.06 0.17

23:00 33.84 27.18 18.12 2.39 1.57 8.03 106.09 0.24

51

Table A7 Descriptive Statistics for Real-Time Prices on the Cinergy Hub

This table represents the summary statistics of twenty-four price series for real-time electricity traded on the Cinergy hub. Each of the twenty-four price series are generated using weekly (settlement day) locational marginal prices (LMPs) obtained from June 6, 2006 to April 11, 2009. LMPs are expressed in terms of dollars per megawatt hour ($/MWh).


0:00 28.89 23.60 17.12 12.59 3.08 6.47 135.23 0.12

1:00 25.37 21.47 13.83 12.26 2.94 5.91 111.99 0.03

2:00 23.13 20.47 10.75 7.89 2.31 1.94 81.33 0.17

3:00 22.60 19.85 12.80 35.02 4.77 -0.59 130.11 0.15

4:00 24.26 20.56 13.54 38.01 5.04 4.29 141.14 0.03

5:00 28.82 24.42 16.99 18.01 3.66 -0.85 139.72 0.02

6:00 40.62 30.50 30.12 8.46 2.58 13.52 201.17 0.18

7:00 46.20 37.10 30.01 3.45 1.70 5.77 187.90 0.32

8:00 53.04 42.10 34.29 3.75 1.84 14.61 189.70 0.27

9:00 44.82 40.07 19.08 1.49 1.13 14.38 117.01 0.10

10:00 52.81 44.74 26.27 7.06 1.99 17.89 203.79 0.04

11:00 57.16 48.58 28.39 1.98 1.40 16.46 158.59 0.22

12:00 58.46 49.36 32.43 2.99 1.61 16.61 182.43 0.14

13:00 63.25 58.05 33.36 1.46 1.12 8.69 198.77 0.27

14:00 62.44 52.74 35.28 1.47 1.27 6.23 186.93 0.33

15:00 59.59 45.04 42.02 6.26 2.08 6.19 288.80 0.38

16:00 62.57 44.79 48.62 5.93 2.13 11.64 316.62 0.44

17:00 58.60 44.45 40.88 6.72 2.19 15.83 271.93 0.36

18:00 60.94 51.24 38.96 8.40 2.31 17.24 287.86 0.11

19:00 63.56 59.50 31.47 3.49 1.41 15.16 218.42 0.23

20:00 61.99 54.30 30.40 0.94 1.06 15.04 161.56 0.29

21:00 60.25 57.56 31.57 2.22 1.32 14.54 181.68 0.27

22:00 43.43 35.99 21.42 0.19 0.90 5.64 113.72 0.23

23:00 34.45 28.46 17.33 1.60 1.41 11.05 95.27 0.21

52

Table A8 Descriptive Statistics for Real-Time Prices on the Michigan Hub

This table represents the summary statistics of twenty-four price series for real-time electricity traded on the Michigan hub. Each of the twenty-four price series are generated using weekly (settlement day) locational marginal prices (LMPs) obtained from June 6, 2006 to April 11, 2009. LMPs are expressed in terms of dollars per megawatt hour ($/MWh).


0:00 30.79 24.17 19.83 16.17 3.37 5.66 166.03 0.12

1:00 27.07 23.29 14.11 4.58 1.99 5.26 86.66 0.13

2:00 24.58 22.24 12.65 10.59 0.95 -41.42 88.46 0.11

3:00 24.65 21.21 13.55 14.24 2.98 -0.73 114.10 0.12

4:00 26.31 21.98 14.84 31.07 4.40 4.47 148.69 0.01

5:00 31.57 26.01 17.97 6.71 2.38 -0.92 123.14 0.03

6:00 44.34 32.93 33.48 7.46 2.47 14.08 206.89 0.20

7:00 48.03 38.15 31.53 1.69 1.30 -29.97 155.16 0.29

8:00 55.80 45.24 35.74 3.80 1.83 5.19 196.48 0.25

9:00 47.96 41.72 21.31 2.23 1.35 15.45 134.01 0.05

10:00 56.68 47.08 32.55 12.58 2.81 18.71 257.69 0.15

11:00 60.09 52.90 29.62 1.90 1.40 17.31 161.17 0.21

12:00 60.44 51.36 33.57 3.63 1.74 17.55 192.64 0.16

13:00 66.54 59.86 35.92 2.13 1.24 9.61 222.17 0.28

14:00 64.72 54.80 35.80 2.92 1.40 9.05 235.34 0.37

15:00 62.50 46.08 42.44 2.77 1.65 6.51 225.88 0.41

16:00 65.97 45.80 50.97 5.39 2.05 12.30 328.23 0.43

17:00 60.52 45.79 40.82 6.88 2.15 16.79 273.08 0.38

18:00 62.79 51.89 38.93 8.07 2.28 18.53 284.28 0.12

19:00 66.62 62.23 31.34 1.08 1.01 18.28 173.04 0.24

20:00 64.66 56.68 31.91 1.62 1.18 18.14 187.48 0.27

21:00 62.62 58.97 32.68 1.87 1.27 16.31 182.33 0.27

22:00 45.24 37.88 21.94 0.15 0.91 12.80 115.64 0.23

23:00 35.90 29.60 18.09 1.46 1.38 11.35 97.01 0.23

53

Table A9 Descriptive Statistics for Real-Time Prices on the Minnesota Hub

This table represents the summary statistics of twenty-four price series for real-time electricity traded on the Minnesota hub. Each of the twenty-four price series are generated using weekly (settlement day) locational marginal prices (LMPs) obtained from June 6, 2006 to April 11, 2009. LMPs are expressed in terms of dollars per megawatt hour ($/MWh).


0:00 27.81 22.56 34.41 42.06 4.18 -128.37 329.04 0.06

1:00 25.25 20.65 27.87 13.68 0.85 -121.49 172.59 0.14

2:00 20.51 18.19 26.45 10.75 0.59 -81.92 171.92 0.13

3:00 19.58 17.36 24.96 22.83 2.92 -74.93 205.90 0.15

4:00 19.91 17.21 24.65 9.28 1.03 -94.82 131.03 0.16

5:00 20.32 18.72 22.54 7.01 -0.28 -88.74 118.93 0.15

6:00 30.32 22.88 24.36 4.67 1.36 -52.50 144.31 0.07

7:00 42.95 35.13 27.71 1.24 1.24 -6.91 143.49 0.32

8:00 59.72 47.30 42.87 7.30 2.31 14.19 271.32 0.30

9:00 56.02 44.81 41.35 21.44 3.65 0.40 363.04 0.21

10:00 58.07 49.49 33.51 3.11 1.59 14.47 200.27 0.02

11:00 61.20 53.07 33.78 1.59 1.14 -9.29 186.62 0.18

12:00 67.78 54.94 55.73 17.64 3.40 -21.07 457.78 0.01

13:00 68.71 61.17 43.46 6.18 1.84 7.41 305.94 0.33

14:00 69.66 58.51 58.06 14.42 3.20 5.17 419.66 0.37

15:00 64.23 50.34 49.65 5.89 2.07 6.20 324.16 0.45

16:00 64.63 45.12 57.81 8.79 2.43 -61.11 373.58 0.31

17:00 62.70 46.36 52.35 9.39 2.60 12.76 353.42 0.25

18:00 64.17 54.52 38.98 1.58 1.32 15.78 202.42 0.23

19:00 72.48 60.56 47.76 5.67 1.90 13.58 324.01 0.18

20:00 71.90 65.61 50.29 25.07 3.69 8.12 466.76 0.22

21:00 65.52 59.38 39.29 9.83 2.22 13.67 311.25 0.16

22:00 48.50 39.60 31.23 2.22 0.76 -71.14 149.25 0.27

23:00 39.81 28.88 32.35 7.14 2.06 -55.55 197.50 0.22

54

Table A10 Descriptive Statistics for Real-Time Prices on the First Energy Hub

This table represents the summary statistics of twenty-four price series for real-time electricity traded on the First Energy hub. Each of the twenty-four price series are generated using weekly (settlement day) locational marginal prices (LMPs) obtained from June 6, 2006 to April 11, 2009. LMPs are expressed in terms of dollars per megawatt hour ($/MWh).


0:00 27.84 23.87 19.79 14.25 2.65 -33.26 157.29 0.18

1:00 23.53 21.73 16.03 4.84 0.08 -47.51 74.03 0.12

2:00 22.87 20.65 11.61 7.71 1.50 -17.03 82.54 0.10

3:00 21.69 20.15 12.70 9.67 0.50 -37.04 85.24 0.13

4:00 23.37 20.71 14.89 30.34 3.67 -24.16 144.37 0.08

5:00 28.15 24.76 16.54 11.25 2.25 -30.13 123.97 0.09

6:00 40.84 30.41 31.04 7.56 2.46 2.77 202.91 0.22

7:00 46.54 37.59 30.29 2.38 1.51 -6.69 174.75 0.31

8:00 54.07 43.64 34.72 3.87 1.85 15.14 191.21 0.26

9:00 44.52 39.69 19.39 1.38 1.02 2.84 120.49 0.07

10:00 51.73 44.25 27.89 6.83 1.74 -17.60 210.76 -0.03

11:00 56.69 48.84 28.66 1.33 1.19 0.12 163.05 0.25

12:00 57.48 50.42 32.22 3.44 1.64 17.46 183.40 0.17

13:00 62.73 55.42 36.85 13.68 2.57 11.11 313.97 0.25

14:00 60.75 50.86 34.33 3.54 1.55 17.62 230.79 0.38

15:00 57.84 43.32 40.16 3.87 1.85 5.08 224.45 0.45

16:00 61.03 40.28 49.69 5.78 2.13 -3.99 316.69 0.41

17:00 56.83 43.34 40.33 6.62 2.00 -30.06 274.40 0.38

18:00 59.68 48.55 38.20 7.60 2.23 8.15 274.67 0.12

19:00 63.05 60.10 30.87 0.94 0.86 -7.24 168.48 0.17

20:00 61.49 54.14 32.10 0.63 0.72 -22.22 163.61 0.26

21:00 60.22 57.15 32.70 1.85 1.23 11.57 180.34 0.25

22:00 43.28 36.29 22.08 0.27 0.81 -12.41 113.87 0.25

23:00 33.05 28.62 19.30 2.12 0.67 -30.80 97.57 0.30

55

Table A11

Minimum Values of Day-Ahead Prices on the Illinois Hub

The following table shows the relative frequency of the lowest day-ahead locational marginal price (LMP) for each day of the week on the Illinois hub. This table is created by using daily LMP data from June 1, 2006 to April 11, 2009 for each of the twenty-four day-ahead time series on the Illinois hub.

Hour Monday Tuesday Wednesday Thursday Friday Saturday Sunday

0:00 0.05 0.08 0.15 0.13 0.05 0.28 0.26

1:00 0.21 0.08 0.15 0.17 0.08 0.08 0.23

2:00 0.19 0.12 0.13 0.15 0.09 0.09 0.24

3:00 0.15 0.10 0.13 0.15 0.10 0.11 0.26

4:00 0.10 0.11 0.13 0.15 0.06 0.11 0.33

5:00 0.07 0.10 0.09 0.11 0.05 0.11 0.47

6:00 0.04 0.07 0.05 0.07 0.01 0.08 0.68

7:00 0.02 0.02 0.02 0.01 0.00 0.09 0.83

8:00 0.03 0.03 0.01 0.00 0.01 0.07 0.85

9:00 0.03 0.02 0.01 0.01 0.01 0.05 0.86

10:00 0.01 0.03 0.03 0.02 0.01 0.01 0.88

11:00 0.02 0.05 0.03 0.03 0.01 0.02 0.85

12:00 0.03 0.04 0.05 0.03 0.01 0.05 0.79

13:00 0.03 0.05 0.05 0.03 0.01 0.07 0.76

14:00 0.02 0.06 0.05 0.04 0.01 0.09 0.72

15:00 0.03 0.07 0.06 0.06 0.01 0.11 0.66

16:00 0.03 0.07 0.08 0.08 0.01 0.19 0.54

17:00 0.03 0.07 0.10 0.11 0.03 0.17 0.49

18:00 0.01 0.09 0.15 0.10 0.08 0.17 0.39

19:00 0.02 0.09 0.13 0.09 0.09 0.29 0.30

20:00 0.03 0.08 0.11 0.07 0.15 0.34 0.21

21:00 0.04 0.09 0.13 0.09 0.15 0.33 0.18

22:00 0.05 0.11 0.13 0.12 0.12 0.29 0.19

23:00 0.04 0.07 0.15 0.13 0.07 0.29 0.25

56

Table A12

Minimum Values of Day-Ahead Prices on the Cinergy Hub

The following table shows the relative frequency of the lowest day-ahead locational marginal price (LMP) for each day of the week on the Cinergy hub. This table is created by using daily LMP data from June 1, 2006 to April 11, 2009 for each of the twenty-four day-ahead time series on the Cinergy hub.


0:00 0.03 0.08 0.16 0.17 0.03 0.27 0.26

1:00 0.25 0.09 0.13 0.15 0.12 0.03 0.24

2:00 0.20 0.12 0.12 0.15 0.10 0.05 0.26

3:00 0.14 0.11 0.13 0.15 0.09 0.11 0.28

4:00 0.11 0.09 0.13 0.11 0.05 0.12 0.38

5:00 0.06 0.06 0.09 0.06 0.04 0.09 0.61

6:00 0.03 0.04 0.03 0.03 0.02 0.05 0.79

7:00 0.01 0.01 0.01 0.01 0.01 0.06 0.89

8:00 0.03 0.01 0.01 0.00 0.01 0.05 0.89

9:00 0.02 0.02 0.02 0.00 0.01 0.03 0.91

10:00 0.01 0.03 0.03 0.01 0.01 0.01 0.89

11:00 0.01 0.03 0.03 0.03 0.01 0.02 0.86

12:00 0.01 0.03 0.07 0.03 0.01 0.05 0.79

13:00 0.01 0.03 0.07 0.03 0.02 0.05 0.79

14:00 0.01 0.03 0.07 0.04 0.01 0.09 0.74

15:00 0.01 0.04 0.09 0.05 0.02 0.13 0.65

16:00 0.01 0.05 0.09 0.07 0.03 0.17 0.56

17:00 0.01 0.07 0.11 0.11 0.04 0.17 0.49

18:00 0.02 0.07 0.15 0.09 0.09 0.18 0.40

19:00 0.01 0.07 0.12 0.09 0.13 0.29 0.29

20:00 0.01 0.05 0.10 0.07 0.19 0.39 0.19

21:00 0.01 0.08 0.13 0.09 0.16 0.36 0.17

22:00 0.03 0.07 0.14 0.11 0.13 0.31 0.21

23:00 0.03 0.09 0.13 0.12 0.06 0.31 0.26

57

Table A13 Minimum Values of Day-Ahead Prices on the Michigan Hub

The following table shows the relative frequency of the lowest day-ahead locational marginal price (LMP) for each day of the week on the Michigan hub. This table is created by using daily LMP data from June 1, 2006 to April 11, 2009 for each of the twenty-four day-ahead time series on the Michigan hub.


0:00 0.05 0.10 0.15 0.13 0.03 0.27 0.27

1:00 0.23 0.07 0.13 0.14 0.11 0.03 0.29

2:00 0.21 0.07 0.15 0.16 0.09 0.04 0.28

3:00 0.15 0.07 0.16 0.15 0.09 0.07 0.31

4:00 0.12 0.07 0.13 0.13 0.05 0.09 0.41

5:00 0.07 0.04 0.07 0.07 0.04 0.09 0.62

6:00 0.03 0.03 0.03 0.04 0.02 0.06 0.79

7:00 0.02 0.01 0.01 0.01 0.01 0.04 0.91

8:00 0.03 0.02 0.01 0.01 0.01 0.03 0.89

9:00 0.02 0.02 0.01 0.02 0.00 0.01 0.91

10:00 0.02 0.03 0.03 0.01 0.01 0.01 0.89

11:00 0.01 0.03 0.04 0.03 0.01 0.01 0.87

12:00 0.02 0.04 0.06 0.04 0.02 0.03 0.79

13:00 0.01 0.03 0.08 0.04 0.03 0.03 0.77

14:00 0.02 0.02 0.06 0.04 0.01 0.10 0.75

15:00 0.01 0.04 0.06 0.05 0.01 0.10 0.72

16:00 0.02 0.04 0.09 0.06 0.03 0.16 0.59

17:00 0.01 0.07 0.11 0.10 0.05 0.16 0.50

18:00 0.01 0.07 0.14 0.11 0.09 0.19 0.39

19:00 0.01 0.05 0.13 0.09 0.12 0.31 0.28

20:00 0.01 0.06 0.11 0.09 0.17 0.37 0.19

21:00 0.02 0.07 0.13 0.08 0.13 0.39 0.17

22:00 0.02 0.07 0.15 0.11 0.14 0.29 0.21

23:00 0.04 0.07 0.12 0.14 0.07 0.27 0.29

58

Table A14 Minimum Values of Day-Ahead Prices on the Minnesota Hub

The following table shows the relative frequency of the lowest day-ahead locational marginal price (LMP) for each day of the week on the Minnesota hub. This table is created by using daily LMP data from June 1, 2006 to April 11, 2009 for each of the twenty-four day-ahead time series on the Minnesota hub.


0:00 0.05 0.06 0.13 0.14 0.09 0.33 0.21

1:00 0.19 0.05 0.18 0.13 0.09 0.11 0.25

2:00 0.17 0.05 0.19 0.13 0.09 0.09 0.27

3:00 0.16 0.05 0.15 0.17 0.09 0.14 0.23

4:00 0.13 0.03 0.18 0.15 0.08 0.13 0.30

5:00 0.11 0.05 0.15 0.14 0.07 0.12 0.35

6:00 0.06 0.02 0.07 0.07 0.04 0.13 0.61

7:00 0.01 0.01 0.03 0.03 0.01 0.11 0.79

8:00 0.03 0.01 0.02 0.01 0.00 0.11 0.83

9:00 0.01 0.01 0.01 0.01 0.01 0.05 0.89

10:00 0.01 0.03 0.01 0.01 0.01 0.05 0.87

11:00 0.01 0.03 0.04 0.01 0.01 0.03 0.86

12:00 0.01 0.03 0.04 0.03 0.02 0.06 0.81

13:00 0.02 0.03 0.06 0.07 0.02 0.11 0.69

14:00 0.01 0.04 0.05 0.05 0.01 0.19 0.65

15:00 0.03 0.05 0.06 0.07 0.03 0.17 0.59

16:00 0.03 0.03 0.09 0.07 0.03 0.23 0.51

17:00 0.03 0.07 0.09 0.08 0.08 0.25 0.39

18:00 0.01 0.09 0.08 0.09 0.09 0.30 0.35

19:00 0.02 0.06 0.09 0.05 0.08 0.35 0.35

20:00 0.03 0.07 0.07 0.07 0.12 0.43 0.21

21:00 0.03 0.05 0.08 0.07 0.14 0.42 0.20

22:00 0.06 0.08 0.08 0.10 0.09 0.39 0.21

23:00 0.06 0.06 0.11 0.11 0.06 0.33 0.27

59

Table A15 Minimum Values of Day-Ahead Prices on the First Energy Hub

The following table shows the relative frequency of the lowest day-ahead locational marginal price (LMP) for each day of the week on the First Energy hub. This table is created by using daily LMP data from June 1, 2006 to April 11, 2009 for each of the twenty-four day-ahead time series on the First Energy hub.


0:00 0.06 0.09 0.15 0.15 0.06 0.21 0.27

1:00 0.20 0.09 0.15 0.13 0.13 0.06 0.23

2:00 0.18 0.11 0.15 0.15 0.09 0.08 0.25

3:00 0.15 0.13 0.15 0.15 0.09 0.08 0.24

4:00 0.11 0.13 0.12 0.11 0.07 0.13 0.33

5:00 0.07 0.08 0.09 0.08 0.05 0.13 0.50

6:00 0.04 0.04 0.04 0.05 0.03 0.15 0.65

7:00 0.03 0.05 0.03 0.01 0.01 0.11 0.77

8:00 0.04 0.05 0.03 0.00 0.00 0.11 0.77

9:00 0.03 0.04 0.03 0.01 0.00 0.07 0.81

10:00 0.02 0.03 0.05 0.01 0.01 0.05 0.83

11:00 0.03 0.03 0.04 0.02 0.01 0.03 0.83

12:00 0.02 0.03 0.07 0.03 0.01 0.07 0.77

13:00 0.02 0.03 0.07 0.03 0.02 0.09 0.75

14:00 0.03 0.03 0.07 0.03 0.02 0.13 0.70

15:00 0.03 0.05 0.07 0.05 0.02 0.15 0.64

16:00 0.03 0.03 0.09 0.07 0.03 0.17 0.57

17:00 0.03 0.05 0.11 0.10 0.05 0.18 0.47

18:00 0.03 0.07 0.12 0.11 0.09 0.27 0.32

19:00 0.02 0.07 0.10 0.09 0.14 0.32 0.26

20:00 0.02 0.06 0.10 0.08 0.17 0.39 0.18

21:00 0.03 0.09 0.11 0.07 0.15 0.41 0.15

22:00 0.02 0.09 0.13 0.13 0.15 0.28 0.20

23:00 0.04 0.13 0.11 0.15 0.09 0.26 0.21

60

Table A16 Minimum Values of Real-Time Prices on the Illinois Hub

The following table shows the relative frequency of the lowest real-time (RT) locational marginal price (LMP) for each day of the week on the Illinois hub. This table is created by using daily LMP data from June 1, 2006 to April 11, 2009 for each of the twenty-four RT time series on the Illinois hub.


0:00 0.14 0.11 0.14 0.09 0.11 0.17 0.24

1:00 0.21 0.11 0.16 0.16 0.11 0.10 0.15

2:00 0.21 0.15 0.17 0.14 0.11 0.04 0.19

3:00 0.15 0.13 0.15 0.13 0.12 0.10 0.22

4:00 0.16 0.09 0.13 0.13 0.13 0.10 0.26

5:00 0.10 0.13 0.15 0.10 0.09 0.13 0.30

6:00 0.09 0.09 0.08 0.07 0.09 0.13 0.45

7:00 0.03 0.09 0.05 0.03 0.05 0.25 0.51

8:00 0.03 0.05 0.04 0.04 0.04 0.21 0.58

9:00 0.05 0.10 0.10 0.03 0.04 0.13 0.55

10:00 0.03 0.08 0.10 0.07 0.03 0.08 0.61

11:00 0.04 0.06 0.10 0.02 0.05 0.11 0.62

12:00 0.07 0.08 0.09 0.03 0.05 0.14 0.54

13:00 0.07 0.08 0.07 0.04 0.07 0.13 0.53

14:00 0.02 0.07 0.09 0.10 0.04 0.20 0.47

15:00 0.05 0.08 0.12 0.09 0.07 0.21 0.39

16:00 0.05 0.08 0.14 0.05 0.13 0.17 0.37

17:00 0.07 0.13 0.11 0.09 0.15 0.18 0.27

18:00 0.08 0.13 0.09 0.13 0.20 0.15 0.22

19:00 0.07 0.09 0.10 0.10 0.20 0.14 0.30

20:00 0.08 0.08 0.08 0.09 0.24 0.21 0.21

21:00 0.08 0.14 0.08 0.07 0.22 0.22 0.19

22:00 0.11 0.14 0.09 0.09 0.13 0.20 0.23

23:00 0.11 0.11 0.11 0.11 0.09 0.15 0.32

61

Table A17 Minimum Values of Real-Time Prices on the Cinergy Hub

The following table shows the relative frequency of the lowest real-time (RT) locational marginal price (LMP) for each day of the week on the Cinergy hub. This table is created by using daily LMP data from June 1, 2006 to April 11, 2009 for each of the twenty-four RT time series on the Cinergy hub.


0:00 0.13 0.10 0.16 0.12 0.10 0.15 0.23

1:00 0.25 0.12 0.13 0.14 0.12 0.07 0.17

2:00 0.21 0.15 0.15 0.14 0.13 0.05 0.17

3:00 0.15 0.14 0.14 0.13 0.09 0.08 0.27

4:00 0.14 0.12 0.12 0.15 0.10 0.09 0.28

5:00 0.11 0.10 0.11 0.08 0.06 0.13 0.41

6:00 0.09 0.07 0.05 0.05 0.07 0.15 0.52

7:00 0.04 0.09 0.07 0.03 0.05 0.22 0.50

8:00 0.04 0.06 0.05 0.03 0.04 0.19 0.59

9:00 0.05 0.08 0.07 0.02 0.05 0.15 0.59

10:00 0.04 0.09 0.10 0.08 0.05 0.06 0.59

11:00 0.02 0.05 0.05 0.03 0.04 0.13 0.68

12:00 0.05 0.08 0.09 0.03 0.05 0.17 0.52

13:00 0.05 0.03 0.08 0.04 0.07 0.18 0.55

14:00 0.01 0.05 0.08 0.07 0.04 0.23 0.52

15:00 0.02 0.07 0.15 0.07 0.05 0.20 0.43

16:00 0.05 0.07 0.11 0.07 0.09 0.20 0.41

17:00 0.03 0.10 0.11 0.11 0.14 0.19 0.33

18:00 0.05 0.12 0.08 0.13 0.20 0.17 0.24

19:00 0.07 0.09 0.10 0.09 0.21 0.17 0.27

20:00 0.08 0.07 0.07 0.09 0.25 0.22 0.22

21:00 0.05 0.12 0.07 0.09 0.21 0.25 0.21

22:00 0.10 0.14 0.09 0.11 0.13 0.19 0.23

23:00 0.11 0.14 0.11 0.11 0.11 0.13 0.29

62

Table A18 Minimum Values of Real-Time Prices on the Michigan Hub

The following table shows the relative frequency of the lowest real-time (RT) locational marginal price (LMP) for each day of the week on the Michigan hub. This table is created by using daily LMP data from June 1, 2006 to April 11, 2009 for each of the twenty-four RT time series on the Michigan hub.


0:00 0.11 0.08 0.16 0.15 0.10 0.17 0.23

1:00 0.23 0.11 0.13 0.13 0.11 0.07 0.21

2:00 0.23 0.15 0.14 0.14 0.13 0.06 0.16

3:00 0.15 0.12 0.16 0.12 0.10 0.10 0.25

4:00 0.15 0.11 0.12 0.12 0.09 0.12 0.29

5:00 0.09 0.07 0.09 0.08 0.07 0.16 0.43

6:00 0.09 0.06 0.05 0.06 0.06 0.17 0.51

7:00 0.05 0.11 0.06 0.03 0.05 0.22 0.49

8:00 0.04 0.06 0.03 0.03 0.03 0.22 0.59

9:00 0.05 0.07 0.08 0.02 0.04 0.15 0.59

10:00 0.03 0.09 0.09 0.08 0.04 0.09 0.57

11:00 0.02 0.05 0.06 0.03 0.03 0.13 0.68

12:00 0.05 0.08 0.08 0.04 0.05 0.19 0.52

13:00 0.05 0.05 0.09 0.05 0.07 0.17 0.52

14:00 0.03 0.05 0.08 0.07 0.03 0.23 0.51

15:00 0.03 0.07 0.13 0.05 0.05 0.21 0.46

16:00 0.05 0.07 0.13 0.07 0.08 0.21 0.39

17:00 0.06 0.10 0.12 0.09 0.15 0.17 0.31

18:00 0.06 0.10 0.09 0.13 0.19 0.16 0.26

19:00 0.08 0.09 0.09 0.09 0.22 0.15 0.27

20:00 0.06 0.06 0.09 0.09 0.23 0.24 0.23

21:00 0.07 0.13 0.09 0.08 0.21 0.23 0.19

22:00 0.10 0.14 0.09 0.10 0.13 0.22 0.22

23:00 0.10 0.12 0.11 0.11 0.11 0.16 0.29

63

Table A19 Minimum Values of Real-Time Prices on the Minnesota Hub

The following table shows the relative frequency of the lowest real-time (RT) locational marginal price (LMP) for each day of the week on the Minnesota hub. This table is created by using daily LMP data from June 1, 2006 to April 11, 2009 for each of the twenty-four RT time series on the Minnesota hub.


0:00 0.15 0.11 0.09 0.11 0.09 0.17 0.27

1:00 0.18 0.11 0.17 0.15 0.13 0.11 0.15

2:00 0.17 0.16 0.16 0.13 0.13 0.11 0.15

3:00 0.09 0.19 0.13 0.16 0.13 0.10 0.19

4:00 0.13 0.16 0.16 0.13 0.13 0.11 0.19

5:00 0.09 0.17 0.13 0.15 0.11 0.11 0.23

6:00 0.11 0.11 0.09 0.10 0.07 0.13 0.39

7:00 0.07 0.04 0.05 0.03 0.09 0.23 0.49

8:00 0.03 0.03 0.02 0.02 0.03 0.25 0.62

9:00 0.04 0.06 0.07 0.03 0.07 0.15 0.59

10:00 0.02 0.08 0.05 0.07 0.05 0.12 0.62

11:00 0.03 0.07 0.05 0.03 0.07 0.11 0.64

12:00 0.04 0.13 0.07 0.05 0.06 0.16 0.49

13:00 0.03 0.09 0.09 0.05 0.07 0.19 0.48

14:00 0.04 0.09 0.07 0.05 0.09 0.21 0.45

15:00 0.03 0.07 0.10 0.08 0.09 0.17 0.46

16:00 0.05 0.08 0.10 0.10 0.15 0.17 0.36

17:00 0.06 0.11 0.11 0.10 0.17 0.19 0.27

18:00 0.07 0.11 0.09 0.10 0.23 0.19 0.21

19:00 0.06 0.11 0.09 0.07 0.20 0.21 0.26

20:00 0.09 0.07 0.09 0.09 0.23 0.25 0.19

21:00 0.08 0.09 0.08 0.09 0.25 0.23 0.18

22:00 0.11 0.13 0.09 0.09 0.17 0.24 0.18

23:00 0.15 0.07 0.10 0.13 0.14 0.17 0.24

64

Table A20 Minimum Values of Real-Time Prices on the First Energy Hub

The following table shows the relative frequency of the lowest real-time (RT) locational marginal price (LMP) for each day of the week on the First Energy hub. This table is created by using daily LMP data from June 1, 2006 to April 11, 2009 for each of the twenty-four RT time series on the First Energy hub.


0:00 0.11 0.10 0.18 0.15 0.10 0.16 0.19

1:00 0.24 0.13 0.13 0.13 0.10 0.07 0.20

2:00 0.20 0.13 0.17 0.15 0.11 0.05 0.20

3:00 0.13 0.13 0.15 0.15 0.13 0.07 0.23

4:00 0.15 0.11 0.12 0.11 0.13 0.11 0.27

5:00 0.12 0.06 0.11 0.09 0.09 0.13 0.40

6:00 0.09 0.08 0.07 0.06 0.08 0.15 0.47

7:00 0.05 0.07 0.06 0.03 0.06 0.19 0.53

8:00 0.03 0.07 0.05 0.05 0.05 0.19 0.56

9:00 0.05 0.09 0.10 0.04 0.05 0.12 0.54

10:00 0.02 0.13 0.11 0.08 0.03 0.10 0.53

11:00 0.02 0.07 0.05 0.03 0.04 0.12 0.67

12:00 0.03 0.09 0.08 0.05 0.06 0.15 0.53

13:00 0.07 0.05 0.10 0.04 0.05 0.19 0.51

14:00 0.02 0.03 0.09 0.09 0.05 0.23 0.49

15:00 0.05 0.08 0.14 0.08 0.05 0.19 0.41

16:00 0.06 0.11 0.12 0.07 0.07 0.18 0.39

17:00 0.06 0.13 0.11 0.13 0.12 0.15 0.29

18:00 0.07 0.15 0.09 0.15 0.18 0.14 0.23

19:00 0.07 0.13 0.07 0.09 0.22 0.18 0.23

20:00 0.07 0.08 0.11 0.09 0.24 0.20 0.21

21:00 0.07 0.11 0.11 0.08 0.21 0.24 0.18

22:00 0.11 0.14 0.08 0.11 0.13 0.20 0.22

23:00 0.12 0.14 0.11 0.14 0.05 0.17 0.26

65

Table A21 Weekly Day-Ahead Augmented Dickey-Fuller Test Statistics

The table below shows the augmented Dickey-Fuller (ADF) test statistics of all twenty four day-ahead price series for each hub within the MISO footprint. These ADF test statistics are obtained using a random walk with drift test equation, which can be expressed as follows: t t t 1 1 t 1 t … p t p t.

The ADF test statistic is ADFτ= -1

SE( ). Critical values are - . 77 - .88 , and - .47 for

significance levels of 10%, 5%, and 1% respectively. The sample period for this analysis is 6/1/2006-4/11/2009.

Hour IL CINERGY MI MN FE

0:00 -7.79 -8.50 -8.44 -6.12 -8.38

1:00 -7.85 -8.74 -9.03 -6.93 -8.39 2:00 -8.10 -8.62 -9.03 -6.55 -8.60 3:00 -7.50 -8.30 -5.50 -4.33 -8.37 4:00 -5.16 -8.30 -5.82 -4.30 -8.09

5:00 -7.28 -8.12 -8.65 -4.62 -7.94 6:00 -5.82 -6.47 -6.81 -5.45 -6.84 7:00 -5.08 -6.08 -6.49 -5.00 -6.40 8:00 -5.82 -6.78 -7.12 -5.80 -6.79 9:00 -7.16 -8.21 -8.62 -6.42 -8.15

10:00 -4.78 -8.21 -8.41 -7.08 -8.23

11:00 -4.83 -5.05 -7.80 -9.01 -4.73 12:00 -2.59 -2.64 -2.80 -8.67 -2.76 13:00 -2.42 -2.31 -2.55 -9.02 -2.64 14:00 -2.30 -2.22 -2.42 -8.32 -2.52 15:00 -2.13 -2.12 -2.21 -4.68 -2.28 16:00 -2.15 -2.14 -2.24 -4.22 -2.19 17:00 -2.31 -2.29 -2.29 -4.29 -2.26 18:00 -2.85 -3.00 -6.61 -7.42 -3.74 19:00 -7.42 -7.83 -7.10 -6.10 -4.94 20:00 -8.13 -8.53 -8.18 -7.26 -4.02

21:00 -7.28 -3.34 -7.86 -7.47 -3.43 22:00 -8.11 -8.78 -8.73 -8.08 -9.21 23:00 -8.93 -9.69 -9.59 -7.91 -9.48

66

Table A22

Weekly Real-Time Augmented Dickey-Fuller Test Statistics

The table below shows the augmented Dickey-Fuller (ADF) test statistics of all twenty four real-time price series for each hub within the MISO footprint. These ADF test statistics were obtained using a random walk with drift test equation, which can be expressed as follows: t t t 1 1 t 1 t … p t p t.


0:00 -5.30 -5.32 -10.74 -11.42 -6.89 1:00 -11.45 -11.76 -10.62 -4.56 -10.70 2:00 -10.83 -10.26 -10.83 -6.28 -10.98 3:00 -11.53 -10.47 -10.76 -10.35 -10.68 4:00 -11.95 -11.79 -12.04 -10.26 -11.13 5:00 -10.75 -11.88 -11.72 -10.37 -11.03 6:00 -6.25 -9.98 -9.92 -11.23 -9.66 7:00 -9.01 -8.68 -8.97 -8.71 -8.79 8:00 -9.75 -5.71 -6.03 -8.90 -5.89 9:00 -11.02 -10.96 -11.51 -9.72 -11.32

10:00 -11.92 -11.64 -10.40 -11.89 -12.47 11:00 -5.63 -4.11 -5.89 -5.66 -5.64 12:00 -10.14 -10.53 -6.56 -12.01 -6.51 13:00 -9.07 -9.07 -8.98 -4.86 -9.37 14:00 -8.77 -3.65 -3.89 -4.58 -3.94 15:00 -4.06 -3.69 -3.74 -3.80 -3.71 16:00 -3.24 -3.29 -3.55 -3.66 -3.42 17:00 -3.95 -3.25 -3.25 -4.04 -3.39 18:00 -4.70 -4.50 -4.59 -4.59 -4.67 19:00 -9.30 -9.54 -5.87 -9.99 -10.14

20:00 -4.41 -3.87 -3.90 -4.28 -3.88

21:00 -5.60 -5.29 -5.46 -10.22 -5.52 22:00 -6.71 -6.19 -9.50 -9.14 -9.34 23:00 -9.48 -9.70 -9.54 -4.30 -5.72

The ADF test statistic is ADFτ= -1

SE( ). Critical values are - . 77 - .88 , and - .47 for


67

Table A23 MISO Weekly Forward Premia

This table shows the average 1 week forward premia and discounts ($/MWh) for each hour of the day across all five MISO hubs. Average forward premia and discounts are calculated using

the following equation: FPi 1

N∑ FitNi 1 -Si,t 1


0:00 0.68 1.4 0.63 4.3 1.49

1:00 1.39 -0.46 -1.34 -2.5 0.82

2:00 2.13 0.21 -0.44 -0.34 -0.06

3:00 2.46 -0.2 -1.55 -1.09 0.26

4:00 1.75 -1.60 -2.62 -1.56 -1.07

5:00 0.64 -3.83 -5.42 -0.29 -3.19

6:00 -3.3 -7.97 -9.76 -4.21 -9.10

7:00 -1.95 -2.64 -1.91 -1.02 -3.48

8:00 -2.43 -1.38 -1.62 -3.64 -2.67

9:00 7.92 10.21 9.67 8.11 9.88

10:00 5.45 8.02 7.25 10.16 8.59

11:00 5.33 6.33 6.68 10.52 6.48

12:00 6.18 6.51 7.92 5.49 7.38

13:00 1.88 1.79 2.05 3.36 2.22

14:00 1.31 1.68 3.02 0.99 3.01

15:00 3.44 3.29 3.75 4.9 4.34

16:00 0.79 1.68 1.5 4.92 1.62

17:00 3.78 3.51 4.08 5.02 3.55

18:00 2.7 3.66 4.25 5.37 2.46

19:00 7.65 8.65 8.59 8.17 6.76

20:00 5.57 7.85 8.10 8.93 7.10

21:00 2.06 4.12 4.65 6.75 2.97

22:00 4.72 6.17 6.95 9.42 5.56

23:00 0.79 2.68 2.79 1.15 2.92

The test statistic for this analysis is t= FP

SE(FP). Critical values are 1.64 1.96, and . 76 for


68

Table A24 1 Week Minimum Variance Hedge Ratios: Illinois Hub (Price Levels)

This table provides summary statistics of weekly minimum variance hedge ratio estimates for the Illinois hub. MV hedge ratios are calculated using a twenty week rolling estimation period. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. 130 weekly hedge ratios are estimated for each hourly time series.

Hour Mean Std. Dev. SE of Mean Minimum Maximum

0:00 0.618 0.526 0.046 -0.114 2.387

1:00 0.843 0.769 0.067 -0.512 2.859

2:00 0.684 0.755 0.066 -0.527 2.754

3:00 0.679 0.532 0.047 -0.633 1.910

4:00 0.639 0.872 0.077 -1.934 2.995

5:00 0.654 0.788 0.069 -1.653 2.810

6:00 0.884 0.793 0.070 -1.216 2.671

7:00 0.775 0.379 0.033 -0.165 1.848

8:00 0.776 0.487 0.043 -0.611 2.243

9:00 0.394 0.320 0.028 -0.181 1.356

10:00 0.493 0.290 0.025 -0.318 1.078

11:00 0.331 0.462 0.040 -1.052 1.151

12:00 0.400 0.538 0.047 -0.949 1.150

13:00 0.518 0.568 0.050 -0.864 1.481

14:00 0.608 0.446 0.039 -0.172 1.971

15:00 0.602 0.349 0.031 0.003 1.586

16:00 0.649 0.374 0.033 -0.363 1.630

17:00 0.396 0.344 0.030 -0.493 1.300

18:00 0.542 0.502 0.044 -0.746 1.406

19:00 0.472 0.235 0.021 -0.038 1.166

20:00 0.353 0.359 0.031 -0.353 1.116

21:00 0.421 0.381 0.033 -0.631 1.423

22:00 0.419 0.184 0.016 0.027 0.965

23:00 0.561 0.318 0.028 -0.181 1.226

The MV hedge ratio is estimated using the following equation: St 1 Ft et, where represents the one week hedge ratio estimate. The sample period for this analysis is 6/1/2006- 4/11/2009.

69

Table A25 1 Week Minimum Variance Hedge Ratios: Cinergy Hub (Price Levels) This table provides summary statistics of weekly minimum variance hedge ratio estimates for the Cinergy hub. MV hedge ratios are calculated using a twenty week rolling estimation period. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. 130 weekly hedge ratios are estimated for each hourly time series.


0:00 0.565 0.448 0.039 -0.151 1.920

1:00 0.906 0.680 0.060 -0.222 2.783

2:00 0.842 0.623 0.055 -0.022 2.336

3:00 0.791 0.463 0.041 -0.142 1.823

4:00 1.040 0.471 0.041 0.481 3.157

5:00 1.096 0.606 0.053 0.180 2.779

6:00 1.164 0.639 0.056 0.199 3.397

7:00 0.645 0.318 0.028 -0.292 1.654

8:00 0.642 0.336 0.029 -0.132 1.547

9:00 0.191 0.165 0.014 -0.198 0.693

10:00 0.383 0.301 0.026 -0.289 1.159

11:00 0.375 0.472 0.041 -0.965 1.458

12:00 0.412 0.522 0.046 -0.774 1.336

13:00 0.599 0.586 0.051 -0.665 1.993

14:00 0.675 0.378 0.033 0.052 1.691

15:00 0.721 0.269 0.024 0.052 1.320

16:00 0.639 0.454 0.040 -0.458 2.407

17:00 0.528 0.317 0.028 -0.424 1.110

18:00 0.660 0.510 0.045 -0.736 1.883

19:00 0.452 0.285 0.025 -0.011 1.300

20:00 0.399 0.372 0.033 -0.401 1.216

21:00 0.446 0.384 0.034 -0.429 1.412

22:00 0.446 0.184 0.016 0.013 0.921

23:00 0.511 0.265 0.023 -0.192 1.171


70

Table A26 1 Week Minimum Variance Hedge Ratios: Michigan Hub (Price Levels)

This table provides summary statistics of weekly minimum variance hedge ratio estimates for the Michigan hub. MV hedge ratios are calculated using a twenty week rolling estimation period. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. 130 weekly hedge ratios are estimated for each hourly time series.


0:00 0.552 0.517 0.045 -0.104 2.250

1:00 0.916 0.619 0.054 -0.052 2.630

2:00 0.852 0.462 0.040 0.090 1.960

3:00 0.740 0.441 0.039 -0.158 1.736

4:00 1.041 0.579 0.051 0.382 3.737

5:00 1.145 0.496 0.044 0.212 3.410

6:00 1.107 0.617 0.054 0.311 3.229

7:00 0.675 0.300 0.026 -0.364 1.611

8:00 0.651 0.333 0.029 -0.122 1.516

9:00 0.243 0.243 0.021 -0.124 0.958

10:00 0.539 0.421 0.037 -0.291 1.851

11:00 0.369 0.420 0.037 -0.668 1.225

12:00 0.412 0.489 0.043 -0.667 1.165

13:00 0.525 0.577 0.051 -0.799 1.469

14:00 0.583 0.373 0.033 -0.030 1.567

15:00 0.701 0.382 0.034 0.016 1.765

16:00 0.767 0.570 0.050 -0.348 2.174

17:00 0.534 0.336 0.029 -0.370 1.120

18:00 0.648 0.464 0.041 -0.670 1.753

19:00 0.503 0.216 0.019 0.044 1.098

20:00 0.421 0.339 0.030 -0.197 1.261

21:00 0.364 0.321 0.028 -0.435 1.046

22:00 0.431 0.188 0.017 0.009 0.885

23:00 0.533 0.302 0.027 -0.170 1.346


71

Table A27 1 Week Minimum Variance Hedge Ratios: Minnesota Hub (Price Levels) This table provides summary statistics of weekly minimum variance hedge ratio estimates for the Minnesota hub. MV hedge ratios are calculated using a twenty week rolling estimation period. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. 130 weekly hedge ratios are estimated for each hourly time series.


0:00 0.526 0.336 0.029 -0.400 1.621

1:00 0.824 0.663 0.058 -1.262 3.707

2:00 1.044 0.811 0.071 -1.120 3.612

3:00 1.095 0.682 0.060 -0.699 3.919

4:00 0.967 0.666 0.058 -0.995 2.258

5:00 0.946 0.815 0.072 -1.722 3.020

6:00 0.596 0.455 0.040 -1.006 2.571

7:00 0.687 0.249 0.022 0.074 1.475

8:00 0.818 0.382 0.034 -0.036 1.427

9:00 0.578 0.364 0.032 -0.057 1.504

10:00 0.574 0.301 0.026 -0.067 1.318

11:00 0.438 0.329 0.029 -0.330 1.166

12:00 0.427 0.488 0.043 -0.865 1.183

13:00 0.644 0.301 0.026 0.134 1.233

14:00 0.748 0.342 0.030 -0.168 1.509

15:00 0.805 0.345 0.030 -0.007 1.347

16:00 0.704 0.397 0.035 -0.011 1.488

17:00 0.657 0.357 0.031 -0.009 1.761

18:00 0.590 0.416 0.036 -0.802 1.431

19:00 0.746 0.274 0.024 0.002 1.546

20:00 0.525 0.404 0.035 -0.040 2.381

21:00 0.675 0.418 0.037 -0.281 2.164

22:00 0.717 0.296 0.026 0.000 1.317

23:00 0.814 0.387 0.034 0.082 2.320


72

Table A28 1 Week Minimum Variance Hedge Ratios: First Energy Hub (Price Levels) This table provides summary statistics of weekly minimum variance hedge ratio estimates for the First Energy hub. MV hedge ratios are calculated using a twenty week rolling estimation period. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. 130 weekly hedge ratios are estimated for each hourly time series.


0:00 0.622 0.463 0.041 0.186 2.179

1:00 0.900 0.588 0.052 0.000 2.369

2:00 0.669 0.428 0.038 0.132 1.793

3:00 0.590 0.350 0.031 -0.039 1.684

4:00 0.903 0.492 0.043 0.372 3.485

5:00 1.102 0.613 0.054 0.147 2.867

6:00 1.133 0.740 0.065 -0.027 3.776

7:00 0.676 0.399 0.035 -0.310 2.148

8:00 0.761 0.391 0.034 -0.165 2.062

9:00 0.208 0.203 0.018 -0.231 0.679

10:00 0.342 0.341 0.030 -0.525 1.160

11:00 0.307 0.448 0.039 -1.095 1.224

12:00 0.392 0.487 0.043 -0.904 1.344

13:00 0.662 0.381 0.033 -0.254 1.812

14:00 0.551 0.351 0.031 -0.169 1.263

15:00 0.579 0.369 0.032 -0.129 1.393

16:00 0.588 0.519 0.046 -0.388 2.432

17:00 0.541 0.322 0.028 -0.284 1.321

18:00 0.525 0.549 0.048 -1.198 1.724

19:00 0.316 0.266 0.023 -0.309 1.311

20:00 0.391 0.382 0.033 -0.319 1.345

21:00 0.419 0.411 0.036 -0.524 1.175

22:00 0.491 0.150 0.013 0.154 0.892

23:00 0.480 0.293 0.026 -0.023 1.320


73

Table A29 2 Week Minimum Variance Hedge Ratios: Illinois Hub (Price Levels) This table provides summary statistics of bi-weekly minimum variance hedge ratio estimates for the Illinois hub. MV hedge ratios are calculated using twenty bi-weekly spot and forward prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. 56 bi-weekly hedge ratios are estimated for each hourly time series.


0:00 0.880 0.420 0.056 0.269 2.157

1:00 0.788 0.370 0.049 0.149 1.674

2:00 0.826 0.370 0.049 0.252 1.756

3:00 0.770 0.265 0.035 0.253 1.543

4:00 1.155 0.485 0.065 0.722 3.553

5:00 0.745 0.294 0.039 0.282 1.382

6:00 0.823 0.297 0.040 0.276 1.427

7:00 0.766 0.214 0.029 0.234 1.530

8:00 1.009 0.271 0.036 0.458 1.706

9:00 0.557 0.172 0.023 0.247 0.977

10:00 0.702 0.249 0.033 0.304 1.451

11:00 0.834 0.484 0.065 -0.038 1.687

12:00 0.559 0.394 0.053 -0.342 1.120

13:00 0.552 0.440 0.059 -0.342 1.136

14:00 0.735 0.438 0.059 0.045 1.557

15:00 0.746 0.382 0.051 0.253 1.385

16:00 0.940 0.577 0.077 0.172 1.986

17:00 0.746 0.485 0.065 0.086 1.991

18:00 0.906 0.497 0.066 0.156 1.648

19:00 0.870 0.409 0.055 0.393 1.747

20:00 0.907 0.249 0.033 0.292 1.378

21:00 0.700 0.640 0.086 0.090 2.162

22:00 0.736 0.391 0.052 -0.067 1.613

23:00 0.711 0.381 0.051 0.305 1.787

The MV hedge ratio is estimated using the following equation: St 1 Ft et, where represents the two week hedge ratio estimate. The sample period for this analysis is 6/1/2006- 4/11/2009.

74

Table A30 2 Week Minimum Variance Hedge Ratios: Cinergy Hub (Price Levels) This table provides summary statistics of bi-weekly minimum variance hedge ratio estimates for the Cinergy hub. MV hedge ratios are calculated using twenty bi-weekly spot and forward prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. 56 bi-weekly hedge ratios are estimated for each hourly time series.


0:00 0.813 0.391 0.052 0.192 1.771

1:00 0.705 0.385 0.051 0.125 1.686

2:00 0.789 0.362 0.048 0.222 1.778

3:00 0.723 0.248 0.033 0.238 1.453

4:00 1.169 0.572 0.077 0.671 3.837

5:00 0.704 0.365 0.049 0.213 1.294

6:00 0.789 0.232 0.031 0.470 1.309

7:00 0.763 0.142 0.019 0.490 1.040

8:00 1.010 0.299 0.040 0.453 1.789

9:00 0.404 0.153 0.020 0.070 0.644

10:00 0.608 0.181 0.024 0.282 1.051

11:00 0.837 0.451 0.060 0.113 1.522

12:00 0.601 0.375 0.050 -0.144 1.378

13:00 0.630 0.322 0.043 -0.159 1.141

14:00 0.798 0.455 0.061 0.108 1.517

15:00 0.781 0.358 0.048 0.302 1.386

16:00 0.966 0.609 0.081 0.279 1.890

17:00 0.827 0.502 0.067 0.197 1.951

18:00 1.091 0.600 0.080 0.250 2.395

19:00 0.943 0.509 0.068 0.227 1.978

20:00 0.897 0.290 0.039 0.441 1.472

21:00 0.682 0.672 0.090 -0.020 2.295

22:00 0.690 0.338 0.045 -0.028 1.453

23:00 0.636 0.367 0.049 0.249 1.604


75

Table A31 2 Week Minimum Variance Hedge Ratios: Michigan Hub (Price Levels) This table provides summary statistics of bi-weekly minimum variance hedge ratio estimates for the Michigan hub. MV hedge ratios are calculated using twenty bi-weekly spot and forward prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. 56 bi-weekly hedge ratios are estimated for each hourly time series.


0:00 0.742 0.478 0.064 0.017 2.085

1:00 0.726 0.411 0.055 0.144 1.827

2:00 0.741 0.330 0.044 0.280 1.646

3:00 0.700 0.261 0.035 0.230 1.593

4:00 1.154 0.624 0.083 0.464 4.002

5:00 0.702 0.402 0.054 0.099 1.437

6:00 0.853 0.214 0.029 0.463 1.248

7:00 0.857 0.143 0.019 0.488 1.070

8:00 1.021 0.316 0.042 0.411 1.816

9:00 0.371 0.150 0.020 0.155 0.684

10:00 0.535 0.164 0.022 0.290 1.021

11:00 0.670 0.321 0.043 0.156 1.221

12:00 0.517 0.351 0.047 -0.208 1.132

13:00 0.527 0.324 0.043 -0.198 1.066

14:00 0.701 0.448 0.060 0.026 1.401

15:00 0.723 0.338 0.045 0.262 1.308

16:00 0.877 0.594 0.079 0.134 1.781

17:00 0.718 0.447 0.060 0.070 1.686

18:00 0.922 0.507 0.068 0.256 1.950

19:00 0.755 0.297 0.040 0.314 1.381

20:00 0.772 0.302 0.040 0.227 1.317

21:00 0.561 0.562 0.075 -0.072 1.789

22:00 0.581 0.332 0.044 -0.038 1.199

23:00 0.570 0.347 0.046 0.147 1.311


76

Table A32 2 Week Minimum Variance Hedge Ratios: Minnesota Hub (Price Levels)

This table provides summary statistics of bi-weekly minimum variance hedge ratio estimates for the Minnesota hub. MV hedge ratios are calculated using twenty bi-weekly spot and forward prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. 56 bi-weekly hedge ratios are estimated for each hourly time series.


0:00 0.686 0.326 0.044 0.140 2.095

1:00 0.953 0.193 0.026 0.649 1.416

2:00 1.299 0.368 0.049 0.611 2.089

3:00 1.321 0.418 0.056 0.805 2.319

4:00 1.225 0.310 0.041 0.672 1.842

5:00 0.939 0.320 0.043 0.583 1.669

6:00 0.804 0.340 0.045 0.293 1.558

7:00 0.830 0.256 0.034 0.576 1.560

8:00 0.975 0.443 0.059 0.407 2.063

9:00 0.700 0.420 0.056 0.379 1.857

10:00 0.855 0.277 0.037 0.546 1.759

11:00 0.778 0.490 0.065 0.088 2.030

12:00 0.419 0.578 0.077 -0.739 1.270

13:00 0.765 0.324 0.043 0.229 1.382

14:00 1.152 0.429 0.057 0.275 1.794

15:00 0.805 0.440 0.059 0.116 1.640

16:00 0.993 0.692 0.093 0.015 2.229

17:00 1.097 0.639 0.085 0.076 2.493

18:00 0.817 0.553 0.074 0.076 1.851

19:00 0.850 0.516 0.069 0.086 1.905

20:00 0.718 0.322 0.043 0.150 1.373

21:00 0.775 0.369 0.049 0.147 1.356

22:00 0.827 0.314 0.042 0.159 1.285

23:00 0.958 0.446 0.060 0.194 2.230


77

Table A33 2 Week Minimum Variance Hedge Ratios: First Energy Hub (Price Levels)

This table provides summary statistics of bi-weekly minimum variance hedge ratio estimates for the First Energy hub. MV hedge ratios are calculated using twenty bi-weekly spot and forward prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. 56 bi-weekly hedge ratios are estimated for each hourly time series.


0:00 0.884 0.345 0.046 0.380 1.973

1:00 0.709 0.426 0.057 0.034 1.570

2:00 0.632 0.387 0.052 -0.140 1.595

3:00 0.572 0.330 0.044 -0.262 1.378

4:00 1.075 0.588 0.079 0.425 3.625

5:00 0.743 0.444 0.059 -0.018 1.510

6:00 0.832 0.304 0.041 0.302 1.456

7:00 0.801 0.139 0.019 0.487 1.197

8:00 1.021 0.333 0.045 0.381 1.753

9:00 0.392 0.175 0.023 -0.132 0.671

10:00 0.665 0.195 0.026 0.399 1.247

11:00 0.679 0.369 0.049 0.047 1.459

12:00 0.490 0.374 0.050 -0.210 1.079

13:00 0.513 0.343 0.046 -0.213 1.032

14:00 0.705 0.432 0.058 -0.099 1.305

15:00 0.702 0.439 0.059 0.066 1.351

16:00 0.870 0.577 0.077 0.081 1.771

17:00 0.842 0.481 0.064 0.143 1.794

18:00 1.014 0.460 0.061 0.288 1.789

19:00 0.726 0.383 0.051 0.233 1.563

20:00 0.955 0.242 0.032 0.516 1.439

21:00 0.666 0.561 0.075 -0.069 2.026

22:00 0.807 0.266 0.036 0.134 1.421

23:00 0.757 0.374 0.050 0.280 1.557


78

Table A34 3 Week Minimum Variance Hedge Ratios: Illinois Hub (Price Levels) This table provides summary statistics of tri-weekly minimum variance hedge ratio estimates for the Illinois hub. MV hedge ratios are calculated using twenty tri-weekly spot and forward prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. 31 tri-weekly hedge ratios are estimated for each hourly time series.


0:00 0.724 0.290 0.052 0.278 1.149

1:00 0.631 0.197 0.035 0.239 1.079

2:00 0.709 0.155 0.028 0.440 0.967

3:00 0.955 0.142 0.025 0.684 1.159

4:00 1.093 0.413 0.074 0.609 2.072

5:00 1.121 0.186 0.033 0.822 1.639

6:00 1.450 0.425 0.076 0.951 2.027

7:00 0.632 0.219 0.039 0.308 0.962

8:00 1.052 0.112 0.020 0.808 1.236

9:00 0.432 0.238 0.043 0.009 0.841

10:00 0.324 0.199 0.036 -0.090 0.563

11:00 0.306 0.175 0.031 -0.026 0.533

12:00 0.147 0.211 0.038 -0.142 0.497

13:00 0.328 0.325 0.058 -0.082 0.790

14:00 0.282 0.311 0.056 -0.107 0.735

15:00 0.471 0.180 0.032 0.252 0.722

16:00 0.451 0.197 0.035 0.200 0.741

17:00 0.495 0.199 0.036 0.153 0.780

18:00 0.308 0.162 0.029 0.038 0.591

19:00 0.209 0.181 0.032 -0.160 0.468

20:00 0.046 0.491 0.088 -0.640 0.798

21:00 0.149 0.402 0.072 -0.453 0.737

22:00 0.515 0.316 0.057 -0.085 0.912

23:00 0.306 0.236 0.042 -0.108 0.649

The MV hedge ratio is estimated using the following equation: St 1 Ft et, where represents the three week hedge ratio estimate. The sample period for this analysis is 6/1/2006-4/11/2009.

79

Table A35 3 Week Minimum Variance Hedge Ratios: Cinergy Hub (Price Levels) This table provides summary statistics of tri-weekly minimum variance hedge ratio estimates for the Cinergy hub. MV hedge ratios are calculated using twenty tri-weekly spot and forward prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. 31 tri-weekly hedge ratios are estimated for each hourly time series.


0:00 0.322 0.153 0.027 0.094 0.673

1:00 0.302 0.402 0.072 -0.125 1.032

2:00 0.295 0.188 0.034 0.032 0.691

3:00 0.448 0.408 0.073 -0.078 1.032

4:00 0.685 0.106 0.019 0.530 0.825

5:00 0.864 0.101 0.018 0.705 1.147

6:00 1.279 0.527 0.095 0.651 1.949

7:00 0.539 0.062 0.011 0.413 0.694

8:00 0.746 0.186 0.033 0.475 1.122

9:00 0.198 0.165 0.030 -0.053 0.585

10:00 0.231 0.121 0.022 0.054 0.541

11:00 0.304 0.140 0.025 0.068 0.560

12:00 0.205 0.148 0.027 -0.141 0.418

13:00 0.450 0.142 0.026 0.192 0.622

14:00 0.419 0.132 0.024 0.171 0.572

15:00 0.547 0.111 0.020 0.376 0.734

16:00 0.384 0.105 0.019 0.191 0.514

17:00 0.396 0.126 0.023 0.168 0.542

18:00 0.267 0.088 0.016 0.055 0.415

19:00 0.176 0.119 0.021 -0.040 0.401

20:00 0.125 0.330 0.059 -0.398 0.541

21:00 0.049 0.134 0.024 -0.203 0.273

22:00 0.482 0.136 0.024 0.118 0.626

23:00 0.217 0.142 0.026 -0.041 0.449


80

Table A36 3 Week Minimum Variance Hedge Ratios: Michigan Hub (Price Levels) This table provides summary statistics of tri-weekly minimum variance hedge ratio estimates for the Michigan hub. MV hedge ratios are calculated using twenty tri-weekly spot and forward prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. 31 tri-weekly hedge ratios are estimated for each hourly time series.


0:00 0.252 0.137 0.025 0.052 0.587

1:00 0.444 0.252 0.045 0.135 1.042

2:00 0.406 0.120 0.022 0.271 0.797

3:00 0.436 0.400 0.072 -0.100 1.050

4:00 0.666 0.133 0.024 0.475 0.847

5:00 0.873 0.107 0.019 0.580 1.023

6:00 1.163 0.500 0.090 0.579 2.031

7:00 0.558 0.071 0.013 0.386 0.717

8:00 0.667 0.206 0.037 0.383 1.087

9:00 0.140 0.144 0.026 -0.100 0.467

10:00 0.200 0.092 0.017 0.050 0.407

11:00 0.329 0.149 0.027 0.082 0.605

12:00 0.167 0.172 0.031 -0.164 0.449

13:00 0.404 0.243 0.044 0.035 0.725

14:00 0.410 0.167 0.030 0.157 0.618

15:00 0.459 0.152 0.027 0.262 0.671

16:00 0.391 0.194 0.035 0.173 0.653

17:00 0.382 0.201 0.036 0.123 0.652

18:00 0.241 0.138 0.025 0.004 0.488

19:00 0.248 0.101 0.018 -0.008 0.464

20:00 0.090 0.321 0.058 -0.392 0.634

21:00 -0.068 0.083 0.015 -0.284 0.050

22:00 0.382 0.158 0.028 0.043 0.612

23:00 0.173 0.108 0.019 -0.036 0.344


81


This table provides summary statistics of tri-weekly minimum variance hedge ratio estimates for the Minnesota hub. MV hedge ratios are calculated using twenty tri-weekly spot and forward prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. 31 tri-weekly hedge ratios are estimated for each hourly time series.


0:00 0.804 0.228 0.041 0.484 1.190

1:00 1.011 0.365 0.065 0.447 1.502

2:00 1.508 0.534 0.096 0.592 2.361

3:00 1.616 0.473 0.085 0.817 2.393

4:00 1.452 0.497 0.089 0.664 2.174

5:00 1.151 0.260 0.047 0.710 1.584

6:00 0.291 0.540 0.097 -0.443 0.870

7:00 0.661 0.201 0.036 0.360 0.965

8:00 1.210 0.442 0.079 0.549 1.779

9:00 0.694 0.196 0.035 0.374 1.021

10:00 0.734 0.211 0.038 0.278 1.089

11:00 0.574 0.281 0.050 0.055 1.121

12:00 0.367 0.213 0.038 -0.184 0.565

13:00 0.689 0.284 0.051 0.373 1.162

14:00 0.870 0.304 0.055 0.500 1.406

15:00 0.805 0.234 0.042 0.453 1.137

16:00 0.671 0.284 0.051 0.364 1.127

17:00 0.767 0.148 0.027 0.325 0.972

18:00 0.547 0.218 0.039 0.209 1.023

19:00 0.976 0.264 0.047 0.674 1.466

20:00 0.908 0.217 0.039 0.464 1.298

21:00 0.934 0.195 0.035 0.628 1.338

22:00 1.176 0.196 0.035 0.772 1.509

23:00 0.933 0.160 0.029 0.516 1.185


82


This table provides summary statistics of tri-weekly minimum variance hedge ratio estimates for the First Energy hub. MV hedge ratios are calculated using twenty tri-weekly spot and forward prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. 31 tri-weekly hedge ratios are estimated for each hourly time series.


0:00 0.105 0.260 0.047 -0.300 0.510

1:00 0.200 0.313 0.056 -0.108 0.646

2:00 0.289 0.139 0.025 0.123 0.751

3:00 0.132 0.126 0.023 -0.048 0.552

4:00 0.401 0.190 0.034 0.129 0.659

5:00 0.489 0.064 0.012 0.310 0.622

6:00 1.114 0.544 0.098 0.459 1.863

7:00 0.491 0.135 0.024 0.300 0.739

8:00 0.688 0.185 0.033 0.417 1.042

9:00 0.099 0.189 0.034 -0.138 0.507

10:00 0.265 0.156 0.028 0.039 0.646

11:00 0.204 0.168 0.030 -0.037 0.556

12:00 0.086 0.115 0.021 -0.138 0.272

13:00 1.145 0.722 0.130 0.265 2.042

14:00 0.361 0.045 0.008 0.224 0.423

15:00 0.511 0.169 0.030 0.239 0.788

16:00 0.427 0.095 0.017 0.170 0.546

17:00 0.475 0.107 0.019 0.301 0.663

18:00 0.090 0.203 0.036 -0.333 0.518

19:00 0.068 0.142 0.025 -0.288 0.309

20:00 0.093 0.170 0.031 -0.155 0.441

21:00 0.016 0.185 0.033 -0.265 0.369

22:00 0.540 0.136 0.024 0.215 0.773

23:00 0.124 0.255 0.046 -0.217 0.518


83

Table A39 4 Week Minimum Variance Hedge Ratios: Illinois Hub (Price Levels)

This table provides summary statistics of monthly minimum variance hedge ratio estimates for the Illinois hub. MV hedge ratios are calculated using twenty monthly spot and forward prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. 19 monthly hedge ratios are estimated for each hourly time series.


0:00 1.039 0.460 0.106 0.787 2.276

1:00 0.590 0.104 0.024 0.436 0.726

2:00 0.772 0.285 0.065 0.541 1.392

3:00 0.596 0.121 0.028 0.410 0.860

4:00 1.321 0.337 0.077 0.825 2.459

5:00 0.748 0.090 0.021 0.423 0.863

6:00 0.633 0.183 0.042 0.380 1.129

7:00 0.613 0.179 0.041 0.380 1.122

8:00 0.897 0.087 0.020 0.732 1.018

9:00 0.583 0.161 0.037 0.448 0.979

10:00 0.629 0.186 0.043 0.439 1.053

11:00 0.660 0.196 0.045 0.379 1.077

12:00 0.285 0.302 0.069 -0.248 0.852

13:00 0.396 0.472 0.108 -0.476 1.106

14:00 1.072 0.211 0.048 0.638 1.468

15:00 0.963 0.100 0.023 0.740 1.144

16:00 1.410 0.162 0.037 1.130 1.648

17:00 0.879 0.163 0.038 0.579 1.159

18:00 1.137 0.257 0.059 0.480 1.411

19:00 0.695 0.088 0.020 0.475 0.845

20:00 0.875 0.083 0.019 0.608 1.032

21:00 0.742 0.275 0.063 0.259 1.230

22:00 0.685 0.206 0.047 0.429 1.145

23:00 0.411 0.205 0.047 0.246 0.953

The MV hedge ratio is estimated using the following equation: St 1 Ft et, where represents the monthly hedge ratio estimate. The sample period for this analysis is 6/1/2006- 4/11/2009.

84

Table A40 4 Week Minimum Variance Hedge Ratios: Cinergy Hub (Price Levels)

This table provides summary statistics of monthly minimum variance hedge ratio estimates for the Cinergy hub. MV hedge ratios are calculated using twenty monthly spot and forward prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. 19 monthly hedge ratios are estimated for each hourly time series.


0:00 0.901 0.365 0.084 0.649 1.867

1:00 0.569 0.092 0.021 0.431 0.696

2:00 0.754 0.281 0.064 0.552 1.372

3:00 0.538 0.110 0.025 0.440 0.792

4:00 1.282 0.342 0.078 0.801 2.512

5:00 0.746 0.086 0.020 0.480 0.899

6:00 0.728 0.249 0.057 0.382 1.345

7:00 0.665 0.165 0.038 0.393 1.055

8:00 0.864 0.185 0.042 0.455 1.098

9:00 0.488 0.120 0.027 0.205 0.610

10:00 0.684 0.142 0.032 0.382 0.926

11:00 0.925 0.204 0.047 0.472 1.213

12:00 0.541 0.253 0.058 -0.026 0.994

13:00 0.814 0.397 0.091 0.141 1.487

14:00 1.452 0.274 0.063 1.139 2.021

15:00 1.141 0.097 0.022 0.956 1.270

16:00 1.538 0.277 0.064 0.934 1.848

17:00 1.227 0.390 0.089 0.500 1.783

18:00 1.908 0.514 0.118 0.488 2.447

19:00 1.062 0.222 0.051 0.537 1.272

20:00 0.935 0.124 0.028 0.541 1.107

21:00 0.705 0.158 0.036 0.307 0.910

22:00 0.604 0.073 0.017 0.446 0.759

23:00 0.363 0.102 0.023 0.262 0.605


85

Table A41 4 Week Minimum Variance Hedge Ratios: Michigan Hub (Price Levels) This table provides summary statistics of monthly minimum variance hedge ratio estimates for the Michigan hub. MV hedge ratios are calculated using twenty monthly spot and forward prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. 19 monthly hedge ratios are estimated for each hourly time series.


0:00 0.836 0.485 0.111 0.517 2.115

1:00 0.588 0.103 0.024 0.440 0.749

2:00 0.740 0.321 0.074 0.534 1.433

3:00 0.487 0.205 0.047 0.329 0.979

4:00 1.216 0.428 0.098 0.588 2.688

5:00 0.840 0.219 0.050 0.655 1.346

6:00 0.678 0.282 0.065 0.278 1.307

7:00 0.735 0.199 0.046 0.505 1.278

8:00 0.850 0.190 0.044 0.510 1.114

9:00 0.518 0.128 0.029 0.411 0.831

10:00 0.605 0.095 0.022 0.480 0.784

11:00 0.665 0.168 0.039 0.413 1.077

12:00 0.413 0.373 0.086 -0.254 1.131

13:00 0.580 0.462 0.106 -0.113 1.337

14:00 1.182 0.224 0.051 0.730 1.444

15:00 1.158 0.101 0.023 0.975 1.363

16:00 1.463 0.180 0.041 1.094 1.657

17:00 1.121 0.305 0.070 0.684 1.658

18:00 1.593 0.401 0.092 0.507 1.991

19:00 0.857 0.145 0.033 0.513 0.989

20:00 0.888 0.114 0.026 0.562 1.041

21:00 0.747 0.198 0.045 0.299 1.127

22:00 0.615 0.066 0.015 0.476 0.789

23:00 0.353 0.108 0.025 0.244 0.620


86


This table provides summary statistics of monthly minimum variance hedge ratio estimates for the Minnesota hub. MV hedge ratios are calculated using twenty monthly spot and forward prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. 19 monthly hedge ratios are estimated for each hourly time series.


0:00 0.616 0.185 0.042 0.197 0.781

1:00 0.835 0.307 0.070 0.504 1.382

2:00 1.003 0.109 0.025 0.882 1.237

3:00 0.649 0.082 0.019 0.489 0.768

4:00 0.824 0.181 0.042 0.349 1.012

5:00 0.512 0.101 0.023 0.363 0.719

6:00 0.567 0.246 0.056 0.273 1.087

7:00 0.615 0.193 0.044 0.374 0.994

8:00 0.756 0.120 0.027 0.597 0.930

9:00 0.528 0.074 0.017 0.367 0.620

10:00 0.772 0.093 0.021 0.620 0.924

11:00 0.589 0.240 0.055 0.078 0.877

12:00 0.155 0.209 0.048 -0.105 0.600

13:00 0.466 0.143 0.033 0.225 0.625

14:00 1.070 0.366 0.084 0.270 1.363

15:00 0.805 0.318 0.073 0.126 1.071

16:00 0.900 0.410 0.094 0.046 1.437

17:00 0.863 0.340 0.078 0.102 1.113

18:00 0.608 0.316 0.072 0.070 0.992

19:00 0.618 0.265 0.061 0.115 0.972

20:00 0.453 0.191 0.044 0.161 0.753

21:00 0.402 0.137 0.032 0.149 0.566

22:00 0.509 0.217 0.050 0.079 0.749

23:00 0.665 0.209 0.048 0.316 0.918


87


This table provides summary statistics of monthly minimum variance hedge ratio estimates for the First Energy hub. MV hedge ratios are calculated using twenty monthly spot and forward prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. 19 monthly hedge ratios are estimated for each hourly time series.


0:00 0.874 0.380 0.087 0.635 1.843

1:00 0.378 0.115 0.026 0.210 0.615

2:00 0.693 0.344 0.079 0.417 1.427

3:00 0.499 0.177 0.041 0.314 0.910

4:00 1.158 0.321 0.074 0.962 2.451

5:00 0.858 0.192 0.044 0.695 1.306

6:00 0.848 0.307 0.070 0.425 1.608

7:00 0.659 0.217 0.050 0.299 1.175

8:00 0.845 0.156 0.036 0.528 1.057

9:00 0.506 0.067 0.015 0.343 0.593

10:00 0.669 0.058 0.013 0.580 0.835

11:00 0.678 0.085 0.020 0.546 0.839

12:00 0.351 0.162 0.037 -0.016 0.610

13:00 0.584 0.315 0.072 -0.122 0.983

14:00 1.120 0.204 0.047 0.727 1.402

15:00 1.138 0.108 0.025 0.974 1.358

16:00 1.401 0.154 0.035 1.097 1.605

17:00 1.193 0.294 0.067 0.705 1.680

18:00 1.836 0.531 0.122 0.533 2.551

19:00 0.614 0.127 0.029 0.354 0.834

20:00 0.832 0.100 0.023 0.562 0.991

21:00 0.625 0.210 0.048 0.215 0.992

22:00 0.658 0.066 0.015 0.539 0.865

23:00 0.514 0.102 0.023 0.356 0.794


88

Table A44 1 Week Minimum Variance Hedge Ratios: Illinois Hub (Price Differences) This table provides summary statistics of weekly minimum variance hedge ratio estimates for the Illinois hub. MV hedge ratios are calculated using a twenty week rolling estimation period. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. 129 weekly hedge ratios are estimated for each hourly time series.


0:00 0.359 0.594 0.052 -0.814 2.458

1:00 0.438 1.566 0.138 -3.706 3.137

2:00 0.227 1.075 0.095 -2.148 2.554

3:00 0.429 0.554 0.049 -1.355 1.469

4:00 0.306 1.355 0.119 -2.865 4.492

5:00 0.310 0.926 0.082 -2.018 2.590

6:00 0.756 1.235 0.109 -2.141 4.410

7:00 0.255 0.492 0.043 -0.523 1.880

8:00 0.421 0.728 0.064 -1.590 1.931

9:00 0.163 0.496 0.044 -0.611 1.777

10:00 0.328 0.483 0.042 -0.853 1.375

11:00 -0.047 0.523 0.046 -1.385 0.879

12:00 0.069 0.593 0.052 -1.576 0.890

13:00 0.256 0.597 0.053 -1.194 1.562

14:00 0.242 0.688 0.061 -0.839 2.142

15:00 0.110 0.499 0.044 -0.837 1.855

16:00 0.173 0.613 0.054 -1.048 2.322

17:00 -0.105 0.615 0.054 -1.501 1.538

18:00 0.017 0.812 0.071 -2.311 1.304

19:00 0.176 0.290 0.026 -0.484 0.765

20:00 0.018 0.487 0.043 -1.226 1.039

21:00 0.011 0.360 0.032 -1.165 0.786

22:00 0.133 0.313 0.028 -0.477 1.287

23:00 0.251 0.429 0.038 -0.812 1.078

The MV hedge ratio is estimated using the following equation: St 1 Ft et, where represents the weekly hedge ratio estimate. The sample period for this analysis is 6/1/2006- 4/11/2009.

89

Table A45 1 Week Minimum Variance Hedge Ratios: Cinergy Hub (Price Differences)

This table provides summary statistics of weekly minimum variance hedge ratio estimates for the Cinergy hub. MV hedge ratios are calculated using a twenty week rolling estimation period. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. 129 weekly hedge ratios are estimated for each hourly time series.


0:00 0.303 0.534 0.047 -0.670 2.016

1:00 0.978 0.804 0.071 -0.113 3.034

2:00 0.764 0.624 0.055 -0.069 2.176

3:00 0.622 0.461 0.041 -0.309 1.492

4:00 1.127 0.659 0.058 0.279 4.573

5:00 1.264 0.648 0.057 0.284 3.521

6:00 1.194 0.880 0.077 -1.979 3.420

7:00 0.215 0.457 0.040 -1.295 1.111

8:00 0.287 0.613 0.054 -1.567 1.480

9:00 0.003 0.222 0.020 -0.499 0.512

10:00 0.227 0.418 0.037 -0.831 1.421

11:00 0.081 0.488 0.043 -1.237 1.062

12:00 0.099 0.580 0.051 -1.355 1.263

13:00 0.359 0.615 0.054 -1.190 1.756

14:00 0.364 0.542 0.048 -0.605 1.822

15:00 0.280 0.334 0.029 -0.727 0.899

16:00 0.276 0.684 0.060 -1.028 2.814

17:00 0.182 0.476 0.042 -0.978 1.038

18:00 0.251 0.808 0.071 -1.624 2.054

19:00 0.259 0.531 0.047 -0.829 1.370

20:00 0.088 0.445 0.039 -0.861 0.881

21:00 0.210 0.385 0.034 -0.909 0.898

22:00 0.181 0.288 0.025 -0.726 0.768

23:00 0.175 0.340 0.030 -0.748 0.909


90

Table A46 1 Week Minimum Variance Hedge Ratios: Michigan Hub (Price Differences)

This table provides summary statistics of weekly minimum variance hedge ratio estimates for the Michigan hub. MV hedge ratios are calculated using a twenty week rolling estimation period. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. 129 weekly hedge ratios are estimated for each hourly time series.


0:00 0.374 0.577 0.051 -0.692 2.216

1:00 0.847 0.513 0.045 0.107 2.232

2:00 0.699 0.605 0.053 -0.296 2.320

3:00 0.485 0.587 0.052 -0.679 1.594

4:00 1.068 0.718 0.063 0.212 4.854

5:00 1.262 0.790 0.070 -0.561 3.160

6:00 1.064 0.744 0.066 -2.047 2.443

7:00 0.110 0.449 0.040 -1.276 0.979

8:00 0.186 0.649 0.057 -1.889 1.372

9:00 0.063 0.315 0.028 -0.401 1.063

10:00 0.461 0.499 0.044 -0.588 1.629

11:00 0.062 0.513 0.045 -1.055 0.952

12:00 0.077 0.597 0.053 -1.207 1.043

13:00 0.233 0.563 0.050 -1.194 1.177

14:00 0.204 0.470 0.041 -0.664 1.543

15:00 0.319 0.530 0.047 -0.828 1.645

16:00 0.507 0.788 0.069 -0.504 2.267

17:00 0.252 0.483 0.043 -0.753 1.219

18:00 0.330 0.669 0.059 -1.544 2.072

19:00 0.324 0.386 0.034 -0.257 1.109

20:00 0.131 0.410 0.036 -0.698 1.065

21:00 0.143 0.375 0.033 -0.892 0.958

22:00 0.170 0.271 0.024 -0.547 0.670

23:00 0.220 0.383 0.034 -0.799 1.118


91

Table A47 1 Week Minimum Variance Hedge Ratios: Minnesota Hub (Price Differences)

This table provides summary statistics of weekly minimum variance hedge ratio estimates for the Minnesota hub. MV hedge ratios are calculated using a twenty week rolling estimation period. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. 129 weekly hedge ratios are estimated for each hourly time series.


0:00 -0.150 0.947 0.083 -2.437 1.337

1:00 0.396 1.278 0.112 -3.104 2.449

2:00 0.586 1.336 0.118 -2.765 3.391

3:00 1.007 0.930 0.082 -0.920 3.904

4:00 0.600 1.038 0.091 -2.458 2.353

5:00 0.440 1.221 0.108 -4.156 2.801

6:00 0.349 0.616 0.054 -2.332 1.942

7:00 0.284 0.629 0.055 -2.639 1.526

8:00 0.477 0.636 0.056 -1.271 1.625

9:00 0.258 0.544 0.048 -0.586 1.595

10:00 0.454 0.456 0.040 -0.746 1.332

11:00 -0.047 0.467 0.041 -1.240 0.834

12:00 -0.122 0.731 0.064 -2.146 1.016

13:00 0.074 0.459 0.040 -1.449 0.914

14:00 0.028 0.660 0.058 -2.057 0.847

15:00 0.247 0.424 0.037 -0.795 1.245

16:00 0.097 0.585 0.052 -1.537 1.098

17:00 0.226 0.429 0.038 -0.768 1.134

18:00 0.125 0.437 0.038 -1.216 1.394

19:00 0.345 0.341 0.030 -0.261 1.825

20:00 0.169 0.422 0.037 -0.584 1.896

21:00 0.337 0.651 0.057 -0.638 2.276

22:00 0.363 0.517 0.045 -0.493 1.584

23:00 0.446 0.698 0.061 -0.944 3.114


92

Table A48 1 Week Minimum Variance Hedge Ratios: First Energy Hub (Price Differences)

This table provides summary statistics of weekly minimum variance hedge ratio estimates for the First Energy hub. MV hedge ratios are calculated using a twenty week rolling estimation period. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. 129 weekly hedge ratios are estimated for each hourly time series.


0:00 0.357 0.517 0.045 -0.552 2.029

1:00 0.883 0.606 0.053 0.036 2.712

2:00 0.485 0.492 0.043 -0.354 1.749

3:00 0.326 0.386 0.034 -0.932 1.394

4:00 0.811 0.635 0.056 0.044 2.995

5:00 1.196 0.742 0.065 0.279 4.097

6:00 1.001 0.890 0.078 -2.293 3.121

7:00 0.268 0.505 0.044 -1.135 1.732

8:00 0.417 0.578 0.051 -1.600 1.392

9:00 0.054 0.286 0.025 -0.532 0.654

10:00 0.191 0.559 0.049 -1.349 1.234

11:00 0.027 0.429 0.038 -1.024 0.805

12:00 0.085 0.429 0.038 -1.166 0.999

13:00 0.300 0.400 0.035 -0.721 1.168

14:00 0.244 0.401 0.035 -0.462 1.501

15:00 0.163 0.239 0.021 -0.723 0.728

16:00 0.126 0.684 0.060 -1.281 2.456

17:00 0.192 0.465 0.041 -1.202 1.212

18:00 0.032 0.715 0.063 -1.644 2.063

19:00 0.034 0.466 0.041 -0.899 0.920

20:00 0.058 0.449 0.039 -0.809 0.940

21:00 0.263 0.447 0.039 -0.990 0.905

22:00 0.287 0.257 0.023 -0.379 0.695

23:00 0.143 0.370 0.033 -0.795 0.840


93

Table A49 2 Week Minimum Variance Hedge Ratios: Illinois Hub (Price Differences)

This table provides summary statistics of bi-weekly minimum variance hedge ratio estimates for the Illinois hub. MV hedge ratios are calculated using twenty bi-weekly spot and forward prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. 55 bi-weekly hedge ratios are estimated for each hourly time series.


0:00 0.830 0.574 0.077 0.236 2.440

1:00 0.780 0.527 0.071 -0.057 1.967

2:00 0.722 0.487 0.066 -0.011 2.104

3:00 0.580 0.360 0.048 0.002 1.762

4:00 1.214 0.628 0.085 0.623 4.437

5:00 0.717 0.456 0.061 0.042 2.098

6:00 0.929 0.837 0.113 -0.288 2.372

7:00 0.866 0.387 0.052 0.251 1.530

8:00 1.020 0.445 0.060 0.047 1.800

9:00 0.550 0.401 0.054 -0.225 1.379

10:00 0.728 0.341 0.046 0.021 1.545

11:00 0.507 0.291 0.039 0.035 1.240

12:00 0.685 0.683 0.092 -0.348 2.048

13:00 0.437 0.792 0.107 -0.603 2.166

14:00 0.918 0.501 0.068 0.311 2.501

15:00 0.661 0.559 0.075 -0.014 2.135

16:00 0.864 0.543 0.073 0.124 1.909

17:00 0.333 0.248 0.033 -0.107 1.347

18:00 0.831 0.590 0.080 -0.037 1.910

19:00 0.675 0.433 0.058 0.185 1.579

20:00 0.772 0.327 0.044 0.295 1.500

21:00 0.560 0.551 0.074 -0.201 1.685

22:00 0.480 0.415 0.056 -0.170 1.430

23:00 0.541 0.385 0.052 0.091 1.412

The MV hedge ratio is estimated using the following equation: St 1 Ft et, where represents the bi-weekly hedge ratio estimate. The sample period for this analysis is 6/1/2006- 4/11/2009.

94


This table provides summary statistics of bi-weekly minimum variance hedge ratio estimates for the Cinergy hub. MV hedge ratios are calculated using twenty bi-weekly spot and forward prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. 55 bi-weekly hedge ratios are estimated for each hourly time series.


0:00 0.749 0.497 0.067 0.202 1.975

1:00 0.578 0.541 0.073 -0.701 2.089

2:00 0.661 0.456 0.062 -0.026 2.197

3:00 0.540 0.350 0.047 -0.024 1.586

4:00 1.136 0.697 0.094 -0.057 4.372

5:00 0.636 0.404 0.054 0.085 2.054

6:00 0.790 0.702 0.095 -0.051 2.281

7:00 0.707 0.260 0.035 0.160 1.206

8:00 0.950 0.337 0.045 0.012 1.576

9:00 0.331 0.361 0.049 -0.314 0.992

10:00 0.691 0.327 0.044 -0.017 1.231

11:00 0.647 0.369 0.050 0.081 1.606

12:00 0.643 0.598 0.081 -0.213 2.066

13:00 0.507 0.880 0.119 -0.721 2.732

14:00 0.792 0.801 0.108 -0.241 2.324

15:00 0.699 0.741 0.100 -0.196 2.509

16:00 0.819 0.857 0.116 -0.089 2.696

17:00 0.143 0.272 0.037 -0.505 1.143

18:00 0.966 0.581 0.078 0.087 1.942

19:00 0.776 0.601 0.081 0.039 1.833

20:00 0.651 0.350 0.047 0.216 1.422

21:00 0.530 0.523 0.070 -0.105 1.589

22:00 0.472 0.365 0.049 -0.085 1.431

23:00 0.467 0.314 0.042 0.073 1.225


95

Table A51 2 Week Minimum Variance Hedge Ratios: Michigan Hub (Price Differences)

This table provides summary statistics of bi-weekly minimum variance hedge ratio estimates for the Michigan hub. MV hedge ratios are calculated using twenty bi-weekly spot and forward prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. 55 bi-weekly hedge ratios are estimated for each hourly time series.


0:00 0.651 0.571 0.077 -0.052 2.318

1:00 0.665 0.543 0.073 -0.582 2.255

2:00 0.690 0.407 0.055 0.037 1.773

3:00 0.580 0.426 0.057 0.108 1.823

4:00 1.249 0.770 0.104 0.115 4.910

5:00 0.840 0.316 0.043 0.414 1.625

6:00 0.692 0.796 0.107 -0.950 1.846

7:00 0.682 0.309 0.042 0.157 1.429

8:00 0.889 0.295 0.040 0.057 1.321

9:00 0.318 0.336 0.045 -0.240 0.879

10:00 0.570 0.237 0.032 0.169 1.024

11:00 0.414 0.197 0.027 -0.064 0.777

12:00 0.382 0.320 0.043 -0.131 1.063

13:00 0.332 0.541 0.073 -0.401 1.613

14:00 0.472 0.388 0.052 -0.062 1.339

15:00 0.460 0.479 0.065 -0.174 1.556

16:00 0.734 0.674 0.091 -0.082 2.084

17:00 0.126 0.305 0.041 -0.518 1.097

18:00 0.817 0.402 0.054 0.275 1.519

19:00 0.596 0.306 0.041 0.124 1.240

20:00 0.587 0.310 0.042 0.188 1.216

21:00 0.453 0.454 0.061 -0.133 1.251

22:00 0.398 0.289 0.039 -0.053 1.004

23:00 0.445 0.368 0.050 0.006 1.256


96

Table A52 2 Week Minimum Variance Hedge Ratios: Minnesota Hub (Price Differences) This table provides summary statistics of bi-weekly minimum variance hedge ratio estimates for the Minnesota hub. MV hedge ratios are calculated using twenty bi-weekly spot and forward prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. 55 bi-weekly hedge ratios are estimated for each hourly time series.


0:00 0.538 0.452 0.061 -0.302 1.690

1:00 0.800 0.415 0.056 -0.002 1.770

2:00 1.085 0.392 0.053 0.295 1.933

3:00 1.095 0.500 0.067 0.156 2.206

4:00 1.396 0.462 0.062 0.429 2.741

5:00 0.934 0.658 0.089 -0.183 2.632

6:00 1.052 0.570 0.077 0.134 2.376

7:00 0.882 0.513 0.069 0.440 2.134

8:00 0.950 0.704 0.095 -0.063 3.194

9:00 0.757 0.598 0.081 -0.086 2.241

10:00 1.108 0.430 0.058 0.444 2.175

11:00 0.705 0.559 0.075 -0.044 1.945

12:00 0.164 0.862 0.116 -1.238 1.398

13:00 0.491 0.774 0.104 -0.467 2.275

14:00 0.669 1.114 0.150 -1.025 2.394

15:00 0.802 0.763 0.103 -0.154 2.364

16:00 0.682 0.810 0.109 -0.400 2.453

17:00 0.870 0.627 0.085 -0.072 2.557

18:00 0.831 0.891 0.120 -0.045 2.655

19:00 0.787 0.642 0.087 0.011 2.291

20:00 0.316 0.418 0.056 -0.215 1.359

21:00 0.601 0.306 0.041 0.118 1.323

22:00 0.619 0.421 0.057 -0.167 1.174

23:00 1.069 0.764 0.103 -0.015 3.100


97


This table provides summary statistics of bi-weekly minimum variance hedge ratio estimates for the First Energy hub. MV hedge ratios are calculated using twenty bi-weekly spot and forward prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. 55 bi-weekly hedge ratios are estimated for each hourly time series.


0:00 0.860 0.520 0.070 0.208 2.198

1:00 0.847 0.680 0.092 -0.023 2.455

2:00 0.523 0.452 0.061 -0.192 1.878

3:00 0.388 0.353 0.048 -0.266 1.469

4:00 1.289 0.929 0.125 -0.015 4.388

5:00 0.757 0.461 0.062 0.045 2.187

6:00 0.798 0.830 0.112 -0.149 2.486

7:00 0.660 0.299 0.040 0.238 1.512

8:00 0.945 0.405 0.055 -0.172 1.825

9:00 0.271 0.339 0.046 -0.298 0.850

10:00 0.748 0.348 0.047 0.186 1.364

11:00 0.511 0.393 0.053 -0.059 1.304

12:00 0.578 0.552 0.074 -0.187 1.802

13:00 0.341 0.677 0.091 -0.644 1.683

14:00 0.378 0.669 0.090 -0.581 2.351

15:00 0.436 0.844 0.114 -0.649 2.024

16:00 0.439 0.887 0.120 -0.843 2.183

17:00 0.189 0.340 0.046 -0.364 1.196

18:00 0.819 0.546 0.074 -0.096 1.827

19:00 0.418 0.579 0.078 -0.415 1.442

20:00 0.605 0.224 0.030 0.246 1.098

21:00 0.400 0.497 0.067 -0.194 1.260

22:00 0.517 0.321 0.043 -0.049 1.317

23:00 0.461 0.272 0.037 0.073 0.986


98


This table provides summary statistics of tri-weekly minimum variance hedge ratio estimates for the Illinois hub. MV hedge ratios are calculated using twenty tri-weekly spot and forward prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. 30 tri-weekly hedge ratios are estimated for each hourly time series.


0:00 0.677 0.328 0.060 0.171 1.181

1:00 -0.471 1.422 0.260 -3.014 1.243

2:00 -0.139 0.898 0.164 -2.022 0.751

3:00 1.012 0.156 0.028 0.634 1.277

4:00 0.590 0.249 0.045 0.085 0.978

5:00 0.891 0.294 0.054 0.113 1.505

6:00 1.786 0.703 0.128 0.902 2.759

7:00 0.885 0.218 0.040 0.596 1.325

8:00 1.037 0.233 0.043 0.649 1.409

9:00 0.452 0.540 0.099 -0.319 1.071

10:00 0.209 0.379 0.069 -0.400 0.739

11:00 -0.005 0.224 0.041 -0.384 0.282

12:00 -0.196 0.494 0.090 -0.801 0.424

13:00 -0.154 0.720 0.131 -1.021 0.740

14:00 -0.013 0.136 0.025 -0.241 0.194

15:00 0.101 0.249 0.045 -0.182 0.402

16:00 -0.219 0.300 0.055 -0.572 0.165

17:00 -0.086 0.179 0.033 -0.285 0.150

18:00 0.047 0.191 0.035 -0.179 0.346

19:00 0.036 0.169 0.031 -0.274 0.307

20:00 -0.377 0.282 0.052 -0.772 0.000

21:00 -0.092 0.285 0.052 -0.507 0.386

22:00 0.469 0.353 0.064 -0.092 0.869

23:00 0.174 0.337 0.061 -0.289 0.656

The MV hedge ratio is estimated using the following equation: St 1 Ft et, where represents the tri-weekly hedge ratio estimate. The sample period for this analysis is 6/1/2006- 4/11/2009.

99

Table A55 3 Week Minimum Variance Hedge Ratios: Cinergy Hub (Price Differences) This table provides summary statistics of tri-weekly minimum variance hedge ratio estimates for the Cinergy hub. MV hedge ratios are calculated using twenty tri-weekly spot and forward prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. 30 tri-weekly hedge ratios are estimated for each hourly time series.


0:00 0.343 0.136 0.025 0.132 0.654

1:00 0.346 0.410 0.075 -0.081 1.184

2:00 0.308 0.201 0.037 0.027 0.680

3:00 0.488 0.452 0.083 -0.070 1.187

4:00 0.772 0.130 0.024 0.564 0.934

5:00 0.862 0.274 0.050 0.454 1.507

6:00 1.428 0.860 0.157 0.437 2.559

7:00 0.366 0.254 0.046 0.001 0.922

8:00 0.681 0.256 0.047 0.402 1.269

9:00 0.107 0.273 0.050 -0.358 0.474

10:00 0.127 0.222 0.041 -0.279 0.461

11:00 0.078 0.231 0.042 -0.307 0.342

12:00 -0.159 0.442 0.081 -0.738 0.343

13:00 -0.070 0.623 0.114 -0.955 0.611

14:00 -0.030 0.183 0.033 -0.380 0.205

15:00 0.044 0.292 0.053 -0.329 0.389

16:00 -0.297 0.397 0.072 -0.761 0.173

17:00 -0.233 0.363 0.066 -0.641 0.173

18:00 0.124 0.139 0.025 -0.234 0.290

19:00 0.034 0.157 0.029 -0.275 0.183

20:00 -0.173 0.347 0.063 -0.757 0.238

21:00 -0.165 0.250 0.046 -0.558 0.284

22:00 0.412 0.159 0.029 0.092 0.595

23:00 0.135 0.121 0.022 -0.077 0.276


100

Table A56 3 Week Minimum Variance Hedge Ratios: Michigan Hub (Price Differences) This table provides summary statistics of tri-weekly minimum variance hedge ratio estimates for the Michigan hub. MV hedge ratios are calculated using twenty tri-weekly spot and forward prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. 30 tri-weekly hedge ratios are estimated for each hourly time series.


0:00 0.254 0.146 0.027 0.061 0.550

1:00 0.474 0.298 0.054 0.170 1.218

2:00 0.405 0.148 0.027 0.258 0.807

3:00 0.464 0.492 0.090 -0.074 1.283

4:00 0.790 0.162 0.030 0.488 1.008

5:00 1.181 0.358 0.065 0.637 2.013

6:00 1.127 0.714 0.130 0.355 2.305

7:00 0.405 0.185 0.034 0.000 0.884

8:00 0.599 0.222 0.041 0.380 1.121

9:00 0.053 0.210 0.038 -0.302 0.303

10:00 0.107 0.193 0.035 -0.260 0.359

11:00 0.098 0.225 0.041 -0.233 0.403

12:00 -0.141 0.399 0.073 -0.624 0.331

13:00 -0.290 0.788 0.144 -1.240 0.634

14:00 -0.081 0.188 0.034 -0.354 0.208

15:00 -0.107 0.392 0.072 -0.550 0.396

16:00 -0.182 0.264 0.048 -0.449 0.168

17:00 -0.164 0.212 0.039 -0.416 0.096

18:00 0.030 0.143 0.026 -0.161 0.236

19:00 0.082 0.117 0.021 -0.200 0.323

20:00 -0.286 0.237 0.043 -0.670 0.030

21:00 -0.313 0.153 0.028 -0.595 -0.043

22:00 0.317 0.166 0.030 0.023 0.515

23:00 0.087 0.129 0.024 -0.141 0.244


101

Table A57 3 Week Minimum Variance Hedge Ratios: Minnesota Hub (Price Differences)

This table provides summary statistics of tri-weekly minimum variance hedge ratio estimates for the Minnesota hub. MV hedge ratios are calculated using twenty tri-weekly spot and forward prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. 30 tri-weekly hedge ratios are estimated for each hourly time series.


0:00 0.626 0.132 0.024 0.209 1.064

1:00 0.515 0.713 0.130 -1.559 1.314

2:00 0.835 0.465 0.085 -0.357 1.439

3:00 1.606 0.662 0.121 0.507 2.398

4:00 1.102 0.443 0.081 0.231 1.617

5:00 1.003 0.236 0.043 0.294 1.243

6:00 -0.071 0.626 0.114 -1.093 0.701

7:00 0.642 0.302 0.055 0.116 1.088

8:00 1.019 0.531 0.097 0.150 1.626

9:00 0.662 0.349 0.064 0.099 1.107

10:00 0.484 0.317 0.058 -0.400 0.890

11:00 0.272 0.213 0.039 -0.109 0.594

12:00 0.004 0.335 0.061 -0.555 0.502

13:00 0.605 0.502 0.092 0.066 1.556

14:00 0.916 0.319 0.058 0.391 1.439

15:00 0.805 0.247 0.045 0.428 1.222

16:00 0.139 0.248 0.045 -0.219 0.791

17:00 0.446 0.174 0.032 0.066 0.759

18:00 0.523 0.235 0.043 0.341 1.336

19:00 0.934 0.366 0.067 0.445 1.565

20:00 0.280 0.170 0.031 -0.023 0.574

21:00 0.611 0.205 0.037 0.066 1.054

22:00 1.020 0.123 0.022 0.825 1.215

23:00 0.712 0.129 0.024 0.415 0.918


102

Table A58 3 Week Minimum Variance Hedge Ratios: First Energy Hub (Price Differences) This table provides summary statistics of tri-weekly minimum variance hedge ratio estimates for the First Energy hub. MV hedge ratios are calculated using twenty tri-weekly spot and forward prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. 30 tri-weekly hedge ratios are estimated for each hourly time series.


0:00 0.125 0.272 0.050 -0.305 0.544

1:00 0.309 0.278 0.051 0.019 0.987

2:00 0.246 0.131 0.024 0.082 0.806

3:00 0.078 0.157 0.029 -0.116 0.677

4:00 0.448 0.193 0.035 0.158 0.849

5:00 0.516 0.177 0.032 0.260 0.876

6:00 1.205 0.856 0.156 0.214 2.474

7:00 0.212 0.352 0.064 -0.187 0.906

8:00 0.613 0.286 0.052 0.268 1.244

9:00 0.044 0.204 0.037 -0.158 0.546

10:00 0.261 0.263 0.048 -0.060 0.824

11:00 0.081 0.189 0.035 -0.228 0.413

12:00 -0.203 0.296 0.054 -0.666 0.141

13:00 1.072 0.723 0.132 0.174 1.930

14:00 0.096 0.174 0.032 -0.171 0.309

15:00 0.308 0.286 0.052 -0.024 0.689

16:00 -0.111 0.076 0.014 -0.263 -0.006

17:00 0.029 0.203 0.037 -0.240 0.281

18:00 -0.019 0.219 0.040 -0.324 0.294

19:00 -0.102 0.118 0.021 -0.348 0.100

20:00 -0.291 0.192 0.035 -0.659 0.063

21:00 -0.027 0.426 0.078 -0.650 0.659

22:00 0.438 0.135 0.025 0.176 0.701

23:00 0.071 0.121 0.022 -0.092 0.319


103


This table provides summary statistics of monthly minimum variance hedge ratio estimates for the Illinois hub. MV hedge ratios are calculated using twenty monthly spot and forward prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. 18 monthly hedge ratios are estimated for each hourly time series.


0:00 1.017 0.520 0.123 0.695 2.232

1:00 0.238 0.164 0.039 0.003 0.567

2:00 0.345 0.428 0.101 0.114 1.360

3:00 0.194 0.233 0.055 0.035 0.782

4:00 0.083 0.527 0.124 -0.408 1.504

5:00 0.879 0.157 0.037 0.592 1.134

6:00 0.839 0.386 0.091 0.291 1.208

7:00 0.754 0.135 0.032 0.568 1.008

8:00 0.811 0.126 0.030 0.579 0.954

9:00 0.504 0.349 0.082 0.069 1.228

10:00 0.670 0.291 0.069 0.181 1.253

11:00 0.167 0.474 0.112 -0.467 1.196

12:00 0.428 0.451 0.106 -0.027 1.292

13:00 -0.313 0.749 0.177 -0.918 1.294

14:00 0.407 0.464 0.109 0.028 1.443

15:00 0.537 0.469 0.110 0.160 1.624

16:00 1.087 0.250 0.059 0.666 1.541

17:00 0.383 0.565 0.133 -0.443 1.253

18:00 0.944 0.287 0.068 0.618 1.621

19:00 0.913 0.159 0.037 0.528 1.127

20:00 0.866 0.154 0.036 0.483 1.089

21:00 1.057 0.185 0.044 0.745 1.415

22:00 0.975 0.173 0.041 0.775 1.325

23:00 0.691 0.145 0.034 0.491 1.007


104


This table provides summary statistics of monthly minimum variance hedge ratio estimates for the Cinergy hub. MV hedge ratios are calculated using twenty monthly spot and forward prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. 18 monthly hedge ratios are estimated for each hourly time series.


0:00 0.741 0.481 0.113 0.406 1.831

1:00 0.221 0.146 0.034 0.048 0.562

2:00 0.364 0.440 0.104 0.114 1.408

3:00 0.227 0.227 0.054 0.087 0.793

4:00 -0.043 0.573 0.135 -0.545 1.461

5:00 0.819 0.096 0.023 0.632 1.024

6:00 0.859 0.459 0.108 0.173 1.368

7:00 0.684 0.251 0.059 0.341 0.992

8:00 0.789 0.216 0.051 0.509 1.054

9:00 0.378 0.118 0.028 0.163 0.530

10:00 0.875 0.246 0.058 0.465 1.271

11:00 0.681 0.394 0.093 0.130 1.364

12:00 0.978 0.442 0.104 0.574 1.967

13:00 0.557 0.375 0.088 0.041 1.305

14:00 1.495 0.391 0.092 1.038 2.416

15:00 0.843 0.208 0.049 0.560 1.218

16:00 1.477 0.220 0.052 1.139 1.956

17:00 1.076 0.782 0.184 0.267 2.817

18:00 2.239 0.533 0.126 0.972 2.909

19:00 1.258 0.304 0.072 0.572 1.581

20:00 0.831 0.133 0.031 0.596 1.042

21:00 0.947 0.125 0.029 0.680 1.153

22:00 0.883 0.089 0.021 0.740 0.979

23:00 0.619 0.078 0.018 0.465 0.744


105

Table A61 4 Week Minimum Variance Hedge Ratios: Michigan Hub (Price Differences) This table provides summary statistics of monthly minimum variance hedge ratio estimates for the Michigan hub. MV hedge ratios are calculated using twenty monthly spot and forward prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. 18 monthly hedge ratios are estimated for each hourly time series.


0:00 0.836 0.571 0.135 0.493 2.145

1:00 0.312 0.170 0.040 0.069 0.603

2:00 0.357 0.428 0.101 0.151 1.356

3:00 0.227 0.257 0.061 0.063 0.876

4:00 -0.130 0.443 0.104 -0.524 1.038

5:00 0.906 0.156 0.037 0.730 1.315

6:00 0.658 0.358 0.084 0.188 1.096

7:00 0.767 0.283 0.067 0.271 1.187

8:00 0.794 0.229 0.054 0.448 1.104

9:00 0.414 0.266 0.063 -0.013 1.025

10:00 0.783 0.143 0.034 0.382 0.921

11:00 0.235 0.415 0.098 -0.406 1.073

12:00 0.472 0.402 0.095 0.037 1.281

13:00 0.061 0.625 0.147 -0.485 1.442

14:00 0.732 0.455 0.107 0.220 1.746

15:00 0.815 0.378 0.089 0.441 1.662

16:00 1.255 0.198 0.047 1.046 1.657

17:00 0.975 0.800 0.189 0.028 2.633

18:00 1.775 0.389 0.092 0.901 2.301

19:00 0.954 0.152 0.036 0.610 1.111

20:00 0.819 0.113 0.027 0.595 1.003

21:00 0.904 0.194 0.046 0.590 1.193

22:00 0.904 0.118 0.028 0.752 1.082

23:00 0.609 0.079 0.019 0.488 0.724


106

Table A62 4 Week Minimum Variance Hedge Ratios: Minnesota Hub (Price Differences) This table provides summary statistics of monthly minimum variance hedge ratio estimates for the Minnesota hub. MV hedge ratios are calculated using twenty monthly spot and forward prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. 18 monthly hedge ratios are estimated for each hourly time series.


0:00 0.354 0.204 0.048 -0.007 0.682

1:00 0.723 0.419 0.099 0.332 1.396

2:00 0.761 0.139 0.033 0.601 1.082

3:00 0.448 0.102 0.024 0.253 0.649

4:00 -0.230 0.387 0.091 -0.814 0.468

5:00 0.384 0.181 0.043 0.129 0.800

6:00 0.847 0.325 0.077 0.307 1.285

7:00 0.892 0.214 0.051 0.560 1.254

8:00 0.706 0.248 0.058 0.402 1.168

9:00 0.589 0.287 0.068 0.216 1.253

10:00 0.990 0.259 0.061 0.487 1.462

11:00 0.604 0.252 0.059 0.137 0.938

12:00 -0.073 0.535 0.126 -0.654 1.374

13:00 0.169 0.429 0.101 -0.360 1.514

14:00 0.116 0.470 0.111 -0.852 1.463

15:00 0.805 0.225 0.053 -0.149 0.918

16:00 0.270 0.166 0.039 -0.090 0.526

17:00 0.706 0.280 0.066 0.145 1.005

18:00 0.887 0.421 0.099 0.213 1.641

19:00 0.942 0.471 0.111 0.196 1.777

20:00 0.226 0.191 0.045 -0.036 0.496

21:00 0.555 0.348 0.082 0.040 1.102

22:00 0.559 0.284 0.067 0.109 0.962

23:00 0.735 0.288 0.068 0.236 1.084


107


This table provides summary statistics of monthly minimum variance hedge ratio estimates for the First Energy hub. MV hedge ratios are calculated using twenty monthly spot and forward prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. 18 monthly hedge ratios are estimated for each hourly time series.


0:00 0.758 0.453 0.107 0.474 1.795

1:00 0.233 0.185 0.044 -0.019 0.664

2:00 0.206 0.492 0.116 -0.170 1.351

3:00 0.141 0.276 0.065 -0.128 0.810

4:00 -0.291 0.554 0.131 -0.837 1.076

5:00 0.896 0.172 0.041 0.666 1.326

6:00 0.875 0.364 0.086 0.324 1.351

7:00 0.841 0.153 0.036 0.548 1.153

8:00 0.847 0.242 0.057 0.516 1.203

9:00 0.451 0.088 0.021 0.262 0.577

10:00 0.837 0.184 0.043 0.507 1.164

11:00 0.342 0.259 0.061 -0.068 0.736

12:00 0.483 0.336 0.079 0.065 1.246

13:00 0.123 0.416 0.098 -0.295 0.983

14:00 0.600 0.486 0.114 0.045 1.689

15:00 0.781 0.405 0.096 0.424 1.689

16:00 1.210 0.211 0.050 0.976 1.612

17:00 0.983 0.794 0.187 0.077 2.614

18:00 2.163 0.563 0.133 0.978 3.235

19:00 0.624 0.198 0.047 0.254 0.946

20:00 0.692 0.102 0.024 0.464 0.846

21:00 0.818 0.134 0.032 0.551 1.058

22:00 0.853 0.113 0.027 0.720 1.028

23:00 0.552 0.137 0.032 0.334 0.779


108

Table A64 1 Week GARCH(1,1) Hedge Ratios: Illinois Hub This table provides summary statistics of weekly GARCH(1,1) hedge ratio estimates for the Illinois hub. GARCH(1,1) hedge ratios are calculated using twenty weekly spot and forward prices. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. 129 weekly hedge ratios are estimated for each hourly time series.


0:00 0.404 0.363 0.032 -0.526 1.666 1:00 0.725 1.055 0.093 -3.049 3.418 2:00 0.348 0.910 0.080 -2.772 1.978 3:00 0.558 0.383 0.034 -0.745 1.631 4:00 0.580 0.709 0.062 -0.857 2.268 5:00 0.365 0.779 0.069 -2.272 2.385 6:00 0.725 0.955 0.084 -1.182 3.641 7:00 0.240 0.699 0.062 -1.846 2.047 8:00 0.277 0.675 0.059 -0.959 2.122 9:00 0.147 0.528 0.046 -1.078 1.848

10:00 0.421 0.538 0.047 -1.048 1.514 11:00 0.129 0.510 0.045 -2.169 0.956 12:00 0.132 0.545 0.048 -1.255 1.244 13:00 0.297 0.532 0.047 -1.078 1.308 14:00 0.098 0.637 0.056 -1.407 1.696 15:00 0.219 0.428 0.038 -1.001 1.519 16:00 0.284 0.441 0.039 -0.923 2.362 17:00 0.045 0.627 0.055 -1.788 1.356 18:00 -0.063 0.813 0.072 -2.711 1.257 19:00 0.193 0.302 0.027 -0.623 0.838 20:00 -0.018 0.473 0.042 -1.226 1.038 21:00 0.028 0.525 0.046 -1.474 1.088 22:00 0.135 0.436 0.038 -0.892 1.487 23:00 0.418 0.379 0.033 -1.018 1.490

The GARCH(1,1) hedge ratio is estimated using the following equation: St 1 Ft et. Bollerslev (1986) assumes that the error term in the above equation is conditional on information obtained in the previous period. The conditional variance of the estimation equation, , is assumed to be normally distributed and is modeled as an autoregressive moving average (ARMA) process (Bollerslev 1986). The ARMA process is expressed as:

t 1 t-1

1 t-1 . The optimal hedge ratio, , minimizes the conditional variance of the

hedge portfolio. The iterative process described by Bollerslev (1986), which uses maximum likelihood estimation (MLE), is utilized to estimate this model. The sample period for this analysis is 6/1/2006-4/11/2009.

109

Table A65 1 Week GARCH(1,1) Hedge Ratios: Cinergy Hub This table provides summary statistics of weekly GARCH(1,1) hedge ratio estimates for the Cinergy hub. GARCH(1,1) hedge ratios are calculated using twenty weekly spot and forward prices. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. 129 weekly hedge ratios are estimated for each hourly time series.


0:00 0.290 0.371 0.033 -0.280 1.620 1:00 0.819 0.949 0.084 -0.381 3.779 2:00 0.586 0.615 0.054 -0.152 2.274 3:00 0.519 0.529 0.047 -0.486 1.644 4:00 0.935 0.485 0.043 0.005 2.585 5:00 0.935 0.512 0.045 0.088 2.519 6:00 0.920 0.756 0.067 -1.777 2.766 7:00 0.191 0.536 0.047 -1.633 1.274 8:00 0.244 0.654 0.058 -1.622 1.407 9:00 0.014 0.281 0.025 -1.071 0.668

10:00 0.329 0.408 0.036 -0.559 1.626 11:00 0.145 0.513 0.045 -1.768 1.031 12:00 0.199 0.455 0.040 -1.100 1.354 13:00 0.293 0.476 0.042 -0.905 1.464 14:00 0.316 0.514 0.045 -1.770 1.743 15:00 0.318 0.331 0.029 -0.562 1.156 16:00 0.331 0.521 0.046 -0.840 1.976 17:00 0.174 0.518 0.046 -1.315 1.392 18:00 0.199 0.638 0.056 -1.978 2.208 19:00 0.324 0.392 0.035 -0.382 1.280 20:00 0.080 0.459 0.040 -0.869 1.015 21:00 0.214 0.483 0.043 -1.085 1.115 22:00 0.270 0.376 0.033 -0.821 1.424 23:00 0.274 0.383 0.034 -0.867 1.225


t 1 t-1



110

Table A66 1 Week GARCH(1,1) Hedge Ratios: Michigan Hub This table provides summary statistics of weekly GARCH(1,1) hedge ratio estimates for the Michigan hub. GARCH(1,1) hedge ratios are calculated using twenty weekly spot and forward prices. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. 129 weekly hedge ratios are estimated for each hourly time series.


0:00 0.304 0.381 0.034 -0.405 1.994 1:00 0.777 0.663 0.058 -0.257 3.143 2:00 0.675 0.713 0.063 -0.344 3.429 3:00 0.551 0.771 0.068 -0.760 2.959 4:00 0.972 0.676 0.059 -0.025 3.701 5:00 0.988 0.512 0.045 -0.261 2.164 6:00 0.890 0.666 0.059 -1.856 2.463 7:00 0.205 0.541 0.048 -1.501 1.311 8:00 0.203 0.640 0.056 -1.750 1.713 9:00 0.073 0.306 0.027 -0.561 0.740

10:00 0.409 0.404 0.036 -0.958 1.263 11:00 0.124 0.552 0.049 -1.815 1.108 12:00 0.186 0.492 0.043 -1.640 1.170 13:00 0.300 0.497 0.044 -0.775 1.231 14:00 0.178 0.371 0.033 -0.713 1.187 15:00 0.347 0.558 0.049 -0.712 2.229 16:00 0.459 0.654 0.058 -0.389 2.267 17:00 0.228 0.498 0.044 -1.018 1.289 18:00 0.058 0.781 0.069 -2.164 2.863 19:00 0.379 0.386 0.034 -0.297 1.147 20:00 0.135 0.455 0.040 -1.041 1.097 21:00 0.171 0.486 0.043 -1.039 1.323 22:00 0.197 0.360 0.032 -0.890 0.915 23:00 0.291 0.410 0.036 -0.883 1.310


t 1 t-1



111

Table A67 1 Week GARCH(1,1) Hedge Ratios: Minnesota Hub This table provides summary statistics of weekly GARCH(1,1) hedge ratio estimates for the Minnesota hub. GARCH(1,1) hedge ratios are calculated using twenty weekly spot and forward prices. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. 129 weekly hedge ratios are estimated for each hourly time series.


0:00 -0.056 0.838 0.074 -2.768 1.808 1:00 0.469 0.725 0.064 -1.445 2.596 2:00 0.635 0.921 0.081 -2.380 2.975 3:00 0.881 0.891 0.078 -1.000 4.158 4:00 0.828 0.860 0.076 -1.855 2.748 5:00 0.549 0.980 0.086 -3.110 3.359 6:00 0.240 0.536 0.047 -1.700 1.497 7:00 0.204 0.753 0.066 -1.859 1.425 8:00 0.584 0.594 0.052 -0.681 1.587 9:00 0.275 0.420 0.037 -0.527 1.206

10:00 0.471 0.393 0.035 -0.234 1.473 11:00 0.154 0.419 0.037 -1.369 1.070 12:00 0.027 0.634 0.056 -2.022 1.220 13:00 0.090 0.474 0.042 -1.409 0.848 14:00 0.239 0.448 0.039 -1.391 0.808 15:00 0.805 0.395 0.035 -0.629 1.640 16:00 0.235 0.551 0.048 -1.193 1.296 17:00 0.362 0.639 0.056 -0.855 2.175 18:00 0.300 0.607 0.053 -1.222 1.973 19:00 0.475 0.420 0.037 -0.641 1.343 20:00 0.078 0.407 0.036 -0.878 1.871 21:00 0.284 0.529 0.047 -1.129 1.542 22:00 0.370 0.466 0.041 -0.659 1.771 23:00 0.437 0.255 0.022 -0.922 1.135


t 1 t-1



112

Table A68 1 Week GARCH(1,1) Hedge Ratios: First Energy Hub This table provides summary statistics of weekly GARCH(1,1) hedge ratio estimates for the First Energy hub. GARCH(1,1) hedge ratios are calculated using twenty weekly spot and forward prices. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. 129 weekly hedge ratios are estimated for each hourly time series.


0:00 0.267 0.365 0.032 -0.500 2.349 1:00 0.828 0.798 0.070 -0.307 3.585 2:00 0.469 0.573 0.050 -0.330 2.010 3:00 0.428 0.394 0.035 -0.212 1.434 4:00 0.795 0.645 0.057 -0.257 3.022 5:00 0.883 0.524 0.046 0.019 2.777 6:00 0.748 0.850 0.075 -2.425 2.693 7:00 0.290 0.527 0.046 -1.743 1.771 8:00 0.409 0.654 0.058 -1.553 1.362 9:00 0.011 0.347 0.031 -0.781 0.952

10:00 0.332 0.521 0.046 -0.820 1.432 11:00 0.156 0.474 0.042 -1.252 1.174 12:00 0.153 0.430 0.038 -1.647 1.277 13:00 0.426 0.465 0.041 -0.872 1.355 14:00 0.215 0.365 0.032 -0.551 1.375 15:00 0.124 0.294 0.026 -0.747 0.816 16:00 0.243 0.507 0.045 -0.669 1.633 17:00 0.171 0.496 0.044 -1.663 1.424 18:00 -0.170 0.726 0.064 -1.686 2.799 19:00 0.106 0.428 0.038 -0.893 1.012 20:00 0.122 0.485 0.043 -0.782 1.222 21:00 0.196 0.549 0.048 -1.247 1.219 22:00 0.308 0.255 0.022 -0.428 0.886 23:00 0.273 0.299 0.026 -0.719 1.158


t 1 t-1



113

Table A69 2 Week GARCH(1,1) Hedge Ratios: Illinois Hub

This table provides summary statistics of bi-weekly GARCH(1,1) hedge ratio estimates for the Illinois hub. GARCH(1,1) hedge ratios are calculated using twenty bi-weekly spot and forward prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. 55 bi-weekly hedge ratios are estimated for each hourly time series.

Hour Mean Std Dev SE of Mean Minimum Maximum

0:00 0.752 0.501 0.068 -0.099 2.344 1:00 0.693 0.586 0.079 -0.290 2.143 2:00 0.578 0.533 0.072 -0.070 1.816 3:00 0.536 0.439 0.059 0.002 1.802 4:00 0.967 0.394 0.053 0.211 1.805 5:00 0.692 0.401 0.054 0.065 1.639 6:00 0.971 0.512 0.069 0.092 1.884 7:00 0.734 0.445 0.060 -0.024 1.734 8:00 0.683 0.460 0.062 -0.754 1.515 9:00 0.463 0.556 0.075 -0.394 1.753

10:00 0.666 0.300 0.040 0.223 1.212 11:00 0.565 0.177 0.024 0.189 1.160 12:00 0.514 0.566 0.076 -0.311 1.636 13:00 0.426 0.726 0.098 -0.635 2.169 14:00 0.712 0.702 0.095 -0.266 2.918 15:00 0.425 0.327 0.044 0.012 1.249 16:00 0.580 0.582 0.078 -0.162 2.239 17:00 0.152 0.376 0.051 -0.280 1.645 18:00 0.907 0.656 0.088 0.070 2.250 19:00 0.649 0.461 0.062 0.071 1.688 20:00 0.748 0.425 0.057 -0.010 1.588 21:00 0.446 0.493 0.066 -0.239 1.598 22:00 0.552 0.504 0.068 -0.231 1.719 23:00 0.366 0.406 0.055 -0.438 1.188


t 1 t-1



114

Table A70 2 Week GARCH(1,1) Hedge Ratios: Cinergy Hub

This table provides summary statistics of bi-weekly GARCH(1,1) hedge ratio estimates for the Cinergy hub. GARCH(1,1) hedge ratios are calculated using twenty bi-weekly spot and forward prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. 55 bi-weekly hedge ratios are estimated for each hourly time series.


0:00 0.665 0.433 0.058 0.113 2.066 1:00 0.567 0.623 0.084 -0.364 2.040 2:00 0.563 0.487 0.066 0.065 1.912 3:00 0.531 0.424 0.057 0.036 1.789 4:00 0.995 0.419 0.057 0.022 1.829 5:00 0.540 0.299 0.040 -0.037 1.850 6:00 0.794 0.451 0.061 0.128 2.119 7:00 0.631 0.377 0.051 -0.333 1.575 8:00 0.826 0.374 0.050 0.078 1.717 9:00 0.278 0.513 0.069 -0.505 1.143

10:00 0.700 0.386 0.052 0.177 1.646 11:00 0.655 0.328 0.044 0.217 1.970 12:00 0.631 0.555 0.075 -0.200 1.960 13:00 0.512 0.660 0.089 -0.795 2.343 14:00 0.751 0.725 0.098 -0.051 2.389 15:00 0.651 0.751 0.101 -0.109 2.961 16:00 0.804 0.743 0.100 -0.155 2.644 17:00 0.145 0.360 0.049 -0.332 1.228 18:00 0.771 0.516 0.070 -0.054 1.752 19:00 0.677 0.598 0.081 -0.279 1.560 20:00 0.531 0.291 0.039 0.139 1.285 21:00 0.366 0.338 0.046 -0.083 1.334 22:00 0.533 0.505 0.068 -0.153 1.788 23:00 0.369 0.243 0.033 -0.069 0.791


t 1 t-1



115

Table A71 2 Week GARCH(1,1) Hedge Ratios: Michigan Hub This table provides summary statistics of bi-weekly GARCH(1,1) hedge ratio estimates for the Michigan hub. GARCH(1,1) hedge ratios are calculated using twenty bi-weekly spot and forward prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. 55 bi-weekly hedge ratios are estimated for each hourly time series.


0:00 0.672 0.502 0.068 0.045 2.139 1:00 0.635 0.751 0.101 -0.355 2.238 2:00 0.488 0.398 0.054 0.010 1.384 3:00 0.689 0.489 0.066 -0.263 1.732 4:00 1.164 0.578 0.078 0.246 2.646 5:00 0.595 0.340 0.046 0.045 1.711 6:00 1.069 0.442 0.060 0.226 2.355 7:00 0.785 0.415 0.056 0.266 2.001 8:00 0.767 0.328 0.044 0.096 1.356 9:00 0.367 0.455 0.061 -0.217 0.985

10:00 0.687 0.320 0.043 0.184 1.277 11:00 0.488 0.213 0.029 -0.024 1.013 12:00 0.365 0.323 0.044 -0.312 1.131 13:00 0.377 0.513 0.069 -0.406 1.498 14:00 0.318 0.513 0.069 -0.553 2.295 15:00 0.422 0.455 0.061 -0.021 1.644 16:00 0.536 0.455 0.061 -0.168 1.828 17:00 0.051 0.313 0.042 -0.290 0.991 18:00 0.656 0.342 0.046 0.159 1.582 19:00 0.594 0.371 0.050 -0.133 1.396 20:00 0.465 0.279 0.038 -0.037 1.003 21:00 0.331 0.364 0.049 -0.136 1.232 22:00 0.494 0.483 0.065 -0.089 2.430 23:00 0.407 0.393 0.053 -0.030 1.316


t 1 t-1



116

Table A72 2 Week GARCH(1,1) Hedge Ratios: Minnesota Hub This table provides summary statistics of bi-weekly GARCH(1,1) hedge ratio estimates for the Minnesota hub. GARCH(1,1) hedge ratios are calculated using twenty bi-weekly spot and forward prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. 55 bi-weekly hedge ratios are estimated for each hourly time series.


0:00 0.451 0.366 0.049 -0.340 0.970 1:00 0.780 0.534 0.072 -0.213 1.705 2:00 0.941 0.544 0.073 -0.179 1.914 3:00 0.922 0.587 0.079 -0.455 2.267 4:00 0.953 0.765 0.103 0.078 2.467 5:00 0.984 1.004 0.135 -0.137 4.968 6:00 1.019 0.612 0.082 0.048 2.414 7:00 0.642 0.320 0.043 0.222 1.710 8:00 0.874 0.527 0.071 0.320 3.106 9:00 0.769 0.654 0.088 -0.037 2.248

10:00 0.972 0.525 0.071 0.232 2.359 11:00 0.704 0.534 0.072 -0.077 1.977 12:00 0.011 0.853 0.115 -1.409 1.323 13:00 0.697 0.753 0.102 -0.367 3.125 14:00 0.862 0.963 0.130 -0.588 2.269 15:00 0.805 0.708 0.095 -0.008 1.970 16:00 0.840 0.792 0.107 -0.296 2.311 17:00 0.694 0.531 0.072 -0.084 2.028 18:00 0.950 0.824 0.111 0.039 2.381 19:00 0.728 0.605 0.082 -0.099 2.187 20:00 0.367 0.453 0.061 -0.253 1.706 21:00 0.531 0.343 0.046 -0.244 1.695 22:00 0.634 0.382 0.052 -0.001 1.312 23:00 0.688 0.504 0.068 -0.178 2.068


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Table A73 2 Week GARCH(1,1) Hedge Ratios: First Energy Hub This table provides summary statistics of bi-weekly GARCH(1,1) hedge ratio estimates for the First Energy hub. GARCH(1,1) hedge ratios are calculated using twenty bi-weekly spot and forward prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. 55 bi-weekly hedge ratios are estimated for each hourly time series.


0:00 0.763 0.480 0.065 0.075 2.007 1:00 0.694 0.696 0.094 -0.178 2.218 2:00 0.360 0.445 0.060 -0.232 1.862 3:00 0.439 0.432 0.058 -0.186 1.679 4:00 1.323 1.331 0.179 -0.184 4.282 5:00 0.708 0.548 0.074 -0.089 2.263 6:00 0.902 0.657 0.089 -0.380 2.552 7:00 0.545 0.451 0.061 -0.261 2.013 8:00 0.819 0.436 0.059 -0.391 1.563 9:00 0.307 0.473 0.064 -0.516 1.174

10:00 0.795 0.428 0.058 0.017 1.622 11:00 0.629 0.554 0.075 -0.074 3.430 12:00 0.574 0.513 0.069 -0.156 1.739 13:00 0.383 0.644 0.087 -0.662 1.827 14:00 0.248 0.733 0.099 -0.837 2.214 15:00 0.301 0.618 0.083 -0.618 2.237 16:00 0.359 0.636 0.086 -0.679 2.263 17:00 0.158 0.672 0.091 -0.574 2.482 18:00 0.415 0.596 0.080 -0.755 1.658 19:00 0.376 0.701 0.094 -0.869 1.603 20:00 0.517 0.241 0.032 0.090 1.054 21:00 0.297 0.378 0.051 -0.258 1.023 22:00 0.611 0.455 0.061 -0.268 2.266 23:00 0.453 0.368 0.050 -0.316 1.423


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Table A74 3 Week GARCH(1,1) Hedge Ratios: Illinois Hub This table provides summary statistics of tri-weekly GARCH(1,1) hedge ratio estimates for the Illinois hub. GARCH(1,1) hedge ratios are calculated using twenty tri-weekly spot and forward prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. 30 tri-weekly hedge ratios are estimated for each hourly time series.


0:00 0.702 0.289 0.053 0.103 1.073 1:00 0.708 0.815 0.149 -1.011 2.100 2:00 0.115 0.560 0.102 -1.171 0.915 3:00 1.059 0.178 0.033 0.776 1.437 4:00 0.743 0.493 0.090 0.000 2.392 5:00 1.226 0.556 0.101 0.478 2.223 6:00 1.235 0.511 0.093 0.624 2.057 7:00 0.806 0.333 0.061 0.184 1.579 8:00 1.008 0.246 0.045 0.563 1.393 9:00 0.409 0.536 0.098 -0.354 1.184

10:00 -0.014 0.268 0.049 -0.452 0.782 11:00 0.042 0.277 0.051 -0.412 0.782 12:00 -0.200 0.625 0.114 -1.283 0.782 13:00 -0.001 0.789 0.144 -1.055 0.880 14:00 -0.013 0.231 0.042 -0.298 0.782 15:00 0.164 0.267 0.049 -0.401 0.782 16:00 -0.194 0.308 0.056 -0.674 0.782 17:00 0.089 0.312 0.057 -0.434 0.782 18:00 -0.005 0.255 0.047 -0.362 0.782 19:00 0.082 0.267 0.049 -0.386 0.782 20:00 -0.360 0.350 0.064 -1.323 0.782 21:00 -0.080 0.434 0.079 -0.837 0.782 22:00 0.556 0.338 0.062 -0.155 1.153 23:00 0.268 0.279 0.051 -0.182 0.782


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Table A75 3 Week GARCH(1,1) Hedge Ratios: Cinergy Hub This table provides summary statistics of tri-weekly GARCH(1,1) hedge ratio estimates for the Cinergy hub. GARCH(1,1) hedge ratios are calculated using twenty tri-weekly spot and forward prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. 30 tri-weekly hedge ratios are estimated for each hourly time series.


0:00 0.327 0.144 0.026 0.016 0.596 1:00 0.329 0.464 0.085 -0.184 1.527 2:00 0.180 0.216 0.039 -0.146 0.545 3:00 0.564 0.580 0.106 -0.140 1.678 4:00 0.644 0.197 0.036 0.262 0.872 5:00 0.737 0.217 0.040 0.448 1.455 6:00 1.034 0.525 0.096 0.438 2.007 7:00 0.615 0.290 0.053 0.153 1.405 8:00 0.624 0.389 0.071 -0.017 1.272 9:00 0.078 0.363 0.066 -0.378 1.072

10:00 -0.006 0.189 0.034 -0.435 0.298 11:00 0.150 0.361 0.066 -0.401 1.416 12:00 -0.108 0.434 0.079 -0.727 0.312 13:00 0.095 0.639 0.117 -1.199 0.985 14:00 -0.095 0.294 0.054 -0.511 0.393 15:00 0.084 0.339 0.062 -0.501 0.444 16:00 -0.259 0.317 0.058 -0.776 0.130 17:00 -0.238 0.534 0.098 -0.984 0.506 18:00 0.047 0.161 0.029 -0.297 0.282 19:00 0.009 0.237 0.043 -0.590 0.481 20:00 -0.156 0.399 0.073 -0.915 0.316 21:00 -0.322 0.170 0.031 -0.543 0.029 22:00 0.429 0.272 0.050 0.071 1.138 23:00 0.184 0.188 0.034 -0.316 0.458


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Table A76 3 Week GARCH(1,1) Hedge Ratios: Michigan Hub This table provides summary statistics of tri-weekly GARCH(1,1) hedge ratio estimates for the Michigan hub. GARCH(1,1) hedge ratios are calculated using twenty tri-weekly spot and forward prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. 30 tri-weekly hedge ratios are estimated for each hourly time series.


0:00 0.242 0.145 0.027 -0.012 0.510 1:00 0.396 0.328 0.060 0.055 1.208 2:00 0.288 0.140 0.026 0.071 0.612 3:00 0.415 0.539 0.098 -0.163 1.486 4:00 0.682 0.205 0.037 0.205 0.919 5:00 1.128 0.395 0.072 0.374 2.068 6:00 0.883 0.333 0.061 0.390 1.710 7:00 0.598 0.216 0.039 0.102 1.179 8:00 0.437 0.313 0.057 -0.061 1.078 9:00 0.014 0.365 0.067 -0.522 0.993

10:00 0.058 0.318 0.058 -0.495 1.066 11:00 0.150 0.335 0.061 -0.282 0.877 12:00 -0.136 0.396 0.072 -0.837 0.307 13:00 -0.172 0.880 0.161 -1.327 0.903 14:00 -0.119 0.254 0.046 -0.484 0.267 15:00 -0.165 0.541 0.099 -0.816 0.497 16:00 -0.219 0.239 0.044 -0.522 0.169 17:00 -0.103 0.351 0.064 -0.640 0.546 18:00 0.026 0.158 0.029 -0.438 0.247 19:00 0.048 0.144 0.026 -0.140 0.537 20:00 -0.271 0.289 0.053 -0.763 0.225 21:00 -0.381 0.159 0.029 -0.582 -0.142 22:00 0.315 0.227 0.041 0.031 0.954 23:00 0.119 0.181 0.033 -0.332 0.388


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Table A77 3 Week GARCH(1,1) Hedge Ratios: Minnesota Hub This table provides summary statistics of tri-weekly GARCH(1,1) hedge ratio estimates for the Minnesota hub. GARCH(1,1) hedge ratios are calculated using twenty tri-weekly spot and forward prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. 30 tri-weekly hedge ratios are estimated for each hourly time series.


0:00 0.582 0.160 0.029 0.130 0.970 1:00 0.801 0.690 0.126 -1.404 2.211 2:00 1.105 0.610 0.111 0.090 2.168 3:00 1.532 0.794 0.145 0.254 2.631 4:00 1.136 0.450 0.082 0.324 1.787 5:00 1.069 0.347 0.063 0.449 1.692 6:00 0.117 0.630 0.115 -0.951 1.030 7:00 0.588 0.353 0.065 0.025 1.204 8:00 0.790 0.411 0.075 0.130 1.347 9:00 0.710 0.358 0.065 0.050 1.088

10:00 0.368 0.384 0.070 -0.338 1.005 11:00 0.500 0.420 0.077 0.038 1.507 12:00 -0.093 0.549 0.100 -0.866 0.661 13:00 0.745 0.494 0.090 0.160 1.913 14:00 1.014 0.410 0.075 0.343 1.728 15:00 0.805 0.359 0.066 0.281 1.748 16:00 0.203 0.302 0.055 -0.177 1.076 17:00 0.498 0.113 0.021 0.288 0.744 18:00 0.411 0.208 0.038 0.145 0.939 19:00 0.728 0.292 0.053 0.301 1.592 20:00 0.132 0.303 0.055 -0.369 0.610 21:00 0.436 0.372 0.068 -0.270 0.946 22:00 1.040 0.192 0.035 0.622 1.357 23:00 0.680 0.262 0.048 -0.085 1.006


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122

Table A78 3 Week GARCH(1,1) Hedge Ratios: First Energy Hub This table provides summary statistics of tri-weekly GARCH(1,1) hedge ratio estimates for the First Energy hub. GARCH(1,1) hedge ratios are calculated using twenty tri-weekly spot and forward prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. 30 tri-weekly hedge ratios are estimated for each hourly time series.


0:00 0.158 0.254 0.046 -0.404 0.567 1:00 0.249 0.276 0.050 -0.050 0.884 2:00 0.141 0.090 0.017 -0.011 0.529 3:00 -0.010 0.129 0.024 -0.179 0.438 4:00 0.385 0.232 0.042 0.040 0.767 5:00 0.588 0.140 0.026 0.361 0.987 6:00 0.910 0.609 0.111 0.327 2.470 7:00 0.349 0.315 0.058 -0.223 1.184 8:00 0.527 0.369 0.067 0.025 1.277 9:00 0.109 0.203 0.037 -0.186 0.522

10:00 0.118 0.312 0.057 -0.340 0.978 11:00 0.021 0.369 0.067 -0.565 0.991 12:00 -0.149 0.280 0.051 -0.799 0.137 13:00 0.428 0.256 0.047 0.111 0.906 14:00 0.133 0.186 0.034 -0.198 0.397 15:00 0.294 0.373 0.068 -0.157 0.755 16:00 -0.179 0.111 0.020 -0.427 0.004 17:00 0.215 0.305 0.056 -0.169 0.723 18:00 -0.095 0.207 0.038 -0.397 0.306 19:00 -0.022 0.228 0.042 -0.530 0.506 20:00 -0.170 0.290 0.053 -0.651 0.303 21:00 -0.213 0.348 0.063 -0.629 0.414 22:00 0.399 0.162 0.029 0.155 0.820 23:00 0.158 0.174 0.032 -0.110 0.499


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123

Table A79 4 Week GARCH(1,1) Hedge Ratios: Illinois Hub This table provides summary statistics of monthly GARCH(1,1) hedge ratio estimates for the Illinois hub. GARCH(1,1) hedge ratios are calculated using twenty monthly spot and forward prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. 18 monthly hedge ratios are estimated for each hourly time series.


0:00 0.997 0.308 0.073 0.615 1.815 1:00 0.331 0.205 0.048 0.056 0.897 2:00 0.392 0.183 0.043 0.203 0.760 3:00 0.155 0.096 0.023 0.006 0.295 4:00 1.107 0.190 0.045 0.839 1.568 5:00 0.752 0.329 0.078 0.385 1.440 6:00 0.625 0.346 0.082 0.149 1.448 7:00 0.919 0.236 0.056 0.431 1.212 8:00 0.663 0.223 0.053 0.295 1.005 9:00 0.500 0.369 0.087 0.001 1.451

10:00 0.473 0.308 0.073 0.014 1.092 11:00 0.260 0.742 0.175 -0.587 1.674 12:00 0.454 0.490 0.115 -0.285 1.437 13:00 -0.565 0.986 0.232 -1.428 1.510 14:00 0.685 0.871 0.205 -1.507 2.098 15:00 0.664 0.471 0.111 0.043 1.615 16:00 0.877 0.441 0.104 0.460 1.810 17:00 0.251 0.863 0.203 -0.766 1.438 18:00 0.857 0.375 0.088 0.071 1.573 19:00 0.870 0.178 0.042 0.531 1.199 20:00 0.765 0.256 0.060 0.162 1.148 21:00 1.026 0.321 0.076 0.468 1.794 22:00 0.938 0.265 0.062 0.547 1.504 23:00 0.430 0.355 0.084 0.101 1.349


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Table A80 4 Week GARCH(1,1) Hedge Ratios: Cinergy Hub This table provides summary statistics of monthly GARCH(1,1) hedge ratio estimates for the Cinergy hub. GARCH(1,1) hedge ratios are calculated using twenty monthly spot and forward prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. 18 monthly hedge ratios are estimated for each hourly time series.


0:00 0.932 0.313 0.074 0.593 1.701 1:00 0.328 0.134 0.032 0.113 0.573 2:00 0.335 0.125 0.029 0.186 0.563 3:00 0.252 0.109 0.026 0.066 0.443 4:00 0.974 0.206 0.049 0.488 1.573 5:00 0.609 0.195 0.046 0.422 0.932 6:00 0.784 0.392 0.092 0.218 1.466 7:00 0.932 0.274 0.064 0.406 1.298 8:00 0.744 0.195 0.046 0.514 1.195 9:00 0.334 0.124 0.029 0.091 0.500

10:00 0.750 0.297 0.070 0.126 1.141 11:00 0.496 0.573 0.135 -0.111 1.715 12:00 1.101 0.715 0.169 0.136 2.401 13:00 0.359 0.471 0.111 -0.570 1.096 14:00 1.576 0.529 0.125 0.688 2.527 15:00 0.835 0.571 0.134 -0.646 1.715 16:00 1.273 0.231 0.055 0.846 1.747 17:00 0.784 1.150 0.271 -0.616 2.746 18:00 1.124 0.465 0.110 0.373 1.881 19:00 0.984 0.352 0.083 0.557 1.477 20:00 0.803 0.210 0.049 0.487 1.259 21:00 0.819 0.145 0.034 0.491 1.070 22:00 0.853 0.198 0.047 0.504 1.102 23:00 0.297 0.154 0.036 -0.097 0.600


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Table A81 4 Week GARCH(1,1) Hedge Ratios: Michigan Hub This table provides summary statistics of monthly GARCH(1,1) hedge ratio estimates for the Michigan hub. GARCH(1,1) hedge ratios are calculated using twenty monthly spot and forward prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. 18 monthly hedge ratios are estimated for each hourly time series.


0:00 0.811 0.668 0.157 0.365 2.611 1:00 0.345 0.237 0.056 0.113 0.955 2:00 0.336 0.307 0.072 0.177 1.498 3:00 0.250 0.094 0.022 0.120 0.516 4:00 0.910 0.185 0.044 0.581 1.357 5:00 0.753 0.292 0.069 0.423 1.486 6:00 1.070 0.434 0.102 0.076 1.736 7:00 1.211 0.319 0.075 0.598 1.594 8:00 0.775 0.171 0.040 0.491 1.042 9:00 0.253 0.295 0.070 -0.067 0.883

10:00 0.666 0.191 0.045 0.377 0.993 11:00 0.393 0.660 0.156 -0.448 1.490 12:00 0.729 0.694 0.163 -0.320 1.991 13:00 0.113 0.573 0.135 -0.539 1.458 14:00 0.845 0.623 0.147 0.116 1.766 15:00 0.914 0.570 0.134 -0.031 1.953 16:00 1.149 0.235 0.055 0.896 1.569 17:00 0.421 1.162 0.274 -1.048 2.546 18:00 1.172 0.434 0.102 0.456 1.774 19:00 0.756 0.200 0.047 0.511 1.075 20:00 0.732 0.097 0.023 0.569 0.951 21:00 0.824 0.295 0.069 0.396 1.485 22:00 0.887 0.162 0.038 0.575 1.159 23:00 0.481 0.185 0.044 0.221 0.931


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126

Table A82 4 Week GARCH(1,1) Hedge Ratios: Minnesota Hub This table provides summary statistics of monthly GARCH(1,1) hedge ratio estimates for the Minnesota hub. GARCH(1,1) hedge ratios are calculated using twenty monthly spot and forward prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. 18 monthly hedge ratios are estimated for each hourly time series.


0:00 0.618 0.248 0.059 -0.004 1.098 1:00 0.657 0.343 0.081 0.208 1.456 2:00 0.559 0.346 0.082 -0.196 1.078 3:00 0.330 0.123 0.029 0.180 0.600 4:00 0.346 0.564 0.133 -1.087 1.031 5:00 0.200 0.242 0.057 -0.122 0.679 6:00 0.797 0.499 0.118 0.202 1.701 7:00 0.947 0.137 0.032 0.774 1.130 8:00 0.510 0.155 0.036 0.285 0.721 9:00 0.501 0.323 0.076 0.170 1.373

10:00 0.965 0.238 0.056 0.427 1.616 11:00 0.624 0.314 0.074 0.084 1.160 12:00 0.399 0.491 0.116 -0.066 1.490 13:00 0.323 0.568 0.134 -0.422 1.864 14:00 0.774 0.613 0.144 -0.875 1.868 15:00 0.805 0.501 0.118 -0.126 1.297 16:00 0.566 0.400 0.094 -0.057 1.726 17:00 0.840 0.361 0.085 0.054 1.292 18:00 0.762 0.371 0.087 0.060 1.267 19:00 1.093 0.400 0.094 0.649 1.961 20:00 0.590 0.338 0.080 0.202 1.280 21:00 0.532 0.457 0.108 -0.161 1.325 22:00 0.540 0.259 0.061 0.074 0.878 23:00 0.486 0.444 0.105 0.005 1.348


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Table A83 4 Week GARCH(1,1) Hedge Ratios: First Energy Hub This table provides summary statistics of monthly GARCH(1,1) hedge ratio estimates for the First Energy hub. GARCH(1,1) hedge ratios are calculated using twenty monthly spot and forward prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. 18 monthly hedge ratios are estimated for each hourly time series.


0:00 0.915 0.317 0.075 0.503 1.726 1:00 0.314 0.195 0.046 -0.202 0.671 2:00 0.277 0.410 0.097 -0.184 1.529 3:00 0.175 0.178 0.042 -0.053 0.613 4:00 0.775 0.168 0.040 0.414 1.249 5:00 0.921 0.259 0.061 0.392 1.140 6:00 0.925 0.568 0.134 0.284 2.294 7:00 1.151 0.206 0.048 0.525 1.353 8:00 0.758 0.197 0.047 0.501 1.175 9:00 0.522 0.119 0.028 0.317 0.707

10:00 0.896 0.280 0.066 0.520 1.612 11:00 0.232 0.419 0.099 -0.347 1.064 12:00 0.590 0.567 0.134 -0.493 1.412 13:00 0.218 0.655 0.154 -0.917 1.180 14:00 0.610 0.768 0.181 -0.509 1.815 15:00 0.851 0.553 0.130 0.133 1.761 16:00 1.223 0.250 0.059 0.860 1.615 17:00 0.453 1.210 0.285 -0.788 2.656 18:00 1.052 0.560 0.132 0.281 2.776 19:00 0.797 0.197 0.047 0.453 1.082 20:00 0.572 0.209 0.049 0.180 0.881 21:00 0.821 0.141 0.033 0.566 1.008 22:00 0.969 0.144 0.034 0.711 1.148 23:00 0.386 0.155 0.037 0.216 0.657


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Table A84 1 Week ARDL(1,1) Short-Run Hedge Ratios: Illinois Hub The table below shows the descriptive statistics of weekly short-run (SR) ARDL(1,1) hedge ratio estimates for the Illinois hub. ARDL(1,1) hedge ratios are calculated using twenty weekly spot and forward prices. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. 129 weekly hedge ratios are estimated for each hourly time series.

Hour Mean SR

Hedge Std Dev. SR

Hedge Std. Error SR

Hedge Min. SR Hedge

Max. SR Hedge

0:00 0.773 0.611 0.054 -0.668 2.561

1:00 0.871 0.948 0.083 -1.378 3.032

2:00 0.687 0.788 0.069 -0.702 2.917

3:00 0.758 0.487 0.043 -0.224 1.940

4:00 0.740 0.890 0.078 -1.611 3.636

5:00 0.607 0.796 0.070 -1.633 2.834

6:00 0.843 0.837 0.074 -1.231 2.843

7:00 0.625 0.546 0.048 -0.463 1.673

8:00 0.669 0.744 0.065 -1.099 2.584

9:00 0.426 0.346 0.030 -0.139 1.439

10:00 0.444 0.343 0.030 -0.409 1.096

11:00 0.320 0.395 0.035 -0.950 1.004

12:00 0.476 0.568 0.050 -0.853 1.790

13:00 0.498 0.625 0.055 -0.927 1.632

14:00 0.630 0.585 0.052 -0.504 2.349

15:00 0.586 0.407 0.036 -0.358 2.112

16:00 0.622 0.467 0.041 -0.319 2.078

17:00 0.290 0.437 0.038 -0.655 1.694

18:00 0.433 0.712 0.063 -1.404 2.031

19:00 0.475 0.262 0.023 -0.299 1.104

20:00 0.494 0.382 0.034 -0.687 1.508

21:00 0.368 0.407 0.036 -1.251 1.392

22:00 0.351 0.225 0.020 -0.208 1.144

23:00 0.556 0.401 0.035 -0.340 1.399 The ARDL(1,1) model is expressed as follows: St 1 St-1 Ft-1 Ft vt. The short-run

hedge ratio, , is obtained by regressing first-differenced weekly real-time prices ( St) on first- differenced contemporaneous day-ahead prices ( Ft), as well as lagged day-ahead and real-time prices. The sample period for this analysis is 6/1/2006-4/11/2009.

129

Table A85 1 Week ARDL(1,1) Long-Run Hedge Ratios: Illinois Hub

The table below shows the descriptive statistics of weekly long-run (LR) ARDL(1,1) hedge ratio estimates for the Illinois hub. ARDL(1,1) hedge ratios are calculated using twenty weekly spot and forward prices. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. 129 weekly hedge ratios are estimated for each hourly time series.

Hour Mean LR

Hedge Std. Dev. LR

Hedge Std. Error LR

Hedge Min. LR Hedge

Max. LR Hedge

0:00 0.680 0.553 0.049 -0.409 2.313

1:00 0.836 0.742 0.065 -0.749 2.668

2:00 0.719 0.789 0.070 -1.826 2.826

3:00 0.731 0.627 0.055 -0.483 2.299

4:00 0.608 0.838 0.074 -1.601 2.489

5:00 0.688 0.848 0.075 -2.063 2.750

6:00 0.968 0.742 0.065 -1.446 2.836

7:00 0.899 0.714 0.063 -0.376 6.107

8:00 1.021 0.936 0.082 -0.028 8.669

9:00 0.452 0.271 0.024 -0.280 0.901

10:00 0.627 0.347 0.031 -0.084 1.700

11:00 0.474 0.499 0.044 -0.503 1.662

12:00 0.420 0.518 0.046 -0.962 1.295

13:00 0.680 0.523 0.046 -0.691 1.671

14:00 0.767 0.312 0.027 0.146 1.728

15:00 0.733 0.363 0.032 -0.011 2.156

16:00 0.773 0.416 0.037 -0.318 1.572

17:00 0.585 0.435 0.038 -0.828 1.547

18:00 0.768 0.423 0.037 -0.601 1.718

19:00 0.471 0.332 0.029 -0.162 1.370

20:00 0.446 0.341 0.030 -0.546 1.214

21:00 0.568 0.593 0.052 -1.100 1.985

22:00 0.501 0.274 0.024 -0.388 1.302

23:00 0.724 0.489 0.043 -0.711 1.616 The ARDL(1,1) model is expressed as follows: St 1 St-1 Ft-1 Ft vt. The long-run

hedge ratio, - 3/ 2, is obtained by regressing first-differenced weekly real-time prices ( St) on first- differenced contemporaneous day-ahead prices ( Ft), as well as lagged day-ahead and real-time prices. The sample period for this analysis is 6/1/2006-4/11/2009.

130

Table A86 1 Week ARDL(1,1) Short-Run Hedge Ratios: Cinergy Hub

The table below shows the descriptive statistics of weekly short-run (SR) ARDL(1,1) hedge ratio estimates for the Cinergy hub. ARDL(1,1) hedge ratios are calculated using twenty weekly spot and forward prices. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. 129 weekly hedge ratios are estimated for each hourly time series.

Hour Mean SR

Hedge Std. Dev. SR

Hedge Std. Error SR

Hedge Min. SR Hedge

Max. SR Hedge

0:00 0.672 0.558 0.049 -0.172 2.129

1:00 0.997 0.762 0.067 -0.222 2.997

2:00 0.867 0.627 0.055 -0.019 2.370

3:00 0.804 0.476 0.042 -0.141 1.983

4:00 1.081 0.510 0.045 0.509 3.585

5:00 1.095 0.651 0.057 0.011 2.818

6:00 1.172 0.696 0.061 0.035 4.267

7:00 0.530 0.370 0.033 -0.569 1.302

8:00 0.588 0.516 0.045 -0.580 1.766

9:00 0.235 0.208 0.018 -0.107 0.750

10:00 0.374 0.317 0.028 -0.372 1.041

11:00 0.395 0.418 0.037 -0.890 1.221

12:00 0.427 0.470 0.041 -0.593 1.944

13:00 0.554 0.594 0.052 -0.803 1.960

14:00 0.678 0.405 0.036 -0.285 1.736

15:00 0.709 0.265 0.023 0.112 1.250

16:00 0.610 0.534 0.047 -0.320 2.548

17:00 0.413 0.398 0.035 -0.591 1.395

18:00 0.472 0.476 0.042 -1.158 1.735

19:00 0.440 0.311 0.027 -0.239 1.187

20:00 0.397 0.410 0.036 -0.385 1.313

21:00 0.358 0.455 0.040 -1.085 1.450

22:00 0.411 0.176 0.016 -0.028 0.843



131

Table A87 1 Week ARDL(1,1) Long-Run Hedge Ratios: Cinergy Hub The table below shows the descriptive statistics of weekly long-run (LR) ARDL(1,1) hedge ratio estimates for the Cinergy hub. ARDL(1,1) hedge ratios are calculated using twenty weekly spot and forward prices. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. 129 weekly hedge ratios are estimated for each hourly time series.

Hour Mean LR

Hedge Std. Dev. LR

Hedge Std. Error LR

Hedge Min. LR Hedge

Max. LR Hedge

0:00 0.592 0.521 0.046 -0.265 1.923

1:00 0.846 0.674 0.059 -0.401 2.419

2:00 0.802 0.653 0.057 -0.136 2.190

3:00 0.799 0.622 0.055 -0.354 3.366

4:00 0.918 0.452 0.040 -0.299 2.545

5:00 1.039 0.807 0.071 -0.098 4.326

6:00 1.253 1.149 0.101 0.017 7.463

7:00 0.642 1.171 0.103 -11.712 2.094

8:00 1.182 3.813 0.336 0.047 43.872

9:00 0.244 0.226 0.020 -0.253 0.926

10:00 0.510 0.355 0.031 -0.123 1.251

11:00 0.514 0.529 0.047 -0.486 1.848

12:00 0.484 0.566 0.050 -0.893 1.502

13:00 0.707 0.533 0.047 -0.573 2.082

14:00 0.751 0.412 0.036 -0.087 1.938

15:00 0.795 0.349 0.031 -0.063 1.775

16:00 0.672 0.509 0.045 -0.960 2.183

17:00 0.632 0.455 0.040 -0.928 1.606

18:00 0.823 0.512 0.045 0.070 2.068

19:00 0.429 0.381 0.034 -0.336 1.322

20:00 0.469 0.494 0.044 -1.957 1.482

21:00 0.355 0.775 0.068 -3.447 1.867

22:00 0.545 0.233 0.020 0.059 1.271



132

Table A88 1 Week ARDL(1,1) Short-Run Hedge Ratios: Michigan Hub The table below shows the descriptive statistics of weekly short-run (SR) ARDL(1,1) hedge ratio estimates for the Michigan hub. ARDL(1,1) hedge ratios are calculated using twenty weekly spot and forward prices. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. 129 weekly hedge ratios are estimated for each hourly time series.

Hour Mean SR

Hedge Std. Dev. SR

Hedge Std. Error SR

Hedge Min. SR Hedge

Max. SR Hedge

0:00 0.618 0.593 0.052 -0.190 2.408

1:00 0.993 0.665 0.059 -0.096 2.673

2:00 0.887 0.500 0.044 0.092 2.056

3:00 0.774 0.500 0.044 -0.320 2.097

4:00 1.106 0.576 0.051 0.407 3.915

5:00 1.244 0.537 0.047 0.375 3.246

6:00 1.126 0.605 0.053 -0.035 3.609

7:00 0.539 0.325 0.029 -0.408 1.350

8:00 0.576 0.548 0.048 -0.763 1.961

9:00 0.262 0.253 0.022 -0.139 0.991

10:00 0.550 0.470 0.041 -0.458 2.171

11:00 0.374 0.348 0.031 -0.595 0.972

12:00 0.444 0.419 0.037 -0.526 1.232

13:00 0.444 0.572 0.050 -0.889 1.382

14:00 0.570 0.387 0.034 -0.345 1.718

15:00 0.679 0.369 0.032 0.025 1.976

16:00 0.735 0.560 0.049 -0.182 2.125

17:00 0.684 0.501 0.044 -0.323 2.047

18:00 0.497 0.464 0.041 -1.029 1.349

19:00 0.482 0.223 0.020 -0.119 1.066

20:00 0.433 0.330 0.029 -0.273 1.303

21:00 0.270 0.378 0.033 -1.058 0.989

22:00 0.383 0.187 0.017 -0.089 0.807



133

Table A89 1 Week ARDL(1,1) Long-Run Hedge Ratios: Michigan Hub The table below shows the descriptive statistics of weekly long-run (LR) ARDL(1,1) hedge ratio estimates for the Michigan hub. ARDL(1,1) hedge ratios are calculated using twenty weekly spot and forward prices. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. 129 weekly hedge ratios are estimated for each hourly time series.

Hour Mean LR

Hedge Std. Dev. LR

Hedge Std. Error LR

Hedge Min. LR Hedge

Max. LR Hedge

0:00 0.502 0.583 0.051 -0.378 2.264

1:00 1.019 0.827 0.073 -0.183 3.417

2:00 0.915 0.511 0.045 0.064 1.939

3:00 0.872 0.671 0.059 -0.201 3.252

4:00 0.979 0.687 0.060 -0.132 3.662

5:00 1.099 0.880 0.077 -0.862 4.573

6:00 1.146 1.191 0.105 -0.382 6.051

7:00 0.776 0.423 0.037 -0.291 2.342

8:00 0.915 0.632 0.056 0.042 6.235

9:00 0.246 0.265 0.023 -0.253 0.833

10:00 0.604 0.407 0.036 -0.124 1.864

11:00 0.471 0.460 0.041 -0.343 1.698

12:00 0.486 0.519 0.046 -0.853 1.395

13:00 0.633 0.557 0.049 -0.764 1.599

14:00 0.662 0.408 0.036 -0.246 1.715

15:00 0.731 0.379 0.033 -0.069 1.775

16:00 0.670 0.488 0.043 -0.749 1.698

17:00 0.724 0.459 0.040 -0.471 2.422

18:00 0.793 0.455 0.040 0.033 2.044

19:00 0.476 0.279 0.025 -0.172 1.118

20:00 0.503 0.365 0.032 -0.193 1.389

21:00 0.250 0.834 0.073 -5.865 1.548

22:00 0.529 0.219 0.019 0.106 1.270



134

Table A90 1 Week ARDL(1,1) Short-Run Hedge Ratios: Minnesota Hub The table below shows the descriptive statistics of weekly short-run (SR) ARDL(1,1) hedge ratio estimates for the Minnesota hub. ARDL(1,1) hedge ratios are calculated using twenty weekly spot and forward prices. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. 129 weekly hedge ratios are estimated for each hourly time series.

Hour Mean SR

Hedge Std. Dev. SR

Hedge Std. Error SR

Hedge Min. SR Hedge

Max. SR Hedge

0:00 0.506 0.668 0.059 -1.271 1.720

1:00 0.779 0.866 0.076 -2.059 4.005

2:00 1.124 0.857 0.075 -0.864 4.063

3:00 1.212 0.781 0.069 -0.704 3.926

4:00 1.146 0.763 0.067 -1.006 3.264

5:00 1.028 1.006 0.089 -1.883 4.070

6:00 0.742 0.471 0.042 -0.582 2.530

7:00 0.608 0.418 0.037 -1.093 1.446

8:00 0.774 0.450 0.040 -0.178 1.525

9:00 0.670 0.481 0.042 -0.144 1.744

10:00 0.625 0.353 0.031 -0.095 1.379

11:00 0.497 0.283 0.025 -0.189 1.171

12:00 0.433 0.532 0.047 -1.018 1.350

13:00 0.563 0.384 0.034 -0.642 1.117

14:00 0.668 0.445 0.039 -0.748 1.598

15:00 0.611 0.444 0.039 -0.552 1.427

16:00 0.670 0.550 0.048 -0.574 1.615

17:00 0.445 0.372 0.033 -0.458 1.138

18:00 0.682 0.690 0.061 -0.967 2.612

19:00 0.889 0.526 0.046 -0.183 2.752

20:00 0.553 0.456 0.040 -0.325 2.007

21:00 0.499 0.457 0.040 -0.710 1.893

22:00 0.672 0.373 0.033 -0.046 1.280

23:00 0.907 0.518 0.046 0.033 2.771 The ARDL(1,1) model is expressed as follows: St 1 St-1 Ft-1 Ft vt. The short-run


135

Table A91 1 Week ARDL(1,1) Long-Run Hedge Ratios: Minnesota Hub

The table below shows the descriptive statistics of weekly long-run (LR) ARDL(1,1) hedge ratio estimates for the Minnesota hub. ARDL(1,1) hedge ratios are calculated using twenty weekly spot and forward prices. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. 129 weekly hedge ratios are estimated for each hourly time series.

Hour Mean LR

Hedge Std. Dev. LR

Hedge Std. Error LR

Hedge Min. LR Hedge

Max. LR Hedge

0:00 0.662 0.898 0.079 -8.761 1.493

1:00 0.838 1.285 0.113 -4.042 3.600

2:00 1.212 1.092 0.096 -1.483 4.402

3:00 1.070 0.850 0.075 -0.969 4.146

4:00 0.841 0.922 0.081 -2.625 2.240

5:00 0.998 0.801 0.071 -1.532 3.006

6:00 0.677 0.799 0.070 -0.421 3.728

7:00 0.717 0.526 0.046 -1.214 2.369

8:00 0.915 0.428 0.038 0.166 2.190

9:00 0.606 0.313 0.028 -0.120 1.786

10:00 0.645 0.293 0.026 0.018 1.345

11:00 0.623 0.417 0.037 -0.248 1.640

12:00 0.619 0.478 0.042 -0.593 1.341

13:00 0.851 0.312 0.027 0.213 1.512

14:00 0.884 0.517 0.046 -0.541 2.646

15:00 0.690 0.557 0.049 -1.501 1.549

16:00 0.819 0.436 0.038 0.095 1.623

17:00 0.580 0.423 0.037 -0.567 1.535

18:00 0.695 0.407 0.036 -0.105 1.633

19:00 0.780 0.262 0.023 -0.072 1.381

20:00 0.692 0.491 0.043 -0.287 3.149

21:00 0.530 1.355 0.119 -12.853 2.452

22:00 0.776 0.287 0.025 0.035 1.357

23:00 0.913 0.372 0.033 0.040 2.656 The ARDL(1,1) model is expressed as follows: St 1 St-1 Ft-1 Ft vt. The long-run


136

Table A92 1 Week ARDL(1,1) Short-Run Hedge Ratios: First Energy Hub The table below shows the descriptive statistics of weekly short-run (SR) ARDL(1,1) hedge ratio estimates for the First Energy hub. ARDL(1,1) hedge ratios are calculated using twenty weekly spot and forward prices. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. 129 weekly hedge ratios are estimated for each hourly time series.

Hour Mean SR

Hedge Std. Dev. SR

Hedge Std. Error SR

Hedge Min. SR Hedge

Max. SR Hedge

0:00 0.643 0.479 0.042 0.053 2.371

1:00 0.945 0.606 0.053 -0.038 2.502

2:00 0.690 0.445 0.039 0.015 1.910

3:00 0.628 0.341 0.030 0.018 1.925

4:00 0.925 0.539 0.047 0.351 3.517

5:00 1.162 0.650 0.057 0.237 2.937

6:00 1.121 0.761 0.067 -0.302 4.196

7:00 0.547 0.446 0.039 -0.620 2.187

8:00 0.700 0.472 0.042 -0.510 1.637

9:00 0.251 0.249 0.022 -0.266 0.832

10:00 0.331 0.328 0.029 -0.536 0.989

11:00 0.263 0.412 0.036 -1.138 0.954

12:00 0.412 0.550 0.048 -0.746 2.581

13:00 0.701 0.456 0.040 -0.119 2.007

14:00 0.530 0.355 0.031 -0.253 1.398

15:00 0.489 0.334 0.029 -0.271 1.253

16:00 0.505 0.564 0.050 -0.547 2.447

17:00 0.457 0.424 0.037 -0.711 1.729

18:00 0.366 0.569 0.050 -1.308 1.806

19:00 0.240 0.293 0.026 -0.224 1.005

20:00 0.339 0.376 0.033 -0.473 1.392

21:00 0.356 0.497 0.044 -0.928 1.294

22:00 0.441 0.176 0.015 0.033 0.798



137

Table A93 1 Week ARDL(1,1) Long-Run Hedge Ratios: First Energy Hub

The table below shows the descriptive statistics of weekly long-run (LR) ARDL(1,1) hedge ratio estimates for the First Energy hub. ARDL(1,1) hedge ratios are calculated using twenty weekly spot and forward prices. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. 129 weekly hedge ratios are estimated for each hourly time series.

Hour Mean LR

Hedge Std. Dev. LR

Hedge Std. Error LR

Hedge Min. LR Hedge

Max. LR Hedge

0:00 0.588 0.602 0.053 -0.559 2.574

1:00 1.003 0.763 0.067 -0.293 2.685

2:00 0.761 0.469 0.041 -0.166 1.866

3:00 0.612 0.530 0.047 -0.719 2.164

4:00 1.101 1.071 0.094 -0.306 6.716

5:00 1.074 0.863 0.076 -0.755 4.320

6:00 1.241 1.365 0.120 -0.572 7.035

7:00 0.724 0.454 0.040 -0.372 2.087

8:00 0.876 0.697 0.061 -0.598 6.447

9:00 0.198 0.290 0.026 -0.278 1.064

10:00 0.392 0.397 0.035 -0.296 1.306

11:00 0.396 0.557 0.049 -0.672 1.752

12:00 0.502 0.596 0.053 -0.711 2.321

13:00 0.788 0.483 0.043 -0.080 4.317

14:00 0.572 0.532 0.047 -1.291 1.616

15:00 0.598 0.551 0.049 -1.882 1.821

16:00 0.660 0.595 0.052 -0.788 2.516

17:00 0.694 0.488 0.043 -0.599 1.556

18:00 0.656 0.637 0.056 -0.622 2.078

19:00 0.345 0.438 0.039 -0.824 1.430

20:00 0.412 0.507 0.045 -0.971 1.633

21:00 0.150 1.200 0.106 -10.095 1.687

22:00 0.512 0.304 0.027 -0.142 1.434



138

Table A94 2 Week ARDL(1,1) Short-Run Hedge Ratios: Illinois Hub The table below shows the descriptive statistics of bi-weekly short-run (SR) ARDL(1,1) hedge ratio estimates for the Illinois hub. ARDL(1,1) hedge ratios are calculated using twenty bi-weekly spot and forward prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. 55 bi-weekly hedge ratios are estimated for each hourly time series.

Hour Mean SR

Hedge Std. Dev. SR

Hedge Std. Error SR

Hedge Min. SR Hedge

Max. SR Hedge

0:00 0.868 0.437 0.059 0.220 2.147

1:00 0.733 0.369 0.050 0.110 1.639

2:00 0.806 0.344 0.046 0.297 1.635

3:00 0.754 0.266 0.036 0.313 1.545

4:00 1.135 0.447 0.060 0.598 3.467

5:00 0.753 0.308 0.042 0.261 1.484

6:00 0.868 0.512 0.069 -0.539 1.615

7:00 0.808 0.271 0.037 0.299 1.506

8:00 0.996 0.344 0.046 0.119 1.830

9:00 0.606 0.227 0.031 0.117 1.045

10:00 0.866 0.292 0.039 0.441 1.556

11:00 0.789 0.440 0.059 -0.049 1.595

12:00 0.685 0.438 0.059 -0.373 1.720

13:00 0.759 0.606 0.082 -0.221 2.181

14:00 0.945 0.659 0.089 -0.014 2.426

15:00 0.938 0.706 0.095 0.072 2.390

16:00 1.148 0.921 0.124 0.121 3.042

17:00 0.704 0.659 0.089 0.096 2.884

18:00 1.007 0.622 0.084 0.085 2.075

19:00 0.905 0.467 0.063 0.372 1.944

20:00 0.852 0.245 0.033 0.308 1.428

21:00 0.665 0.499 0.067 0.090 1.936

22:00 0.754 0.429 0.058 -0.160 1.770



139

Table A95 2 Week ARDL(1,1) Long-Run Hedge Ratios: Illinois Hub The table below shows the descriptive statistics of bi-weekly long-run (LR) ARDL(1,1) hedge ratio estimates for the Illinois hub. ARDL(1,1) hedge ratios are calculated using twenty bi-weekly spot and forward prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. 55 bi-weekly hedge ratios are estimated for each hourly time series.

Hour Mean LR

Hedge Std. Dev. LR

Hedge Std. Error LR

Hedge Min. LR Hedge

Max. LR Hedge

0:00 0.607 0.452 0.061 -0.242 1.950

1:00 0.663 0.386 0.052 0.006 1.597

2:00 0.792 0.320 0.043 0.199 1.590

3:00 0.790 0.191 0.026 0.431 1.272

4:00 1.056 0.388 0.052 0.361 2.960

5:00 0.701 0.276 0.037 0.105 1.179

6:00 0.477 0.604 0.081 -2.054 1.210

7:00 0.669 0.254 0.034 -0.041 1.453

8:00 0.988 0.394 0.053 -0.025 1.672

9:00 0.501 0.169 0.023 0.122 0.748

10:00 0.599 0.405 0.055 0.057 1.776

11:00 0.908 0.670 0.090 -0.339 2.076

12:00 0.631 0.444 0.060 -0.610 1.562

13:00 0.720 0.391 0.053 -0.289 1.577

14:00 0.648 0.460 0.062 -0.127 1.630

15:00 0.800 0.323 0.044 0.310 1.826

16:00 0.973 0.572 0.077 0.226 2.926

17:00 0.764 2.267 0.306 -0.397 17.059

18:00 0.966 0.391 0.053 0.278 2.092

19:00 0.909 0.302 0.041 0.179 1.518

20:00 1.001 0.597 0.081 -0.908 2.523

21:00 0.568 0.510 0.069 -1.535 1.513

22:00 0.602 0.432 0.058 -0.839 1.419



140

Table A96 2 Week ARDL(1,1) Short-Run Hedge Ratios: Cinergy Hub The table below shows the descriptive statistics of bi-weekly short-run (SR) ARDL(1,1) hedge ratio estimates for the Cinergy hub. ARDL(1,1) hedge ratios are calculated using twenty bi-weekly spot and forward prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. 55 bi-weekly hedge ratios are estimated for each hourly time series.

Hour Mean SR

Hedge Std. Dev. SR

Hedge Std. Error SR

Hedge Min. SR Hedge

Max. SR Hedge

0:00 0.817 0.445 0.060 0.155 1.850

1:00 0.636 0.372 0.050 0.164 1.724

2:00 0.756 0.327 0.044 0.322 1.680

3:00 0.692 0.273 0.037 0.324 1.480

4:00 1.163 0.557 0.075 0.372 3.805

5:00 0.646 0.311 0.042 0.188 1.417

6:00 0.814 0.401 0.054 -0.120 1.570

7:00 0.740 0.227 0.031 0.368 1.118

8:00 0.974 0.337 0.045 0.120 2.226

9:00 0.451 0.171 0.023 0.137 0.720

10:00 0.708 0.165 0.022 0.352 1.173

11:00 0.809 0.440 0.059 0.123 1.540

12:00 0.750 0.388 0.052 -0.117 1.442

13:00 0.838 0.506 0.068 -0.074 2.265

14:00 1.206 0.651 0.088 0.069 2.491

15:00 0.975 0.656 0.088 0.059 2.767

16:00 1.257 0.810 0.109 0.185 3.121

17:00 0.848 0.665 0.090 0.030 3.147

18:00 1.238 0.682 0.092 0.250 2.428

19:00 0.988 0.593 0.080 0.147 2.071

20:00 0.791 0.300 0.040 0.354 1.504

21:00 0.697 0.574 0.077 -0.029 2.034

22:00 0.732 0.423 0.057 -0.171 1.773



141

Table A97 2 Week ARDL(1,1) Long-Run Hedge Ratios: Cinergy Hub

The table below shows the descriptive statistics of bi-weekly long-run (LR) ARDL(1,1) hedge ratio estimates for the Cinergy hub. ARDL(1,1) hedge ratios are calculated using twenty bi-weekly spot and forward prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. 55 bi-weekly hedge ratios are estimated for each hourly time series.

Hour Mean LR

Hedge Std. Dev. LR

Hedge Std. Error LR

Hedge Min. LR Hedge

Max. LR Hedge

0:00 0.484 0.438 0.059 -0.392 1.598

1:00 0.679 0.434 0.058 0.021 1.530

2:00 0.765 0.311 0.042 0.068 1.606

3:00 0.812 0.188 0.025 0.358 1.395

4:00 1.184 0.420 0.057 0.670 3.291

5:00 0.719 0.446 0.060 0.136 1.461

6:00 0.536 0.416 0.056 -1.105 0.961

7:00 0.711 0.197 0.027 0.104 1.024

8:00 1.053 0.370 0.050 -0.017 1.873

9:00 0.426 0.183 0.025 -0.094 0.700

10:00 0.442 0.274 0.037 0.090 1.329

11:00 0.919 0.585 0.079 -0.027 1.950

12:00 0.720 0.543 0.073 -0.269 1.806

13:00 0.812 0.274 0.037 0.128 1.368

14:00 0.822 0.418 0.056 -0.033 1.552

15:00 0.806 0.289 0.039 0.379 1.796

16:00 1.000 0.550 0.074 0.160 2.682

17:00 0.929 1.887 0.254 -0.069 14.450

18:00 1.225 0.694 0.094 0.264 3.344

19:00 0.862 0.523 0.070 -0.189 1.816

20:00 0.950 0.650 0.088 -2.289 2.176

21:00 0.700 0.477 0.064 -0.193 1.731

22:00 0.510 0.447 0.060 -1.164 1.296



142

Table A98 2 Week ARDL(1,1) Short-Run Hedge Ratios: Michigan Hub

The table below shows the descriptive statistics of bi-weekly short-run (SR) ARDL(1,1) hedge ratio estimates for the Michigan hub. ARDL(1,1) hedge ratios are calculated using twenty bi-weekly spot and forward prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. 55 bi-weekly hedge ratios are estimated for each hourly time series.

Hour Mean SR

Hedge Std. Dev. SR

Hedge Std. Error SR

Hedge Min. SR Hedge

Max. SR Hedge

0:00 0.760 0.468 0.063 0.086 2.041

1:00 0.637 0.442 0.060 0.045 1.889

2:00 0.743 0.333 0.045 0.305 1.844

3:00 0.629 0.327 0.044 0.165 1.248

4:00 1.153 0.639 0.086 0.315 4.176

5:00 0.627 0.335 0.045 0.107 1.292

6:00 0.946 0.301 0.041 0.365 1.544

7:00 0.861 0.264 0.036 0.476 1.485

8:00 0.958 0.309 0.042 0.147 1.824

9:00 0.389 0.185 0.025 0.136 0.765

10:00 0.608 0.119 0.016 0.369 0.885

11:00 0.614 0.297 0.040 0.112 1.046

12:00 0.540 0.398 0.054 -0.300 1.293

13:00 0.695 0.531 0.072 -0.151 2.096

14:00 1.009 0.613 0.083 0.003 2.156

15:00 0.879 0.541 0.073 0.104 2.167

16:00 1.123 0.766 0.103 0.096 2.767

17:00 1.169 0.818 0.110 0.013 3.315

18:00 0.997 0.539 0.073 0.257 1.886

19:00 0.760 0.339 0.046 0.188 1.495

20:00 0.711 0.260 0.035 0.273 1.290

21:00 0.524 0.427 0.058 -0.089 1.477

22:00 0.616 0.388 0.052 -0.105 1.349



143

Table A99 2 Week ARDL(1,1) Long-Run Hedge Ratios: Michigan Hub

The table below shows the descriptive statistics of bi-weekly long-run (LR) ARDL(1,1) hedge ratio estimates for the Michigan hub. ARDL(1,1) hedge ratios are calculated using twenty bi-weekly spot and forward prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. 55 bi-weekly hedge ratios are estimated for each hourly time series.

Hour Mean LR

Hedge Std. Dev. LR

Hedge Std. Error LR

Hedge Min. LR Hedge

Max. LR Hedge

0:00 0.422 0.511 0.069 -0.330 1.916

1:00 0.717 0.379 0.051 0.019 1.315

2:00 0.752 0.289 0.039 0.349 1.534

3:00 0.791 0.203 0.027 0.265 1.372

4:00 1.108 0.448 0.060 0.280 3.185

5:00 0.592 0.630 0.085 -0.289 1.672

6:00 0.613 0.321 0.043 -0.352 1.300

7:00 0.774 0.271 0.037 0.169 1.331

8:00 1.126 0.390 0.053 -0.086 1.793

9:00 0.415 0.136 0.018 0.144 0.662

10:00 0.418 0.312 0.042 0.046 1.488

11:00 0.756 0.514 0.069 -0.152 1.688

12:00 0.688 0.512 0.069 -0.430 1.740

13:00 0.736 0.288 0.039 0.043 1.347

14:00 0.752 0.474 0.064 -0.273 1.611

15:00 0.799 0.270 0.036 0.364 1.698

16:00 0.917 0.568 0.077 0.169 2.494

17:00 0.922 0.772 0.104 0.026 5.967

18:00 1.014 0.597 0.080 0.148 2.572

19:00 0.683 0.380 0.051 -0.177 1.302

20:00 0.776 0.913 0.123 -4.433 2.142

21:00 0.457 0.338 0.046 -0.241 1.145

22:00 0.477 0.378 0.051 -0.601 1.198



144

Table A100 2 Week ARDL(1,1) Short-Run Hedge Ratios: Minnesota Hub

The table below shows the descriptive statistics of bi-weekly short-run (SR) ARDL(1,1) hedge ratio estimates for the Minnesota hub. ARDL(1,1) hedge ratios are calculated using twenty bi-weekly spot and forward prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. 55 bi-weekly hedge ratios are estimated for each hourly time series.

Hour Mean SR

Hedge Std. Dev. SR

Hedge Std. Error SR

Hedge Min. SR Hedge

Max. SR Hedge

0:00 0.639 0.339 0.046 -0.031 1.857

1:00 0.837 0.337 0.045 0.139 1.626

2:00 1.204 0.401 0.054 0.378 2.072

3:00 1.328 0.531 0.072 0.356 2.251

4:00 1.375 0.390 0.053 0.472 2.615

5:00 0.898 0.445 0.060 0.374 2.106

6:00 0.979 0.563 0.076 0.210 2.197

7:00 0.905 0.405 0.055 0.497 1.928

8:00 1.018 0.628 0.085 0.352 2.976

9:00 0.660 0.543 0.073 0.115 1.920

10:00 0.960 0.300 0.040 0.536 2.083

11:00 0.808 0.524 0.071 0.083 2.339

12:00 0.479 0.573 0.077 -0.616 1.467

13:00 0.717 0.444 0.060 0.071 1.665

14:00 0.929 0.837 0.113 -0.141 2.218

15:00 1.003 0.590 0.080 0.130 2.201

16:00 1.044 0.919 0.124 -0.347 2.788

17:00 0.631 0.504 0.068 0.009 1.957

18:00 0.894 0.775 0.104 0.067 2.365

19:00 0.943 0.655 0.088 0.038 2.335

20:00 0.583 0.398 0.054 -0.015 1.452

21:00 0.720 0.326 0.044 0.161 1.378

22:00 0.983 0.387 0.052 0.115 1.520



145

Table A101 2 Week ARDL(1,1) Long-Run Hedge Ratios: Minnesota Hub The table below shows the descriptive statistics of bi-weekly long-run (LR) ARDL(1,1) hedge ratio estimates for the Minnesota hub. ARDL(1,1) hedge ratios are calculated using twenty bi-weekly spot and forward prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. 55 bi-weekly hedge ratios are estimated for each hourly time series.

Hour Mean LR

Hedge Std. Dev. LR

Hedge Std. Error LR

Hedge Min. LR Hedge

Max. LR Hedge

0:00 0.781 0.355 0.048 0.347 1.961

1:00 0.988 0.180 0.024 0.335 1.411

2:00 1.363 0.431 0.058 0.708 3.047

3:00 1.332 0.466 0.063 0.765 2.562

4:00 1.103 0.388 0.052 -0.010 1.726

5:00 0.922 0.241 0.032 0.503 1.622

6:00 0.621 0.386 0.052 -0.315 1.410

7:00 0.775 0.202 0.027 0.405 1.223

8:00 0.982 0.523 0.071 0.319 2.141

9:00 0.507 0.530 0.072 -0.496 1.843

10:00 0.660 0.230 0.031 0.069 1.240

11:00 0.660 0.426 0.057 -0.501 1.863

12:00 0.755 0.325 0.044 -0.014 1.343

13:00 0.973 0.357 0.048 0.205 1.644

14:00 0.654 0.693 0.093 -1.650 1.645

15:00 1.132 0.410 0.055 0.187 2.129

16:00 1.068 0.647 0.087 0.100 2.801

17:00 1.231 5.393 0.727 -0.392 40.395

18:00 0.616 0.433 0.058 -0.042 1.358

19:00 0.607 0.492 0.066 -0.086 1.641

20:00 0.875 0.350 0.047 -0.143 1.463

21:00 0.555 0.504 0.068 -1.094 1.308

22:00 0.799 0.267 0.036 0.075 1.195



146

Table A102 2 Week ARDL(1,1) Short-Run Hedge Ratios: First Energy Hub The table below shows the descriptive statistics of bi-weekly short-run (SR) ARDL(1,1) hedge ratio estimates for the First Energy hub. ARDL(1,1) hedge ratios are calculated using twenty bi-weekly spot and forward prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. 55 bi-weekly hedge ratios are estimated for each hourly time series.

Hour Mean SR

Hedge Std. Dev. SR

Hedge Std. Error SR

Hedge Min. SR Hedge

Max. SR Hedge

0:00 0.968 0.356 0.048 0.433 1.981

1:00 0.732 0.426 0.057 -0.045 1.623

2:00 0.587 0.381 0.051 -0.223 1.507

3:00 0.523 0.400 0.054 -0.447 1.382

4:00 1.148 0.587 0.079 0.399 3.484

5:00 0.702 0.427 0.058 -0.044 1.619

6:00 0.880 0.495 0.067 0.144 1.858

7:00 0.802 0.226 0.030 0.483 1.252

8:00 1.019 0.429 0.058 -0.034 2.585

9:00 0.431 0.204 0.027 -0.105 0.703

10:00 0.783 0.194 0.026 0.446 1.286

11:00 0.672 0.383 0.052 0.111 1.566

12:00 0.614 0.426 0.057 -0.245 1.387

13:00 0.709 0.394 0.053 0.010 1.558

14:00 0.963 0.508 0.068 -0.004 1.990

15:00 0.837 0.673 0.091 -0.210 2.337

16:00 0.920 0.830 0.112 -0.234 2.965

17:00 0.745 0.727 0.098 -0.033 3.342

18:00 1.237 0.675 0.091 0.166 2.545

19:00 0.773 0.452 0.061 -0.005 1.797

20:00 0.749 0.272 0.037 0.243 1.513

21:00 0.663 0.483 0.065 -0.073 1.722

22:00 0.840 0.368 0.050 0.053 1.688



147

Table A103 2 Week ARDL(1,1) Long-Run Hedge Ratios: First Energy Hub The table below shows the descriptive statistics of bi-weekly long-run (LR) ARDL(1,1) hedge ratio estimates for the First Energy hub. ARDL(1,1) hedge ratios are calculated using twenty bi-weekly spot and forward prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. 55 bi-weekly hedge ratios are estimated for each hourly time series.

Hour Mean LR

Hedge Std. Dev. LR

Hedge Std. Error LR

Hedge Min. LR Hedge

Max. LR Hedge

0:00 0.488 0.536 0.072 -0.673 1.826

1:00 0.271 0.746 0.101 -2.409 1.203

2:00 0.620 0.389 0.053 -0.345 1.438

3:00 0.621 0.272 0.037 -0.160 1.159

4:00 0.773 0.323 0.043 -1.047 1.463

5:00 0.738 0.469 0.063 -0.033 1.467

6:00 0.622 0.448 0.060 -0.238 1.846

7:00 0.760 0.162 0.022 0.455 1.323

8:00 1.110 0.408 0.055 0.071 1.889

9:00 0.401 0.141 0.019 -0.002 0.618

10:00 0.481 0.319 0.043 -0.002 1.789

11:00 0.640 0.353 0.048 0.088 1.428

12:00 0.454 0.371 0.050 -0.323 1.208

13:00 0.605 0.251 0.034 0.099 1.160

14:00 0.760 0.422 0.057 0.015 1.503

15:00 0.780 0.340 0.046 0.231 1.629

16:00 0.994 0.520 0.070 0.378 3.051

17:00 -9.363 75.161 10.135 -556.631 1.557

18:00 1.266 0.581 0.078 0.328 2.705

19:00 0.596 0.302 0.041 -0.217 1.226

20:00 0.557 1.987 0.268 -11.487 1.615

21:00 0.706 0.430 0.058 -0.419 1.587

22:00 0.687 0.326 0.044 -0.655 1.229



148

Table A104 3 Week ARDL(1,1) Short-Run Hedge Ratios: Illinois Hub

The table below shows the descriptive statistics of tri-weekly short-run (SR) ARDL(1,1) hedge ratio estimates for the Illinois hub. ARDL(1,1) hedge ratios are calculated using twenty tri-weekly spot and forward prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. 30 tri-weekly hedge ratios are estimated for each hourly time series.

Hour Mean SR

Hedge Std. Dev. SR

Hedge Std. Error SR

Hedge Min. SR Hedge

Max. SR Hedge

0:00 0.732 0.302 0.055 0.152 1.150

1:00 0.249 0.562 0.103 -0.952 1.001

2:00 0.350 0.431 0.079 -0.775 0.786

3:00 0.929 0.116 0.021 0.684 1.142

4:00 0.943 0.259 0.047 0.614 1.700

5:00 1.002 0.161 0.029 0.551 1.409

6:00 1.400 0.539 0.098 0.693 2.143

7:00 0.650 0.138 0.025 0.410 0.941

8:00 1.084 0.078 0.014 0.976 1.348

9:00 0.494 0.329 0.060 -0.043 0.991

10:00 0.336 0.236 0.043 -0.148 0.628

11:00 0.191 0.186 0.034 -0.148 0.400

12:00 -0.055 0.409 0.075 -0.616 0.469

13:00 0.294 0.376 0.069 -0.278 0.779

14:00 0.169 0.248 0.045 -0.145 0.507

15:00 0.282 0.245 0.045 -0.008 0.617

16:00 0.130 0.275 0.050 -0.193 0.538

17:00 0.298 0.247 0.045 0.007 0.640

18:00 0.281 0.167 0.031 -0.012 0.526

19:00 0.303 0.202 0.037 -0.179 0.551

20:00 0.346 0.735 0.134 -0.634 1.445

21:00 0.174 0.372 0.068 -0.439 0.653

22:00 0.506 0.313 0.057 -0.118 0.892



149

Table A105 3 Week ARDL(1,1) Long-Run Hedge Ratios: Illinois Hub The table below shows the descriptive statistics of tri-weekly long-run (LR) ARDL(1,1) hedge ratio estimates for the Illinois hub. ARDL(1,1) hedge ratios are calculated using twenty tri-weekly spot and forward prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. 30 tri-weekly hedge ratios are estimated for each hourly time series.

Hour Mean LR

Hedge Std. Dev. LR

Hedge Std. Error LR

Hedge Min. LR Hedge

Max. LR Hedge

0:00 0.831 0.380 0.069 0.010 1.408

1:00 1.344 0.545 0.099 0.741 2.511

2:00 1.106 0.550 0.100 0.384 2.196

3:00 0.978 0.194 0.035 0.600 1.315

4:00 1.224 0.555 0.101 0.616 2.524

5:00 1.203 0.238 0.043 0.949 1.832

6:00 1.369 0.233 0.043 1.094 1.718

7:00 0.692 0.373 0.068 0.171 1.261

8:00 1.067 0.183 0.033 0.702 1.267

9:00 0.467 0.147 0.027 0.253 0.723

10:00 0.406 0.088 0.016 0.204 0.606

11:00 0.574 0.223 0.041 0.196 1.012

12:00 0.193 0.269 0.049 -0.228 0.639

13:00 0.563 0.144 0.026 0.290 0.833

14:00 0.366 0.625 0.114 -0.410 1.217

15:00 0.615 0.293 0.054 0.193 1.013

16:00 0.722 0.282 0.051 0.367 1.112

17:00 0.885 0.283 0.052 0.444 1.262

18:00 0.682 0.156 0.029 0.329 0.980

19:00 0.450 0.332 0.061 -0.168 0.933

20:00 1.334 1.301 0.237 -0.486 3.178

21:00 0.571 0.469 0.086 -0.276 1.182

22:00 0.389 0.402 0.073 -0.429 0.876



150

Table A106 3 Week ARDL(1,1) Short-Run Hedge Ratios: Cinergy Hub The table below shows the descriptive statistics of tri-weekly short-run (SR) ARDL(1,1) hedge ratio estimates for the Cinergy hub. ARDL(1,1) hedge ratios are calculated using twenty tri-weekly spot and forward prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. 30 tri-weekly hedge ratios are estimated for each hourly time series.

Hour Mean SR

Hedge Std. Dev. SR

Hedge Std. Error SR

Hedge Max. SR Hedge

Min. SR Hedge

0:00 0.351 0.143 0.026 0.735 0.138

1:00 0.234 0.375 0.068 0.962 -0.201

2:00 0.285 0.188 0.034 0.701 0.035

3:00 0.382 0.368 0.067 0.919 -0.091

4:00 0.650 0.123 0.022 0.815 0.493

5:00 0.805 0.067 0.012 1.014 0.638

6:00 1.267 0.607 0.111 2.044 0.561

7:00 0.490 0.121 0.022 0.737 0.235

8:00 0.760 0.215 0.039 1.106 0.459

9:00 0.173 0.169 0.031 0.521 -0.086

10:00 0.209 0.125 0.023 0.502 0.030

11:00 0.236 0.183 0.033 0.447 -0.104

12:00 0.015 0.289 0.053 0.428 -0.407

13:00 0.458 0.141 0.026 0.625 0.194

14:00 0.235 0.179 0.033 0.437 -0.122

15:00 0.254 0.264 0.048 0.534 -0.113

16:00 -0.003 0.345 0.063 0.404 -0.443

17:00 0.155 0.295 0.054 0.489 -0.208

18:00 0.262 0.094 0.017 0.410 -0.009

19:00 0.249 0.146 0.027 0.509 -0.116

20:00 0.253 0.536 0.098 0.873 -0.632

21:00 0.107 0.156 0.029 0.409 -0.167

22:00 0.488 0.166 0.030 0.652 0.034

23:00 0.180 0.144 0.026 0.401 -0.097 The ARDL(1,1) model is expressed as follows: St 1 St-1 Ft-1 Ft vt. The short-run


151

Table A107 3 Week ARDL(1,1) Long-Run Hedge Ratios: Cinergy Hub The table below shows the descriptive statistics of tri-weekly long-run (LR) ARDL(1,1) hedge ratio estimates for the Cinergy hub. ARDL(1,1) hedge ratios are calculated using twenty tri-weekly spot and forward prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. 30 tri-weekly hedge ratios are estimated for each hourly time series.

Hour Mean LR

Hedge Std. Dev. LR

Hedge Std. Error LR

Hedge Min. LR Hedge

Max. LR Hedge

0:00 0.409 0.198 0.036 -0.015 1.082

1:00 0.283 0.468 0.085 -0.334 0.937

2:00 0.279 0.202 0.037 0.005 0.709

3:00 0.411 0.448 0.082 -0.136 0.967

4:00 0.610 0.061 0.011 0.517 0.726

5:00 0.870 0.105 0.019 0.649 1.137

6:00 1.240 0.378 0.069 0.696 1.824

7:00 0.655 0.113 0.021 0.511 0.993

8:00 0.756 0.196 0.036 0.398 1.045

9:00 0.281 0.211 0.039 -0.046 0.687

10:00 0.305 0.207 0.038 -0.010 0.638

11:00 0.568 0.233 0.043 0.255 1.066

12:00 0.393 0.179 0.033 0.098 0.951

13:00 0.767 0.165 0.030 0.513 1.089

14:00 0.635 0.345 0.063 0.120 1.031

15:00 0.715 0.211 0.039 0.387 1.041

16:00 0.630 0.211 0.039 0.311 0.908

17:00 0.809 0.179 0.033 0.518 1.101

18:00 0.563 0.097 0.018 0.356 0.725

19:00 0.356 0.174 0.032 -0.014 0.611

20:00 0.907 0.778 0.142 -0.326 2.223

21:00 0.684 0.207 0.038 0.286 1.113

22:00 0.479 0.335 0.061 -0.330 0.813



152

Table A108 3 Week ARDL(1,1) Short-Run Hedge Ratios: Michigan Hub The table below shows the descriptive statistics of tri-weekly short-run (SR) ARDL(1,1) hedge ratio estimates for the Michigan hub. ARDL(1,1) hedge ratios are calculated using twenty tri-weekly spot and forward prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. 30 tri-weekly hedge ratios are estimated for each hourly time series.

Hour Mean SR

Hedge Std. Dev. SR

Hedge Std. Error SR

Hedge Min. SR Hedge

Max. SR Hedge

0:00 0.276 0.135 0.025 0.022 0.635

1:00 0.394 0.222 0.040 0.114 0.982

2:00 0.405 0.117 0.021 0.281 0.809

3:00 0.388 0.386 0.071 -0.101 0.978

4:00 0.670 0.126 0.023 0.441 0.840

5:00 0.932 0.130 0.024 0.727 1.288

6:00 1.101 0.556 0.102 0.486 2.109

7:00 0.511 0.110 0.020 0.207 0.733

8:00 0.678 0.221 0.040 0.383 1.012

9:00 0.124 0.137 0.025 -0.116 0.414

10:00 0.177 0.092 0.017 0.024 0.365

11:00 0.267 0.195 0.036 -0.071 0.576

12:00 -0.018 0.335 0.061 -0.447 0.473

13:00 0.382 0.268 0.049 -0.072 0.712

14:00 0.215 0.212 0.039 -0.129 0.502

15:00 0.089 0.397 0.072 -0.437 0.539

16:00 0.089 0.289 0.053 -0.268 0.463

17:00 0.705 0.312 0.057 0.331 1.511

18:00 0.224 0.145 0.026 -0.010 0.417

19:00 0.324 0.113 0.021 -0.019 0.517

20:00 0.272 0.613 0.112 -0.602 1.054

21:00 -0.010 0.116 0.021 -0.304 0.153

22:00 0.386 0.199 0.036 -0.026 0.668



153

Table A109 3 Week ARDL(1,1) Long-Run Hedge Ratios: Michigan Hub The table below shows the descriptive statistics of tri-weekly long-run (LR) ARDL(1,1) hedge ratio estimates for the Michigan hub. ARDL(1,1) hedge ratios are calculated using twenty tri-weekly spot and forward prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. 30 tri-weekly hedge ratios are estimated for each hourly time series.

Hour Mean LR

Hedge Std. Dev. LR

Hedge Std. Error LR

Hedge Min. LR Hedge

Max. LR Hedge

0:00 0.347 0.203 0.037 -0.243 0.983

1:00 0.464 0.287 0.052 0.060 0.983

2:00 0.414 0.126 0.023 0.298 0.777

3:00 0.404 0.423 0.077 -0.202 0.956

4:00 0.557 0.106 0.019 0.412 0.742

5:00 0.357 0.304 0.056 -0.206 0.851

6:00 1.171 0.512 0.094 0.536 2.107

7:00 0.532 0.144 0.026 0.382 1.058

8:00 0.650 0.300 0.055 0.174 1.045

9:00 0.290 0.236 0.043 -0.046 0.724

10:00 0.318 0.216 0.040 0.005 0.607

11:00 0.607 0.241 0.044 0.229 0.978

12:00 0.221 0.296 0.054 -0.282 0.778

13:00 0.923 0.184 0.034 0.661 1.274

14:00 0.658 0.381 0.069 0.101 1.125

15:00 0.541 0.367 0.067 -0.046 0.959

16:00 0.641 0.287 0.052 0.278 1.040

17:00 0.914 0.344 0.063 0.164 1.566

18:00 0.608 0.176 0.032 0.269 0.912

19:00 0.476 0.211 0.039 0.116 0.837

20:00 1.123 1.075 0.196 -0.494 2.851

21:00 0.602 0.216 0.039 0.240 1.069

22:00 0.392 0.360 0.066 -0.352 0.860



154

Table A110 3 Week ARDL(1,1) Short-Run Hedge Ratios: Minnesota Hub The table below shows the descriptive statistics of tri-weekly short-run (SR) ARDL(1,1) hedge ratio estimates for the Minnesota hub. ARDL(1,1) hedge ratios are calculated using twenty tri-weekly spot and forward prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. 30 tri-weekly hedge ratios are estimated for each hourly time series.

Hour Mean SR

Hedge Std. Dev. SR

Hedge Std. Error SR

Hedge Min. SR Hedge

Max. SR Hedge

0:00 0.820 0.291 0.053 0.481 1.397

1:00 0.990 0.414 0.075 0.442 1.601

2:00 1.569 0.620 0.113 0.574 2.556

3:00 1.678 0.511 0.093 0.733 2.426

4:00 1.509 0.519 0.095 0.636 2.179

5:00 1.160 0.274 0.050 0.673 1.553

6:00 0.169 0.515 0.094 -0.594 0.784

7:00 0.601 0.197 0.036 0.279 0.885

8:00 1.231 0.499 0.091 0.495 2.289

9:00 0.720 0.250 0.046 0.310 1.124

10:00 0.722 0.260 0.047 0.088 1.241

11:00 0.658 0.342 0.062 0.168 1.472

12:00 0.502 0.215 0.039 -0.036 0.812

13:00 0.826 0.339 0.062 0.383 1.475

14:00 0.934 0.342 0.062 0.487 1.491

15:00 0.783 0.337 0.061 0.382 1.271

16:00 0.547 0.447 0.082 0.048 1.351

17:00 0.197 0.265 0.048 -0.107 0.538

18:00 0.564 0.305 0.056 0.096 1.498

19:00 0.900 0.269 0.049 0.450 1.358

20:00 0.882 0.172 0.031 0.536 1.160

21:00 0.839 0.199 0.036 0.487 1.200

22:00 1.231 0.284 0.052 0.797 1.802



155

Table A111 3 Week ARDL(1,1) Long-Run Hedge Ratios: Minnesota Hub The table below shows the descriptive statistics of tri-weekly long-run (LR) ARDL(1,1) hedge ratio estimates for the Minnesota hub. ARDL(1,1) hedge ratios are calculated using twenty tri-weekly spot and forward prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. 30 tri-weekly hedge ratios are estimated for each hourly time series.

Hour Mean LR

Hedge Std. Dev. LR

Hedge Std. Error LR

Hedge Min. LR Hedge

Max. LR Hedge

0:00 0.829 0.136 0.025 0.561 1.030

1:00 1.109 0.467 0.085 0.459 1.699

2:00 1.782 0.709 0.129 0.633 2.987

3:00 1.660 0.395 0.072 1.009 2.429

4:00 1.523 0.504 0.092 0.754 2.292

5:00 1.182 0.272 0.050 0.779 1.714

6:00 0.425 0.650 0.119 -0.647 1.166

7:00 0.752 0.215 0.039 0.463 1.131

8:00 1.284 0.368 0.067 0.805 1.778

9:00 0.902 0.219 0.040 0.541 1.223

10:00 1.186 0.248 0.045 0.534 1.690

11:00 1.387 0.539 0.098 0.672 2.525

12:00 1.663 1.026 0.187 0.215 3.265

13:00 1.369 0.519 0.095 0.480 2.377

14:00 1.002 0.183 0.033 0.735 1.366

15:00 0.819 0.125 0.023 0.679 1.146

16:00 0.928 0.164 0.030 0.642 1.259

17:00 0.826 0.284 0.052 0.466 1.214

18:00 0.784 0.398 0.073 -0.281 1.192

19:00 0.937 0.423 0.077 0.181 1.537

20:00 1.819 0.651 0.119 0.952 2.700

21:00 1.547 0.680 0.124 0.660 2.497

22:00 1.368 0.289 0.053 0.968 1.899



156

Table A112 3 Week ARDL(1,1) Short-Run Hedge Ratios: First Energy Hub The table below shows the descriptive statistics of tri-weekly short-run (SR) ARDL(1,1) hedge ratio estimates for the First Energy hub. ARDL(1,1) hedge ratios are calculated using twenty tri-weekly spot and forward prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. 30 tri-weekly hedge ratios are estimated for each hourly time series.

Hour Mean SR

Hedge Std. Dev. SR

Hedge Std. Error SR

Hedge Min. SR Hedge

Max. SR Hedge

0:00 0.133 0.245 0.045 -0.230 0.543

1:00 0.084 0.249 0.045 -0.216 0.487

2:00 0.304 0.138 0.025 0.120 0.761

3:00 0.120 0.154 0.028 -0.132 0.588

4:00 0.431 0.185 0.034 0.142 0.743

5:00 0.502 0.080 0.015 0.313 0.751

6:00 1.048 0.572 0.104 0.365 1.904

7:00 0.416 0.199 0.036 0.162 0.761

8:00 0.704 0.226 0.041 0.378 1.053

9:00 0.078 0.186 0.034 -0.135 0.490

10:00 0.253 0.147 0.027 0.049 0.582

11:00 0.161 0.183 0.033 -0.108 0.514

12:00 -0.035 0.170 0.031 -0.306 0.276

13:00 1.201 0.810 0.148 0.239 2.163

14:00 0.262 0.067 0.012 0.129 0.380

15:00 0.413 0.206 0.038 0.161 0.720

16:00 0.157 0.089 0.016 0.003 0.280

17:00 0.291 0.042 0.008 0.213 0.379

18:00 0.134 0.184 0.034 -0.286 0.497

19:00 0.125 0.150 0.027 -0.223 0.322

20:00 0.217 0.311 0.057 -0.249 0.777

21:00 0.077 0.229 0.042 -0.268 0.571

22:00 0.561 0.159 0.029 0.113 0.806



157

Table A113 3 Week ARDL(1,1) Long-Run Hedge Ratios: First Energy Hub The table below shows the descriptive statistics of tri-weekly long-run (LR) ARDL(1,1) hedge ratio estimates for the First Energy hub. ARDL(1,1) hedge ratios are calculated using twenty tri-weekly spot and forward prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. 30 tri-weekly hedge ratios are estimated for each hourly time series.

Hour Mean LR

Hedge Std. Dev. LR

Hedge Std. Error LR

Hedge Min. LR Hedge

Max. LR Hedge

0:00 0.188 0.187 0.034 -0.182 0.765

1:00 0.182 0.440 0.080 -0.283 0.854

2:00 0.302 0.182 0.033 0.054 0.758

3:00 0.081 0.137 0.025 -0.071 0.513

4:00 0.350 0.216 0.039 -0.003 0.595

5:00 0.409 0.142 0.026 0.101 0.613

6:00 1.095 0.470 0.086 0.481 1.939

7:00 0.666 0.122 0.022 0.556 1.051

8:00 0.704 0.165 0.030 0.415 0.962

9:00 0.137 0.242 0.044 -0.202 0.530

10:00 0.252 0.169 0.031 0.002 0.517

11:00 0.356 0.250 0.046 0.044 0.971

12:00 0.352 0.253 0.046 -0.087 0.831

13:00 1.171 0.682 0.124 0.320 2.091

14:00 0.640 0.338 0.062 0.166 1.119

15:00 0.737 0.122 0.022 0.284 0.976

16:00 0.824 0.100 0.018 0.631 0.978

17:00 1.022 0.118 0.022 0.747 1.369

18:00 0.546 0.251 0.046 -0.372 1.069

19:00 0.402 0.243 0.044 -0.080 0.820

20:00 1.155 0.655 0.119 0.201 2.251

21:00 0.478 0.255 0.047 0.111 0.942

22:00 0.719 0.360 0.066 -0.276 1.248



158

Table A114 4 Week ARDL(1,1) Short-Run Hedge Ratios: Illinois Hub The table below shows the descriptive statistics of monthly short-run (SR) ARDL(1,1) hedge ratio estimates for the Illinois hub. ARDL(1,1) hedge ratios are calculated using twenty monthly spot and forward prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. 18 monthly hedge ratios are estimated for each hourly time series.

Hour Mean SR

Hedge Std. Dev. SR

Hedge Std. Error SR

Hedge Min. SR Hedge

Max. SR Hedge

0:00 1.095 0.315 0.074 0.902 1.978

1:00 0.756 0.298 0.070 0.469 1.221

2:00 0.949 0.274 0.065 0.637 1.391

3:00 0.469 0.141 0.033 0.274 0.781

4:00 2.831 1.065 0.251 0.851 4.121

5:00 0.828 0.136 0.032 0.450 1.023

6:00 0.711 0.196 0.046 0.399 0.955

7:00 0.768 0.138 0.033 0.575 1.103

8:00 0.903 0.101 0.024 0.637 1.033

9:00 0.442 0.244 0.057 0.206 0.956

10:00 0.728 0.200 0.047 0.359 1.012

11:00 0.416 0.220 0.052 0.064 0.890

12:00 0.305 0.409 0.096 -0.299 1.100

13:00 0.021 0.559 0.132 -0.655 1.197

14:00 0.838 0.231 0.054 0.525 1.241

15:00 1.173 0.393 0.093 0.572 1.658

16:00 1.515 0.188 0.044 1.101 1.742

17:00 1.158 0.259 0.061 0.750 1.617

18:00 1.236 0.259 0.061 0.612 1.597

19:00 0.935 0.190 0.045 0.530 1.283

20:00 0.946 0.153 0.036 0.604 1.343

21:00 0.868 0.173 0.041 0.415 1.160

22:00 0.879 0.152 0.036 0.622 1.166



159

Table A115 4 Week ARDL(1,1) Long-Run Hedge Ratios: Illinois Hub The table below shows the descriptive statistics of monthly long-run (LR) ARDL(1,1) hedge ratio estimates for the Illinois hub. ARDL(1,1) hedge ratios are calculated using twenty monthly spot and forward prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. 18 monthly hedge ratios are estimated for each hourly time series.

Hour Mean LR

Hedge Std. Dev. LR

Hedge Std. Error LR

Hedge Min. LR Hedge

Max. LR Hedge

0:00 0.902 0.292 0.069 0.716 1.791

1:00 0.592 0.130 0.031 0.384 0.786

2:00 0.809 0.245 0.058 0.596 1.441

3:00 0.647 0.122 0.029 0.315 0.771

4:00 1.931 1.404 0.331 0.593 7.346

5:00 0.632 0.149 0.035 0.285 0.763

6:00 0.513 0.104 0.025 0.341 0.751

7:00 0.405 0.107 0.025 0.278 0.777

8:00 0.837 0.166 0.039 0.559 1.038

9:00 0.586 0.035 0.008 0.513 0.673

10:00 0.505 0.086 0.020 0.326 0.648

11:00 0.793 0.118 0.028 0.509 0.961

12:00 0.307 0.294 0.069 -0.396 0.673

13:00 0.683 0.339 0.080 -0.034 1.268

14:00 1.345 0.415 0.098 0.718 1.987

15:00 1.033 0.147 0.035 0.837 1.229

16:00 1.478 0.247 0.058 0.987 1.850

17:00 1.005 0.257 0.061 0.416 1.346

18:00 1.232 0.259 0.061 0.616 1.560

19:00 0.492 0.189 0.045 -0.002 0.664

20:00 0.815 0.179 0.042 0.253 1.071

21:00 0.372 0.295 0.070 -0.044 1.065

22:00 0.414 0.203 0.048 0.104 0.909



160

Table A116 4 Week ARDL(1,1) Short-Run Hedge Ratios: Cinergy Hub

The table below shows the descriptive statistics of monthly short-run (SR) ARDL(1,1) hedge ratio estimates for the Cinergy hub. ARDL(1,1) hedge ratios are calculated using twenty monthly spot and forward prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. 18 monthly hedge ratios are estimated for each hourly time series.

Hour Mean SR

Hedge Std. Dev. SR

Hedge Std. Error SR

Hedge Min. SR Hedge

Max. SR Hedge

0:00 0.969 0.253 0.060 0.796 1.649

1:00 0.688 0.252 0.059 0.444 1.168

2:00 0.930 0.266 0.063 0.631 1.372

3:00 0.435 0.131 0.031 0.306 0.769

4:00 2.995 1.258 0.296 0.872 4.587

5:00 0.780 0.090 0.021 0.475 0.908

6:00 0.804 0.234 0.055 0.430 1.060

7:00 0.742 0.241 0.057 0.367 1.070

8:00 0.886 0.214 0.050 0.597 1.172

9:00 0.393 0.086 0.020 0.206 0.497

10:00 0.902 0.251 0.059 0.380 1.281

11:00 0.917 0.321 0.076 0.368 1.362

12:00 0.738 0.318 0.075 0.288 1.430

13:00 0.696 0.377 0.089 0.087 1.318

14:00 1.545 0.267 0.063 1.212 2.079

15:00 1.254 0.272 0.064 0.839 1.764

16:00 1.452 0.161 0.038 1.049 1.639

17:00 1.290 0.437 0.103 0.672 2.096

18:00 2.202 0.451 0.106 1.029 2.614

19:00 1.349 0.268 0.063 0.607 1.537

20:00 0.906 0.112 0.026 0.541 1.039

21:00 0.784 0.149 0.035 0.370 0.985

22:00 0.800 0.087 0.020 0.599 0.924



161

Table A117 4 Week ARDL(1,1) Long-Run Hedge Ratios: Cinergy Hub

The table below shows the descriptive statistics of monthly long-run (LR) ARDL(1,1) hedge ratio estimates for the Cinergy hub. ARDL(1,1) hedge ratios are calculated using twenty monthly spot and forward prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. 18 monthly hedge ratios are estimated for each hourly time series.

Hour Mean LR

Hedge Std. Dev. LR

Hedge Std. Error LR

Hedge Min. LR Hedge

Max. LR Hedge

0:00 0.817 0.241 0.057 0.624 1.484

1:00 0.556 0.149 0.035 0.335 0.794

2:00 0.761 0.222 0.052 0.554 1.304

3:00 0.551 0.082 0.019 0.296 0.679

4:00 2.372 2.975 0.701 0.796 14.208

5:00 0.675 0.058 0.014 0.472 0.739

6:00 0.619 0.209 0.049 0.304 1.168

7:00 0.507 0.085 0.020 0.397 0.775

8:00 0.900 0.138 0.033 0.695 1.094

9:00 0.582 0.059 0.014 0.396 0.660

10:00 0.610 0.113 0.027 0.370 0.809

11:00 1.065 0.172 0.040 0.623 1.299

12:00 0.426 0.390 0.092 -0.485 1.072

13:00 0.889 0.442 0.104 0.213 1.616

14:00 1.476 0.385 0.091 1.054 2.292

15:00 1.228 0.138 0.033 0.899 1.398

16:00 1.670 0.250 0.059 1.069 1.994

17:00 1.375 0.370 0.087 0.456 1.837

18:00 1.778 0.400 0.094 0.855 2.274

19:00 0.959 0.205 0.048 0.363 1.138

20:00 0.988 0.162 0.038 0.463 1.175

21:00 0.446 0.242 0.057 0.214 1.024

22:00 0.397 0.191 0.045 0.199 0.870



162

Table A118 4 Week ARDL(1,1) Short-Run Hedge Ratios: Michigan Hub The table below shows the descriptive statistics of monthly short-run (SR) ARDL(1,1) hedge ratio estimates for the Michigan hub. ARDL(1,1) hedge ratios are calculated using twenty monthly spot and forward prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. 18 monthly hedge ratios are estimated for each hourly time series.

Hour Mean SR

Hedge Std. Dev. SR

Hedge Std. Error SR

Hedge Min. SR Hedge

Max. SR Hedge

0:00 0.881 0.361 0.085 0.667 1.856

1:00 0.790 0.214 0.050 0.583 1.205

2:00 0.966 0.239 0.056 0.705 1.437

3:00 0.435 0.179 0.042 0.201 0.895

4:00 2.774 1.000 0.236 0.630 3.875

5:00 0.869 0.180 0.042 0.678 1.350

6:00 0.884 0.197 0.047 0.587 1.228

7:00 0.870 0.231 0.054 0.541 1.274

8:00 0.836 0.181 0.043 0.549 1.071

9:00 0.285 0.171 0.040 0.037 0.696

10:00 0.667 0.128 0.030 0.385 0.831

11:00 0.433 0.196 0.046 0.153 0.903

12:00 0.364 0.352 0.083 -0.214 1.081

13:00 0.322 0.490 0.116 -0.238 1.380

14:00 1.098 0.216 0.051 0.814 1.501

15:00 1.130 0.257 0.061 0.619 1.538

16:00 1.320 0.106 0.025 1.089 1.545

17:00 0.998 0.359 0.085 0.134 1.636

18:00 1.789 0.357 0.084 0.876 2.128

19:00 1.069 0.197 0.046 0.530 1.219

20:00 0.826 0.097 0.023 0.572 1.011

21:00 0.737 0.157 0.037 0.289 1.072

22:00 0.831 0.109 0.026 0.648 1.017



163

Table A119 4 Week ARDL(1,1) Long-Run Hedge Ratios: Michigan Hub The table below shows the descriptive statistics of monthly long-run (LR) ARDL(1,1) hedge ratio estimates for the Michigan hub. ARDL(1,1) hedge ratios are calculated using twenty monthly spot and forward prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. 18 monthly hedge ratios are estimated for each hourly time series.

Hour Mean LR

Hedge Std. Dev. LR

Hedge Std. Error LR

Hedge Min. LR Hedge

Max. LR Hedge

0:00 0.658 0.296 0.070 0.439 1.515

1:00 0.593 0.107 0.025 0.440 0.780

2:00 0.781 0.291 0.069 0.568 1.522

3:00 0.486 0.159 0.037 0.205 0.878

4:00 1.836 0.907 0.214 0.736 5.174

5:00 0.763 0.219 0.052 0.560 1.348

6:00 0.545 0.469 0.111 0.065 1.751

7:00 0.478 0.160 0.038 0.225 0.870

8:00 0.874 0.172 0.041 0.596 1.119

9:00 0.568 0.074 0.017 0.502 0.757

10:00 0.527 0.085 0.020 0.379 0.701

11:00 0.837 0.100 0.023 0.687 1.070

12:00 0.396 0.346 0.082 -0.328 1.031

13:00 0.753 0.326 0.077 0.237 1.215

14:00 1.304 0.410 0.097 0.687 1.988

15:00 1.267 0.101 0.024 1.089 1.445

16:00 1.629 0.244 0.058 1.097 1.926

17:00 0.895 0.254 0.060 0.221 1.144

18:00 1.502 0.323 0.076 0.750 1.908

19:00 0.741 0.174 0.041 0.242 0.879

20:00 0.987 0.144 0.034 0.553 1.189

21:00 0.513 0.283 0.067 0.253 1.314

22:00 0.367 0.172 0.041 0.164 0.760



164

164

Table A120 4 Week ARDL(1,1) Short-Run Hedge Ratios: Minnesota Hub

The table below shows the descriptive statistics of monthly short-run (SR) ARDL(1,1) hedge ratio estimates for the Minnesota hub. ARDL(1,1) hedge ratios are calculated using twenty monthly spot and forward prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. 18 monthly hedge ratios are estimated for each hourly time series.

Hour Mean SR

Hedge Std. Dev. SR

Hedge Std. Error SR

Hedge Min. SR Hedge

Max. SR Hedge

0:00 0.439 0.140 0.033 0.184 0.637

1:00 0.955 0.267 0.063 0.659 1.501

2:00 1.139 0.124 0.029 0.957 1.356

3:00 0.626 0.067 0.016 0.525 0.738

4:00 0.745 0.169 0.040 0.279 0.899

5:00 0.488 0.104 0.025 0.372 0.726

6:00 0.673 0.205 0.048 0.362 1.065

7:00 0.757 0.191 0.045 0.427 1.068

8:00 0.677 0.092 0.022 0.527 0.821

9:00 0.569 0.174 0.041 0.242 0.854

10:00 0.723 0.150 0.035 0.454 0.918

11:00 0.588 0.207 0.049 0.070 0.783

12:00 0.303 0.266 0.063 -0.116 0.968

13:00 0.561 0.257 0.061 0.073 0.890

14:00 1.596 0.700 0.165 0.280 2.751

15:00 0.998 0.414 0.098 0.132 1.417

16:00 0.775 0.280 0.066 0.041 1.149

17:00 1.182 0.401 0.095 0.603 1.944

18:00 0.742 0.383 0.090 0.105 1.507

19:00 0.740 0.323 0.076 0.110 1.310

20:00 0.283 0.180 0.042 0.026 0.548

21:00 0.321 0.163 0.038 0.085 0.593

22:00 0.489 0.242 0.057 0.076 0.838



165

Table A121 4 Week ARDL(1,1) Long-Run Hedge Ratios: Minnesota Hub The table below shows the descriptive statistics of monthly long-run (LR) ARDL(1,1) hedge ratio estimates for the Minnesota hub. ARDL(1,1) hedge ratios are calculated using twenty monthly spot and forward prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. 18 monthly hedge ratios are estimated for each hourly time series.

Hour Mean LR

Hedge Std. Dev. LR

Hedge Std. Error LR

Hedge Min. LR Hedge

Max. LR Hedge

0:00 0.837 0.084 0.020 0.638 0.996

1:00 0.745 0.180 0.042 0.536 1.131

2:00 0.988 0.117 0.028 0.852 1.242

3:00 0.668 0.072 0.017 0.531 0.787

4:00 1.120 0.235 0.055 0.457 1.469

5:00 0.518 0.083 0.020 0.312 0.602

6:00 0.397 0.168 0.040 0.174 0.748

7:00 0.572 0.114 0.027 0.411 0.770

8:00 0.756 0.193 0.046 0.360 0.957

9:00 0.577 0.133 0.031 0.408 0.843

10:00 0.737 0.086 0.020 0.588 0.925

11:00 0.921 0.325 0.076 0.134 1.355

12:00 0.433 0.244 0.058 -0.054 0.809

13:00 0.961 0.388 0.092 0.285 1.373

14:00 1.618 0.588 0.139 0.345 2.290

15:00 1.049 0.312 0.073 0.241 1.297

16:00 1.225 0.374 0.088 0.276 1.529

17:00 1.262 0.288 0.068 0.590 1.686

18:00 0.229 0.199 0.047 -0.134 0.551

19:00 0.491 0.157 0.037 0.113 0.721

20:00 0.735 0.180 0.042 0.378 0.969

21:00 0.520 0.111 0.026 0.313 0.681

22:00 0.603 0.211 0.050 0.260 0.923



166

Table A122 4 Week ARDL(1,1) Short-Run Hedge Ratios: First Energy Hub

The table below shows the descriptive statistics of monthly short-run (SR) ARDL(1,1) hedge ratio estimates for the First Energy hub. ARDL(1,1) hedge ratios are calculated using twenty monthly spot and forward prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. 18 monthly hedge ratios are estimated for each hourly time series.

Hour Mean SR

Hedge Std. Dev. SR

Hedge Std. Error SR

Hedge Min. SR Hedge

Max. SR Hedge

0:00 0.969 0.208 0.049 0.734 1.547

1:00 0.739 0.152 0.036 0.463 0.992

2:00 0.748 0.275 0.065 0.449 1.427

3:00 0.412 0.180 0.042 0.189 0.845

4:00 2.092 0.426 0.100 1.010 2.469

5:00 0.889 0.159 0.037 0.687 1.303

6:00 1.008 0.185 0.044 0.695 1.284

7:00 0.857 0.155 0.036 0.577 1.132

8:00 0.939 0.248 0.058 0.611 1.273

9:00 0.508 0.071 0.017 0.355 0.621

10:00 0.884 0.153 0.036 0.620 1.110

11:00 0.575 0.136 0.032 0.300 0.760

12:00 0.467 0.238 0.056 0.041 0.978

13:00 0.404 0.310 0.073 -0.195 0.971

14:00 1.014 0.224 0.053 0.738 1.492

15:00 1.223 0.335 0.079 0.683 1.753

16:00 1.295 0.131 0.031 1.026 1.563

17:00 1.357 0.380 0.090 0.860 2.086

18:00 2.311 0.562 0.132 0.956 3.106

19:00 1.014 0.234 0.055 0.388 1.227

20:00 0.845 0.114 0.027 0.531 0.999

21:00 0.730 0.134 0.032 0.345 0.968

22:00 0.852 0.115 0.027 0.647 1.017



167

Table A123 4 Week ARDL(1,1) Long-Run Hedge Ratios: First Energy Hub The table below shows the descriptive statistics of monthly long-run (LR) ARDL(1,1) hedge ratio estimates for the First Energy hub. ARDL(1,1) hedge ratios are calculated using twenty monthly spot and forward prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. 18 monthly hedge ratios are estimated for each hourly time series.

Hour Mean LR

Hedge Std. Dev. LR

Hedge Std. Error LR

Hedge Min. LR Hedge

Max. LR Hedge

0:00 0.628 0.184 0.043 0.034 1.040

1:00 0.362 0.112 0.026 0.142 0.571

2:00 0.750 0.278 0.065 0.497 1.450

3:00 0.563 0.095 0.022 0.443 0.805

4:00 1.614 0.362 0.085 1.076 2.680

5:00 0.753 0.153 0.036 0.648 1.200

6:00 0.703 0.385 0.091 0.262 1.699

7:00 0.372 0.111 0.026 0.158 0.693

8:00 0.834 0.135 0.032 0.620 1.009

9:00 0.518 0.063 0.015 0.322 0.616

10:00 0.550 0.069 0.016 0.441 0.695

11:00 0.815 0.142 0.033 0.499 1.012

12:00 0.274 0.252 0.059 -0.277 0.720

13:00 0.651 0.274 0.065 -0.108 1.055

14:00 1.258 0.372 0.088 0.742 1.961

15:00 1.241 0.094 0.022 1.072 1.435

16:00 1.526 0.222 0.052 1.047 1.847

17:00 1.306 0.320 0.075 0.488 1.762

18:00 1.590 0.452 0.107 0.719 2.208

19:00 0.527 0.170 0.040 0.086 0.662

20:00 0.812 0.192 0.045 0.219 1.042

21:00 0.284 0.274 0.065 0.008 0.950

22:00 0.446 0.126 0.030 0.279 0.778



168

Table A124 1 Week Method of Group Averages Hedge Ratios (Price Levels) The following table shows weekly hedge ratio estimates obtained using the method of group averages (MGA). A holdout sample of the first twenty weekly forward and spot prices is used to produce a static MGA hedge ratio estimate for each hour of the day across all five hubs.

Hour IL Cinergy MI MN FE

0:00 1.523 1.381 1.434 0.058 1.281

1:00 1.099 1.117 0.727 2.276 0.985

2:00 1.385 1.771 1.085 2.371 0.979

3:00 1.545 1.355 0.486 0.863 0.880

4:00 0.868 0.723 0.436 1.041 0.620

5:00 1.673 1.528 0.959 1.534 1.390

6:00 1.812 2.686 0.455 2.116 1.205

7:00 0.809 1.482 0.815 1.752 0.946

8:00 1.001 0.323 0.213 0.699 0.542

9:00 0.746 0.129 0.595 0.222 0.228

10:00 0.263 0.154 0.314 0.248 0.243

11:00 0.358 0.377 0.416 0.240 0.286

12:00 0.498 0.463 0.515 0.435 0.355

13:00 0.766 0.528 0.725 0.596 0.495

14:00 1.047 1.033 0.860 0.673 0.946

15:00 1.192 0.962 0.849 0.782 1.192

16:00 0.906 0.543 0.545 0.663 0.729

17:00 0.716 0.534 0.510 0.594 0.698

18:00 0.634 0.293 0.276 0.353 0.362

19:00 0.066 0.000 0.057 0.190 0.217

20:00 0.355 0.153 0.196 0.085 0.250

21:00 0.712 0.636 0.666 0.392 0.739

22:00 0.483 0.293 0.305 0.003 0.416

23:00 0.729 0.524 0.555 0.364 0.502

MGA hedge ratios are calculated by fitting a line between day-ahead prices that fall above the median (and their corresponding real-time prices) and day-ahead prices that fall below the median (along with their respective real-time prices). The MGA hedge ratio can be expressed

as MGA RT h -RT l

DA h -DA l. RT h is the average real-time price observed in the group with the highest day-

ahead prices. RT l is the average real-time price observed in the group with the lowest day-ahead prices. DA h and DA l represent the average day-ahead price in the highest and lowest group, respectively. The sample period for this analysis is 6/1/2006-4/11/2009.

169

Table A125 2 Week Method of Group Averages Hedge Ratios (Price Levels) The following table shows bi-weekly hedge ratio estimates obtained using the method of group averages (MGA). A holdout sample of the first twenty bi-weekly forward and spot prices is used to produce a static MGA hedge ratio estimate for each hour of the day across all five hubs.


0:00 1.437 1.264 1.417 0.160 1.292

1:00 0.517 0.596 0.562 1.184 0.557

2:00 1.411 1.458 1.136 1.154 1.241

3:00 1.548 1.516 1.159 1.294 1.425

4:00 1.103 1.028 0.611 1.670 0.821

5:00 1.417 1.486 0.911 1.760 1.289

6:00 1.255 1.154 0.839 0.700 1.103

7:00 0.932 0.799 0.991 0.704 1.041

8:00 1.406 1.132 1.061 0.828 1.221

9:00 1.058 0.346 0.712 0.528 0.465

10:00 0.743 0.738 0.616 1.006 0.819

11:00 0.652 0.518 0.544 0.364 0.690

12:00 0.224 0.563 0.441 0.065 0.451

13:00 0.543 0.469 0.535 0.274 0.542

14:00 0.251 0.413 0.334 0.457 0.540

15:00 0.501 0.438 0.534 0.444 0.566

16:00 0.483 0.435 0.431 0.245 0.526

17:00 0.250 0.230 0.279 0.245 0.351

18:00 0.303 0.338 0.372 0.186 0.440

19:00 0.567 0.448 0.509 0.233 0.393

20:00 0.974 0.703 0.784 0.442 0.912

21:00 0.579 0.395 0.384 0.311 0.581

22:00 0.814 0.718 0.692 0.365 0.833

23:00 0.851 0.759 0.754 0.288 0.906


as MGA RT h -RT l



170

Table A126 3 Week Method of Group Averages Hedge Ratios (Price Levels) The following table shows tri-weekly hedge ratio estimates obtained using the method of group averages (MGA). A holdout sample of the first twenty tri-weekly forward and spot prices is used to produce a static MGA hedge ratio estimate for each hour of the day across all five hubs.


0:00 0.266 0.271 0.063 1.442 0.233

1:00 0.686 0.634 0.515 0.888 0.637

2:00 0.536 0.483 0.426 0.921 0.477

3:00 0.807 0.665 0.298 0.892 0.288

4:00 0.620 0.511 0.450 0.697 0.414

5:00 0.784 0.619 0.521 0.647 0.458

6:00 1.191 1.345 1.043 -0.059 1.578

7:00 0.170 0.389 0.367 0.491 0.333

8:00 0.934 0.592 0.598 0.579 0.590

9:00 0.168 0.092 -0.057 0.413 0.062

10:00 -0.112 0.254 0.267 0.334 0.359

11:00 0.164 0.297 0.255 0.073 0.147

12:00 0.210 0.354 0.207 1.124 0.177

13:00 0.353 0.541 0.500 0.404 1.036

14:00 0.265 0.743 0.609 0.662 0.594

15:00 0.420 0.722 0.541 1.122 0.672

16:00 0.254 0.288 0.254 0.380 0.249

17:00 0.288 0.328 0.330 0.405 0.382

18:00 0.008 -0.035 0.056 0.276 0.301

19:00 -0.180 -0.027 0.018 0.988 0.043

20:00 -0.372 -0.031 -0.028 1.513 0.071

21:00 -0.233 -0.102 -0.052 1.152 0.097

22:00 0.012 0.357 0.320 0.526 0.488

23:00 0.177 0.299 0.174 0.828 0.269


as MGA RT h -RT l



171

Table A127 4 Week Method of Group Averages Hedge Ratios (Price Levels) The following table shows monthly hedge ratio estimates obtained using the method of group averages (MGA). A holdout sample of the first twenty monthly forward and spot prices is used to produce a static MGA hedge ratio estimate for each hour of the day across all five hubs.


0:00 1.761 1.585 1.813 0.471 1.577

1:00 0.499 0.712 0.754 1.290 0.640

2:00 1.096 1.163 1.088 1.422 1.205

3:00 0.999 1.015 1.073 0.806 1.089

4:00 0.880 0.776 0.755 0.870 1.320

5:00 1.163 1.103 1.109 0.915 1.495

6:00 0.829 1.575 1.363 0.904 1.700

7:00 1.171 1.162 1.267 1.092 1.327

8:00 0.750 0.487 0.737 0.727 0.612

9:00 1.016 0.327 0.810 0.556 0.334

10:00 1.376 0.766 0.943 0.768 0.818

11:00 0.801 0.949 0.909 0.520 0.746

12:00 0.399 0.874 0.729 -0.080 0.626

13:00 0.125 1.140 1.020 0.188 0.756

14:00 0.793 1.167 1.047 0.605 0.987

15:00 0.833 1.055 1.218 0.276 1.067

16:00 0.936 1.039 1.078 0.277 1.075

17:00 0.560 0.911 0.998 0.255 1.028

18:00 0.719 0.988 0.958 -0.004 1.298

19:00 1.069 0.737 0.692 0.492 0.532

20:00 1.417 1.045 0.950 0.098 0.767

21:00 0.937 0.907 0.951 0.566 0.761

22:00 0.907 0.703 0.469 0.079 1.023

23:00 0.816 0.745 0.776 0.687 0.988


as MGA RT h -RT l



172

Table A128 1 Week Method of Group Averages Hedge Ratios (Price Differences) The following table shows weekly hedge ratio estimates obtained using the method of group averages (MGA). A holdout sample of the first twenty weekly forward and spot prices is used to produce a static MGA hedge ratio estimate for each hour of the day across all five hubs.


0:00 1.207 1.021 1.146 -0.459 1.191

1:00 0.566 0.715 0.497 1.317 0.693

2:00 1.637 1.525 1.021 1.695 1.161

3:00 0.556 1.239 0.258 0.592 0.708

4:00 -0.214 0.630 0.398 -0.240 0.740

5:00 2.510 2.051 1.102 -0.407 1.836

6:00 4.803 3.521 1.780 1.633 3.064

7:00 1.815 1.287 0.290 0.977 1.196

8:00 1.266 0.157 0.156 0.210 0.229

9:00 1.142 0.059 0.723 0.128 0.198

10:00 0.316 -0.140 0.016 0.342 0.085

11:00 0.216 0.083 0.203 -0.048 0.392

12:00 0.107 -0.389 0.071 -0.567 0.056

13:00 0.041 -0.431 -0.124 -0.400 0.090

14:00 -0.063 -0.189 -0.018 -0.626 0.532

15:00 0.095 -0.388 0.209 -0.426 0.290

16:00 0.188 0.307 0.496 -0.632 0.500

17:00 -0.302 -0.339 0.010 -0.932 -0.072

18:00 -0.949 -0.392 -0.217 -0.581 -0.222

19:00 0.201 -0.092 -0.059 0.018 0.120

20:00 0.089 -0.287 -0.129 -0.139 0.148

21:00 0.566 -0.236 -0.019 -0.078 0.396

22:00 0.606 0.174 0.229 -0.053 0.589

23:00 0.621 0.319 0.326 -0.257 0.461


as MGA RT h -RT l



173

Table A129 2 Week Method of Group Averages Hedge Ratios (Price Differences) The following table shows bi-weekly hedge ratio estimates obtained using the method of group averages (MGA). A holdout sample of the first twenty bi-weekly forward and spot prices is used to produce a static MGA hedge ratio estimate for each hour of the day across all five hubs.


0:00 1.665 1.556 1.731 -0.242 1.290

1:00 0.661 0.620 0.654 1.288 0.587

2:00 1.749 1.846 1.424 1.281 1.458

3:00 1.775 1.803 1.151 1.543 1.524

4:00 1.112 1.193 0.641 1.367 0.888

5:00 2.232 2.103 1.202 1.088 1.764

6:00 2.717 1.624 1.186 1.508 2.521

7:00 1.082 0.908 1.195 1.038 1.176

8:00 1.904 1.070 1.072 0.697 1.193

9:00 1.286 -0.014 0.739 0.218 0.149

10:00 1.536 0.709 0.715 0.952 0.727

11:00 1.133 0.630 0.466 0.140 0.742

12:00 1.498 0.766 0.852 0.179 0.905

13:00 1.631 0.628 1.239 0.217 0.923

14:00 1.930 1.581 1.313 0.410 1.529

15:00 1.675 1.076 1.077 0.192 1.403

16:00 1.408 0.848 1.193 0.108 1.318

17:00 0.356 0.443 0.708 0.204 0.793

18:00 0.401 0.483 0.460 0.209 0.447

19:00 0.445 0.183 0.464 0.137 0.234

20:00 1.050 0.694 0.747 0.249 0.562

21:00 1.191 0.855 1.078 0.366 0.991

22:00 0.892 0.893 0.846 0.283 0.799

23:00 1.410 1.111 1.082 0.372 1.023


as MGA RT h -RT l



174

Table A130 3 Week Method of Group Averages Hedge Ratios (Price Differences) The following table shows tri-weekly hedge ratio estimates obtained using the method of group averages (MGA). A holdout sample of the first twenty tri-weekly forward and spot prices is used to produce a static MGA hedge ratio estimate for each hour of the day across all five hubs.


0:00 0.088 0.087 -0.054 1.375 0.282

1:00 0.899 0.633 0.401 1.073 0.482

2:00 -0.067 0.295 0.194 1.131 0.310

3:00 0.820 0.491 0.263 0.621 0.103

4:00 0.612 0.459 0.341 0.479 0.233

5:00 0.955 0.863 1.071 0.777 0.630

6:00 1.821 1.686 0.939 0.013 1.365

7:00 1.037 0.665 0.549 0.048 0.463

8:00 0.915 0.518 0.458 0.344 0.533

9:00 -0.220 -0.276 -0.250 0.076 -0.061

10:00 -0.411 -0.256 -0.345 0.246 0.059

11:00 -0.130 -0.203 -0.027 0.077 -0.253

12:00 -0.358 -0.081 -0.089 -0.572 -0.109

13:00 -0.535 -0.508 -0.706 0.147 0.859

14:00 0.201 -0.013 -0.109 0.585 0.043

15:00 0.212 0.249 0.072 0.893 0.604

16:00 -0.248 -0.368 -0.191 0.232 -0.328

17:00 0.034 -0.355 0.067 0.242 0.149

18:00 0.103 0.033 0.175 0.412 -0.210

19:00 -0.280 -0.177 -0.119 1.181 -0.262

20:00 -0.849 -0.543 -0.451 0.474 -0.424

21:00 -0.426 -0.319 -0.244 0.619 -0.076

22:00 -0.194 0.166 0.261 0.789 0.123

23:00 -0.191 0.029 -0.078 0.715 -0.082


as MGA RT h -RT l



175

Table A131 4 Week Method of Group Averages Hedge Ratios (Price Differences) The following table shows monthly hedge ratio estimates obtained using the method of group averages (MGA). A holdout sample of the first twenty monthly forward and spot prices is used to produce a static MGA hedge ratio estimate for each hour of the day across all five hubs.


0:00 1.790 1.498 1.908 0.196 1.532

1:00 0.443 0.597 0.584 1.264 0.595

2:00 0.987 1.133 1.121 0.998 1.038

3:00 0.697 0.795 0.848 0.611 0.795

4:00 0.853 0.820 0.666 0.427 0.781

5:00 1.421 1.461 1.273 0.608 1.270

6:00 0.164 0.601 0.426 1.283 0.109

7:00 0.921 0.916 1.243 1.512 1.091

8:00 0.948 0.611 0.718 0.610 0.700

9:00 1.141 0.338 0.866 0.465 0.509

10:00 1.606 0.981 1.273 0.964 1.139

11:00 1.117 0.762 0.638 0.368 0.529

12:00 0.721 0.571 0.827 0.113 0.237

13:00 0.946 0.679 0.806 0.248 0.613

14:00 1.040 1.277 1.135 0.359 1.241

15:00 1.287 0.954 1.240 0.395 1.117

16:00 1.441 1.081 1.280 0.231 1.246

17:00 0.836 1.121 1.558 0.518 1.495

18:00 0.651 1.423 1.203 0.469 1.503

19:00 0.578 0.457 0.335 0.547 0.072

20:00 0.786 0.671 0.647 0.412 0.729

21:00 1.388 0.802 1.128 0.394 0.966

22:00 1.033 0.816 0.831 0.246 0.620

23:00 0.955 0.861 0.845 0.469 0.818


as MGA RT h -RT l



176

Table A132

Standard Deviation of Dollar Returns on 1 Week Hedged Portfolios: Illinois Hub

The table below shows the standard deviation of dollar returns for one week hedged portfolios on the Illinois hub. Weekly day-ahead and real-time price levels are used in constructing these hedged positions. In the case of the method of group averages (MGA) approach, an estimation period is used to calculate a static hedge ratio, which is then applied to the remainder of the sample. MV hedge ratios are calculated using a twenty week rolling estimation period. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. The standard deviations shown are in terms of dollars per megawatt hour ($/MWh). 129 weekly dollar returns from 6/1/2006-4/11/2009 are used in this analysis.

Hour Unhedged Naïve MV MGA

0:00 15.282 14.610 21.870 17.423

1:00 18.505 18.123 25.384 18.270

2:00 14.176 14.072 22.719 15.195

3:00 11.196 10.811 17.559 12.809

4:00 19.357 19.191 32.031 19.026

5:00 15.706 15.803 25.859 18.138

6:00 27.056 24.382 35.089 27.623

7:00 28.772 26.383 32.140 25.616

8:00 37.462 32.064 39.595 32.068

9:00 21.303 22.876 25.569 20.785

10:00 30.143 29.173 33.664 28.646

11:00 29.464 28.727 40.459 27.435

12:00 34.205 33.665 51.091 31.903

13:00 34.134 31.751 51.885 30.454

14:00 35.995 33.902 41.424 34.365

15:00 39.416 33.834 41.154 36.056

16:00 50.859 41.670 50.764 41.305

17:00 42.014 38.238 46.872 36.603

18:00 38.840 35.729 48.542 34.914

19:00 32.523 31.725 38.011 31.813

20:00 34.452 34.783 41.216 32.930

21:00 33.514 32.154 42.356 31.231

22:00 22.868 23.448 23.278 21.348

23:00 17.893 17.266 21.576 16.389

177

Table A133 Standard Deviation of Dollar Returns on 1 Week Hedged Portfolios: Cinergy Hub

The table below shows the standard deviation of dollar returns for one week hedged portfolios on the Cinergy hub. Weekly day-ahead and real-time price levels are used in constructing these hedged positions. In the case of the method of group averages (MGA) approach, an estimation period is used to calculate a static hedge ratio, which is then applied to the remainder of the sample. MV hedge ratios are calculated using a twenty week rolling estimation period. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. The standard deviations shown are in terms of dollars per megawatt hour ($/MWh). 129 weekly dollar returns from 6/1/2006-4/11/2009 are used in this analysis.


0:00 15.317 15.406 22.030 17.574

1:00 14.395 13.806 22.263 14.030

2:00 10.043 9.188 16.912 12.174

3:00 13.256 11.987 16.372 12.527

4:00 14.340 12.145 21.075 12.379

5:00 17.619 15.292 23.531 15.671

6:00 30.715 26.242 31.921 35.631

7:00 30.973 28.342 32.308 32.584

8:00 35.554 31.621 36.664 32.486

9:00 19.613 24.964 21.814 19.016

10:00 27.526 28.702 33.589 26.602

11:00 29.591 28.756 41.212 27.327

12:00 33.787 33.364 50.044 31.365

13:00 34.357 30.409 53.874 29.602

14:00 34.326 30.069 39.168 30.360

15:00 41.542 33.847 41.306 33.623

16:00 50.910 42.347 55.591 42.442

17:00 42.402 36.239 46.890 35.449

18:00 40.706 38.406 49.512 37.993

19:00 32.353 31.839 41.849 32.354

20:00 31.298 30.406 40.739 30.153

21:00 32.420 31.649 45.270 30.209

22:00 21.783 22.095 22.038 20.189

23:00 17.725 18.153 22.188 16.519

178

Table A134 Standard Deviation of Dollar Returns on 1 Week Hedged Portfolios: Michigan Hub The table below shows the standard deviation of dollar returns for one week hedged portfolios on the Michigan hub. Weekly day-ahead and real-time price levels are used in constructing these hedged positions. In the case of the method of group averages (MGA) approach, an estimation period is used to calculate a static hedge ratio, which is then applied to the remainder of the sample. MV hedge ratios are calculated using a twenty week rolling estimation period. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. The standard deviations shown are in terms of dollars per megawatt hour ($/MWh). 129 weekly dollar returns from 6/1/2006-4/11/2009 are used in this analysis.


0:00 17.132 17.481 25.235 20.123

1:00 14.673 14.076 21.796 13.763

2:00 12.087 11.250 16.149 11.422

3:00 13.865 12.872 17.401 12.859

4:00 15.678 13.677 25.343 14.368

5:00 18.569 16.424 23.680 16.437

6:00 34.447 30.332 36.829 31.744

7:00 32.434 29.691 33.389 28.974

8:00 37.137 33.685 38.263 35.022

9:00 20.891 27.205 25.180 22.101

10:00 34.021 33.368 44.457 32.186

11:00 29.844 29.253 39.507 27.575

12:00 33.677 32.971 48.742 31.055

13:00 34.390 31.579 55.514 30.211

14:00 32.747 29.194 36.513 28.045

15:00 40.920 34.056 44.448 33.152

16:00 52.362 44.055 59.704 44.038

17:00 42.350 37.441 47.821 36.225

18:00 40.717 37.829 49.237 38.172

19:00 32.204 30.652 36.914 31.507

20:00 32.962 32.096 41.168 31.616

21:00 33.019 33.149 44.296 31.235

22:00 22.288 23.202 22.922 20.600

23:00 18.585 18.778 23.951 17.162

179

Table A135 Standard Deviation of Dollar Returns on 1 Week Hedged Portfolios: Minnesota Hub The table below shows the standard deviation of dollar returns for one week hedged portfolios on the Minnesota hub. Weekly day-ahead and real-time price levels are used in constructing these hedged positions. In the case of the method of group averages (MGA) approach, an estimation period is used to calculate a static hedge ratio, which is then applied to the remainder of the sample. MV hedge ratios are calculated using a twenty week rolling estimation period. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. The standard deviations shown are in terms of dollars per megawatt hour ($/MWh). 129 weekly dollar returns from 6/1/2006-4/11/2009 are used in this analysis.


0:00 36.199 34.592 39.380 35.831

1:00 26.581 23.065 27.781 29.167

2:00 26.358 23.093 28.577 28.083

3:00 26.584 22.959 26.450 23.181

4:00 26.246 22.680 26.239 22.633

5:00 23.314 19.525 25.476 20.028

6:00 23.902 23.010 25.156 32.465

7:00 27.929 25.294 28.046 35.652

8:00 44.645 35.168 45.607 35.789

9:00 43.380 36.978 48.268 40.241

10:00 34.952 33.371 39.519 32.646

11:00 35.146 34.130 40.563 33.116

12:00 56.134 54.054 65.533 53.579

13:00 40.061 34.715 42.496 34.766

14:00 52.989 44.785 50.088 45.847

15:00 43.024 32.012 40.679 32.360

16:00 53.223 40.330 49.560 42.064

17:00 45.440 37.531 46.677 37.938

18:00 38.221 35.291 43.618 34.761

19:00 49.950 42.836 54.843 46.633

20:00 52.735 49.083 60.911 51.571

21:00 40.814 36.361 45.214 37.143

22:00 32.753 27.363 34.226 32.711

23:00 33.566 28.386 37.816 29.961

180

Table A136 Standard Deviation of Dollar Returns on 1 Week Hedged Portfolios: First Energy Hub The table below shows the standard deviation of dollar returns for one week hedged portfolios on the First Energy hub. Weekly day-ahead and real-time price levels are used in constructing these hedged positions. In the case of the method of group averages (MGA) approach, an estimation period is used to calculate a static hedge ratio, which is then applied to the remainder of the sample. MV hedge ratios are calculated using a twenty week rolling estimation period. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. The standard deviations shown are in terms of dollars per megawatt hour ($/MWh). 129 weekly dollar returns from 6/1/2006-4/11/2009 are used in this analysis.


0:00 17.505 17.200 23.459 18.750

1:00 16.847 16.314 22.681 16.287

2:00 11.036 10.957 14.818 10.896

3:00 13.180 12.620 15.518 12.417

4:00 15.857 14.103 19.360 14.241

5:00 17.095 14.998 23.465 15.506

6:00 31.624 27.603 35.868 27.784

7:00 31.044 27.895 34.463 27.602

8:00 36.038 31.209 38.461 31.195

9:00 20.152 27.417 23.880 19.628

10:00 29.227 31.492 37.447 28.139

11:00 29.200 29.480 40.869 27.496

12:00 33.341 34.418 48.518 31.569

13:00 37.922 33.916 50.036 33.493

14:00 32.001 29.771 36.156 29.191

15:00 37.966 33.524 43.478 36.204

16:00 50.824 43.441 55.680 42.612

17:00 41.598 36.616 43.458 35.181

18:00 39.822 39.103 52.313 37.826

19:00 31.685 34.938 39.960 30.723

20:00 32.856 32.788 43.479 31.433

21:00 33.126 33.673 45.606 32.000

22:00 22.535 22.454 21.241 20.433

23:00 20.039 20.434 25.091 18.860

181

Table A137 Standard Deviation of Dollar Returns on 2 Week Hedged Portfolios: Illinois Hub The table below shows the standard deviation of dollar returns for bi-weekly hedged portfolios on the Illinois hub. Bi-weekly day-ahead and real-time price levels are used in constructing these hedged positions. In the case of the method of group averages (MGA) approach, an estimation period is used to calculate a static hedge ratio, which is then applied to the remainder of the sample. MV hedge ratios are calculated using twenty bi-weekly day-ahead and real-time prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. The standard deviations shown are in terms of dollars per megawatt hour ($/MWh). 55 bi-weekly dollar returns from 6/1/2006-4/11/2009 are used in this analysis.


0:00 15.904 13.985 20.198 15.418

1:00 14.455 12.319 16.666 12.792

2:00 12.618 10.900 15.813 11.911

3:00 10.481 8.311 11.243 10.271

4:00 19.201 16.137 27.300 16.044

5:00 12.697 9.951 13.053 10.963

6:00 21.163 18.283 19.987 19.325

7:00 28.375 25.468 27.054 25.169

8:00 31.833 22.094 27.073 23.407

9:00 17.618 16.612 17.157 17.201

10:00 24.968 22.359 26.307 21.727

11:00 31.567 27.101 35.961 27.542

12:00 35.149 33.926 38.347 34.022

13:00 35.281 33.077 43.182 32.287

14:00 37.714 33.204 41.751 34.867

15:00 35.269 29.647 36.343 29.189

16:00 48.691 38.160 51.988 40.707

17:00 46.490 41.904 60.109 43.667

18:00 44.064 38.404 51.142 41.144

19:00 31.742 25.783 36.402 26.303

20:00 30.892 25.830 33.213 25.803

21:00 32.656 28.276 47.294 28.878

22:00 23.662 21.602 28.684 21.149

23:00 16.350 16.052 21.871 15.449

182

Table A138 Standard Deviation of Dollar Returns on 2 Week Hedged Portfolios: Cinergy Hub The table below shows the standard deviation of dollar returns for bi-weekly hedged portfolios on the Cinergy hub. Bi-weekly day-ahead and real-time price levels are used in constructing these hedged positions. In the case of the method of group averages (MGA) approach, an estimation period is used to calculate a static hedge ratio, which is then applied to the remainder of the sample. MV hedge ratios are calculated using twenty bi-weekly day-ahead and real-time prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. The standard deviations shown are in terms of dollars per megawatt hour ($/MWh). 55 bi-weekly dollar returns from 6/1/2006-4/11/2009 are used in this analysis.


0:00 15.907 14.778 21.151 15.583

1:00 12.086 10.751 16.488 10.787

2:00 8.817 7.584 14.914 9.057

3:00 6.939 6.105 10.136 8.296

4:00 17.743 15.496 29.237 15.474

5:00 9.868 7.451 12.820 8.868

6:00 22.073 19.429 20.070 20.060

7:00 27.588 23.858 24.710 23.297

8:00 30.977 21.200 25.673 21.175

9:00 15.427 16.392 15.322 13.268

10:00 23.464 22.421 24.640 21.387

11:00 30.373 26.375 35.116 27.065

12:00 34.344 33.970 39.879 32.887

13:00 35.844 32.586 40.031 32.832

14:00 36.448 30.439 41.079 32.181

15:00 35.839 29.410 37.434 30.332

16:00 48.408 37.523 51.905 41.041

17:00 49.772 44.297 62.082 47.222

18:00 50.588 44.246 64.512 47.496

19:00 38.269 30.169 43.279 33.076

20:00 30.810 25.091 32.728 25.545

21:00 32.202 28.419 50.131 29.557

22:00 22.673 21.241 27.311 20.494

23:00 16.283 16.677 22.602 15.672

183

Table A139 Standard Deviation of Dollar Returns on 2 Week Hedged Portfolios: Michigan Hub

The table below shows the standard deviation of dollar returns for bi-weekly hedged portfolios on the Michigan hub. Bi-weekly day-ahead and real-time price levels are used in constructing these hedged positions. In the case of the method of group averages (MGA) approach, an estimation period is used to calculate a static hedge ratio, which is then applied to the remainder of the sample. MV hedge ratios are calculated using twenty bi-weekly day-ahead and real-time prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. The standard deviations shown are in terms of dollars per megawatt hour ($/MWh). 55 bi-weekly dollar returns from 6/1/2006-4/11/2009 are used in this analysis.


0:00 18.504 17.683 24.835 19.288

1:00 13.609 12.415 19.041 12.411

2:00 8.917 8.066 15.210 8.486

3:00 10.425 10.398 13.593 10.867

4:00 19.293 17.141 32.820 17.638

5:00 14.278 12.703 17.479 12.639

6:00 32.284 30.033 29.738 29.856

7:00 33.482 29.254 29.668 29.230

8:00 31.547 21.010 26.698 20.933

9:00 17.778 20.314 16.460 17.585

10:00 24.281 24.122 24.616 22.443

11:00 29.366 27.114 29.709 26.570

12:00 33.016 33.395 37.969 31.744

13:00 31.324 29.776 36.091 28.400

14:00 34.498 29.848 39.876 30.815

15:00 36.248 30.691 38.315 29.897

16:00 49.949 40.531 53.724 42.474

17:00 50.664 46.950 62.715 47.754

18:00 50.374 45.222 62.397 47.067

19:00 35.548 29.932 35.890 30.277

20:00 30.750 26.491 35.894 26.138

21:00 32.886 30.283 49.701 30.385

22:00 23.196 23.436 30.068 21.801

23:00 16.926 17.297 22.839 16.107

184

Table A140 Standard Deviation of Dollar Returns on 2 Week Hedged Portfolios: Minnesota Hub The table below shows the standard deviation of dollar returns for bi-weekly hedged portfolios on the Minnesota hub. Bi-weekly day-ahead and real-time price levels are used in constructing these hedged positions. In the case of the method of group averages (MGA) approach, an estimation period is used to calculate a static hedge ratio, which is then applied to the remainder of the sample. MV hedge ratios are calculated using twenty bi-weekly day-ahead and real-time prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. The standard deviations shown are in terms of dollars per megawatt hour ($/MWh). 55 bi-weekly dollar returns from 6/1/2006-4/11/2009 are used in this analysis.


0:00 19.479 16.275 23.208 18.225

1:00 15.011 11.959 13.543 12.390

2:00 22.558 19.100 23.338 19.082

3:00 19.950 15.461 19.347 15.395

4:00 23.310 20.260 24.108 21.391

5:00 17.397 14.802 17.756 18.312

6:00 19.696 17.846 19.792 17.107

7:00 27.021 22.525 25.266 21.675

8:00 37.752 29.112 33.846 29.150

9:00 26.833 25.167 28.227 22.932

10:00 29.531 26.239 31.092 26.274

11:00 33.760 29.818 38.391 30.794

12:00 47.457 47.165 60.409 47.140

13:00 41.119 37.743 43.919 39.045

14:00 66.020 58.727 69.700 61.654

15:00 42.039 29.460 43.301 34.425

16:00 49.985 37.667 53.123 45.177

17:00 51.301 40.011 61.842 47.234

18:00 42.167 34.327 50.582 39.695

19:00 47.112 36.216 53.298 43.124

20:00 42.294 36.449 44.432 37.507

21:00 34.300 28.649 40.859 31.213

22:00 31.406 25.997 32.150 28.020

23:00 31.886 27.296 34.220 29.577

185

Table A141 Standard Deviation of Dollar Returns on 2 Week Hedged Portfolios: First Energy Hub The table below shows the standard deviation of dollar returns for bi-weekly hedged portfolios on the First Energy hub. Bi-weekly day-ahead and real-time price levels are used in constructing these hedged positions. In the case of the method of group averages (MGA) approach, an estimation period is used to calculate a static hedge ratio, which is then applied to the remainder of the sample. MV hedge ratios are calculated using twenty bi-weekly day-ahead and real-time prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. The standard deviations shown are in terms of dollars per megawatt hour ($/MWh). 55 bi-weekly dollar returns from 6/1/2006-4/11/2009 are used in this analysis.


0:00 17.272 15.432 19.584 16.190

1:00 18.836 17.951 22.484 17.906

2:00 10.156 10.351 14.874 11.332

3:00 9.000 9.835 12.448 11.966

4:00 19.636 17.344 28.298 17.491

5:00 11.544 9.061 15.201 9.727

6:00 26.237 23.685 24.958 24.000

7:00 29.353 25.392 26.136 25.559

8:00 31.501 21.060 26.072 21.211

9:00 17.045 18.361 15.718 14.601

10:00 25.231 23.991 24.913 23.088

11:00 28.796 26.537 31.080 25.832

12:00 33.237 35.358 39.226 32.408

13:00 30.946 30.507 36.576 28.545

14:00 33.955 29.042 36.687 29.197

15:00 35.676 32.780 42.664 30.818

16:00 48.201 39.372 49.996 40.748

17:00 49.649 43.607 57.556 45.791

18:00 48.986 43.234 57.223 45.490

19:00 36.207 32.864 39.037 33.411

20:00 31.372 24.767 33.632 24.824

21:00 32.718 29.014 47.244 29.248

22:00 23.326 20.193 25.240 19.893

23:00 18.641 18.449 23.102 18.076

186

Table A142 Standard Deviation of Dollar Returns on 3 Week Hedged Portfolios: Illinois Hub The table below shows the standard deviation of dollar returns for tri-weekly hedged portfolios on the Illinois hub. Tri-weekly day-ahead and real-time price levels are used in constructing these hedged positions. In the case of the method of group averages (MGA) approach, an estimation period is used to calculate a static hedge ratio, which is then applied to the remainder of the sample. MV hedge ratios are calculated using twenty tri-weekly day-ahead and real-time prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. The standard deviations shown are in terms of dollars per megawatt hour ($/MWh). 30 tri-weekly dollar returns from 6/1/2006-4/11/2009 are used in this analysis.


0:00 12.051 9.362 13.346 10.899

1:00 26.947 26.897 28.150 26.818

2:00 18.706 18.240 18.677 18.283

3:00 6.246 4.794 5.114 4.610

4:00 22.004 21.224 22.070 21.365

5:00 17.448 16.740 16.113 16.722

6:00 21.417 17.261 25.068 17.473

7:00 31.819 26.663 29.532 30.112

8:00 39.402 32.511 32.506 32.595

9:00 17.541 14.773 15.813 15.896

10:00 22.896 23.675 23.913 23.679

11:00 27.395 26.886 27.733 25.937

12:00 29.145 33.330 29.800 27.978

13:00 35.777 30.426 39.346 30.896

14:00 32.788 28.408 33.595 28.506

15:00 32.958 23.413 25.386 23.913

16:00 44.137 33.311 37.590 38.544

17:00 42.987 33.042 40.364 37.360

18:00 39.593 37.182 40.133 39.504

19:00 29.294 29.165 32.606 31.525

20:00 35.578 33.602 49.763 38.975

21:00 36.238 33.482 46.590 37.959

22:00 21.654 16.460 23.640 21.537

23:00 12.231 11.378 12.360 11.436

187

Table A143 Standard Deviation of Dollar Returns on 3 Week Hedged Portfolios: Cinergy Hub The table below shows the standard deviation of dollar returns for tri-weekly hedged portfolios on the Cinergy hub. Tri-weekly day-ahead and real-time price levels are used in constructing these hedged positions. In the case of the method of group averages (MGA) approach, an estimation period is used to calculate a static hedge ratio, which is then applied to the remainder of the sample. MV hedge ratios are calculated using twenty tri-weekly day-ahead and real-time prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. The standard deviations shown are in terms of dollars per megawatt hour ($/MWh). 30 tri-weekly dollar returns from 6/1/2006-4/11/2009 are used in this analysis.


0:00 11.456 13.544 13.962 11.106

1:00 7.158 10.642 14.759 8.708

2:00 6.891 8.299 9.333 6.780

3:00 6.302 8.007 11.512 6.883

4:00 6.963 5.263 5.651 5.321

5:00 11.435 9.994 9.299 9.898

6:00 24.530 21.090 32.998 22.501

7:00 33.232 31.874 30.579 30.889

8:00 36.551 32.806 36.500 31.955

9:00 20.962 28.657 23.816 20.331

10:00 23.656 31.815 25.715 23.072

11:00 28.031 28.530 28.444 25.399

12:00 33.357 38.719 34.117 32.133

13:00 35.348 29.095 30.339 27.253

14:00 33.034 30.226 28.990 27.013

15:00 32.490 25.692 24.753 21.717

16:00 44.458 40.113 37.378 37.619

17:00 40.857 36.629 37.609 33.883

18:00 40.148 44.115 39.668 40.695

19:00 29.998 36.546 32.168 30.293

20:00 33.360 31.832 40.140 33.710

21:00 35.170 40.204 38.913 35.680

22:00 21.195 18.847 18.830 17.813

23:00 12.041 16.174 12.009 11.683

188

Table A144 Standard Deviation of Dollar Returns on 3 Week Hedged Portfolios: Michigan Hub The table below shows the standard deviation of dollar returns for tri-weekly hedged portfolios on the Michigan hub. Tri-weekly day-ahead and real-time price levels are used in constructing these hedged positions. In the case of the method of group averages (MGA) approach, an estimation period is used to calculate a static hedge ratio, which is then applied to the remainder of the sample. MV hedge ratios are calculated using twenty tri-weekly day-ahead and real-time prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. The standard deviations shown are in terms of dollars per megawatt hour ($/MWh). 30 tri-weekly dollar returns from 6/1/2006-4/11/2009 are used in this analysis.


0:00 12.145 14.878 14.672 12.006

1:00 8.314 10.012 11.332 8.261

2:00 7.199 7.696 8.127 6.515

3:00 7.301 9.503 12.234 7.407

4:00 9.110 7.951 8.525 7.949

5:00 17.704 16.527 17.547 16.681

6:00 26.353 24.096 36.242 24.244

7:00 36.783 34.994 33.328 34.286

8:00 38.148 36.499 39.631 34.562

9:00 18.892 30.075 21.836 19.419

10:00 23.817 32.650 24.921 23.364

11:00 28.297 27.491 27.813 26.109

12:00 31.793 36.729 32.513 30.832

13:00 36.130 29.844 36.230 29.473

14:00 33.639 29.073 28.588 26.710

15:00 32.852 26.195 25.946 23.018

16:00 43.986 35.243 37.000 38.250

17:00 41.714 35.002 40.593 35.692

18:00 40.102 39.746 40.368 39.508

19:00 30.339 31.850 31.070 30.142

20:00 34.464 33.653 40.215 34.680

21:00 35.790 42.336 38.129 35.985

22:00 21.637 19.111 19.854 18.133

23:00 12.318 17.295 12.069 11.937

189

Table A145 Standard Deviation of Dollar Returns on 3 Week Hedged Portfolios: Minnesota Hub The table below shows the standard deviation of dollar returns for tri-weekly hedged portfolios on the Minnesota hub. Tri-weekly day-ahead and real-time price levels are used in constructing these hedged positions. In the case of the method of group averages (MGA) approach, an estimation period is used to calculate a static hedge ratio, which is then applied to the remainder of the sample. MV hedge ratios are calculated using twenty tri-weekly day-ahead and real-time prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. The standard deviations shown are in terms of dollars per megawatt hour ($/MWh). 30 tri-weekly dollar returns from 6/1/2006-4/11/2009 are used in this analysis.


0:00 17.021 13.878 14.938 17.016

1:00 29.210 27.369 30.031 27.453

2:00 31.056 27.623 27.970 27.812

3:00 20.988 15.509 15.937 15.962

4:00 27.889 24.289 25.929 25.113

5:00 23.038 20.004 20.328 20.676

6:00 24.188 22.148 27.235 24.595

7:00 34.710 30.565 30.621 30.911

8:00 59.075 46.389 49.288 50.479

9:00 35.202 28.188 29.989 29.995

10:00 36.874 35.353 36.605 34.640

11:00 37.865 33.528 38.853 37.139

12:00 32.933 35.528 34.804 36.823

13:00 33.475 28.721 32.444 29.413

14:00 34.789 23.035 29.791 24.649

15:00 33.619 24.019 31.427 25.144

16:00 44.701 33.252 38.947 37.249

17:00 48.441 39.113 44.004 42.360

18:00 46.945 40.611 45.847 43.685

19:00 51.161 41.775 48.665 41.753

20:00 45.046 40.326 41.754 45.411

21:00 39.908 35.193 37.880 35.747

22:00 35.197 23.802 24.965 27.737

23:00 26.671 20.460 22.041 20.520

190

Table A146 Standard Deviation of Dollar Returns on 3 Week Hedged Portfolios: First Energy Hub The table below shows the standard deviation of dollar returns for tri-weekly hedged portfolios on the First Energy hub. Tri-weekly day-ahead and real-time price levels are used in constructing these hedged positions. In the case of the method of group averages (MGA) approach, an estimation period is used to calculate a static hedge ratio, which is then applied to the remainder of the sample. MV hedge ratios are calculated using twenty tri-weekly day-ahead and real-time prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. The standard deviations shown are in terms of dollars per megawatt hour ($/MWh). 30 tri-weekly dollar returns from 6/1/2006-4/11/2009 are used in this analysis.


0:00 13.058 17.900 17.407 13.485

1:00 11.609 15.277 15.777 13.222

2:00 7.342 8.121 9.047 6.551

3:00 6.908 9.382 9.288 6.765

4:00 7.245 7.147 7.645 5.704

5:00 11.642 11.924 11.066 10.787

6:00 24.787 23.680 33.636 28.089

7:00 33.228 34.569 32.208 31.529

8:00 36.612 33.971 37.090 32.230

9:00 20.347 36.410 27.902 20.413

10:00 24.192 34.263 27.638 24.406

11:00 29.094 33.406 32.335 28.368

12:00 31.462 41.027 32.761 31.506

13:00 33.436 36.180 70.097 36.751

14:00 32.101 33.802 30.353 29.317

15:00 31.066 34.185 35.623 28.665

16:00 43.569 41.160 41.799 39.667

17:00 39.199 39.050 37.989 35.201

18:00 40.855 47.261 47.066 40.938

19:00 35.319 44.459 37.803 35.365

20:00 36.655 39.766 39.040 36.471

21:00 36.676 45.701 42.532 36.726

22:00 23.060 21.441 21.468 19.355

23:00 12.226 19.191 14.792 12.912

191

Table A147 Standard Deviation of Dollar Returns on 4 Week Hedged Portfolios: Illinois Hub The table below shows the standard deviation of dollar returns for monthly hedged portfolios on the Illinois hub. Monthly day-ahead and real-time price levels are used in constructing these hedged positions. In the case of the method of group averages (MGA) approach, an estimation period is used to calculate a static hedge ratio, which is then applied to the remainder of the sample. MV hedge ratios are calculated using twenty monthly day-ahead and real-time prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. The standard deviations shown are in terms of dollars per megawatt hour ($/MWh). 18 monthly dollar returns from 6/1/2006-4/11/2009 are used in this analysis.


0:00 20.504 16.774 27.841 20.906

1:00 11.526 9.724 8.815 9.544

2:00 11.988 9.737 9.229 10.030

3:00 9.915 7.993 6.911 7.987

4:00 28.609 25.184 35.669 25.413

5:00 11.680 7.480 9.341 7.931

6:00 13.981 10.821 13.431 10.131

7:00 23.889 23.624 26.523 25.759

8:00 33.176 20.597 20.852 21.751

9:00 14.614 10.982 13.153 11.244

10:00 20.720 16.340 18.216 21.020

11:00 28.806 21.540 29.729 21.530

12:00 39.350 39.059 45.983 37.680

13:00 29.977 24.391 43.808 28.260

14:00 37.086 24.816 27.848 25.962

15:00 33.929 20.536 20.950 20.911

16:00 49.135 25.534 20.046 26.584

17:00 44.393 39.769 40.816 39.662

18:00 51.213 39.966 49.201 41.973

19:00 37.025 29.739 33.107 29.970

20:00 34.762 25.112 27.560 26.737

21:00 38.900 33.517 48.063 33.451

22:00 24.197 19.190 23.266 18.908

23:00 15.549 16.231 18.846 14.852

192

Table A148 Standard Deviation of Dollar Returns on 4 Week Hedged Portfolios: Cinergy Hub The table below shows the standard deviation of dollar returns for monthly hedged portfolios on the Cinergy hub. Monthly day-ahead and real-time price levels are used in constructing these hedged positions. In the case of the method of group averages (MGA) approach, an estimation period is used to calculate a static hedge ratio, which is then applied to the remainder of the sample. MV hedge ratios are calculated using twenty monthly day-ahead and real-time prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. The standard deviations shown are in terms of dollars per megawatt hour ($/MWh). 18 monthly dollar returns from 6/1/2006-4/11/2009 are used in this analysis.


0:00 19.704 17.757 25.552 21.004

1:00 11.133 9.940 9.014 9.488

2:00 11.208 9.611 9.086 10.174

3:00 7.954 7.850 6.184 7.930

4:00 28.301 25.877 37.217 26.169

5:00 9.700 6.846 8.171 7.179

6:00 21.309 20.602 25.998 24.116

7:00 24.709 24.382 25.922 26.210

8:00 34.260 21.242 27.703 25.915

9:00 14.300 10.789 13.504 9.592

10:00 23.065 19.477 26.535 18.447

11:00 34.187 26.015 32.799 26.107

12:00 44.114 44.230 47.374 43.635

13:00 36.520 29.935 45.482 30.264

14:00 36.145 22.911 25.361 22.167

15:00 35.040 22.071 24.154 21.999

16:00 49.153 25.618 23.782 24.935

17:00 44.065 39.411 50.547 39.218

18:00 66.564 54.496 82.402 54.601

19:00 49.473 35.788 47.380 38.212

20:00 35.781 26.129 29.988 26.065

21:00 38.236 33.312 42.855 33.238

22:00 20.899 18.328 19.217 17.044

23:00 15.075 16.918 16.258 14.953

193

Table A149 Standard Deviation of Dollar Returns on 4 Week Hedged Portfolios: Michigan Hub The table below shows the standard deviation of dollar returns for monthly hedged portfolios on the Michigan hub. Monthly day-ahead and real-time price levels are used in constructing these hedged positions. In the case of the method of group averages (MGA) approach, an estimation period is used to calculate a static hedge ratio, which is then applied to the remainder of the sample. MV hedge ratios are calculated using twenty monthly day-ahead and real-time prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. The standard deviations shown are in terms of dollars per megawatt hour ($/MWh). 18 monthly dollar returns from 6/1/2006-4/11/2009 are used in this analysis.


0:00 21.153 19.185 30.701 24.822

1:00 12.686 11.602 10.316 11.090

2:00 11.384 10.508 11.697 10.910

3:00 9.701 11.328 10.655 11.780

4:00 29.864 27.563 43.044 27.815

5:00 11.127 9.503 11.343 9.983

6:00 22.271 22.393 27.365 25.097

7:00 30.826 27.966 31.704 30.556

8:00 36.218 22.082 28.088 23.877

9:00 14.047 12.651 13.267 9.964

10:00 20.377 18.689 17.238 18.081

11:00 28.913 24.947 30.458 24.514

12:00 42.211 43.661 52.548 42.042

13:00 31.010 26.331 47.937 26.452

14:00 37.287 25.503 32.820 25.354

15:00 34.566 21.000 25.205 21.845

16:00 52.418 28.304 25.630 27.090

17:00 45.236 41.408 50.102 41.397

18:00 65.548 53.597 74.290 53.921

19:00 41.120 31.262 37.242 32.351

20:00 35.347 25.667 27.897 25.729

21:00 39.384 34.542 47.109 34.447

22:00 21.450 18.396 19.676 17.577

23:00 15.425 17.257 16.470 15.310

194

Table A150 Standard Deviation of Dollar Returns on 4 Week Hedged Portfolios: Minnesota Hub The table below shows the standard deviation of dollar returns for monthly hedged portfolios on the Minnesota hub. Monthly day-ahead and real-time price levels are used in constructing these hedged positions. In the case of the method of group averages (MGA) approach, an estimation period is used to calculate a static hedge ratio, which is then applied to the remainder of the sample. MV hedge ratios are calculated using twenty monthly day-ahead and real-time prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. The standard deviations shown are in terms of dollars per megawatt hour ($/MWh). 18 monthly dollar returns from 6/1/2006-4/11/2009 are used in this analysis.


0:00 19.361 17.504 20.112 16.197

1:00 12.826 9.999 15.628 11.785

2:00 16.662 13.686 14.604 15.758

3:00 17.187 15.051 14.517 14.655

4:00 33.955 31.693 34.625 31.708

5:00 17.900 16.524 15.860 16.240

6:00 20.342 22.800 24.923 21.997

7:00 30.110 32.553 36.029 33.731

8:00 47.351 38.050 37.356 38.472

9:00 34.609 31.735 31.020 30.000

10:00 32.861 27.175 28.916 26.248

11:00 36.685 31.226 31.276 31.469

12:00 43.636 42.260 42.577 44.299

13:00 29.564 27.765 26.251 27.683

14:00 39.106 25.140 22.732 29.113

15:00 32.808 17.888 18.434 27.083

16:00 53.655 35.732 31.676 47.570

17:00 48.916 40.493 43.417 45.531

18:00 46.924 39.107 38.699 46.978

19:00 53.155 44.041 48.514 46.198

20:00 36.332 27.974 30.695 34.570

21:00 32.853 33.792 31.652 30.939

22:00 22.203 14.922 22.226 20.826

23:00 19.751 18.689 19.193 16.316

195

Table A151 Standard Deviation of Dollar Returns on 4 Week Hedged Portfolios: First Energy Hub The table below shows the standard deviation of dollar returns for monthly hedged portfolios on the First Energy hub. Monthly day-ahead and real-time price levels are used in constructing these hedged positions. In the case of the method of group averages (MGA) approach, an estimation period is used to calculate a static hedge ratio, which is then applied to the remainder of the sample. MV hedge ratios are calculated using twenty monthly day-ahead and real-time prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. The standard deviations shown are in terms of dollars per megawatt hour ($/MWh). 18 monthly dollar returns from 6/1/2006-4/11/2009 are used in this analysis.


0:00 20.281 17.873 24.654 21.068

1:00 16.204 17.568 16.155 16.531

2:00 13.759 14.282 13.070 15.293

3:00 9.993 11.822 9.759 12.388

4:00 29.041 27.350 37.073 27.595

5:00 12.319 10.398 11.171 12.429

6:00 22.573 21.331 27.740 25.348

7:00 24.449 25.974 29.026 30.077

8:00 34.044 21.796 26.295 24.344

9:00 14.758 12.243 10.077 9.999

10:00 21.816 19.194 18.918 17.781

11:00 29.093 25.669 26.315 24.764

12:00 41.581 43.391 43.716 41.298

13:00 30.187 26.612 36.185 25.656

14:00 37.450 27.631 32.898 27.660

15:00 34.538 22.012 24.456 22.043

16:00 49.464 30.603 30.300 29.902

17:00 44.960 39.973 47.219 40.052

18:00 63.424 52.156 81.235 50.501

19:00 43.724 40.532 42.209 40.077

20:00 34.344 25.453 26.952 25.948

21:00 38.040 33.679 45.254 33.413

22:00 21.942 18.744 19.971 18.902

23:00 21.932 21.734 20.993 21.663

196

Table A152 Standard Deviation of Dollar Returns on 1 Week Hedged Portfolios: Illinois Hub The table below shows the standard deviation of dollar returns for one week hedged portfolios on the Illinois hub. First differences of weekly day-ahead and real-time prices are used in constructing these hedged positions. In the case of the method of group averages (MGA) approach, an estimation period is used to calculate a static hedge ratio, which is then applied to the remainder of the sample. MV, ARDL(1,1), and GARCH(1,1) hedge ratios are calculated using a twenty week rolling estimation period. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. The standard deviations shown are in terms of dollars per megawatt hour ($/MWh). 128 weekly dollar returns from 6/1/2006-4/11/2009 are used in this analysis.

Hour Unhedged Naïve MV ARDL(1,1) MGA GARCH(1,1)

0:00 20.183 21.495 21.483 21.446 22.552 20.942

1:00 25.783 26.105 28.539 26.888 25.636 26.373

2:00 19.198 20.840 22.548 22.611 23.597 21.295

3:00 15.445 16.411 17.298 16.935 15.458 17.028

4:00 27.383 28.564 34.226 32.079 27.452 30.118

5:00 20.508 22.202 24.542 24.255 29.665 24.433

6:00 32.860 33.012 37.700 35.564 61.491 34.510

7:00 33.911 36.671 35.532 35.803 43.399 37.025

8:00 46.429 46.629 48.405 48.287 48.057 48.900

9:00 26.387 32.592 28.454 28.733 34.323 28.220

10:00 39.827 42.234 41.774 40.950 39.460 42.169

11:00 36.713 43.844 39.270 38.798 37.237 39.815

12:00 44.416 47.824 46.525 45.949 44.194 45.682

13:00 39.847 42.886 42.699 42.588 39.690 41.266

14:00 44.691 50.677 49.111 48.122 44.788 50.525

15:00 44.993 52.434 46.720 47.033 45.038 47.616

16:00 56.896 64.454 59.835 58.911 57.317 58.312

17:00 46.571 54.100 52.599 52.199 47.257 52.363

18:00 48.768 52.716 54.379 50.392 55.582 52.190

19:00 36.648 42.897 37.039 38.539 36.422 37.611

20:00 43.545 51.422 45.952 49.625 43.757 45.522

21:00 40.659 45.980 42.903 43.756 42.527 43.293

22:00 29.139 34.160 31.174 30.729 30.743 32.435

23:00 22.229 25.094 23.523 23.058 22.789 22.807

197

Table A153 Standard Deviation of Dollar Returns on 1 Week Hedged Portfolios: Cinergy Hub The table below shows the standard deviation of dollar returns for one week hedged portfolios on the Cinergy hub. First differences of weekly day-ahead and real-time prices are used in constructing these hedged positions. In the case of the method of group averages (MGA) approach, an estimation period is used to calculate a static hedge ratio, which is then applied to the remainder of the sample. MV, ARDL(1,1), and GARCH(1,1) hedge ratios are calculated using a twenty week rolling estimation period. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. The standard deviations shown are in terms of dollars per megawatt hour ($/MWh). 128 weekly dollar returns from 6/1/2006-4/11/2009 are used in this analysis.


0:00 20.809 23.281 22.400 23.543 23.407 21.950

1:00 20.403 19.782 20.217 19.786 19.531 20.347

2:00 13.139 13.063 13.649 13.643 15.179 14.168

3:00 17.568 17.392 17.276 17.361 17.909 17.537

4:00 20.337 18.187 22.741 21.244 18.585 19.112

5:00 24.721 22.039 23.859 23.346 23.078 23.494

6:00 38.479 36.123 40.131 37.815 51.975 39.160

7:00 36.140 39.798 36.636 36.622 42.570 37.525

8:00 44.774 46.273 47.426 45.789 44.171 47.094

9:00 27.346 36.960 28.447 29.438 27.387 28.431

10:00 38.767 42.838 42.388 39.979 39.371 41.401

11:00 37.691 43.431 40.293 40.731 37.651 40.501

12:00 45.397 48.154 46.858 46.887 48.089 45.615

13:00 41.634 42.797 45.041 44.486 45.389 41.967

14:00 42.015 45.995 46.534 44.688 42.881 47.104

15:00 48.506 51.595 49.791 50.050 51.212 50.291

16:00 54.652 61.745 57.017 56.866 54.962 56.483

17:00 48.435 52.818 54.882 53.038 51.203 57.072

18:00 55.472 58.859 61.961 55.796 58.479 61.239

19:00 41.144 45.275 43.735 43.576 41.799 41.707

20:00 38.466 44.443 41.194 42.148 39.732 40.581

21:00 39.501 45.378 40.782 40.524 40.123 41.885

22:00 27.220 32.739 28.478 28.258 26.944 29.157

23:00 22.529 27.261 24.396 24.572 22.700 23.961

198

Table A154 Standard Deviation of Dollar Returns on 1 Week Hedged Portfolios: Michigan Hub The table below shows the standard deviation of dollar returns for one week hedged portfolios on the Michigan hub. First differences of weekly day-ahead and real-time prices are used in constructing these hedged positions. In the case of the method of group averages (MGA) approach, an estimation period is used to calculate a static hedge ratio, which is then applied to the remainder of the sample. MV, ARDL(1,1), and GARCH(1,1) hedge ratios are calculated using a twenty week rolling estimation period. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. The standard deviations shown are in terms of dollars per megawatt hour ($/MWh). 128 weekly dollar returns from 6/1/2006-4/11/2009 are used in this analysis.


0:00 23.458 25.688 24.877 26.093 26.601 23.967

1:00 19.567 18.937 19.272 19.156 18.650 19.215

2:00 16.417 16.460 16.879 16.746 16.512 17.989

3:00 18.453 18.581 18.321 18.266 18.113 19.292

4:00 22.415 20.243 25.571 23.901 21.162 23.772

5:00 25.940 23.152 25.388 24.722 23.063 24.842

6:00 43.626 41.447 44.017 43.105 43.338 43.438

7:00 38.548 42.642 39.339 39.209 38.626 41.404

8:00 46.944 49.469 50.847 48.492 46.462 48.798

9:00 28.751 40.001 29.124 30.358 35.200 29.521

10:00 44.828 46.840 49.370 46.523 44.746 46.060

11:00 37.728 44.522 40.306 40.257 38.069 40.621

12:00 44.579 47.905 45.305 45.674 44.366 44.294

13:00 41.500 44.636 46.075 45.267 42.010 45.835

14:00 39.347 44.608 43.818 42.380 39.382 42.656

15:00 46.900 51.389 50.698 49.430 46.649 53.477

16:00 55.820 62.204 59.021 58.149 57.267 59.598

17:00 48.043 53.254 52.688 51.980 48.020 54.784

18:00 55.249 57.161 58.795 56.317 56.304 56.925

19:00 40.440 43.374 39.970 40.507 40.812 40.631

20:00 40.501 46.185 42.726 43.965 40.754 43.245

21:00 39.924 47.190 41.609 41.423 39.935 43.245

22:00 27.680 34.254 28.447 28.859 27.534 28.925

23:00 23.282 27.813 25.031 25.173 23.282 24.045

199

Table A155 Standard Deviation of Dollar Returns on 1 Week Hedged Portfolios: Minnesota Hub The table below shows the standard deviation of dollar returns for one week hedged portfolios on the Minnesota hub. First differences of weekly day-ahead and real-time prices are used in constructing these hedged positions. In the case of the method of group averages (MGA) approach, an estimation period is used to calculate a static hedge ratio, which is then applied to the remainder of the sample. MV, ARDL(1,1), and GARCH(1,1) hedge ratios are calculated using a twenty week rolling estimation period. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. The standard deviations shown are in terms of dollars per megawatt hour ($/MWh). 128 weekly dollar returns from 6/1/2006-4/11/2009 are used in this analysis.


0:00 41.861 45.248 46.565 43.381 42.572 46.182

1:00 32.663 31.798 34.079 34.307 32.453 32.131

2:00 34.365 34.247 35.093 35.598 36.136 35.370

3:00 34.816 33.041 34.532 34.624 33.402 34.876

4:00 34.275 33.056 35.633 35.287 35.008 35.454

5:00 30.375 29.507 31.214 30.931 31.726 29.893

6:00 32.198 33.270 33.588 33.350 36.284 33.456

7:00 32.033 34.051 34.544 32.457 33.895 33.581

8:00 54.319 50.911 51.467 50.812 52.635 50.707

9:00 55.990 54.337 53.835 55.605 55.046 56.333

10:00 48.052 49.377 47.429 47.615 46.825 46.906

11:00 45.068 52.436 45.810 48.490 45.092 46.576

12:00 79.784 82.505 81.295 80.007 82.602 81.581

13:00 46.981 50.267 48.144 48.159 49.129 46.760

14:00 58.796 62.124 60.989 61.149 61.831 59.933

15:00 46.867 48.451 49.685 48.852 50.226 48.605

16:00 59.074 62.332 61.526 61.642 62.498 60.689

17:00 50.724 53.651 52.440 51.216 58.628 52.216

18:00 46.979 52.650 50.074 49.044 50.276 49.798

19:00 64.461 66.558 66.506 66.316 64.386 65.533

20:00 66.355 68.993 68.761 67.793 67.176 67.691

21:00 52.667 51.699 51.398 51.512 53.232 51.611

22:00 39.498 40.200 38.752 38.292 39.919 38.331

23:00 39.815 40.352 43.229 40.050 41.517 39.116

200

Table A156 Standard Deviation of Dollar Returns on 1 Week Hedged Portfolios: First Energy Hub The table below shows the standard deviation of dollar returns for one week hedged portfolios on the First Energy hub. First differences of weekly day-ahead and real-time prices are used in constructing these hedged positions. In the case of the method of group averages (MGA) approach, an estimation period is used to calculate a static hedge ratio, which is then applied to the remainder of the sample. MV, ARDL(1,1), and GARCH(1,1) hedge ratios are calculated using a twenty week rolling estimation period. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. The standard deviations shown are in terms of dollars per megawatt hour ($/MWh). 128 weekly dollar returns from 6/1/2006-4/11/2009 are used in this analysis.


0:00 22.277 24.558 23.650 24.842 25.886 23.148

1:00 32.663 31.798 34.079 34.307 32.453 32.131

2:00 34.365 34.247 35.093 35.598 36.136 35.370

3:00 34.816 33.041 34.532 34.624 33.402 34.876

4:00 34.275 33.056 35.633 35.287 35.008 35.454

5:00 22.930 20.802 23.127 22.207 22.314 22.108

6:00 38.791 37.264 40.863 38.785 51.354 41.394

7:00 36.377 39.265 36.551 36.305 41.158 37.267

8:00 45.417 44.984 48.023 45.885 44.160 47.908

9:00 28.368 40.098 29.668 31.330 29.168 29.416

10:00 42.525 47.312 46.588 43.988 42.345 46.795

11:00 36.521 44.314 38.917 40.314 37.999 39.778

12:00 44.149 49.732 45.711 47.325 44.048 44.629

13:00 46.920 49.970 50.995 51.850 46.648 51.600

14:00 37.717 44.806 40.301 40.651 39.443 40.749

15:00 42.293 49.225 44.641 45.500 42.529 44.894

16:00 55.227 62.628 58.873 57.163 57.257 58.886

17:00 46.866 52.729 50.582 48.960 47.060 52.374

18:00 53.937 59.596 56.168 54.152 54.280 54.728

19:00 41.822 51.557 42.346 44.489 42.074 42.749

20:00 40.868 48.277 44.125 45.203 41.021 43.647

21:00 40.758 47.436 40.882 40.667 41.605 42.323

22:00 27.695 32.357 28.765 28.023 28.156 29.053

23:00 23.815 27.841 25.151 25.755 24.125 24.711

201

Table A157 Standard Deviation of Dollar Returns on 2 Week Hedged Portfolios: Illinois Hub The table below shows the standard deviation of dollar returns for bi-weekly hedged portfolios on the Illinois hub. First differences of bi-weekly day-ahead and real-time prices are used in constructing these hedged positions. In the case of the method of group averages (MGA) approach, an estimation period is used to calculate a static hedge ratio, which is then applied to the remainder of the sample. MV, ARDL(1,1), and GARCH(1,1) hedge ratios are calculated using twenty bi-weekly day-ahead and real-time prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. The standard deviations shown are in terms of dollars per megawatt hour ($/MWh). 54 bi-weekly dollar returns from 6/1/2006-4/11/2009 are used in this analysis.


0:00 20.450 18.999 20.445 20.700 22.441 20.352

1:00 20.778 18.916 22.121 20.815 18.972 21.087

2:00 17.325 15.770 18.151 17.488 18.532 16.881

3:00 13.569 12.745 13.917 13.370 16.908 13.528

4:00 28.572 25.666 30.794 29.327 25.574 27.025

5:00 18.502 16.469 18.223 16.743 22.158 16.471

6:00 26.883 27.612 32.214 30.764 44.702 30.598

7:00 37.354 34.877 34.961 35.532 35.091 35.323

8:00 35.042 30.124 34.401 32.294 36.214 33.460

9:00 22.806 24.535 25.276 23.783 27.877 26.496

10:00 34.656 34.347 35.128 34.903 38.423 33.136

11:00 38.157 38.851 38.707 38.521 39.604 38.169

12:00 54.859 55.511 55.713 55.461 58.142 54.875

13:00 52.011 56.421 54.316 55.736 63.143 55.312

14:00 52.181 50.690 52.839 55.195 59.728 54.127

15:00 41.260 43.901 44.396 48.073 53.679 41.817

16:00 53.865 52.180 55.668 58.040 56.005 65.009

17:00 50.228 53.426 55.326 63.103 49.593 55.607

18:00 62.090 59.313 59.608 59.830 59.742 59.615

19:00 37.967 36.237 35.903 37.840 35.243 35.124

20:00 30.685 28.554 28.966 28.484 28.852 30.481

21:00 35.829 37.291 37.086 36.873 38.939 37.370

22:00 29.241 31.276 30.451 30.452 30.498 29.090

23:00 20.707 22.651 21.885 22.445 26.426 21.855

202

Table A158 Standard Deviation of Dollar Returns on 2 Week Hedged Portfolios: Cinergy Hub The table below shows the standard deviation of dollar returns for bi-weekly hedged portfolios on the Cinergy hub. First differences of bi-weekly day-ahead and real-time prices are used in constructing these hedged positions. In the case of the method of group averages (MGA) approach, an estimation period is used to calculate a static hedge ratio, which is then applied to the remainder of the sample. MV, ARDL(1,1), and GARCH(1,1) hedge ratios are calculated using twenty bi-weekly day-ahead and real-time prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. The standard deviations shown are in terms of dollars per megawatt hour ($/MWh). 54 bi-weekly dollar returns from 6/1/2006-4/11/2009 are used in this analysis.


0:00 20.537 19.910 20.290 21.052 22.673 20.621

1:00 17.463 16.521 20.033 18.856 16.280 20.703

2:00 11.320 10.628 13.862 13.099 14.862 12.140

3:00 8.770 8.885 10.113 9.974 13.473 9.878

4:00 25.753 23.878 28.935 28.724 23.854 23.734

5:00 12.117 11.496 13.318 11.789 17.955 11.692

6:00 25.600 26.487 29.497 28.930 32.074 29.333

7:00 32.882 30.460 30.385 30.956 30.253 30.136

8:00 31.254 25.477 29.213 27.594 25.571 27.618

9:00 20.271 22.583 20.980 19.683 20.357 21.970

10:00 34.357 32.401 32.362 31.715 31.848 33.272

11:00 36.774 35.618 35.560 35.355 34.918 35.343

12:00 50.527 51.181 50.857 49.803 50.300 50.729

13:00 52.025 53.903 53.357 52.156 52.396 54.816

14:00 48.269 49.581 48.705 47.820 53.930 50.839

15:00 43.573 44.989 43.586 44.151 45.586 44.273

16:00 54.252 54.828 54.109 53.241 53.845 52.738

17:00 56.359 61.606 59.011 63.709 57.321 59.520

18:00 70.517 66.829 68.679 67.053 67.795 68.548

19:00 48.253 44.596 44.766 44.102 46.742 44.152

20:00 29.944 28.630 27.527 27.344 27.294 27.811

21:00 35.109 37.200 35.675 36.338 36.126 35.435

22:00 28.572 30.710 29.300 29.463 29.890 28.688

23:00 20.898 23.659 21.983 22.352 24.653 21.375

203

Table A159 Standard Deviation of Dollar Returns on 2 Week Hedged Portfolios: Michigan Hub

The table below shows the standard deviation of dollar returns for bi-weekly hedged portfolios on the Michigan hub. First differences of bi-weekly day-ahead and real-time prices are used in constructing these hedged positions. In the case of the method of group averages (MGA) approach, an estimation period is used to calculate a static hedge ratio, which is then applied to the remainder of the sample. MV, ARDL(1,1), and GARCH(1,1) hedge ratios are calculated using twenty bi-weekly day-ahead and real-time prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. The standard deviations shown are in terms of dollars per megawatt hour ($/MWh). 54 bi-weekly dollar returns from 6/1/2006-4/11/2009 are used in this analysis.


0:00 25.012 25.152 25.260 25.838 29.464 24.650

1:00 20.644 19.693 23.221 21.994 19.514 24.024

2:00 12.323 11.816 14.583 14.194 13.557 12.855

3:00 14.213 14.927 16.159 15.509 15.449 17.187

4:00 28.672 26.862 33.810 32.782 27.193 27.258

5:00 19.542 18.556 19.627 18.919 18.955 19.429

6:00 40.908 42.128 45.916 44.053 43.054 44.068

7:00 39.864 38.359 37.671 38.749 39.128 37.669

8:00 32.653 26.502 29.728 28.270 26.651 28.585

9:00 23.741 28.461 25.378 24.530 25.525 25.313

10:00 35.853 35.435 34.618 34.472 34.107 35.688

11:00 35.916 36.978 35.543 35.474 34.639 35.986

12:00 48.364 50.580 49.478 49.174 49.613 48.933

13:00 45.124 49.719 46.371 48.261 52.332 46.428

14:00 44.395 47.724 45.507 47.651 51.122 45.722

15:00 43.564 48.005 45.551 49.962 48.985 48.414

16:00 56.308 58.830 57.800 61.160 61.517 56.415

17:00 57.360 65.129 61.254 67.214 61.381 62.327

18:00 73.285 70.842 71.758 72.687 70.852 71.431

19:00 45.091 44.389 42.886 43.357 42.439 42.681

20:00 29.833 31.166 28.321 28.634 28.761 28.702

21:00 35.936 39.907 36.777 36.575 40.897 36.560

22:00 29.182 34.150 30.268 32.323 32.310 30.018

23:00 21.882 25.259 23.150 23.280 26.097 22.626

204

Table A160 Standard Deviation of Dollar Returns on 2 Week Hedged Portfolios: Minnesota Hub The table below shows the standard deviation of dollar returns for bi-weekly hedged portfolios on the Minnesota hub. First differences of bi-weekly day-ahead and real-time prices are used in constructing these hedged positions. In the case of the method of group averages (MGA) approach, an estimation period is used to calculate a static hedge ratio, which is then applied to the remainder of the sample. MV, ARDL(1,1), and GARCH(1,1) hedge ratios are calculated using twenty bi-weekly day-ahead and real-time prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. The standard deviations shown are in terms of dollars per megawatt hour ($/MWh). 54 bi-weekly dollar returns from 6/1/2006-4/11/2009 are used in this analysis.


0:00 25.853 23.054 26.485 24.690 27.847 24.050

1:00 18.535 17.511 20.516 19.564 18.611 19.664

2:00 25.622 22.958 25.304 25.298 23.139 25.676

3:00 26.104 23.174 26.788 26.160 23.603 26.489

4:00 34.444 31.494 34.708 34.459 31.336 34.833

5:00 24.748 23.056 25.952 25.313 23.171 29.721

6:00 26.643 23.973 26.461 26.127 25.138 26.644

7:00 34.197 28.999 29.739 30.292 29.036 30.611

8:00 43.571 38.694 44.768 42.621 38.826 40.601

9:00 39.253 34.081 36.920 36.471 36.859 37.540

10:00 43.196 37.293 39.113 38.657 37.318 40.204

11:00 39.923 38.279 37.864 37.374 39.056 37.417

12:00 62.866 68.139 64.973 65.658 63.285 65.824

13:00 51.367 52.655 50.617 50.794 50.964 49.934

14:00 71.873 72.688 71.595 72.352 71.538 70.738

15:00 42.418 38.276 37.371 38.709 40.760 36.928

16:00 50.633 48.551 48.253 47.025 49.805 48.485

17:00 52.494 47.579 47.048 47.453 50.709 48.583

18:00 50.770 46.257 45.173 45.478 49.072 45.041

19:00 52.380 46.196 47.813 46.646 50.938 45.800

20:00 43.641 49.193 45.151 45.837 43.586 46.077

21:00 40.728 39.018 40.166 39.908 38.870 40.532

22:00 42.425 40.333 42.041 40.302 40.979 41.033

23:00 48.977 43.826 49.610 44.928 46.384 47.192

205

Table A161 Standard Deviation of Dollar Returns on 2 Week Hedged Portfolios: First Energy Hub The table below shows the standard deviation of dollar returns for bi-weekly hedged portfolios on the First Energy hub. First differences of bi-weekly day-ahead and real-time prices are used in constructing these hedged positions. In the case of the method of group averages (MGA) approach, an estimation period is used to calculate a static hedge ratio, which is then applied to the remainder of the sample. MV, ARDL(1,1), and GARCH(1,1) hedge ratios are calculated using twenty bi-weekly day-ahead and real-time prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. The standard deviations shown are in terms of dollars per megawatt hour ($/MWh). 54 bi-weekly dollar returns from 6/1/2006-4/11/2009 are used in this analysis.


0:00 23.254 20.822 21.737 21.760 21.594 21.580

1:00 27.059 24.771 27.688 26.241 25.176 27.834

2:00 14.293 14.625 15.797 15.473 16.869 15.804

3:00 12.556 13.862 13.521 13.611 16.745 13.418

4:00 31.541 28.403 34.577 31.350 31.336 33.550

5:00 14.698 12.966 14.978 14.053 16.750 15.749

6:00 31.265 32.209 35.151 34.717 48.379 34.561

7:00 35.465 34.163 33.281 34.643 34.913 33.951

8:00 32.474 25.367 29.781 27.808 25.782 30.151

9:00 22.040 25.437 23.115 21.836 21.269 23.514

10:00 36.473 33.723 34.273 33.388 33.123 34.063

11:00 35.263 36.493 35.271 34.483 35.020 34.717

12:00 49.625 53.065 50.975 51.104 52.168 49.623

13:00 44.890 50.464 47.337 49.432 49.683 47.862

14:00 42.888 46.339 45.018 45.524 51.177 45.026

15:00 42.879 51.098 45.347 45.866 57.455 46.392

16:00 53.990 59.005 54.807 52.973 62.809 57.129

17:00 54.519 59.667 57.081 56.852 57.720 58.652

18:00 70.778 67.950 71.508 69.322 68.633 70.731

19:00 49.261 49.153 49.053 47.854 48.279 49.542

20:00 29.362 27.705 26.928 27.004 26.420 27.208

21:00 34.971 39.205 35.976 37.773 39.118 35.443

22:00 29.348 29.755 29.206 29.048 28.605 29.901

23:00 22.452 25.120 23.407 23.616 25.308 23.667

206

Table A162 Standard Deviation of Dollar Returns on 3 Week Hedged Portfolios: Illinois Hub The table below shows the standard deviation of dollar returns for tri-weekly hedged portfolios on the Illinois hub. First differences of tri-weekly day-ahead and real-time prices are used in constructing these hedged positions. In the case of the method of group averages (MGA) approach, an estimation period is used to calculate a static hedge ratio, which is then applied to the remainder of the sample. MV, ARDL(1,1), and GARCH(1,1) hedge ratios are calculated using twenty tri-weekly day-ahead and real-time prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. The standard deviations shown are in terms of dollars per megawatt hour ($/MWh). 29 tri-weekly dollar returns from 6/1/2006-4/11/2009 are used in this analysis.


0:00 15.982 11.608 13.470 12.973 15.378 13.392

1:00 39.171 40.162 43.064 40.691 40.021 41.207

2:00 27.083 27.463 29.747 28.155 27.107 28.066

3:00 8.234 6.730 6.822 6.537 6.558 6.849

4:00 31.515 31.558 31.662 31.750 31.400 31.519

5:00 25.634 25.857 25.752 25.858 25.811 26.658

6:00 27.672 24.380 28.914 26.323 27.016 26.270

7:00 40.834 35.355 36.569 37.314 35.334 38.001

8:00 51.490 45.249 46.038 45.269 45.483 46.519

9:00 24.696 18.509 26.961 23.739 27.313 26.885

10:00 36.147 36.116 38.604 36.219 39.001 38.439

11:00 29.127 35.668 31.352 30.024 30.015 32.514

12:00 41.022 45.508 49.360 45.616 45.383 48.551

13:00 44.550 41.269 58.004 44.457 55.099 57.850

14:00 31.628 43.979 32.877 32.624 31.831 33.566

15:00 29.864 35.218 31.294 28.611 26.884 31.945

16:00 39.514 50.058 43.238 37.644 42.209 41.795

17:00 42.393 53.602 46.121 43.866 42.247 44.339

18:00 50.165 54.163 50.548 48.755 49.426 51.159

19:00 37.150 47.821 38.613 38.692 40.107 39.489

20:00 39.873 50.377 44.298 44.428 47.552 43.550

21:00 44.573 45.718 47.335 47.078 47.032 46.438

22:00 29.933 23.155 28.807 27.476 32.857 27.878

23:00 17.100 14.999 17.251 15.446 18.848 16.218

207

Table A163 Standard Deviation of Dollar Returns on 3 Week Hedged Portfolios: Cinergy Hub The table below shows the standard deviation of dollar returns for tri-weekly hedged portfolios on the Cinergy hub. First differences of tri-weekly day-ahead and real-time prices are used in constructing these hedged positions. In the case of the method of group averages (MGA) approach, an estimation period is used to calculate a static hedge ratio, which is then applied to the remainder of the sample. MV, ARDL(1,1), and GARCH(1,1) hedge ratios are calculated using twenty tri-weekly day-ahead and real-time prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. The standard deviations shown are in terms of dollars per megawatt hour ($/MWh). 29 tri-weekly dollar returns from 6/1/2006-4/11/2009 are used in this analysis.


0:00 14.797 17.573 15.408 16.054 14.251 14.717

1:00 10.444 16.053 16.313 14.993 12.918 14.172

2:00 10.068 12.344 11.430 11.576 9.693 10.830

3:00 7.941 10.975 10.919 9.559 8.381 11.222

4:00 11.183 8.390 8.552 8.571 8.928 8.987

5:00 15.327 14.313 14.616 13.970 13.926 15.195

6:00 31.708 29.604 39.597 34.834 35.927 30.292

7:00 42.242 46.253 45.281 43.470 42.899 42.380

8:00 47.776 44.138 48.492 45.307 42.698 49.125

9:00 30.776 39.951 34.549 32.698 35.673 41.474

10:00 38.534 47.621 42.168 39.267 41.750 39.685

11:00 31.498 38.213 33.785 32.186 34.541 42.483

12:00 48.011 54.132 58.277 52.389 48.966 54.918

13:00 45.236 40.294 59.100 38.843 60.375 50.581

14:00 31.923 46.591 35.088 32.509 32.040 40.798

15:00 29.144 37.189 34.558 27.963 24.496 30.743

16:00 42.295 61.801 56.104 43.214 51.630 57.220

17:00 41.545 61.612 57.015 45.556 50.041 72.014

18:00 52.674 65.766 52.591 51.321 52.179 54.521

19:00 39.850 59.459 42.378 43.287 42.460 45.394

20:00 40.540 50.563 47.399 46.067 50.342 47.505

21:00 42.967 63.422 48.332 49.393 41.997 45.237

22:00 29.907 28.786 26.914 26.119 27.048 28.707

23:00 16.905 22.940 16.443 15.419 16.639 15.466

208

Table A164 Standard Deviation of Dollar Returns on 3 Week Hedged Portfolios: Michigan Hub The table below shows the standard deviation of dollar returns for tri-weekly hedged portfolios on the Michigan hub. First differences of tri-weekly day-ahead and real-time prices are used in constructing these hedged positions. In the case of the method of group averages (MGA) approach, an estimation period is used to calculate a static hedge ratio, which is then applied to the remainder of the sample. MV, ARDL(1,1), and GARCH(1,1) hedge ratios are calculated using twenty tri-weekly day-ahead and real-time prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. The standard deviations shown are in terms of dollars per megawatt hour ($/MWh). 29 tri-weekly dollar returns from 6/1/2006-4/11/2009 are used in this analysis.


0:00 15.380 19.335 16.666 17.038 15.771 16.158

1:00 12.758 15.513 15.896 14.089 12.394 14.699

2:00 10.991 11.981 11.408 11.460 10.357 10.900

3:00 9.996 13.738 13.497 11.726 10.240 13.428

4:00 14.779 12.721 12.896 12.851 13.360 13.294

5:00 25.219 23.648 24.601 23.726 23.733 24.970

6:00 33.669 33.305 41.773 38.301 32.909 31.823

7:00 45.461 47.418 46.149 44.961 44.030 44.889

8:00 50.457 47.422 50.719 47.372 45.500 50.931

9:00 27.229 41.867 30.565 29.511 31.781 42.023

10:00 38.984 48.874 41.999 39.306 43.682 40.753

11:00 32.538 36.286 34.793 33.458 32.803 36.776

12:00 45.320 50.719 53.072 49.444 46.211 51.153

13:00 45.369 41.532 67.019 42.700 62.210 64.164

14:00 31.525 43.941 34.506 32.463 32.376 35.513

15:00 28.864 37.079 40.162 34.585 27.504 43.495

16:00 40.056 52.812 42.729 37.749 42.321 43.039

17:00 41.477 57.827 46.722 43.174 41.313 52.113

18:00 51.304 58.002 51.717 50.203 50.391 53.859

19:00 40.297 52.727 41.070 41.537 41.199 40.969

20:00 40.272 52.435 44.706 44.903 43.286 45.622

21:00 43.970 67.285 44.893 46.128 42.287 44.254

22:00 30.270 29.687 27.371 26.824 25.986 26.938

23:00 17.252 24.754 17.272 16.194 18.078 16.847

209

Table A165 Standard Deviation of Dollar Returns on 3 Week Hedged Portfolios: Minnesota Hub The table below shows the standard deviation of dollar returns for tri-weekly hedged portfolios on the Minnesota hub. First differences of tri-weekly day-ahead and real-time prices are used in constructing these hedged positions. In the case of the method of group averages (MGA) approach, an estimation period is used to calculate a static hedge ratio, which is then applied to the remainder of the sample. MV, ARDL(1,1), and GARCH(1,1) hedge ratios are calculated using twenty tri-weekly day-ahead and real-time prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. The standard deviations shown are in terms of dollars per megawatt hour ($/MWh). 29 tri-weekly dollar returns from 6/1/2006-4/11/2009 are used in this analysis.


0:00 22.035 20.162 18.671 22.542 23.915 19.107

1:00 41.124 40.863 42.173 42.062 40.939 42.235

2:00 43.048 41.822 42.863 43.037 41.830 43.893

3:00 29.521 23.281 26.208 23.942 25.341 27.727

4:00 38.025 35.664 36.958 36.878 36.562 37.209

5:00 30.176 28.000 28.397 28.757 28.145 28.878

6:00 32.263 32.706 37.275 35.031 32.218 35.768

7:00 47.736 43.263 45.310 44.889 47.266 46.204

8:00 69.060 60.299 64.989 62.670 64.970 63.887

9:00 52.811 42.554 48.114 46.487 51.448 48.057

10:00 53.841 54.162 54.811 55.561 52.386 54.907

11:00 45.146 47.308 46.760 50.425 44.696 50.374

12:00 50.989 51.771 53.425 49.797 56.816 56.303

13:00 49.783 42.361 46.703 44.549 48.160 45.564

14:00 45.597 36.883 39.492 39.186 39.566 40.534

15:00 40.639 32.378 34.386 35.142 32.743 35.627

16:00 48.047 48.585 48.274 46.426 47.319 48.152

17:00 53.086 53.226 54.302 53.235 52.302 52.982

18:00 60.889 56.565 57.341 58.244 57.395 57.471

19:00 65.643 60.519 67.454 64.868 61.664 65.615

20:00 59.964 60.752 59.733 59.223 57.690 62.884

21:00 50.786 47.359 47.510 48.200 46.834 53.977

22:00 46.564 35.051 35.793 35.010 36.045 35.568

23:00 36.218 29.363 30.108 29.345 29.423 32.079

210

Table A166 Standard Deviation of Dollar Returns on 3 Week Hedged Portfolios: First Energy Hub The table below shows the standard deviation of dollar returns for tri-weekly hedged portfolios on the First Energy hub. First differences of tri-weekly day-ahead and real-time prices are used in constructing these hedged positions. In the case of the method of group averages (MGA) approach, an estimation period is used to calculate a static hedge ratio, which is then applied to the remainder of the sample. MV, ARDL(1,1), and GARCH(1,1) hedge ratios are calculated using twenty tri-weekly day-ahead and real-time prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. The standard deviations shown are in terms of dollars per megawatt hour ($/MWh). 29 tri-weekly dollar returns from 6/1/2006-4/11/2009 are used in this analysis.


0:00 16.515 24.569 20.108 20.197 17.369 19.665

1:00 17.479 21.903 18.901 17.634 18.332 19.864

2:00 10.810 12.714 11.847 11.936 10.105 11.059

3:00 8.759 13.350 11.057 11.272 8.753 9.909

4:00 11.135 10.928 10.268 9.951 9.993 10.191

5:00 15.441 17.086 15.102 15.222 15.147 15.546

6:00 31.601 33.347 38.643 35.335 37.436 31.170

7:00 42.805 53.160 48.022 47.241 45.317 49.431

8:00 48.227 47.364 51.663 47.998 44.328 52.463

9:00 28.050 50.257 37.584 34.899 28.102 35.800

10:00 39.437 50.827 47.305 40.698 39.084 49.774

11:00 35.945 46.131 39.205 39.462 37.694 44.892

12:00 45.774 57.211 49.807 46.902 46.349 50.028

13:00 42.971 51.337 71.180 72.287 48.286 48.168

14:00 30.487 51.852 33.845 34.117 30.699 34.151

15:00 29.301 50.717 37.792 38.008 38.379 39.759

16:00 42.411 61.089 42.582 41.305 44.800 41.678

17:00 41.598 66.273 44.877 45.336 43.274 50.418

18:00 54.920 71.672 56.929 56.909 54.615 54.857

19:00 52.295 68.626 53.873 54.847 52.452 55.252

20:00 45.070 61.707 48.807 50.855 44.564 50.869

21:00 46.979 71.373 62.157 58.251 46.105 56.762

22:00 32.275 32.492 30.245 30.269 30.290 29.657

23:00 16.728 27.734 18.267 15.963 17.054 17.242

211

Table A167 Standard Deviation of Dollar Returns on 4 Week Hedged Portfolios: Illinois Hub The table below shows the standard deviation of dollar returns for monthly hedged portfolios on the Illinois hub. First differences of monthly day-ahead and real-time prices are used in constructing these hedged positions. In the case of the method of group averages (MGA) approach, an estimation period is used to calculate a static hedge ratio, which is then applied to the remainder of the sample. MV, ARDL(1,1), and GARCH(1,1) hedge ratios are calculated using twenty monthly day-ahead and real-time prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. The standard deviations shown are in terms of dollars per megawatt hour ($/MWh). 17 monthly dollar returns from 6/1/2006-4/11/2009 are used in this analysis.


0:00 28.928 27.216 30.263 26.430 28.720 27.517

1:00 13.239 15.518 13.756 13.699 13.596 13.341

2:00 13.091 16.238 17.093 14.919 16.166 13.832

3:00 10.215 13.573 11.383 10.592 11.816 10.209

4:00 39.687 41.509 42.227 49.625 41.102 43.458

5:00 14.846 11.243 11.904 12.277 11.966 13.215

6:00 16.923 16.073 15.498 15.294 16.178 15.500

7:00 27.509 24.832 24.483 24.737 24.646 26.228

8:00 32.186 33.320 32.793 33.165 33.127 34.197

9:00 13.121 12.274 13.063 11.556 13.555 12.166

10:00 26.442 25.268 26.221 25.513 27.442 25.644

11:00 33.869 34.758 34.086 33.523 35.097 34.581

12:00 60.425 57.653 59.697 60.381 58.165 60.459

13:00 35.595 38.641 36.845 36.874 38.363 38.408

14:00 30.040 31.955 29.380 30.470 32.182 42.817

15:00 28.548 32.104 30.982 37.975 35.297 31.181

16:00 37.344 33.088 35.918 39.240 36.772 34.020

17:00 58.337 68.144 68.905 69.007 65.993 70.256

18:00 46.496 40.212 39.716 39.371 41.219 43.231

19:00 53.981 48.873 49.012 49.219 50.002 50.623

20:00 38.677 34.718 35.046 35.981 34.838 37.162

21:00 34.703 32.949 33.292 32.214 34.542 34.973

22:00 29.487 24.141 24.702 24.435 24.101 24.987

23:00 23.927 20.986 21.883 21.329 20.985 22.938

212

Table A168 Standard Deviation of Dollar Returns on 4 Week Hedged Portfolios: Cinergy Hub The table below shows the standard deviation of dollar returns for monthly hedged portfolios on the Cinergy hub. First differences of monthly day-ahead and real-time prices are used in constructing these hedged positions. In the case of the method of group averages (MGA) approach, an estimation period is used to calculate a static hedge ratio, which is then applied to the remainder of the sample. MV, ARDL(1,1), and GARCH(1,1) hedge ratios are calculated using twenty monthly day-ahead and real-time prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. The standard deviations shown are in terms of dollars per megawatt hour ($/MWh). 17 monthly dollar returns from 6/1/2006-4/11/2009 are used in this analysis.


0:00 28.224 28.815 31.876 28.347 30.599 30.163

1:00 12.843 15.825 13.591 13.616 14.022 13.192

2:00 12.249 15.936 17.110 14.437 16.780 13.438

3:00 8.763 12.427 10.343 9.521 11.180 9.180

4:00 40.384 42.858 42.975 50.605 42.265 44.966

5:00 12.428 10.328 10.249 10.868 12.082 10.572

6:00 26.872 26.868 29.388 27.188 26.028 27.263

7:00 28.291 31.280 30.640 30.130 30.516 32.669

8:00 33.030 33.366 32.891 33.105 32.702 32.748

9:00 12.231 11.951 10.946 10.644 10.858 10.909

10:00 33.076 30.285 31.192 31.859 30.300 31.940

11:00 45.563 42.375 43.775 44.406 42.937 43.112

12:00 70.666 66.721 68.079 68.622 68.150 68.527

13:00 51.533 50.452 51.048 51.929 50.445 51.186

14:00 33.666 31.150 30.937 31.521 31.224 35.321

15:00 38.478 38.546 39.282 41.176 38.361 43.190

16:00 39.578 32.959 38.169 34.109 33.020 35.434

17:00 59.588 67.402 85.419 71.733 68.802 93.518

18:00 53.323 46.900 48.280 48.001 46.543 47.863

19:00 72.488 64.231 65.630 63.378 67.947 66.434

20:00 41.023 37.344 37.858 38.202 37.688 37.957

21:00 34.005 33.298 34.619 32.560 32.722 33.369

22:00 25.516 20.789 21.184 21.228 20.928 22.156

23:00 24.425 21.979 22.698 22.354 21.922 22.816

213

Table A169 Standard Deviation of Dollar Returns on 4 Week Hedged Portfolios: Michigan Hub The table below shows the standard deviation of dollar returns for monthly hedged portfolios on the Michigan hub. First differences of monthly day-ahead and real-time prices are used in constructing these hedged positions. In the case of the method of group averages (MGA) approach, an estimation period is used to calculate a static hedge ratio, which is then applied to the remainder of the sample. MV, ARDL(1,1), and GARCH(1,1) hedge ratios are calculated using twenty monthly day-ahead and real-time prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. The standard deviations shown are in terms of dollars per megawatt hour ($/MWh). 17 monthly dollar returns from 6/1/2006-4/11/2009 are used in this analysis.


0:00 30.635 30.914 35.580 30.033 34.772 29.755

1:00 17.150 18.724 17.600 17.476 17.417 16.600

2:00 14.290 17.967 18.941 16.927 18.763 14.760

3:00 15.177 17.858 16.463 15.624 17.107 15.423

4:00 43.834 46.531 45.472 56.428 45.388 48.069

5:00 14.705 13.027 12.742 13.244 14.044 13.325

6:00 33.380 33.180 34.433 33.320 32.323 33.183

7:00 35.461 37.712 37.267 38.095 40.055 43.097

8:00 35.806 35.044 35.085 34.793 34.675 34.945

9:00 12.935 15.041 14.149 13.153 14.129 13.890

10:00 29.569 27.792 27.580 27.675 28.635 27.454

11:00 38.864 40.545 37.587 38.034 39.377 37.822

12:00 67.574 66.326 65.519 66.349 66.282 67.084

13:00 39.705 43.202 37.511 39.645 42.064 40.114

14:00 32.165 34.718 32.874 35.059 35.418 35.160

15:00 30.958 34.686 34.601 36.807 37.200 38.683

16:00 40.035 36.962 42.917 38.552 39.104 39.962

17:00 60.401 71.821 92.599 75.256 81.311 77.383

18:00 49.902 42.597 43.775 44.042 42.437 42.872

19:00 61.905 56.222 57.035 56.559 58.923 57.809

20:00 39.477 33.934 34.632 34.848 34.830 34.605

21:00 34.785 35.309 37.193 33.617 36.171 35.575

22:00 26.098 20.649 21.143 21.136 20.893 22.339

23:00 25.032 22.216 23.257 22.788 22.167 23.766

214

Table A170 Standard Deviation of Dollar Returns on 4 Week Hedged Portfolios: Minnesota Hub The table below shows the standard deviation of dollar returns for monthly hedged portfolios on the Minnesota hub. First differences of monthly day-ahead and real-time prices are used in constructing these hedged positions. In the case of the method of group averages (MGA) approach, an estimation period is used to calculate a static hedge ratio, which is then applied to the remainder of the sample. MV, ARDL(1,1), and GARCH(1,1) hedge ratios are calculated using twenty monthly day-ahead and real-time prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. The standard deviations shown are in terms of dollars per megawatt hour ($/MWh). 17 monthly dollar returns from 6/1/2006-4/11/2009 are used in this analysis.


0:00 26.263 29.516 25.444 27.259 26.321 27.397

1:00 14.648 16.878 19.601 19.767 18.465 16.569

2:00 19.261 20.440 21.070 20.469 20.432 20.482

3:00 19.084 19.217 18.868 18.357 18.447 18.721

4:00 40.308 42.559 42.525 42.904 40.904 41.438

5:00 24.614 24.103 24.274 23.855 23.689 24.864

6:00 30.014 29.622 31.051 29.516 30.809 31.922

7:00 32.338 31.350 32.674 31.066 35.691 31.920

8:00 62.921 58.007 59.468 58.445 59.326 59.113

9:00 43.188 34.928 39.817 38.915 38.496 39.944

10:00 29.569 27.792 27.580 45.198 42.719 43.649

11:00 45.646 40.662 41.501 42.794 42.954 42.958

12:00 66.508 60.461 69.671 64.911 65.565 65.048

13:00 45.102 39.903 45.423 43.888 43.535 46.300

14:00 31.592 25.903 31.810 25.038 29.102 27.139

15:00 28.838 22.222 25.769 22.153 25.543 22.995

16:00 49.374 44.752 46.773 44.934 47.707 45.801

17:00 68.106 66.555 65.966 66.369 66.611 66.407

18:00 62.920 51.868 51.257 52.513 57.052 53.130

19:00 79.107 64.410 64.913 64.952 70.262 60.100

20:00 43.490 38.419 42.583 42.658 39.991 39.936

21:00 38.433 44.608 44.194 39.549 39.905 43.509

22:00 22.519 14.992 14.900 15.907 19.257 15.042

23:00 28.622 24.417 23.190 25.041 25.305 26.268

215

Table A171 Standard Deviation of Dollar Returns on 4 Week Hedged Portfolios: First Energy Hub The table below shows the standard deviation of dollar returns for monthly hedged portfolios on the First Energy hub. First differences of monthly day-ahead and real-time prices are used in constructing these hedged positions. In the case of the method of group averages (MGA) approach, an estimation period is used to calculate a static hedge ratio, which is then applied to the remainder of the sample. MV, ARDL(1,1), and GARCH(1,1) hedge ratios are calculated using twenty monthly day-ahead and real-time prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. The standard deviations shown are in terms of dollars per megawatt hour ($/MWh). 17 monthly dollar returns from 6/1/2006-4/11/2009 are used in this analysis.


0:00 29.139 28.658 32.273 27.962 30.336 27.745

1:00 23.009 26.922 24.333 25.264 24.946 24.540

2:00 17.528 23.550 22.851 21.800 23.867 19.919

3:00 13.632 18.889 15.246 15.079 17.368 14.250

4:00 41.533 45.402 44.865 54.851 44.325 46.284

5:00 16.413 16.028 15.648 15.660 17.306 17.102

6:00 31.381 30.649 31.698 31.051 31.026 30.773

7:00 31.471 31.206 30.915 31.191 31.670 32.847

8:00 34.296 33.517 33.282 33.047 33.311 33.580

9:00 12.664 12.824 11.581 11.283 11.526 11.474

10:00 31.588 28.783 29.087 29.145 28.793 29.347

11:00 41.917 40.279 41.373 40.679 40.497 42.259

12:00 69.642 65.996 68.481 68.256 68.419 70.841

13:00 44.586 46.118 44.310 45.214 44.692 48.443

14:00 33.388 36.102 33.534 35.558 37.849 42.419

15:00 32.757 33.630 33.885 37.566 34.494 37.234

16:00 46.733 44.116 48.347 45.449 45.505 47.272

17:00 59.424 69.072 86.368 73.734 76.428 79.316

18:00 50.790 43.158 53.466 54.646 43.656 46.480

19:00 74.267 70.231 71.188 70.274 73.716 71.086

20:00 38.336 35.613 35.997 36.118 35.438 36.540

21:00 33.551 33.052 33.664 32.337 32.879 32.984

22:00 27.816 22.849 23.136 23.095 23.596 23.135

23:00 34.709 34.159 34.337 33.658 33.927 34.426

216

Table A172 1 Week Hedging Effectiveness (Price Levels): Illinois Hub

The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 129 weekly, out-of-sample dollar returns between two hedging strategies on the Illinois hub. MGA portfolios utilize twenty weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV estimates. MV hedge ratios are calculated using twenty weekly spot and forward prices. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Unhedged-

Naïve Unhedged-

MV Unhedged-

MGA Naïve-

MV Naive- MGA

MV- MGA

0:00 0.73 -5.62 -1.67 -6.58 -6.25 3.20

1:00 0.56 -4.61 0.31 -5.24 -2.17 5.10

2:00 0.15 -6.28 -1.13 -6.84 -4.45 5.63

3:00 0.59 -6.64 -1.75 -7.22 -6.06 4.21

4:00 0.24 -7.43 0.55 -7.96 1.81 8.11

5:00 -0.14 -7.41 -2.20 -7.08 -5.27 4.67

6:00 2.31 -4.16 -0.29 -5.56 -3.49 3.13

7:00 1.42 -1.84 2.29 -4.03 2.26 4.90

8:00 2.89 -0.78 2.89 -3.93 -1.16 3.93

9:00 -1.01 -2.66 0.42 -1.63 5.21 3.24

10:00 0.60 -1.87 3.47 -3.04 0.43 3.07

11:00 0.43 -4.64 3.21 -4.87 1.12 5.90

12:00 0.28 -6.43 2.33 -6.16 1.75 7.68

13:00 1.14 -6.12 2.26 -6.65 2.51 7.59

14:00 0.92 -2.32 0.69 -2.83 -4.25 2.60

15:00 2.22 -0.79 1.16 -3.27 -4.39 1.98

16:00 3.23 0.04 3.70 -3.57 1.22 4.03

17:00 1.46 -2.39 2.86 -3.44 2.08 5.09

18:00 1.51 -4.05 2.98 -4.80 1.02 5.83

19:00 0.38 -2.89 5.06 -3.24 -0.04 3.42

20:00 -0.18 -3.18 2.25 -2.94 1.52 4.28

21:00 0.80 -4.45 1.85 -4.83 1.81 5.87

22:00 -0.40 -0.38 2.05 0.14 2.68 2.27

23:00 0.57 -3.56 1.83 -3.73 2.82 5.25

# of Neg. Coeff. 4 23 5 23 10 0

Sign. at 5% 0 18 1 22 8 0

217

Table A172 (Continued)

Note: Morgan’s t-statistic can be expressed as t R(N- )

.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1

s ]. . Critical values are

1.64 1.96, and . 76 for significance levels of 10%, 5%, and 1% respectively. The sample period for this analysis is 6/1/2006-4/11/2009.

218

Table A173 1 Week Hedging Effectiveness (Price Levels): Cinergy Hub

The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 129 weekly, out-of-sample dollar returns between two hedging strategies on the Cinergy hub. MGA portfolios utilize twenty weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV estimates. MV hedge ratios are calculated using twenty weekly spot and forward prices. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Unhedged-

Naïve Unhedged-

MV Unhedged-

MGA Naïve-

MV Naive-MGA

MV- MGA

0:00 -0.09 -5.69 -1.84 -6.11 -6.42 3.46

1:00 0.88 -6.13 0.49 -7.55 -2.81 7.28

2:00 1.41 -6.32 -2.29 -8.46 -7.08 4.42

3:00 2.12 -3.08 0.92 -5.51 -2.47 4.63

4:00 3.75 -5.03 4.68 -9.25 -1.33 8.29

5:00 3.51 -4.25 1.95 -7.33 -1.02 6.75

6:00 3.66 -0.62 -1.75 -3.36 -4.96 -1.38

7:00 1.48 -0.70 -0.66 -3.02 -5.10 -0.16

8:00 2.02 -0.48 4.95 -3.64 -0.63 2.26

9:00 -3.26 -2.02 2.45 2.31 4.11 2.95

10:00 -0.67 -2.91 3.28 -3.02 1.39 3.64

11:00 0.47 -4.39 3.28 -5.03 1.24 5.75

12:00 0.21 -5.84 2.54 -5.97 1.79 7.33

13:00 1.89 -6.43 4.25 -7.73 0.76 8.75

14:00 1.93 -2.33 1.75 -3.93 -3.75 3.73

15:00 3.09 0.12 3.30 -3.47 2.13 3.70

16:00 2.86 -2.19 5.21 -4.38 -0.06 6.26

17:00 2.32 -2.28 4.85 -3.75 0.58 5.63

18:00 1.00 -3.51 4.00 -3.83 0.24 4.83

19:00 0.24 -4.28 -5.38 -4.78 -0.24 4.27

20:00 0.49 -4.15 4.11 -4.73 0.16 4.92

21:00 0.43 -6.45 1.89 -5.29 2.13 6.88

22:00 -0.21 -0.21 3.50 0.05 1.74 1.94

23:00 -0.37 -4.24 1.91 -3.69 2.89 6.63

# of Neg. Coeff. 5 23 5 22 12 2

Sign. at 5% 1 19 2 22 7 0

219



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



220

Table A174 1 Week Hedging Effectiveness (Price Levels): Michigan Hub

The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 129 weekly, out-of-sample dollar returns between two hedging strategies on the Michigan hub. MGA portfolios utilize twenty weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV estimates. MV hedge ratios are calculated using twenty weekly spot and forward prices. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Unhedged-

Naïve Unhedged-

MV Unhedged-

MGA Naïve-

MV Naive-MGA

MV- MGA

0:00 -0.34 -6.18 -2.20 -6.10 -6.48 3.36

1:00 0.86 -5.50 1.78 -6.98 1.59 7.24

2:00 1.30 -3.81 0.96 -6.01 -3.04 5.80

3:00 1.57 -3.46 3.28 -5.48 0.04 5.21

4:00 3.24 -6.20 4.98 -9.66 -1.90 7.93

5:00 3.15 -3.62 3.26 -6.59 -0.45 6.55

6:00 3.25 -1.06 4.80 -3.65 -1.96 2.60

7:00 1.51 -0.50 2.31 -2.87 2.02 3.63

8:00 1.71 -0.47 5.01 -3.17 -0.82 1.56

9:00 -3.65 -3.16 -1.05 1.21 7.47 2.42

10:00 0.35 -3.88 3.07 -5.18 0.90 5.19

11:00 0.33 -3.87 2.94 -4.26 1.54 5.25

12:00 0.35 -5.58 2.48 -5.77 1.90 7.16

13:00 1.33 -6.92 2.67 -7.45 2.21 8.50

14:00 1.60 -1.77 2.42 -3.08 3.42 3.85

15:00 2.68 -1.58 3.53 -4.07 2.09 4.92

16:00 2.72 -2.66 5.00 -4.70 0.01 6.02

17:00 1.84 -2.73 4.43 -3.72 0.86 5.92

18:00 1.32 -3.67 4.24 -4.11 -0.21 4.97

19:00 0.72 -2.63 5.74 -3.27 -0.42 3.15

20:00 0.47 -3.94 3.72 -4.19 0.32 4.91

21:00 -0.07 -6.20 1.35 -4.43 2.88 6.25

22:00 -0.57 -0.49 3.27 0.23 2.26 2.26

23:00 -0.16 -4.62 2.02 -4.30 2.88 7.07

# of Neg. Coeff. 5 24 2 22 8 0

Sign. at 5% 1 18 1 22 3 0

221



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



222

Table A175 1 Week Hedging Effectiveness (Price Levels): Minnesota Hub

The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 129 weekly, out-of-sample dollar returns between two hedging strategies on the Minnesota hub. MGA portfolios utilize twenty weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV estimates. MV hedge ratios are calculated using twenty weekly spot and forward prices. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Unhedged-

Naïve Unhedged-

MV Unhedged-

MGA Naïve-

MV Naive-MGA

MV- MGA

0:00 0.99 -2.26 3.98 -3.49 -0.80 2.64

1:00 3.12 -0.69 -1.13 -4.20 -4.47 -0.83

2:00 3.25 -1.22 -0.80 -4.15 -3.75 0.29

3:00 4.03 0.09 4.40 -3.73 -1.68 3.34

4:00 4.02 0.01 3.90 -3.68 1.19 3.79

5:00 4.12 -1.29 2.36 -4.68 -0.94 4.11

6:00 0.69 -0.90 -3.74 -1.76 -7.71 -3.63

7:00 1.41 -0.07 -2.82 -2.33 -8.44 -3.67

8:00 4.11 -0.32 5.54 -6.42 -0.79 5.38

9:00 2.71 -1.67 6.23 -5.10 -1.71 3.08

10:00 0.74 -1.77 4.27 -3.72 0.43 3.12

11:00 0.48 -2.20 3.92 -2.94 0.61 3.36

12:00 0.89 -2.95 2.51 -3.65 0.35 4.08

13:00 2.56 -1.03 4.26 -4.42 -0.06 4.52

14:00 3.68 1.03 4.81 -3.01 -1.35 2.23

15:00 4.79 0.86 5.96 -4.64 -0.59 4.58

16:00 4.91 1.10 6.52 -4.00 -1.72 3.14

17:00 3.18 -0.43 5.11 -3.98 -0.37 3.94

18:00 1.29 -2.21 4.28 -3.51 0.34 4.18

19:00 2.49 -1.75 6.36 -4.54 -1.58 3.28

20:00 1.29 -3.17 4.97 -3.52 -0.95 3.70

21:00 2.14 -1.57 4.54 -3.57 -0.59 3.26

22:00 2.75 -0.73 7.98 -3.57 -2.73 0.75

23:00 2.92 -1.88 5.72 -4.88 -1.31 4.02

# of Neg. Coeff. 0 19 4 24 19 3

Sign. at 5% 0 5 2 23 5 2

223



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



224

Table A176 1 Week Hedging Effectiveness (Price Levels): First Energy Hub

The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 129 weekly, out-of-sample dollar returns between two hedging strategies on the First Energy hub. MGA portfolios utilize twenty weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV estimates. MV hedge ratios are calculated using twenty weekly spot and forward prices. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Unhedged-

Naïve Unhedged-

MV Unhedged-

MGA Naïve-

MV Naive-MGA

MV- MGA

0:00 0.29 -4.64 -0.96 -5.80 -5.42 3.83

1:00 0.71 -4.57 0.75 -6.09 2.36 6.12

2:00 0.12 -4.06 0.21 -5.21 4.27 5.31

3:00 0.83 -2.61 1.27 -3.76 2.42 4.12

4:00 2.55 -2.58 3.81 -5.16 -0.50 4.57

5:00 2.88 -4.49 1.60 -7.70 -1.70 7.10

6:00 3.15 -1.98 2.50 -4.39 -0.65 4.16

7:00 1.71 -1.69 1.97 -4.55 2.77 4.88

8:00 2.43 -0.95 4.49 -4.93 0.01 4.08

9:00 -4.17 -3.15 1.10 2.49 5.73 4.61

10:00 -1.21 -3.65 2.26 -3.12 2.33 4.63

11:00 -0.15 -4.67 3.15 -4.67 1.48 5.78

12:00 -0.53 -5.80 2.34 -4.91 2.10 6.84

13:00 1.86 -4.67 4.14 -6.64 0.36 7.57

14:00 1.00 -2.19 1.31 -2.83 4.57 3.20

15:00 1.73 -2.44 0.60 -4.10 -5.30 2.61

16:00 2.54 -2.14 3.84 -4.02 0.96 5.23

17:00 1.93 -1.13 3.49 -2.75 1.69 4.38

18:00 0.35 -5.15 2.66 -4.20 0.96 5.75

19:00 -1.59 -4.64 2.03 -2.22 2.59 5.58

20:00 0.04 -4.78 3.04 -4.61 0.96 5.82

21:00 -0.29 -5.98 0.78 -4.41 3.31 5.65

22:00 0.05 1.11 3.15 1.19 2.15 1.02

23:00 -0.32 -4.17 1.86 -4.20 2.53 6.62

# of Neg. Coeff. 7 23 1 22 5 0

Sign. at 5% 1 20 0 22 2 0

225



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



226


The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 55 bi-weekly, out-of-sample dollar returns between two hedging strategies on the Illinois hub. MGA portfolios utilize twenty bi-weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV estimates. MV hedge ratios are calculated using twenty bi-weekly spot and forward prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Unhedged-

Naïve Unhedged-

MV Unhedged-

MGA Naïve-

MV Naive-MGA

MV- MGA

0:00 1.46 -2.65 0.27 -4.23 -2.46 2.64

1:00 2.13 -1.37 3.26 -4.12 -0.92 3.07

2:00 1.65 -2.04 0.50 -5.04 -2.29 3.70

3:00 2.19 -0.68 0.15 -3.90 -3.57 0.87

4:00 2.91 -2.99 2.71 -5.87 0.78 6.14

5:00 2.56 -0.30 1.19 -3.44 -2.09 1.77

6:00 1.58 0.86 0.82 -1.10 -2.14 0.35

7:00 1.14 0.68 1.34 -0.78 1.63 0.99

8:00 3.96 1.71 2.50 -2.96 -1.11 1.60

9:00 0.47 0.26 0.19 -0.31 -4.63 -0.02

10:00 1.17 -0.67 1.93 -2.09 1.03 2.87

11:00 2.05 -1.40 2.85 -2.62 -0.54 2.69

12:00 0.50 -1.05 2.07 -1.30 -0.05 1.46

13:00 0.77 -2.25 1.91 -2.72 0.58 3.31

14:00 1.38 -1.09 3.56 -2.10 -0.65 1.96

15:00 1.61 -0.29 3.46 -2.02 0.24 2.38

16:00 2.65 -0.60 4.28 -2.99 -1.12 2.41

17:00 1.25 -2.78 3.14 -4.60 -0.62 3.78

18:00 1.97 -1.69 3.45 -3.40 -1.32 2.61

19:00 2.20 -1.44 3.57 -3.70 -0.40 3.83

20:00 2.17 -1.11 2.24 -3.28 0.40 3.35

21:00 1.92 -5.76 2.89 -5.34 -0.59 6.29

22:00 1.03 -2.54 1.53 -3.01 1.16 3.53

23:00 0.19 -3.42 0.65 -3.42 2.46 4.13

# of Neg. Coeff. 0 20 0 24 16 1

Sign. at 5% 0 8 0 20 6 0

227



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1


1.67 , and .67 for significance levels of 10%, 5%, and 1% respectively. The sample period for this analysis is 6/1/2006-4/11/2009.

228


The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 55 bi-weekly, out-of-sample dollar returns between two hedging strategies on the Cinergy hub. MGA portfolios utilize twenty bi-weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV estimates. MV hedge ratios are calculated using twenty bi-weekly spot and forward prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Unhedged-

Naïve Unhedged-

MV Unhedged-

MGA Naïve-

MV Naive-MGA

MV- MGA

0:00 0.87 -3.34 0.20 -4.19 -2.33 3.23

1:00 1.50 -2.71 2.46 -4.96 -0.10 4.42

2:00 1.42 -4.46 -0.21 -9.21 -3.76 6.33

3:00 1.05 -3.37 -1.31 -6.77 -5.88 2.01

4:00 2.52 -4.19 2.47 -6.58 0.81 6.64

5:00 2.67 -2.30 0.80 -5.46 -3.03 3.20

6:00 1.37 1.29 0.92 -0.56 -2.02 0.01

7:00 1.49 1.47 2.12 -0.65 1.02 1.40

8:00 4.17 1.85 3.69 -2.24 0.07 2.15

9:00 -0.48 0.07 2.77 0.60 2.19 1.73

10:00 0.47 -0.50 1.25 -1.38 1.72 2.12

11:00 1.84 -1.34 2.98 -2.58 -0.62 2.45

12:00 0.15 -1.67 1.05 -1.83 0.99 2.31

13:00 1.24 -1.39 2.46 -2.75 -0.17 2.86

14:00 2.11 -1.30 3.72 -2.92 -0.97 2.70

15:00 1.96 -0.47 3.88 -2.78 -0.46 2.66

16:00 2.84 -0.65 4.59 -3.16 -1.48 2.34

17:00 1.57 -2.51 3.29 -4.60 -1.06 3.36

18:00 2.35 -2.49 3.51 -4.23 -1.76 3.29

19:00 3.01 -1.26 4.49 -3.58 -1.81 2.84

20:00 2.50 -0.84 3.30 -3.26 -0.61 3.55

21:00 1.69 -6.81 3.04 -5.88 -0.80 7.22

22:00 0.72 -2.48 1.50 -2.72 1.26 3.58

23:00 -0.25 -3.87 0.49 -3.33 2.55 4.45

# of Neg. Coeff. 2 20 2 23 16 0

Sign. at 5% 0 11 0 19 5 0

229



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



230


The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 55 bi-weekly, out-of-sample dollar returns between two hedging strategies on the Michigan hub. MGA portfolios utilize twenty bi-weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV estimates. MV hedge ratios are calculated using twenty bi-weekly spot and forward prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Unhedged-

Naïve Unhedged-

MV Unhedged-

MGA Naïve-

MV Naive-MGA

MV- MGA

0:00 0.87 -3.34 0.20 -4.19 -2.33 3.23

1:00 1.50 -2.71 2.46 -4.96 -0.10 4.42

2:00 1.42 -4.46 -0.21 -9.21 -3.76 6.33

3:00 1.05 -3.37 -1.31 -6.77 -5.88 2.01

4:00 2.52 -4.19 2.47 -6.58 0.81 6.64

5:00 2.67 -2.30 0.80 -5.46 -3.03 3.20

6:00 1.37 1.29 0.92 -0.56 -2.02 0.01

7:00 1.49 1.47 2.12 -0.65 1.02 1.40

8:00 4.17 1.85 3.69 -2.24 0.07 2.15

9:00 -0.48 0.07 2.77 0.60 2.19 1.73

10:00 0.47 -0.50 1.25 -1.38 1.72 2.12

11:00 1.84 -1.34 2.98 -2.58 -0.62 2.45

12:00 0.15 -1.67 1.05 -1.83 0.99 2.31

13:00 1.24 -1.39 2.46 -2.75 -0.17 2.86

14:00 2.11 -1.30 3.72 -2.92 -0.97 2.70

15:00 1.96 -0.47 3.88 -2.78 -0.46 2.66

16:00 2.84 -0.65 4.59 -3.16 -1.48 2.34

17:00 1.57 -2.51 3.29 -4.60 -1.06 3.36

18:00 2.35 -2.49 3.51 -4.23 -1.76 3.29

19:00 3.01 -1.26 4.49 -3.58 -1.81 2.84

20:00 2.50 -0.84 3.30 -3.26 -0.61 3.55

21:00 1.69 -6.81 3.04 -5.88 -0.80 7.22

22:00 0.72 -2.48 1.50 -2.72 1.26 3.58

23:00 -0.25 -3.87 0.49 -3.33 2.55 4.45

# of Neg. Coeff. 2 20 2 23 16 0

Sign. at 5% 0 11 0 19 5 0

231



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



232


The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 55 bi-weekly, out-of-sample dollar returns between two hedging strategies on the Minnesota hub. MGA portfolios utilize twenty bi-weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV estimates. MV hedge ratios are calculated using twenty bi-weekly spot and forward prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Unhedged-

Naïve Unhedged-

MV Unhedged-

MGA Naïve-

MV Naive-MGA

MV- MGA

0:00 1.79 -1.40 4.60 -3.94 -1.25 2.01

1:00 2.33 0.90 1.72 -3.08 -1.62 2.68

2:00 2.50 -0.29 2.18 -2.82 0.08 3.21

3:00 3.48 0.28 2.72 -3.51 0.15 4.34

4:00 2.16 -0.38 0.84 -4.12 -1.15 2.61

5:00 1.79 -0.21 -0.40 -3.38 -3.28 -0.37

6:00 0.99 -0.06 1.95 -1.19 1.23 2.05

7:00 1.68 0.75 2.79 -1.88 0.96 3.15

8:00 2.77 1.21 3.34 -1.62 -0.06 1.72

9:00 0.56 -0.56 2.39 -1.09 1.48 2.47

10:00 1.20 -0.67 1.18 -2.43 -1.98 2.40

11:00 1.49 -1.49 3.12 -2.36 -0.55 2.48

12:00 0.10 -3.17 1.69 -2.40 0.01 3.21

13:00 1.20 -0.96 2.72 -2.05 -0.62 1.85

14:00 2.38 -0.72 3.19 -3.02 -1.69 1.91

15:00 4.10 -0.28 5.98 -4.38 -2.60 2.44

16:00 3.24 -0.51 5.59 -2.96 -2.47 1.37

17:00 3.33 -1.78 5.28 -4.82 -2.69 2.70

18:00 2.59 -2.23 4.71 -4.28 -2.11 3.06

19:00 3.17 -1.11 5.39 -4.59 -2.50 2.03

20:00 1.72 -0.64 3.24 -2.54 -0.52 2.54

21:00 2.19 -1.62 4.00 -4.20 -1.37 2.72

22:00 2.24 -0.25 3.97 -2.92 -1.24 1.70

23:00 2.06 -0.59 3.73 -2.60 -1.38 1.31

# of Neg. Coeff. 0 20 1 24 18 1

Sign. at 5% 0 2 0 20 6 0

233



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



234


The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 55 bi-weekly, out-of-sample dollar returns between two hedging strategies on the First Energy hub. MGA portfolios utilize twenty bi-weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV estimates. MV hedge ratios are calculated using twenty bi-weekly spot and forward prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Unhedged-

Naïve Unhedged-

MV Unhedged-

MGA Naïve-

MV Naive-MGA

MV- MGA

0:00 1.37 -1.41 0.64 -3.23 -1.87 2.31 1:00 0.82 -1.98 1.55 -3.20 0.09 3.01 2:00 -0.19 -3.31 -0.96 -3.71 -4.15 2.70 3:00 -0.83 -3.17 -2.32 -2.31 -5.81 0.35 4:00 2.16 -2.99 2.47 -4.74 -0.73 4.51 5:00 2.42 -2.19 1.42 -4.93 -2.05 4.17 6:00 1.26 0.68 1.01 -0.94 -1.44 0.65 7:00 1.57 1.47 1.45 -0.67 -1.50 0.49 8:00 4.38 1.85 3.54 -2.34 -0.23 2.07 9:00 -0.58 0.89 2.08 1.47 2.90 0.99

10:00 0.52 0.15 1.07 -0.58 1.99 1.30 11:00 0.94 -0.85 1.76 -1.51 0.89 1.95 12:00 -0.74 -1.86 0.62 -1.09 1.86 2.23 13:00 0.15 -1.86 1.48 -1.91 1.42 2.98 14:00 1.70 -0.76 3.05 -2.11 -0.11 2.26 15:00 0.80 -1.70 2.30 -2.71 1.16 3.58 16:00 2.24 -0.36 3.65 -2.30 -0.67 2.13 17:00 1.72 -1.78 3.21 -3.67 -0.92 3.06 18:00 2.26 -1.86 3.20 -3.90 -1.52 3.04 19:00 1.24 -0.86 2.66 -1.97 -0.32 1.92 20:00 2.83 -0.90 3.08 -4.97 -0.25 5.20 21:00 1.57 -6.04 2.54 -5.42 -0.22 6.68 22:00 1.58 -1.08 2.06 -2.90 0.83 3.48 23:00 0.11 -2.37 0.37 -2.45 2.34 2.75

# of Neg. Coeff. 4 19 2 23 15 0

Sign. at 5% 0 6 1 16 3 0

235



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



236


The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 30 tri-weekly, out-of-sample dollar returns between two hedging strategies on the Illinois hub. MGA portfolios utilize twenty tri-weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV estimates. MV hedge ratios are calculated using twenty tri-weekly spot and forward prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Unhedged-

Naïve Unhedged-

MV Unhedged-

MGA Naïve-

MV Naive-MGA

MV- MGA

0:00 2.15 -0.87 3.72 -3.10 -1.59 1.86

1:00 0.05 -1.34 0.20 -1.54 0.27 1.85

2:00 0.49 0.04 0.83 -0.56 -0.10 0.65

3:00 1.66 1.27 2.27 -0.70 0.93 1.14

4:00 0.78 -0.05 1.04 -0.62 -0.37 0.55

5:00 0.65 1.14 0.85 1.07 0.07 -0.99

6:00 1.90 -0.91 1.53 -3.29 -0.46 3.55

7:00 1.53 1.24 3.15 -1.02 -1.20 -0.36

8:00 1.92 1.69 2.03 0.01 -0.32 -0.07

9:00 1.03 0.74 3.77 -0.44 -0.48 -0.04

10:00 -0.25 -0.45 -2.23 -0.09 0.00 0.09

11:00 0.13 -0.12 2.21 -0.28 0.28 0.79

12:00 -0.92 -0.28 1.12 0.66 1.46 0.64

13:00 1.09 -1.21 2.83 -1.58 -0.14 2.47

14:00 0.87 -0.30 3.21 -0.95 -0.02 1.66

15:00 1.93 3.85 4.39 -0.47 -0.15 0.75

16:00 1.87 3.46 4.06 -0.82 -1.13 -0.50

17:00 1.82 0.97 3.77 -1.58 -1.03 1.42

18:00 0.50 -0.29 2.50 -0.66 -0.49 0.34

19:00 0.03 -1.31 -3.00 -0.81 -0.48 0.37

20:00 0.55 -2.99 -2.74 -2.71 -1.15 2.17

21:00 0.90 -3.08 -2.56 -2.81 -1.21 2.51

22:00 2.09 -0.74 4.52 -2.85 -2.06 0.78

23:00 0.49 -0.09 2.59 -0.55 -0.04 0.68

# of Neg. Coeff. 2 15 4 21 19 5

Sign. at 5% 0 2 4 5 1 0

237



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1


1.697 . 4 , and .7 for significance levels of 10%, 5%, and 1% respectively. The sample period for this analysis is 6/1/2006-4/11/2009.

238


The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 30 tri-weekly, out-of-sample dollar returns between two hedging strategies on the Cinergy hub. MGA portfolios utilize twenty tri-weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV estimates. MV hedge ratios are calculated using twenty tri-weekly spot and forward prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Unhedged-

Naïve Unhedged-

MV Unhedged-

MGA Naïve-

MV Naive-MGA

MV- MGA

0:00 -1.18 -1.74 0.66 -0.40 1.86 2.82

1:00 -2.88 -5.46 -1.80 -2.60 4.74 4.52

2:00 -1.24 -2.43 0.18 -1.21 2.57 3.89

3:00 -1.68 -3.88 -0.79 -2.52 3.44 3.68

4:00 1.75 1.54 3.33 -0.75 -0.11 0.67

5:00 1.09 1.77 1.87 1.23 0.18 -0.95

6:00 1.26 -1.81 0.57 -4.15 -1.43 3.81

7:00 0.35 1.05 1.51 0.77 0.40 -0.28

8:00 0.84 0.01 1.71 -2.30 0.43 1.62

9:00 -1.87 -0.91 1.39 2.11 2.20 1.24

10:00 -1.90 -0.74 0.45 2.46 2.70 1.52

11:00 -0.11 -0.13 1.88 0.03 0.95 1.45

12:00 -1.03 -0.36 0.61 0.77 1.93 0.59

13:00 1.16 2.90 2.70 -0.26 0.65 1.15

14:00 0.51 1.81 1.41 0.27 2.07 0.59

15:00 1.27 2.49 2.59 0.24 2.17 1.19

16:00 0.59 3.79 3.13 0.44 0.44 -0.18

17:00 0.63 1.24 3.04 -0.17 0.55 1.89

18:00 -0.61 0.23 -2.30 0.82 0.51 -0.45

19:00 -1.25 -0.82 -1.86 1.04 1.16 0.68

20:00 0.35 -1.80 -2.63 -1.64 -0.42 1.69

21:00 -1.12 -1.96 -1.05 0.32 0.92 1.45

22:00 0.71 0.97 2.78 0.01 0.44 0.69

23:00 -1.85 0.03 0.45 1.97 2.82 0.29

# of Neg. Coeff. 12 12 6 10 3 4

Sign. at 5% 1 3 2 4 0 0

239



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



240


The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 30 tri-weekly, out-of-sample dollar returns between two hedging strategies on the Michigan hub. MGA portfolios utilize twenty tri-weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV estimates. MV hedge ratios are calculated using twenty tri-weekly spot and forward prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Unhedged-

Naïve Unhedged-

MV Unhedged-

MGA Naïve-

MV Naive-MGA

MV- MGA

0:00 -1.41 -1.85 1.02 0.18 1.58 2.14

1:00 -1.25 -2.27 0.07 -1.21 2.65 3.29

2:00 -0.42 -0.92 1.25 -0.71 1.66 2.90

3:00 -2.00 -3.34 -0.28 -1.94 2.73 3.58

4:00 1.02 0.63 2.27 -0.80 0.00 0.96

5:00 0.86 0.13 1.44 -1.33 -0.23 1.26

6:00 0.78 -1.94 0.70 -3.77 -1.13 3.78

7:00 0.42 1.24 1.60 0.99 0.26 -0.71

8:00 0.34 -0.28 1.20 -1.75 0.94 1.84

9:00 -2.73 -1.06 -1.78 3.18 2.49 0.80

10:00 -2.02 -0.48 0.32 2.72 2.87 1.30

11:00 0.20 0.20 2.06 -0.10 0.44 0.93

12:00 -1.03 -0.31 0.89 0.74 1.53 0.58

13:00 1.26 -0.04 2.66 -1.18 0.13 1.89

14:00 0.89 2.42 2.13 0.11 1.05 0.65

15:00 1.24 2.88 3.22 0.06 1.08 1.21

16:00 1.38 3.63 3.72 -0.30 -0.59 -0.59

17:00 1.12 0.44 3.08 -1.01 -0.16 2.05

18:00 0.07 -0.16 2.05 -0.13 0.05 0.56

19:00 -0.32 -0.37 2.26 0.19 0.37 0.48

20:00 0.21 -1.60 -2.02 -1.23 -0.26 1.55

21:00 -1.40 -2.08 -0.74 0.80 1.29 2.02

22:00 0.72 0.92 3.06 -0.27 0.38 1.25

23:00 -2.10 0.26 0.75 2.49 2.70 0.16

# of Neg. Coeff. 10 14 4 14 5 2

Sign. at 5% 2 3 0 1 0 0

241



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



242


The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 30 tri-weekly, out-of-sample dollar returns between two hedging strategies on the Minnesota hub. MGA portfolios utilize twenty tri-weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV estimates. MV hedge ratios are calculated using twenty tri-weekly spot and forward prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Unhedged-

Naïve Unhedged-

MV Unhedged-

MGA Naïve-

MV Naive-MGA

MV- MGA

0:00 1.31 0.81 0.00 -0.76 -2.95 -1.10 1:00 1.20 -0.46 1.29 -1.80 -0.47 1.80 2:00 2.31 1.37 2.38 -0.22 -1.52 0.10 3:00 4.39 2.29 4.57 -0.30 -2.90 -0.02 4:00 2.42 0.97 2.72 -1.17 -1.73 0.55 5:00 1.92 1.68 2.35 -0.37 -1.14 -0.37 6:00 0.77 -1.31 -2.71 -1.37 -0.87 1.15 7:00 1.10 1.86 2.06 -0.02 -0.17 -0.21 8:00 3.03 1.77 3.68 -0.67 -2.13 -0.27 9:00 1.66 1.65 3.07 -0.62 -0.67 0.00

10:00 0.36 0.06 1.58 -0.59 0.25 0.60 11:00 1.13 -0.26 2.73 -1.32 -1.01 0.47 12:00 -0.65 -0.60 -0.88 0.17 -2.75 -0.45 13:00 1.17 0.35 2.50 -0.92 -0.27 1.09 14:00 2.99 1.30 4.00 -1.94 -1.00 1.70 15:00 2.10 0.43 1.68 -2.59 -1.71 1.97 16:00 2.10 1.55 3.79 -1.33 -1.07 0.60 17:00 1.82 1.12 3.05 -1.45 -0.99 0.61 18:00 1.36 0.45 2.62 -1.40 -0.87 1.15 19:00 1.72 0.32 1.74 -1.52 0.30 1.52 20:00 0.93 0.53 -0.05 -0.47 -1.97 -1.05 21:00 1.16 0.37 0.90 -1.06 -0.85 0.92 22:00 3.54 2.41 4.70 -0.58 -2.25 -0.91 23:00 2.07 1.30 2.48 -1.36 -0.10 1.03

# of Neg. Coeff. 1 4 3 23 22 9

Sign. at 5% 0 0 1 1 5 0

243



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



244


The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 30 tri-weekly, out-of-sample dollar returns between two hedging strategies on the First Energy hub. MGA portfolios utilize twenty tri-weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV estimates. MV hedge ratios are calculated using twenty tri-weekly spot and forward prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Unhedged-

Naïve Unhedged-

MV Unhedged-

MGA Naïve-

MV Naive-MGA

MV- MGA

0:00 1.31 0.81 0.00 -0.76 -2.95 -1.10 1:00 1.20 -0.46 1.29 -1.80 -0.47 1.80 2:00 2.31 1.37 2.38 -0.22 -1.52 0.10 3:00 4.39 2.29 4.57 -0.30 -2.90 -0.02 4:00 2.42 0.97 2.72 -1.17 -1.73 0.55 5:00 1.92 1.68 2.35 -0.37 -1.14 -0.37 6:00 0.77 -1.31 -2.71 -1.37 -0.87 1.15 7:00 1.10 1.86 2.06 -0.02 -0.17 -0.21 8:00 3.03 1.77 3.68 -0.67 -2.13 -0.27 9:00 1.66 1.65 3.07 -0.62 -0.67 0.00

10:00 0.36 0.06 1.58 -0.59 0.25 0.60 11:00 1.13 -0.26 2.73 -1.32 -1.01 0.47 12:00 -0.65 -0.60 -0.88 0.17 -2.75 -0.45 13:00 1.17 0.35 2.50 -0.92 -0.27 1.09 14:00 2.99 1.30 4.00 -1.94 -1.00 1.70 15:00 2.10 0.43 1.68 -2.59 -1.71 1.97 16:00 2.10 1.55 3.79 -1.33 -1.07 0.60 17:00 1.82 1.12 3.05 -1.45 -0.99 0.61 18:00 1.36 0.45 2.62 -1.40 -0.87 1.15 19:00 1.72 0.32 1.74 -1.52 0.30 1.52 20:00 0.93 0.53 -0.05 -0.47 -1.97 -1.05 21:00 1.16 0.37 0.90 -1.06 -0.85 0.92 22:00 3.54 2.41 4.70 -0.58 -2.25 -0.91 23:00 2.07 1.30 2.48 -1.36 -0.10 1.03

# of Neg. Coeff. 1 4 3 23 22 9

Sign. at 5% 0 0 1 1 5 0

245



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



246


The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 18 monthly, out-of-sample dollar returns between two hedging strategies on the Illinois hub. MGA portfolios utilize twenty monthly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV estimates. MV hedge ratios are calculated using twenty monthly spot and forward prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Unhedged-

Naïve Unhedged-

MV Unhedged-

MGA Naïve-

MV Naive-MGA

MV-MGA

0:00 1.20 0.81 -0.08 -2.73 -1.76 2.09

1:00 0.86 1.39 1.88 0.82 0.16 -1.36

2:00 1.04 0.84 0.84 0.29 -1.29 -0.48

3:00 0.94 1.16 0.95 0.99 1.81 -0.99

4:00 1.49 0.72 1.59 -3.05 -0.78 2.78

5:00 2.12 4.24 1.67 -1.29 -1.13 0.80

6:00 1.12 1.32 1.60 -1.58 1.21 2.44

7:00 0.05 0.06 -0.33 -1.23 -2.56 0.26

8:00 2.60 3.17 3.21 -0.18 -0.75 -0.87

9:00 1.25 1.20 1.15 -1.05 -4.94 0.91

10:00 1.03 0.99 -0.06 -0.64 -2.94 -0.80

11:00 1.59 1.85 1.99 -2.40 0.01 2.73

12:00 0.05 0.06 0.77 -1.33 0.42 1.83

13:00 1.08 1.14 2.82 -3.61 -0.83 2.57

14:00 2.51 2.72 2.93 -0.99 -0.93 0.66

15:00 2.57 2.88 3.02 -0.24 -0.33 0.03

16:00 5.10 3.02 5.28 1.55 -2.46 -1.70

17:00 0.73 0.66 1.34 -0.47 0.04 0.28

18:00 2.12 1.62 2.48 -1.94 -1.21 1.38

19:00 1.30 2.05 1.18 -1.07 -0.53 0.89

20:00 1.96 2.37 1.18 -1.22 -0.69 0.21

21:00 1.05 1.05 1.14 -3.18 0.19 3.28

22:00 1.21 1.07 1.40 -1.51 0.64 1.57

23:00 -0.20 -0.20 0.24 -1.32 2.12 2.20

# of Neg. Coeff. 1 1 3 20 15 6

Sign. at 5% 0 0 0 5 4 0

247



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1


1.7 4 .1 1, and .878 for significance levels of 10%, 5%, and 1% respectively. The sample period for this analysis is 6/1/2006-4/11/2009.

248


The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 18 monthly, out-of-sample dollar returns between two hedging strategies on the Cinergy hub. MGA portfolios utilize twenty monthly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV estimates. MV hedge ratios are calculated using twenty monthly spot and forward prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Unhedged-

Naïve Unhedged-

MV Unhedged-

MGA Naïve-

MV Naive-MGA

MV- MGA

0:00 0.63 0.43 -0.29 -2.33 -1.85 1.74

1:00 0.60 0.94 1.14 0.89 0.73 -0.79

2:00 0.78 0.62 0.44 0.30 -1.59 -0.66

3:00 0.06 0.06 0.01 2.16 -2.80 -2.23

4:00 1.13 0.51 1.29 -3.12 -0.58 2.70

5:00 1.58 2.48 1.29 -1.01 -1.51 0.67

6:00 0.22 0.21 -0.59 -3.27 -2.00 0.68

7:00 0.07 0.07 -0.27 -0.73 -2.33 -0.11

8:00 2.80 5.75 3.99 -1.81 -1.66 0.93

9:00 1.16 1.82 4.54 -0.91 0.48 2.36

10:00 0.81 1.05 1.33 -2.30 0.89 3.42

11:00 1.85 2.42 1.93 -1.92 -0.35 1.98

12:00 -0.02 -0.02 0.10 -0.86 0.90 1.03

13:00 1.30 0.96 1.09 -2.91 -0.42 2.89

14:00 3.18 2.33 2.84 -0.66 0.82 0.87

15:00 2.65 2.37 2.52 -1.30 0.21 1.43

16:00 5.94 2.91 5.83 0.37 2.96 -0.24

17:00 0.80 0.52 0.91 -1.84 0.35 1.78

18:00 2.53 1.18 2.54 -3.17 -1.63 3.14

19:00 2.65 3.20 3.04 -2.50 -1.55 2.28

20:00 2.05 2.40 1.98 -1.35 0.26 1.31

21:00 1.00 1.50 1.12 -3.20 0.15 3.72

22:00 0.62 0.77 1.29 -0.57 0.95 2.43

23:00 -0.54 -0.69 0.04 0.48 2.25 2.05

# of Neg. Coeff. 2 2 3 19 12 5

Sign. at 5% 0 0 0 8 2 1

249



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



250


The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 18 monthly, out-of-sample dollar returns between two hedging strategies on the Michigan hub. MGA portfolios utilize twenty monthly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV estimates. MV hedge ratios are calculated using twenty monthly spot and forward prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Unhedged-

Naïve Unhedged-

MV Unhedged-

MGA Naïve-

MV Naive-MGA

MV- MGA

0:00 0.58 0.40 -0.69 -2.68 -2.25 1.56

1:00 0.48 0.69 0.92 1.25 0.87 -1.20

2:00 0.39 0.32 0.20 -0.59 -1.96 0.40

3:00 -0.75 -0.72 -0.91 0.55 -3.12 -0.89

4:00 0.96 0.45 1.14 -3.76 -0.41 3.29

5:00 0.73 0.71 0.48 -1.05 -1.88 0.74

6:00 -0.03 -0.03 -0.59 -2.38 -2.12 0.88

7:00 0.52 0.53 0.04 -1.28 -1.77 0.32

8:00 2.85 5.91 3.49 -1.59 -1.09 1.60

9:00 0.43 0.42 1.40 -0.27 3.71 1.73

10:00 0.37 0.39 0.53 0.91 2.21 -0.57

11:00 0.80 0.81 0.96 -1.80 0.88 2.02

12:00 -0.26 -0.21 0.04 -1.52 1.08 1.80

13:00 0.88 0.78 0.84 -3.85 -1.04 3.81

14:00 2.50 2.46 2.41 -2.22 0.55 2.22

15:00 2.61 2.46 2.04 -2.82 -0.58 1.75

16:00 5.07 2.98 4.86 0.69 2.23 -0.42

17:00 0.60 0.43 0.60 -1.71 0.74 1.71

18:00 2.26 1.26 2.30 -2.78 -1.33 2.69

19:00 1.72 2.37 2.24 -1.45 -0.54 1.55

20:00 1.96 2.50 2.05 -0.74 -0.21 0.76

21:00 0.92 1.00 0.98 -3.49 0.34 3.64

22:00 0.73 0.99 1.93 -0.67 0.33 1.57

23:00 -0.51 -0.65 0.04 0.51 2.41 1.34

# of Neg. Coeff. 4 4 3 19 13 4

Sign. at 5% 0 0 0 8 3 0

251



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



252


The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 18 monthly, out-of-sample dollar returns between two hedging strategies on the Minnesota hub. MGA portfolios utilize twenty monthly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV estimates. MV hedge ratios are calculated using twenty monthly spot and forward prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Unhedged-

Naïve Unhedged-

MV Unhedged-

MGA Naïve-

MV Naive-MGA

MV- MGA

0:00 0.48 0.85 1.66 -0.78 0.58 2.13

1:00 1.11 1.01 0.34 -4.02 -2.32 3.88

2:00 1.05 0.94 0.24 -1.14 -1.68 -1.15

3:00 0.74 1.18 1.08 0.42 0.66 -0.19

4:00 0.74 0.85 0.84 -2.15 -0.04 2.42

5:00 0.46 0.82 0.60 0.39 1.06 -0.26

6:00 -0.63 -0.67 -0.46 -1.52 2.22 2.30

7:00 -0.42 -0.48 -0.59 -2.10 -2.36 1.11

8:00 1.37 2.62 1.81 0.19 -0.20 -0.60

9:00 0.46 0.77 1.28 0.22 0.58 0.99

10:00 0.97 1.01 1.44 -1.33 0.60 1.64

11:00 0.94 1.25 1.74 -0.01 -0.08 -0.04

12:00 0.24 0.60 -1.49 -0.05 -0.33 -0.77

13:00 0.33 0.49 1.83 0.40 0.02 -0.49

14:00 3.07 1.99 3.85 0.45 -1.87 -1.12

15:00 3.28 2.77 5.38 -0.14 -2.48 -1.73

16:00 3.27 2.69 4.54 0.88 -2.78 -2.87

17:00 1.44 1.12 2.39 -0.63 -1.11 -0.31

18:00 1.33 1.94 -2.66 0.06 -1.34 -2.06

19:00 1.26 2.38 2.00 -0.57 -0.55 0.44

20:00 1.37 2.62 3.24 -0.46 -1.16 -1.18

21:00 -0.16 -0.26 0.55 0.44 1.09 0.23

22:00 1.71 2.92 4.73 -1.69 -1.45 0.47

23:00 0.24 0.33 1.06 -0.14 1.57 1.06

# of Neg. Coeff. 3 3 4 15 15 13

Sign. at 5% 0 0 1 2 4 1

253



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



254


The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 18 monthly, out-of-sample dollar returns between two hedging strategies on the First Energy hub. MGA portfolios utilize twenty monthly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV estimates. MV hedge ratios are calculated using twenty monthly spot and forward prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Unhedged-

Naïve Unhedged-

]MV Unhedged-

MGA Naïve-

MV Naive-MGA

MV- MGA

0:00 0.75 0.52 -0.17 -1.84 -1.77 1.15

1:00 -0.63 -0.97 -0.23 1.05 1.35 -0.43

2:00 -0.22 -0.16 -0.55 0.56 -2.15 -1.08

3:00 -0.82 -0.84 -1.01 1.72 -3.18 -2.08

4:00 0.68 0.33 0.44 -2.55 -0.30 2.94

5:00 0.90 0.89 -0.04 -0.49 -1.94 -0.60

6:00 0.38 0.31 -0.55 -2.82 -1.87 0.83

7:00 -0.31 -0.31 -0.94 -1.15 -2.85 -0.31

8:00 2.52 5.27 3.41 -1.35 -1.11 1.16

9:00 0.76 1.21 3.95 0.82 0.84 0.07

10:00 0.57 0.67 1.03 0.17 1.52 1.04

11:00 0.68 1.23 1.14 -0.23 0.66 0.95

12:00 -0.33 -0.45 0.08 -0.09 1.03 0.87

13:00 0.68 0.66 1.12 -2.28 0.69 2.59

14:00 2.04 2.09 2.06 -1.68 -0.40 1.68

15:00 2.46 2.29 2.30 -1.60 -0.07 1.64

16:00 3.56 2.39 3.40 0.09 1.34 0.13

17:00 0.85 0.57 0.81 -1.45 -0.46 1.47

18:00 2.20 1.05 1.92 -3.08 0.96 3.53

19:00 0.53 0.98 1.13 -0.37 0.15 0.84

20:00 1.78 2.36 2.21 -0.59 -0.37 0.52

21:00 0.83 1.00 1.15 -2.98 0.20 3.60

22:00 0.76 0.95 0.71 -0.73 -1.52 0.60

23:00 0.05 0.06 0.07 0.64 1.54 -0.59

# of Neg. Coeff. 5 5 7 17 13 6

Sign. at 5% 0 0 0 5 3 0

255



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1


1.96 .1 1, and .878 for significance levels of 10%, 5%, and 1% respectively. The sample period for this analysis is 6/1/2006-4/11/2009.

256

Table A192 1 Week Hedging Effectiveness (Price Differences): Illinois Hub (Hedged vs. Unhedged Portfolios)

The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 128 weekly, out-of-sample dollar returns between hedged and unhedged portfolios on the Illinois hub. MGA portfolios utilize twenty weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV, ARDL, and GARCH estimates. Hedge ratios utilizing rolling estimation windows are calculated using twenty weekly spot and forward prices. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Unhedged-

Naïve Unhedged-

MV Unhedged-

ARDL Unhedged-

MGA Unhedged-

GARCH

0:00 -1.30 -1.93 -1.51 -1.99 -1.20 1:00 -0.44 -2.45 -1.06 0.35 -0.66 2:00 -2.18 -3.27 -3.10 -3.81 -2.29 3:00 -1.37 -3.01 -2.11 -0.03 -2.66 4:00 -1.62 -4.71 -3.96 -0.44 -3.19 5:00 -2.30 -5.30 -4.86 -5.83 -5.03 6:00 -0.14 -3.83 -2.36 -8.06 -1.75 7:00 -2.01 -1.71 -1.66 -4.16 -2.57

8:00 -0.12 -1.24 -0.98 -0.76 -1.67 9:00 -3.92 -2.19 -2.39 -4.51 -1.91

10:00 -1.36 -1.66 -1.02 0.63 -1.75 11:00 -3.90 -2.42 -2.38 -1.21 -3.16 12:00 -1.69 -1.72 -1.30 0.99 -1.19 13:00 -1.48 -2.27 -2.06 1.81 -1.28 14:00 -2.77 -3.35 -2.46 -0.67 -3.78 15:00 -3.28 -1.55 -1.74 -0.20 -2.04 16:00 -3.16 -2.37 -1.66 -0.88 -1.34 17:00 -3.33 -4.09 -5.59 -0.94 -3.56 18:00 -1.90 -2.81 -1.09 -3.55 -1.87 19:00 -2.84 -0.43 -1.43 0.47 -1.00

257

20:00 -3.95 -2.34 -4.37 -1.10 -1.93 21:00 -3.06 -3.58 -2.95 -1.82 -2.86 22:00 -3.04 -2.88 -1.94 -1.52 -3.48 23:00 -2.18 -2.00 -1.05 -0.65 -0.81

# of Neg. Coeff. 24 24 24 19 24 Sign. at 5% 14 17 12 7 11


.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1

s ]. . Critical values are 1.64 1.96, and . 76 for


258

Table A193 1 Week Hedging Effectiveness (Price Differences): Illinois Hub (Comparisons of Hedging Techniques)

The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 128 weekly, out-of-sample dollar returns between hedged portfolios on the Illinois hub. MGA portfolios utilize twenty weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV, ARDL, and GARCH estimates. Hedge ratios utilizing rolling estimation windows are calculated using twenty weekly spot and forward prices. These hedge ratios are updated weekly by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day- ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Naïve-

MV Naive-ARDL

Naive-MGA

Naive-GARCH

MV-ARDL

MV-MGA

MV-GARCH

ARDL-MGA

ARDL-GARCH

MGA-GARCH

0:00 0.01 0.08 -5.33 0.90 0.06 -1.03 0.94 -1.46 1.25 2.04 1:00 -2.57 -1.09 1.47 -0.42 2.80 3.03 3.80 1.58 1.18 -1.10 2:00 -1.88 -2.19 -6.37 -0.64 -0.13 -0.95 2.74 -1.08 2.34 2.55 3:00 -1.23 -1.15 3.04 -1.15 0.83 3.22 0.82 3.24 -0.27 -3.68 4:00 -3.97 -3.51 1.26 -2.25 3.57 4.48 4.20 3.62 3.01 -2.76 5:00 -2.55 -2.60 -8.16 -2.51 0.87 -3.08 0.27 -3.59 -0.41 3.23 6:00 -3.15 -3.01 -10.14 -1.47 1.71 -6.25 3.96 -8.00 1.14 7.87 7:00 0.94 1.05 -6.81 -0.23 -0.35 -3.90 -1.95 -4.76 -1.03 2.76 8:00 -1.07 -1.12 -3.17 -1.25 0.18 0.18 -0.53 0.14 -0.48 -0.40 9:00 2.57 3.36 -8.71 2.58 -0.49 -3.32 0.68 -4.27 0.69 3.31

10:00 0.30 1.07 2.28 0.04 1.58 2.35 -0.75 1.97 -1.94 -2.48 11:00 1.90 3.19 4.64 1.99 0.40 1.59 -0.63 2.12 -1.21 -2.50 12:00 0.52 1.05 2.01 0.89 0.53 1.82 1.17 1.62 0.21 -1.32 13:00 0.08 0.14 1.62 0.80 0.18 2.41 2.57 2.21 1.78 -1.46 14:00 0.68 1.47 2.56 0.06 0.98 3.16 -1.53 2.24 -1.64 -3.72 15:00 2.07 3.52 3.61 1.74 -0.21 1.40 -1.18 2.00 -0.38 -1.92 16:00 1.47 2.77 3.69 2.65 0.63 1.67 1.22 1.55 0.47 -0.98 17:00 0.48 0.74 2.34 0.57 0.37 3.84 0.29 3.86 -0.13 -3.07 18:00 -0.51 1.04 -0.75 0.17 2.68 -0.53 2.46 -1.94 -1.29 1.63 19:00 3.12 3.32 3.66 2.72 -1.79 0.82 -1.35 2.25 1.04 -1.45

259

20:00 2.45 1.33 4.23 2.59 -2.60 2.11 0.92 4.70 2.85 -1.68 21:00 1.56 1.74 4.67 1.32 -0.81 0.29 -0.54 1.54 0.42 -0.54 22:00 1.89 2.92 5.38 1.04 0.91 0.41 -2.45 -0.02 -2.55 -1.45 23:00 1.28 2.34 4.69 2.24 0.85 0.87 1.76 0.50 0.68 -0.03

# of Neg. Coeff.

8 7 8 8 7 7 9 8 11 17 Sign. at 5% 4 4 7 2 1 4 1 4 1 6


.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



260

Table A194 1 Week Hedging Effectiveness (Price Differences): Cinergy Hub (Hedged vs. Unhedged Portfolios)

The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 128 weekly, out-of-sample dollar returns between hedged and unhedged portfolios on the Cinergy hub. MGA portfolios utilize twenty weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV, ARDL, and GARCH estimates. Hedge ratios utilizing rolling estimation windows are calculated using twenty weekly spot and forward prices. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Unhedged-

Naïve Unhedged-

MV Unhedged-

ARDL Unhedged-

MGA Unhedged-

GARCH

0:00 -2.24 -2.23 -2.78 -2.32 -1.65 1:00 0.78 0.21 0.71 1.53 0.07 2:00 0.10 -0.64 -0.60 -1.97 -1.35 3:00 0.25 0.48 0.28 -0.39 0.06 4:00 3.08 -1.77 -0.78 4.02 1.35 5:00 3.51 0.70 1.28 1.07 1.40 6:00 1.89 -1.01 0.44 -3.73 -0.47 7:00 -2.15 -0.53 -0.49 -3.05 -1.32 8:00 -0.73 -1.91 -0.60 1.83 -1.58 9:00 -5.09 -2.85 -2.95 -0.31 -2.25

10:00 -1.99 -2.03 -0.95 -2.03 -1.59 11:00 -2.96 -2.96 -2.59 0.23 -2.74 12:00 -1.26 -1.21 -1.23 -3.17 -0.22 13:00 -0.56 -2.90 -2.35 -4.29 -0.32 14:00 -1.88 -3.45 -1.97 -2.10 -3.33 15:00 -1.34 -1.56 -1.10 -3.02 -1.65 16:00 -2.63 -2.22 -1.62 -0.35 -1.52 17:00 -1.70 -4.99 -3.99 -3.11 -5.16 18:00 -1.31 -2.77 -0.22 -2.96 -2.37 19:00 -1.69 -1.30 -1.31 -2.78 -0.44

261

20:00 -2.83 -2.33 -2.60 -1.97 -1.93 21:00 -2.95 -1.29 -0.95 -1.24 -1.61 22:00 -3.06 -2.25 -1.16 0.79 -2.44 23:00 -3.33 -2.92 -2.52 -0.34 -2.14



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



262

Table A195 1 Week Hedging Effectiveness (Price Differences): Cinergy Hub (Comparisons of Hedging Techniques) The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 128 weekly, out-of-sample dollar returns between hedged portfolios on the Cinergy hub. MGA portfolios utilize twenty weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV, ARDL, and GARCH estimates. Hedge ratios utilizing rolling estimation windows are calculated using twenty weekly spot and forward prices. These hedge ratios are updated week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day- ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Naïve-

MV Naive-ARDL

Naive-MGA

Naive-GARCH

MV-ARDL

MV- MGA

MV-GARCH

ARDL-MGA

ARDL-GARCH

MGA-GARCH

0:00 0.98 -0.36 -5.87 1.75 -1.82 -1.10 0.80 0.18 3.16 1.88 1:00 -0.95 -0.01 1.09 -1.02 1.73 1.35 -0.33 0.55 -1.40 -1.53 2:00 -1.31 -1.46 -5.91 -2.10 0.03 -2.48 -1.54 -2.92 -1.30 1.38 3:00 0.32 0.10 -3.08 -0.38 -0.35 -1.35 -1.22 -1.46 -0.51 0.74 4:00 -5.06 -4.57 -1.47 -2.02 5.04 3.97 5.47 3.23 4.25 -0.91 5:00 -2.67 -2.39 -1.25 -3.79 1.74 0.95 0.78 0.31 -0.43 -0.45 6:00 -2.61 -2.71 -5.96 -1.97 1.39 -3.45 1.74 -5.26 -0.76 3.65 7:00 1.98 2.79 -6.16 1.29 0.02 -3.02 -2.12 -3.91 -1.06 2.38 8:00 -0.61 0.39 1.21 -0.41 1.76 2.57 0.51 1.12 -1.10 -2.15 9:00 4.23 5.21 5.39 4.22 -1.30 2.47 0.05 3.40 1.26 -2.03

10:00 0.28 2.30 1.50 1.08 2.87 1.52 1.82 0.40 -2.36 -1.08 11:00 1.43 1.87 3.24 1.36 -0.38 2.92 -0.32 2.91 0.19 -2.78 12:00 0.58 0.78 0.02 1.11 -0.04 -0.75 1.34 -0.63 1.06 1.83 13:00 -1.19 -0.93 -0.90 0.49 1.35 -0.19 4.41 -0.48 3.06 1.99 14:00 -0.31 1.08 1.25 -0.63 2.64 2.26 -0.80 1.05 -2.56 -2.32 15:00 0.92 1.18 0.12 0.64 -0.23 -0.91 -0.57 -0.52 -0.18 0.53 16:00 1.46 2.59 3.64 2.25 0.09 1.27 0.37 2.21 0.57 -1.45 17:00 -0.64 -0.08 0.48 -1.20 2.49 2.63 -2.56 1.21 -3.80 -3.58 18:00 -0.79 1.20 0.11 -0.59 3.61 1.54 0.58 -1.33 -2.61 -1.23 19:00 0.85 1.13 1.31 1.90 0.25 0.90 1.82 0.87 1.80 0.06

263

20:00 1.52 1.46 1.76 1.87 -1.07 0.98 1.30 1.26 1.62 -0.59 21:00 1.91 2.34 2.15 1.26 0.36 0.66 -1.45 0.32 -1.24 -1.26 22:00 2.61 4.00 3.87 2.08 0.35 3.32 -1.44 2.24 -1.08 -3.05 23:00 2.23 2.92 4.73 2.66 -0.33 2.94 1.42 3.99 1.19 -2.19

# of Neg. Coeff. 10 8 8 10 8 8 10 8 14 15 Sign. at 5% 3 3 5 4 0 3 2 3 4 7


.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



264

Table A196 1 Week Hedging Effectiveness (Price Differences): Michigan Hub (Hedged vs. Unhedged Portfolios)

The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 128 weekly, out-of-sample dollar returns between hedged and unhedged portfolios on the Michigan hub. MGA portfolios utilize twenty weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV, ARDL, and GARCH estimates. Hedge ratios utilizing rolling estimation windows are calculated using twenty weekly spot and forward prices. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Unhedged-

Naïve Unhedged-

MV Unhedged-

ARDL Unhedged-

MGA Unhedged-

GARCH

0:00 -1.91 -1.76 -2.51 -2.39 -0.76 1:00 0.76 0.37 0.47 2.21 0.46 2:00 -0.06 -0.59 -0.40 -0.12 -1.93 3:00 -0.17 0.21 0.26 1.77 -1.15 4:00 2.98 -2.12 -1.15 4.41 -1.09 5:00 3.55 0.44 1.10 3.32 1.14 6:00 1.69 -0.24 0.32 0.13 0.15 7:00 -2.31 -0.90 -0.64 -0.14 -2.52 8:00 -1.17 -2.67 -0.88 1.39 -1.38 9:00 -5.56 -0.67 -2.06 -4.10 -1.29

10:00 -0.92 -2.37 -1.01 2.26 -0.68 11:00 -3.56 -2.68 -2.52 -0.81 -2.20 12:00 -1.57 -0.59 -0.97 1.35 0.22 13:00 -1.57 -3.85 -3.16 -2.00 -3.88 14:00 -2.60 -4.06 -2.55 -0.91 -3.12 15:00 -2.00 -3.09 -1.80 0.51 -4.70 16:00 -2.61 -2.30 -1.57 -1.14 -2.56 17:00 -2.25 -4.76 -4.14 0.93 -5.83 18:00 -0.88 -2.17 -0.89 -2.23 -1.16 19:00 -1.30 0.37 -0.05 -2.71 -0.14

265

20:00 -2.83 -2.22 -2.90 -0.91 -2.59 21:00 -3.43 -1.76 -1.55 -0.25 -2.16 22:00 -3.46 -1.35 -1.28 0.30 -1.91 23:00 -3.03 -2.44 -2.04 0.00 -1.00



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



266

Table A197 1 Week Hedging Effectiveness (Price Differences): Michigan Hub (Comparisons of Hedging Techniques)

The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 128 weekly, out-of-sample dollar returns between hedged portfolios on the Michigan hub. MGA portfolios utilize twenty weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV, ARDL, and GARCH estimates. Hedge ratios utilizing rolling estimation windows are calculated using twenty weekly spot and forward prices. These hedge ratios are updated weekly by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day- ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Naïve-

MV Naive-ARDL

Naive-MGA

Naive-GARCH

MV-ARDL

MV- MGA

MV-GARCH

ARDL-MGA

ARDL-GARCH

MGA-GARCH

0:00 0.87 -0.50 -5.71 2.12 -2.00 -1.63 1.79 -0.56 3.67 2.79 1:00 -0.99 -0.56 0.67 -0.69 0.48 1.35 0.18 0.93 -0.18 -1.26 2:00 -0.86 -0.91 -3.30 -2.79 0.45 0.75 -3.19 0.74 -2.81 -2.67 3:00 0.53 0.79 0.85 -1.36 0.22 0.42 -2.79 0.26 -2.55 -1.97 4:00 -5.34 -4.64 -2.03 -4.71 5.64 3.46 3.26 2.55 0.26 -2.55 5:00 -3.20 -3.03 1.05 -4.36 1.26 3.50 1.08 3.39 -0.32 -4.69 6:00 -1.77 -2.36 -1.87 -1.64 0.47 0.34 0.77 -0.21 -0.20 -0.05 7:00 1.80 2.80 3.19 0.61 0.15 0.76 -3.52 0.81 -2.16 -2.31 8:00 -0.60 0.68 1.64 0.35 1.92 3.12 2.00 1.35 -0.23 -1.93 9:00 5.14 6.21 9.36 4.99 -1.68 -3.60 -0.86 -4.41 1.07 3.41

10:00 -1.97 0.26 0.98 0.60 4.48 2.45 4.01 1.08 0.45 -0.74 11:00 1.89 2.99 4.26 1.69 0.05 2.06 -0.32 2.88 -0.30 -1.86 12:00 1.20 1.45 1.79 1.74 -0.41 0.77 1.54 1.28 1.43 0.06 13:00 -0.66 -0.33 1.18 -0.63 1.48 3.20 0.37 2.46 -0.89 -3.05 14:00 0.41 1.65 2.54 1.17 1.86 3.96 1.47 2.46 -0.31 -3.02 15:00 0.31 1.50 2.66 -0.96 1.05 3.48 -2.10 2.75 -2.90 -5.40 16:00 1.26 2.28 4.04 1.20 1.00 1.07 -0.66 0.83 -1.83 -1.70 17:00 0.22 0.54 2.28 -0.53 0.97 4.78 -2.56 4.19 -3.21 -5.81 18:00 -0.59 0.45 0.33 0.09 1.98 1.48 1.68 0.01 -0.44 -0.43 19:00 1.90 2.08 1.08 1.60 -0.76 -0.62 -1.12 -0.22 -0.19 0.13

267

20:00 1.64 1.52 2.41 1.43 -1.16 1.82 -1.16 2.28 0.66 -2.14 21:00 2.20 2.61 3.37 1.37 0.28 1.77 -1.76 1.53 -1.75 -2.17 22:00 3.41 4.40 4.58 2.90 -0.68 1.84 -1.01 2.53 -0.08 -2.07 23:00 2.09 2.66 4.49 2.95 -0.25 2.79 2.57 3.20 2.14 -1.19



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



268

Table A198 1 Week Hedging Effectiveness (Price Differences): Minnesota Hub (Hedged vs. Unhedged Portfolios)

The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 128 weekly, out-of-sample dollar returns between hedged and unhedged portfolios on the Minnesota hub. MGA portfolios utilize twenty weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV, ARDL, and GARCH estimates. Hedge ratios utilizing rolling estimation windows are calculated using twenty weekly spot and forward prices. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Unhedged-

Naïve Unhedged-

MV Unhedged-

ARDL Unhedged-

MGA Unhedged-

GARCH

0:00 -2.31 -2.81 -1.70 -1.02 -2.80 1:00 0.83 -1.08 -1.11 0.15 0.52 2:00 0.12 -0.56 -0.90 -1.12 -0.87 3:00 2.00 0.25 0.15 2.70 -0.06 4:00 1.36 -1.07 -0.71 -3.50 -0.92 5:00 0.94 -0.67 -0.42 -3.75 0.41 6:00 -0.97 -1.55 -1.19 -2.37 -1.59 7:00 -1.30 -1.96 -0.39 -1.23 -1.27 8:00 1.58 1.44 1.65 3.77 1.78 9:00 0.71 1.18 0.17 3.17 -0.29

10:00 -0.58 0.38 0.24 1.52 0.73 11:00 -3.30 -0.66 -2.48 -0.21 -1.48 12:00 -1.10 -1.08 -0.14 -2.01 -1.24 13:00 -1.57 -1.21 -0.88 -2.53 0.23 14:00 -1.56 -1.65 -1.49 -2.26 -0.95 15:00 -0.73 -2.66 -1.40 -3.68 -1.83 16:00 -1.48 -2.01 -1.61 -2.46 -1.53 17:00 -1.34 -1.66 -0.40 -4.08 -1.32 18:00 -2.53 -3.04 -1.55 -2.47 -2.55 19:00 -0.85 -1.54 -0.91 1.61 -0.71

269

20:00 -0.96 -2.02 -0.96 -2.12 -1.16 21:00 0.45 1.10 0.97 -3.40 1.02 22:00 -0.33 0.75 0.92 -3.65 1.35 23:00 -0.29 -1.90 -0.14 -3.63 0.62



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



270

Table A199 1 Week Hedging Effectiveness (Price Differences): Minnesota Hub (Comparisons of Hedging Techniques)

The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 128 weekly, out-of-sample dollar returns between hedged portfolios on the Minnesota hub. MGA portfolios utilize twenty weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV, ARDL, and GARCH estimates. Hedge ratios utilizing rolling estimation windows are calculated using twenty weekly spot and forward prices. These hedge ratios are updated weekly by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day- ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Naïve-

MV Naive-ARDL

Naive-MGA

Naive-GARCH

MV- ARDL

MV- MGA

MV-GARCH

ARDL-MGA

ARDL-GARCH

MGA-GARCH

0:00 -0.50 1.36 1.26 -0.39 2.27 2.64 0.57 0.60 -2.30 -2.41 1:00 -2.46 -3.00 -1.96 -0.62 -0.17 1.58 2.02 2.24 3.39 0.45 2:00 -1.12 -1.93 -2.91 -1.58 -0.82 -1.13 -0.32 -0.70 0.25 0.77 3:00 -2.64 -2.85 -0.98 -3.06 -0.20 1.57 -0.67 1.53 -0.44 -2.16 4:00 -3.74 -3.16 -1.77 -3.62 0.64 0.43 0.33 0.17 -0.28 -0.30 5:00 -1.71 -1.66 -1.75 -0.45 0.48 -0.34 3.38 -0.49 1.92 1.28 6:00 -0.37 -0.13 -4.58 -0.20 0.41 -1.97 0.29 -2.63 -0.17 1.94 7:00 -0.29 1.54 4.43 0.27 2.40 0.38 1.25 -1.42 -1.03 0.18 8:00 -0.36 0.11 -0.99 0.14 0.66 -0.69 1.41 -1.04 0.11 1.11 9:00 0.27 -1.00 -0.35 -1.06 -1.41 -0.73 -2.05 0.28 -0.48 -1.26

10:00 1.48 2.04 1.67 1.83 -0.22 0.56 0.88 0.71 0.91 -0.08 11:00 2.93 3.28 3.14 3.18 -1.65 0.62 -0.93 2.29 1.83 -1.36 12:00 0.47 1.62 -0.03 0.35 0.83 -0.60 -0.36 -0.93 -0.94 0.46 13:00 1.06 1.65 0.40 1.63 -0.02 -0.66 2.63 -0.47 1.29 1.73 14:00 0.47 0.80 0.09 1.22 -0.10 -0.42 1.08 -0.25 1.40 0.85 15:00 -0.66 -0.31 -0.59 -0.08 0.98 -0.31 2.03 -0.62 0.29 0.96 16:00 0.42 0.54 -0.05 0.82 -0.10 -0.43 1.11 -0.30 0.81 0.87 17:00 0.68 1.88 -1.27 0.83 1.18 -2.29 0.42 -2.47 -1.02 2.30 18:00 1.05 2.00 0.69 1.25 0.96 -0.12 0.40 -0.52 -0.74 0.25 19:00 0.03 0.16 0.89 0.58 0.12 1.63 1.17 0.96 0.60 -0.78 20:00 0.08 0.56 0.58 0.43 0.85 1.19 0.81 0.35 0.07 -0.43

271

21:00 0.15 0.13 -0.66 0.05 -0.13 -1.50 -0.31 -1.29 -0.12 1.44 22:00 0.75 1.30 0.12 1.02 0.65 -1.11 0.92 -1.16 -0.05 1.70 23:00 -1.15 0.21 -0.51 1.18 2.14 0.91 1.98 -0.73 0.68 1.56



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



272

Table A200 1 Week Hedging Effectiveness (Price Differences): First Energy Hub (Hedged vs. Unhedged Portfolios)

The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 128 weekly, out-of-sample dollar returns between hedged and unhedged portfolios on the First Energy hub. MGA portfolios utilize twenty weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV, ARDL, and GARCH estimates. Hedge ratios utilizing rolling estimation windows are calculated using twenty weekly spot and forward prices. These hedge ratios are updated every week by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Unhedged-

Naïve Unhedged-

MV Unhedged-

ARDL Unhedged-

MGA Unhedged-

GARCH

0:00 -1.90 -1.77 -2.54 -2.59 -1.49 1:00 0.74 0.55 0.26 1.51 -0.58 2:00 -1.08 -1.29 -0.88 -1.63 -1.91 3:00 -1.30 -0.76 -0.46 -0.47 -0.67 4:00 1.80 0.58 -0.69 2.46 0.53 5:00 2.59 -0.17 0.67 0.42 1.02 6:00 1.14 -1.38 0.00 -3.63 -1.72 7:00 -1.57 -0.16 0.07 -2.23 -0.77 8:00 0.21 -1.75 -0.25 2.61 -1.40 9:00 -5.94 -2.40 -3.78 -1.71 -1.65

10:00 -2.20 -2.26 -1.09 0.91 -2.09 11:00 -4.02 -2.46 -3.72 -1.79 -3.07 12:00 -2.48 -1.49 -2.31 0.74 -0.47 13:00 -1.41 -4.37 -3.09 1.35 -3.79 14:00 -3.25 -2.43 -2.31 -1.39 -2.59 15:00 -2.98 -2.79 -2.30 -0.32 -3.40 16:00 -3.06 -3.24 -1.76 -1.60 -3.55 17:00 -2.50 -3.48 -2.19 -1.08 -3.59 18:00 -2.59 -1.22 -0.18 -0.67 -0.46 19:00 -4.22 -0.51 -2.47 -0.82 -0.98

273

20:00 -3.48 -3.39 -3.85 -0.45 -2.64 21:00 -3.09 -0.09 0.07 -0.93 -0.85 22:00 -2.42 -1.46 -0.34 -0.38 -1.73 23:00 -2.73 -2.26 -2.20 -0.42 -1.49



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



274

Table A201 1 Week Hedging Effectiveness (Price Differences): First Energy Hub (Comparisons of Hedging Techniques) The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 128 weekly, out-of-sample dollar returns between hedged portfolios on the First Energy hub. MGA portfolios utilize twenty weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV, ARDL, and GARCH estimates. Hedge ratios utilizing rolling estimation windows are calculated using twenty weekly spot and forward prices. These hedge ratios are updated weekly by dropping the oldest spot and forward price in the estimation window and replacing them with the current weekly day- ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Naïve-

MV Naive-ARDL

Naive-MGA

Naive-GARCH

MV- ARDL

MV- MGA

MV-GARCH

ARDL-MGA

ARDL-GARCH

MGA-GARCH

0:00 0.97 -0.41 -6.22 1.36 -2.14 -2.02 0.87 -1.23 2.21 2.24 1:00 -0.33 -0.99 1.02 -1.88 -1.10 0.90 -2.50 1.53 -1.71 -2.10 2:00 0.04 0.59 -5.11 -0.87 0.81 -1.07 -2.07 -1.83 -2.08 0.10 3:00 1.09 1.74 3.34 1.30 0.24 0.22 0.10 0.06 -0.15 -0.18 4:00 -1.14 -3.07 0.09 -1.27 -3.63 1.03 -0.24 2.75 2.85 -1.24 5:00 -3.34 -2.61 -2.17 -3.34 2.83 0.90 1.89 -0.14 0.22 0.23 6:00 -2.28 -1.97 -5.95 -2.35 1.09 -3.14 -0.87 -4.94 -1.22 2.82 7:00 1.54 2.36 -5.60 1.06 0.37 -2.28 -1.47 -3.17 -1.14 1.81 8:00 -1.68 -0.85 0.51 -1.54 2.12 3.02 0.14 1.18 -1.61 -2.39 9:00 4.93 5.94 6.98 4.72 -1.86 0.67 0.82 4.80 1.75 -0.27

10:00 0.37 2.26 2.50 0.31 2.95 2.49 -0.24 1.37 -2.77 -2.32 11:00 2.29 2.17 5.46 1.96 -1.28 0.65 -1.66 2.28 0.48 -1.27 12:00 1.56 1.13 2.67 2.21 -1.41 1.55 1.28 2.48 2.46 -0.58 13:00 -0.50 -1.15 1.68 -0.86 -0.79 5.01 -0.79 3.57 0.26 -4.38 14:00 2.37 3.07 5.36 1.97 -0.43 0.77 -0.52 1.79 -0.08 -1.00 15:00 2.33 2.64 4.06 2.11 -0.98 3.21 -0.53 3.51 0.60 -3.51 16:00 1.24 2.79 4.52 1.46 0.95 0.81 -0.01 -0.09 -1.15 -1.05 17:00 0.83 1.75 2.26 0.12 1.99 3.23 -1.93 1.81 -2.55 -3.49 18:00 1.08 2.32 1.99 1.53 1.83 1.08 1.20 -0.10 -0.43 -0.28 19:00 3.98 3.76 4.68 3.96 -2.03 0.27 -0.47 2.64 1.94 -0.75

275

20:00 1.80 1.67 4.00 2.15 -1.23 3.13 0.89 4.32 1.83 -2.58 21:00 2.56 3.12 4.51 1.67 0.27 -0.44 -1.84 -0.69 -1.27 -0.32 22:00 2.16 3.65 5.34 1.87 1.16 0.62 -0.95 -0.27 -1.33 -0.81 23:00 1.99 2.24 4.70 2.46 -0.92 1.47 1.02 3.50 1.59 -0.94



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



276


The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 54 bi-weekly, out-of-sample dollar returns between hedged and unhedged portfolios on the Illinois hub. MGA portfolios utilize twenty bi-weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV, ARDL, and GARCH estimates. Hedge ratios utilizing rolling estimation windows are calculated using twenty bi-weekly spot and forward prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Unhedged-

Naïve Unhedged-

MV Unhedged-

ARDL Unhedged-

MGA Unhedged-

GARCH

0:00 0.86 0.00 -0.15 -0.77 0.06 1:00 1.38 -0.79 -0.03 2.03 -0.22 2:00 1.17 -0.54 -0.11 -0.56 0.36 3:00 0.63 -0.29 0.16 -1.67 0.04 4:00 2.16 -0.84 -0.32 2.00 0.91 5:00 1.47 0.19 1.36 -1.38 1.77 6:00 -0.34 -2.00 -1.79 -4.07 -1.57 7:00 1.01 1.10 0.86 0.86 1.27 8:00 1.90 0.26 1.16 -0.26 0.83 9:00 -0.67 -1.42 -0.58 -1.65 -1.93

10:00 0.12 -0.22 -0.10 -1.00 0.97 11:00 -0.28 -0.46 -0.19 -0.51 -0.01 12:00 -0.25 -0.44 -0.30 -0.87 -0.01 13:00 -1.49 -1.18 -1.29 -2.44 -1.41 14:00 0.44 -0.21 -0.85 -1.25 -0.69 15:00 -0.75 -1.16 -1.78 -2.34 -0.28 16:00 0.43 -0.50 -0.88 -0.40 -2.14 17:00 -0.85 -1.74 -2.72 0.46 -1.83 18:00 0.81 1.02 0.71 1.72 0.86 19:00 0.55 0.99 0.04 1.90 1.49

277

20:00 0.77 0.81 0.96 0.64 0.09 21:00 -0.51 -0.70 -0.53 -0.93 -0.87 22:00 -0.81 -0.89 -0.61 -0.55 0.10 23:00 -0.93 -0.88 -1.09 -2.12 -1.07



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1

s ]. . Critical values are 1.67 , and .67 for


278

Table A203 2 Week Hedging Effectiveness (Price Differences): Illinois Hub (Comparisons of Hedging Techniques) The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 54 bi-weekly, out-of-sample dollar returns between hedged portfolios on the Illinois hub. MGA portfolios utilize twenty bi-weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV, ARDL, and GARCH estimates. Hedge ratios utilizing rolling estimation windows are calculated using twenty bi-weekly spot and forward prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day- ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Naïve-

MV Naive-ARDL

Naive-MGA

Naive-GARCH

MV-ARDL

MV-MGA

MV-GARCH

ARDL-MGA

ARDL-GARCH

MGA- GARCH

0:00 -1.33 -2.04 -3.23 -1.37 -0.42 -1.12 0.70 -1.10 0.65 1.17 1:00 -4.16 -3.27 -0.12 -3.18 3.23 3.23 5.70 2.70 -0.70 -2.87 2:00 -3.38 -3.07 -2.88 -1.37 1.46 -0.30 5.96 -0.95 0.75 1.10 3:00 -1.80 -1.35 -4.65 -1.05 1.93 -2.19 2.93 -3.00 -0.35 2.35 4:00 -3.23 -2.75 0.58 -2.22 2.95 3.50 10.15 3.01 2.07 -2.56 5:00 -2.09 -0.51 -3.68 0.00 3.37 -2.03 5.54 -3.01 0.47 2.94 6:00 -2.84 -2.92 -6.24 -3.24 1.55 -3.68 6.88 -4.12 0.23 4.62 7:00 -0.08 -0.70 -1.03 -0.28 -1.05 -0.11 -1.70 0.41 0.20 -0.13 8:00 -3.03 -1.93 -2.65 -2.40 4.00 -0.56 3.96 -1.29 -1.20 0.79 9:00 -0.35 0.50 -5.06 -0.86 2.02 -0.99 -6.97 -1.95 -2.44 0.49

10:00 -0.56 -0.59 -3.08 0.90 0.23 -1.35 7.47 -1.85 1.37 2.08 11:00 0.08 0.21 -2.28 0.58 0.21 -0.43 3.34 -0.61 0.31 0.96 12:00 -0.09 0.03 -2.10 0.29 0.26 -0.77 8.55 -1.03 0.57 1.01 13:00 0.71 0.30 -3.96 0.39 -0.82 -2.02 -8.05 -2.21 0.29 1.89 14:00 -1.86 -1.94 -3.05 -1.96 -1.45 -1.88 -9.40 -1.03 0.52 1.29 15:00 -0.23 -1.78 -4.71 0.98 -2.61 -2.38 12.69 -1.58 2.74 2.96 16:00 -2.06 -2.37 -2.44 -4.27 -1.48 -0.12 -29.79 0.69 -3.27 -2.64 17:00 -0.85 -3.29 1.57 -0.65 -3.57 2.98 -1.51 3.61 2.76 -2.46 18:00 -0.13 -0.32 -0.21 -0.14 -0.18 -0.08 -0.06 0.04 0.16 0.06 19:00 0.18 -1.16 0.54 0.54 -1.62 0.58 7.92 1.41 1.80 0.10

279

20:00 -0.30 0.07 -2.11 -1.38 0.85 0.08 -12.23 -0.32 -2.85 -1.09 21:00 0.09 0.25 -3.13 -0.04 0.21 -0.70 -2.44 -0.98 -0.40 0.59 22:00 0.42 0.63 2.93 1.03 0.00 -0.03 9.30 -0.04 1.08 0.73 23:00 0.56 0.19 -5.00 0.44 -1.15 -2.24 0.14 -2.31 0.57 1.88



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



280


The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 54 bi-weekly, out-of-sample dollar returns between hedged and unhedged portfolios on the Cinergy hub. MGA portfolios utilize twenty bi-weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV, ARDL, and GARCH estimates. Hedge ratios utilizing rolling estimation windows are calculated using twenty bi-weekly spot and forward prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Unhedged-

Naïve Unhedged-

MV Unhedged-

ARDL Unhedged-

MGA Unhedged-

GARCH

0:00 0.38 0.19 -0.35 -0.89 -0.07 1:00 0.76 -1.86 -1.11 1.53 -2.36 2:00 0.61 -1.92 -1.31 -2.04 -0.71 3:00 -0.11 -1.34 -1.17 -3.19 -1.13 4:00 1.63 -1.35 -1.22 1.38 1.48 5:00 0.51 -0.96 0.32 -2.93 0.42 6:00 -0.39 -1.45 -1.43 -1.95 -1.55 7:00 1.02 1.42 0.98 1.21 2.09 8:00 2.39 1.00 1.74 2.20 2.09 9:00 -0.99 -0.87 0.59 -2.57 -1.77

10:00 0.78 1.19 1.38 1.39 0.58 11:00 0.46 1.00 0.89 1.16 0.94 12:00 -0.24 -0.24 0.37 0.11 -0.13 13:00 -0.71 -0.89 -0.06 -0.22 -1.98 14:00 -0.47 -0.26 0.17 -1.35 -1.42 15:00 -0.45 -0.01 -0.21 -0.60 -0.43 16:00 -0.15 0.05 0.25 0.13 0.63 17:00 -1.52 -1.24 -1.87 -0.61 -1.49 18:00 1.18 0.72 1.03 1.81 0.84 19:00 1.17 1.77 1.69 2.70 2.12

281

20:00 0.47 1.53 1.33 1.33 1.60 21:00 -0.73 -0.39 -0.69 -0.41 -0.27 22:00 -0.84 -0.60 -0.48 -0.57 -0.09 23:00 -1.29 -0.91 -1.04 -1.62 -0.53



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



282

Table A205 2 Week Hedging Effectiveness (Price Differences): Cinergy Hub (Comparisons of Hedging Techniques)

The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 54 bi-weekly, out-of-sample dollar returns between hedged portfolios on the Cinergy hub. MGA portfolios utilize twenty bi-weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV, ARDL, and GARCH estimates. Hedge ratios utilizing rolling estimation windows are calculated using twenty bi-weekly spot and forward prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day- ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Naïve-

MV Naive-ARDL

Naive-MGA

Naive-GARCH

MV- ARDL

MV- MGA

MV-GARCH

ARDL-MGA

ARDL-GARCH

MGA-GARCH

0:00 -0.37 -1.31 -3.18 -0.73 -1.46 -1.40 -2.93 -1.07 0.76 1.21 1:00 -4.39 -3.54 0.49 -4.95 4.76 4.47 -7.49 3.78 -5.57 -5.22 2:00 -4.98 -4.73 -5.17 -2.16 1.66 -0.83 7.22 -1.79 1.26 2.12 3:00 -2.42 -3.03 -7.02 -1.46 0.57 -3.20 1.21 -3.82 0.20 3.04 4:00 -3.28 -3.08 0.11 0.31 0.49 3.54 13.44 3.36 3.84 0.26 5:00 -2.19 -0.47 -6.05 -0.28 4.14 -2.86 5.03 -4.14 0.20 4.01 6:00 -2.11 -2.56 -4.44 -3.47 0.72 -1.33 0.60 -1.74 -0.59 1.67 7:00 0.09 -0.59 0.90 0.23 -1.11 0.19 1.29 1.00 0.75 0.10 8:00 -2.80 -1.94 -0.50 -1.76 2.78 2.49 7.60 1.67 -0.03 -1.49 9:00 0.70 1.75 0.94 0.24 1.57 0.76 -4.86 -0.65 -1.95 -1.67

10:00 0.03 0.84 0.73 -0.69 1.06 0.84 -5.91 -0.30 -2.34 -1.66 11:00 0.03 0.17 0.74 0.20 0.37 0.70 1.69 0.45 0.02 -0.56 12:00 0.14 0.97 1.35 0.22 0.89 0.32 1.62 -0.49 -0.91 -0.28 13:00 0.19 1.20 1.54 -0.41 0.63 0.45 -10.07 -0.21 -1.99 -1.66 14:00 0.44 1.02 -2.86 -0.73 0.56 -1.59 -18.30 -2.28 -1.77 1.00 15:00 0.59 0.44 -2.56 0.34 -0.43 -0.77 -4.47 -0.71 -0.08 0.56 16:00 0.30 0.80 1.73 0.96 0.44 0.13 10.54 -0.30 0.24 0.62 17:00 0.98 -1.09 2.24 0.70 -1.88 1.04 -5.31 2.38 1.59 -1.20 18:00 -1.04 -0.13 -0.58 -0.85 1.35 0.57 1.40 -0.33 -0.88 -0.50 19:00 -0.07 0.30 -0.83 0.16 0.63 -1.18 4.96 -1.31 -0.03 1.46

283

20:00 0.64 1.03 1.49 0.43 0.29 0.23 -2.23 0.07 -0.53 -0.45 21:00 0.72 0.49 2.64 0.80 -0.86 -0.26 2.35 0.15 0.90 0.38 22:00 0.72 0.90 3.06 0.95 -0.17 -0.34 4.50 -0.35 0.69 0.63 23:00 1.18 1.12 -4.54 1.43 -0.92 -1.65 3.57 -1.69 1.35 1.82



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



284


The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 54 bi-weekly, out-of-sample dollar returns between hedged and unhedged portfolios on the Michigan hub. MGA portfolios utilize twenty bi-weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV, ARDL, and GARCH estimates. Hedge ratios utilizing rolling estimation windows are calculated using twenty bi-weekly spot and forward prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Unhedged-

Naïve Unhedged-

MV Unhedged-

ARDL Unhedged-

MGA Unhedged-

GARCH

0:00 -0.08 -0.21 -0.56 -1.54 0.30 1:00 0.74 -1.60 -0.93 1.34 -2.12 2:00 0.43 -1.65 -1.28 -0.79 -0.51 3:00 -0.63 -1.67 -1.26 -0.96 -2.33 4:00 1.51 -1.82 -1.52 1.93 0.93 5:00 0.76 -0.05 0.58 0.38 0.08 6:00 -0.54 -2.03 -1.35 -0.81 -1.31 7:00 0.59 1.18 0.44 0.24 1.18 8:00 2.34 1.35 1.87 2.13 2.57 9:00 -1.72 -1.53 -0.64 -0.83 -1.27

10:00 0.14 0.73 0.70 0.81 0.08 11:00 -0.35 0.34 0.29 0.89 -0.05 12:00 -0.72 -0.85 -0.41 -0.47 -0.40 13:00 -1.48 -1.01 -1.24 -1.92 -0.85 14:00 -1.03 -0.67 -1.00 -1.64 -0.88 15:00 -1.21 -1.02 -1.62 -1.39 -1.79 16:00 -0.55 -0.44 -0.93 -0.98 -0.04 17:00 -1.92 -1.40 -2.22 -1.36 -1.80 18:00 0.65 0.54 0.15 1.40 0.72 19:00 0.19 1.12 0.67 1.48 1.16

285

20:00 -0.41 0.85 0.53 0.42 0.79 21:00 -1.18 -0.55 -0.39 -1.39 -0.43 22:00 -1.64 -0.81 -1.43 -1.18 -0.57 23:00 -1.45 -1.02 -1.01 -1.70 -0.70



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



286


The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 54 bi-weekly, out-of-sample dollar returns between hedged portfolios on the Michigan hub. MGA portfolios utilize twenty bi-weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV, ARDL, and GARCH estimates. Hedge ratios utilizing rolling estimation windows are calculated using twenty bi-weekly spot and forward prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day- ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Naïve-

MV Naive-ARDL

Naive-MGA

Naive-GARCH

MV- ARDL

MV- MGA

MV-GARCH

ARDL-MGA

ARDL-GARCH

MGA-GARCH

0:00 -0.08 -0.64 -3.53 0.45 -0.86 -1.77 4.72 -1.76 1.93 2.23 1:00 -4.04 -2.98 0.39 -4.70 3.79 3.74 -7.70 2.93 -5.67 -4.50 2:00 -5.22 -4.03 -3.68 -1.94 0.80 1.38 6.67 0.94 1.71 0.77 3:00 -2.27 -1.38 -3.16 -4.04 1.31 1.16 -8.63 0.11 -2.77 -2.88 4:00 -3.60 -3.18 -0.75 -0.63 2.58 2.98 15.24 2.62 3.57 -0.07 5:00 -1.94 -0.65 -1.49 -1.45 1.03 1.28 1.37 -0.05 -1.00 -0.70 6:00 -1.93 -2.20 -2.26 -2.63 1.31 1.33 6.60 0.97 -0.02 -1.18 7:00 0.62 -0.41 -1.53 0.60 -0.91 -0.96 0.01 -0.33 0.87 0.93 8:00 -2.49 -1.69 -0.71 -1.43 2.39 2.12 4.94 1.38 -0.29 -1.18 9:00 1.20 2.05 4.25 1.22 0.99 -0.07 0.52 -0.77 -0.75 0.10

10:00 0.52 0.80 1.54 -0.16 0.23 0.61 -10.03 0.74 -1.54 -1.62 11:00 0.62 0.79 1.44 0.49 0.09 1.01 -4.24 1.10 -0.70 -1.96 12:00 0.45 0.80 2.16 0.75 0.31 -0.07 6.02 -0.31 0.27 0.38 13:00 1.11 0.75 -3.77 1.21 -0.96 -1.65 -0.44 -1.69 1.11 1.78 14:00 1.05 0.03 -3.60 0.91 -1.07 -1.88 -2.01 -1.37 0.81 1.76 15:00 0.93 -0.90 -3.70 -0.16 -1.76 -1.20 -15.49 0.44 0.75 0.21 16:00 0.40 -0.96 -3.20 0.84 -1.38 -1.17 8.95 -0.14 1.61 1.42 17:00 1.35 -0.95 3.28 0.85 -2.42 -0.06 -11.79 2.45 1.77 -0.37 18:00 -0.52 -1.07 0.00 -0.30 -0.57 0.62 4.83 0.71 0.67 -0.44 19:00 0.61 0.57 0.93 0.65 -0.56 0.42 2.32 0.79 0.63 -0.18

287

20:00 1.42 1.69 2.87 1.08 -0.44 -0.34 -2.82 -0.14 -0.06 0.04 21:00 1.23 1.44 -4.00 1.27 0.31 -1.49 2.60 -1.71 0.02 1.52 22:00 1.74 1.02 4.16 1.73 -1.98 -1.11 1.77 0.01 1.94 1.13 23:00 1.28 1.39 -4.78 1.42 -0.36 -1.64 3.12 -1.78 1.04 1.73



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



288


The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 54 bi-weekly, out-of-sample dollar returns between hedged and unhedged portfolios on the Minnesota hub. MGA portfolios utilize twenty bi-weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV, ARDL, and GARCH estimates. Hedge ratios utilizing rolling estimation windows are calculated using twenty bi-weekly spot and forward prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Unhedged-

Naïve Unhedged-

MV Unhedged-

ARDL Unhedged-

MGA Unhedged-

GARCH

0:00 1.37 -0.34 0.55 -4.42 1.22 1:00 0.67 -1.20 -0.63 -0.04 -0.75 2:00 1.81 0.15 0.15 1.32 -0.03 3:00 2.05 -0.35 -0.02 1.15 -0.21 4:00 2.00 -0.11 -0.01 1.54 -0.18 5:00 1.10 -0.63 -0.31 0.95 -1.93 6:00 1.57 0.08 0.27 0.60 0.00 7:00 2.10 2.22 1.73 2.01 2.46 8:00 1.62 -0.32 0.26 2.26 0.85 9:00 1.66 1.04 1.41 3.65 0.74

10:00 2.13 1.30 1.62 2.23 1.01 11:00 0.60 0.94 1.09 2.27 1.13 12:00 -1.79 -0.92 -1.41 -0.77 -1.29 13:00 -0.46 0.40 0.29 0.66 0.73 14:00 -0.29 0.10 -0.18 0.29 0.45 15:00 1.44 2.50 1.46 3.08 2.92 16:00 0.61 1.18 1.29 2.29 0.98 17:00 1.62 2.66 1.91 2.98 2.15 18:00 1.55 2.43 2.28 2.88 2.28 19:00 1.99 1.55 1.75 3.57 2.19

289

20:00 -1.59 -0.93 -0.96 0.06 -1.35 21:00 0.62 0.28 0.34 1.83 0.10 22:00 0.82 0.20 0.77 2.02 0.74 23:00 2.27 -0.16 1.21 3.16 0.64



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



290


The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 54 bi-weekly, out-of-sample dollar returns between hedged portfolios on the Minnesota hub. MGA portfolios utilize twenty bi-weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV, ARDL, and GARCH estimates. Hedge ratios utilizing rolling estimation windows are calculated using twenty bi-weekly spot and forward prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day- ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Naïve-

MV Naive-ARDL

Naive-MGA

Naive-GARCH

MV-ARDL

MV-MGA

MV-GARCH

ARDL-MGA

ARDL-GARCH

MGA-GARCH

0:00 -2.63 -1.33 -1.96 -0.74 2.29 -0.61 11.87 -1.28 0.66 2.06 1:00 -3.79 -3.05 -2.49 -2.46 4.17 1.87 4.60 1.08 -0.19 -0.92 2:00 -3.02 -2.62 -0.41 -3.56 0.02 3.51 -2.87 3.32 -0.57 -4.33 3:00 -4.56 -3.01 -0.53 -4.21 1.04 3.52 1.85 3.45 -0.34 -2.79 4:00 -2.55 -2.33 0.28 -2.75 0.65 3.40 -0.53 3.37 -0.32 -2.96 5:00 -2.74 -3.31 -0.83 -3.83 1.16 2.62 -13.03 3.15 -3.18 -3.81 6:00 -2.04 -2.28 -1.31 -2.22 0.58 0.91 -1.01 0.71 -0.82 -1.04 7:00 -0.67 -1.46 -0.36 -1.19 -1.02 0.60 -4.00 1.34 -0.28 -1.09 8:00 -2.18 -1.85 -0.14 -0.86 2.12 2.14 18.78 1.67 2.05 -0.77 9:00 -1.20 -1.11 -1.10 -1.34 0.56 0.03 -5.28 -0.25 -0.98 -0.34

10:00 -1.46 -1.57 -0.18 -1.83 0.61 1.42 -7.45 1.57 -1.53 -1.84 11:00 0.20 0.52 -0.32 0.41 0.77 -0.61 8.02 -0.82 -0.07 0.82 12:00 0.86 1.05 2.02 0.61 -0.45 0.72 -9.71 1.39 -0.09 -1.06 13:00 0.75 1.29 0.77 1.17 -0.13 -0.20 4.39 -0.12 0.69 0.61 14:00 0.38 0.19 0.70 0.89 -0.52 0.02 5.90 0.44 1.44 0.40 15:00 0.46 -0.33 -1.05 0.67 -1.15 -2.01 4.69 -0.98 1.56 2.44

16:00 0.11 0.64 -0.41 0.03 1.01 -0.85 -2.33 -1.08 -1.34 0.67 17:00 0.33 0.08 -1.27 -0.60 -0.41 -2.32 -12.37 -1.50 -0.80 1.60

291

18:00 0.47 0.37 -1.20 0.59 -0.51 -1.94 1.04 -1.82 0.74 1.87 19:00 -0.73 -0.22 -1.75 0.17 1.91 -1.17 15.19 -1.44 0.92 1.87 20:00 1.39 1.70 2.13 1.08 -0.54 1.21 -11.60 1.43 -0.19 -1.74 21:00 -0.89 -0.86 0.08 -1.05 0.44 1.16 -4.67 0.70 -0.78 -1.49 22:00 -1.20 0.03 -0.35 -0.52 1.37 0.80 8.57 -0.32 -0.60 -0.04 23:00 -2.37 -0.62 -1.75 -2.23 4.74 0.95 9.50 -0.54 -2.32 -0.37



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



292


The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 54 bi-weekly, out-of-sample dollar returns between hedged and unhedged portfolios on the First Energy hub. MGA portfolios utilize twenty bi-weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV, ARDL, and GARCH estimates. Hedge ratios utilizing rolling estimation windows are calculated using twenty bi-weekly spot and forward prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Unhedged-

Naïve Unhedged-

MV Unhedged-

ARDL Unhedged-

MGA Unhedged-

GARCH

0:00 1.42 1.07 0.93 0.76 1.34 1:00 1.57 -0.29 0.51 2.22 -0.37 2:00 -0.25 -1.29 -0.90 -1.45 -1.48 3:00 -1.08 -1.13 -1.09 -2.51 -0.91 4:00 2.48 -1.02 0.08 0.06 -0.71 5:00 1.29 -0.18 0.46 -0.98 -0.61 6:00 -0.40 -1.40 -1.34 -3.57 -1.27 7:00 0.53 1.39 0.37 0.19 1.26 8:00 2.77 1.26 2.03 2.20 1.39 9:00 -1.29 -1.52 0.16 1.80 -1.59

10:00 0.96 1.24 1.39 1.60 1.32 11:00 -0.44 -0.01 0.58 0.12 0.46 12:00 -0.96 -0.72 -0.64 -0.78 0.00 13:00 -1.84 -1.50 -1.85 -1.70 -1.87 14:00 -1.31 -1.55 -1.19 -2.18 -1.48 15:00 -2.49 -1.42 -1.34 -3.36 -2.52 16:00 -1.44 -0.35 0.42 -1.99 -1.94 17:00 -1.51 -1.42 -1.02 -1.17 -1.77 18:00 0.92 -0.28 0.43 1.57 0.03 19:00 0.03 0.12 0.62 1.34 -0.13

293

20:00 0.60 1.55 1.24 1.86 1.76 21:00 -1.46 -0.81 -1.47 -1.44 -0.49 22:00 -0.16 0.12 0.15 0.35 -0.36 23:00 -1.23 -0.81 -0.83 -1.30 -1.09



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



294

Table A211 2 Week Hedging Effectiveness (Price Differences): First Energy Hub (Comparisons of Hedging Techniques)

The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 54 bi-weekly, out-of-sample dollar returns between hedged portfolios on the First Energy hub. MGA portfolios utilize twenty bi-weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV, ARDL, and GARCH estimates. Hedge ratios utilizing rolling estimation windows are calculated using twenty bi-weekly spot and forward prices. These hedge ratios are updated every two weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current bi-weekly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Naïve-

MV Naive-ARDL

Naive-MGA

Naive-GARCH

MV- ARDL

MV- MGA

MV-GARCH

ARDL-MGA

ARDL-GARCH

MGA-GARCH

0:00 -1.14 -1.52 -1.49 -0.84 -0.04 0.12 1.20 0.17 0.27 0.01 1:00 -2.41 -2.07 -0.65 -2.75 1.87 1.64 -1.83 1.17 -2.39 -1.88 2:00 -1.45 -1.23 -4.08 -1.23 0.71 -0.88 -0.05 -1.38 -0.46 0.76 3:00 0.42 0.36 -5.24 0.55 -0.31 -2.53 1.00 -2.76 0.63 2.71 4:00 -3.07 -2.08 -0.91 -2.71 4.97 0.87 3.32 0.00 -1.63 -0.58 5:00 -2.58 -1.73 -3.96 -3.12 2.53 -1.35 -5.15 -2.15 -3.23 0.79 6:00 -1.50 -1.90 -5.66 -1.85 0.38 -3.44 2.92 -3.99 0.22 4.11 7:00 0.72 -0.63 -1.73 0.11 -1.30 -1.02 -3.33 -0.26 0.36 0.42 8:00 -2.70 -1.85 -0.74 -2.52 2.79 1.96 -1.27 1.20 -1.69 -1.86 9:00 0.89 2.15 1.83 0.69 1.09 2.62 -3.07 0.64 -1.14 -2.22

10:00 -0.38 0.38 0.73 -0.21 1.11 1.43 2.12 0.55 -0.70 -0.89 11:00 0.49 1.08 2.05 0.83 1.06 0.14 4.96 -0.43 -0.44 0.20 12:00 0.77 0.94 2.72 1.30 -0.16 -0.49 12.08 -0.58 1.34 1.08 13:00 0.96 0.72 3.53 0.85 -0.98 -0.76 -4.95 -0.19 0.78 0.63 14:00 0.49 0.57 -3.80 0.43 -0.30 -1.63 -0.08 -2.39 0.24 1.49 15:00 1.70 2.56 -5.51 1.60 -0.33 -2.79 -6.31 -3.89 -0.36 2.77 16:00 1.00 2.32 -3.71 0.59 0.90 -1.59 -9.63 -2.93 -2.23 1.38 17:00 0.98 1.49 2.83 0.35 0.14 -0.31 -15.40 -0.61 -0.79 -0.38 18:00 -2.26 -0.84 -0.40 -0.97 1.57 1.89 3.83 0.30 -0.50 -1.18 19:00 0.03 0.79 0.36 -0.11 0.63 0.46 -4.03 -0.25 -0.67 -0.56

295

20:00 0.53 0.61 1.01 0.26 -0.14 1.02 -1.56 1.03 -0.22 -0.95 21:00 1.34 0.88 3.71 1.45 -1.50 -1.31 5.04 -0.84 1.60 1.42 22:00 0.30 0.65 2.17 -0.07 0.15 0.45 -4.15 0.56 -0.66 -0.78 23:00 1.19 1.39 -4.01 1.00 -0.48 -1.29 -1.72 -1.51 -0.09 1.10



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



296


The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 29 tri-weekly, out-of-sample dollar returns between hedged and unhedged portfolios on the Illinois hub. MGA portfolios utilize twenty tri-weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV, ARDL, and GARCH estimates. Hedge ratios utilizing rolling estimation windows are calculated using twenty tri-weekly spot and forward prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Unhedged-

Naïve Unhedged-

MV Unhedged-

ARDL Unhedged-

MGA Unhedged-

GARCH

0:00 2.62 2.42 2.73 4.66 2.62 1:00 -0.84 -1.99 -2.26 -0.80 -1.94 2:00 -0.32 -2.11 -1.59 -0.30 -1.34 3:00 1.34 1.19 1.72 1.80 1.14 4:00 -0.04 -0.21 -0.19 0.16 0.00 5:00 -0.17 -0.10 -0.18 -0.14 -0.51 6:00 1.32 -0.26 0.33 0.15 0.35 7:00 1.58 1.59 1.80 1.53 0.96 8:00 1.74 1.65 1.64 1.84 1.57 9:00 2.17 -1.39 0.67 -5.02 -1.34

10:00 0.01 -2.05 -0.06 -1.99 -2.64 11:00 -1.40 -2.43 -0.66 -1.33 -2.70 12:00 -0.77 -2.45 -1.91 -2.08 -2.10 13:00 0.55 -3.61 0.08 -3.84 -3.32 14:00 -2.29 -1.61 -1.19 -0.16 -1.48 15:00 -0.89 -1.28 1.05 2.04 -1.34 16:00 -1.61 -1.11 1.38 -1.52 -0.74 17:00 -1.69 -2.27 -0.97 0.56 -0.97 18:00 -0.61 -0.40 1.16 1.05 -0.52

297

19:00 -1.72 -1.28 -0.64 -1.55 -1.40 20:00 -1.98 -1.35 -1.39 -1.65 -1.22 21:00 -0.29 -1.85 -1.70 -1.46 -0.78 22:00 1.80 0.55 1.21 -4.74 0.83 23:00 0.82 -0.18 2.32 -4.02 1.26



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1

s ]. . Critical values are 1.699 . 4 , and .7 6 for


298


The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 29 tri-weekly, out-of-sample dollar returns between hedged portfolios on the Illinois hub. MGA portfolios utilize twenty tri-weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV, ARDL, and GARCH estimates. Hedge ratios utilizing rolling estimation windows are calculated using twenty tri-weekly spot and forward prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Naïve-

MV Naive-ARDL

Naive-MGA

Naive-GARCH

MV-ARDL

MV- MGA

MV-GARCH

ARDL-MGA

ARDL-GARCH

MGA- GARCH

0:00 -1.73 -1.49 -2.42 -1.55 2.49 -2.04 0.24 -2.42 -1.04 2.21 1:00 -1.01 -0.39 1.20 -0.90 1.51 1.10 0.81 0.53 -0.45 -1.09 2:00 -1.07 -0.57 0.28 -0.39 1.61 2.16 2.35 1.49 0.18 -1.33 3:00 -0.61 1.04 0.76 -0.48 1.07 0.81 -0.22 -0.18 -0.90 -0.73 4:00 -0.16 -0.69 0.34 0.07 -0.13 0.81 0.25 0.68 0.41 -0.26 5:00 0.29 0.00 0.81 -0.89 -0.28 -0.17 -0.79 0.29 -0.84 -0.91 6:00 -1.59 -0.95 -1.27 -0.92 2.68 1.10 2.42 -0.44 0.10 0.47 7:00 -1.15 -1.17 0.15 -2.02 -0.98 1.05 -1.64 1.09 -0.56 -1.90 8:00 -0.82 -0.06 -0.72 -1.17 0.75 0.63 -1.68 -0.37 -1.08 -1.09 9:00 -3.14 -2.36 -2.68 -3.30 5.21 -0.18 0.13 -1.90 -5.86 0.21

10:00 -0.67 -0.04 -0.59 -0.57 2.71 -0.19 0.17 -1.14 -1.62 0.39 11:00 0.84 1.40 1.08 0.59 0.93 1.44 -1.15 0.00 -1.26 -2.10 12:00 -0.46 -0.01 0.02 -0.36 3.31 2.26 0.60 0.18 -1.84 -1.35 13:00 -1.95 -0.53 -1.70 -1.94 4.07 1.34 0.11 -3.45 -3.85 -0.93 14:00 1.87 2.02 2.82 1.63 0.44 0.55 -0.93 0.48 -0.86 -0.70 15:00 0.62 1.16 1.68 0.51 2.68 2.06 -0.82 1.21 -2.68 -2.13 16:00 0.79 1.79 0.99 0.98 2.42 0.55 2.20 -3.13 -1.89 0.26 17:00 0.95 1.59 1.77 1.24 1.01 2.09 1.32 1.17 -0.22 -0.99 18:00 0.51 0.97 0.81 0.38 1.06 0.73 -0.53 -0.90 -0.89 -0.69 19:00 1.44 1.94 1.00 1.18 -0.04 -0.66 -0.62 -0.34 -0.24 0.33

299

20:00 0.76 0.95 0.31 0.88 -0.03 -1.51 1.17 -0.53 0.23 1.77 21:00 -0.32 -0.30 -0.24 -0.13 0.32 0.22 0.79 0.02 0.41 0.35 22:00 -1.90 -1.59 -2.28 -1.93 3.66 -1.59 0.90 -2.11 -0.41 1.64 23:00 -0.87 -0.21 -1.33 -0.50 3.22 -1.61 2.87 -3.24 -1.84 2.86



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



300


The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 29 tri-weekly, out-of-sample dollar returns between hedged and unhedged portfolios on the Cinergy hub. MGA portfolios utilize twenty tri-weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV, ARDL, and GARCH estimates. Hedge ratios utilizing rolling estimation windows are calculated using twenty tri-weekly spot and forward prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Unhedged-

Naïve Unhedged-

MV Unhedged-

ARDL Unhedged-

MGA Unhedged-

GARCH

0:00 -0.98 -0.37 -0.66 2.00 0.06 1:00 -2.90 -3.53 -3.14 -1.78 -2.68 2:00 -1.29 -1.27 -1.38 0.64 -1.05 3:00 -2.04 -2.56 -1.77 -0.52 -2.53 4:00 1.87 2.08 2.54 3.38 2.22 5:00 0.50 0.40 0.85 0.79 0.07 6:00 0.55 -1.32 -0.60 -0.72 0.38 7:00 -0.77 -1.00 -0.40 -0.18 -0.04 8:00 0.59 -0.11 0.41 1.57 -0.21 9:00 -1.51 -1.30 -0.63 -2.74 -2.27

10:00 -1.41 -1.28 -0.29 -1.81 -0.76 11:00 -1.16 -2.63 -0.29 -2.45 -2.23 12:00 -0.85 -2.63 -1.95 -1.56 -2.17 13:00 0.69 -4.06 2.68 -5.12 -1.85 14:00 -2.28 -2.89 -0.55 -1.13 -3.34 15:00 -1.26 -2.47 0.73 2.36 -0.76 16:00 -2.23 -2.19 -0.23 -2.61 -2.29 17:00 -2.33 -3.31 -1.51 -2.47 -4.70

301

18:00 -1.37 0.06 0.53 1.41 -1.04 19:00 -2.44 -1.63 -0.92 -1.52 -2.54 20:00 -1.45 -2.66 -1.49 -2.60 -2.69 21:00 -3.47 -3.94 -3.33 0.41 -1.59 22:00 0.21 0.99 1.19 3.11 0.30 23:00 -1.67 0.73 2.53 2.15 2.14



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



302

Table A215 3 Week Hedging Effectiveness (Price Differences): Cinergy Hub (Comparisons of Hedging Techniques)

The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 29 tri-weekly, out-of-sample dollar returns between hedged portfolios on the Cinergy hub. MGA portfolios utilize twenty tri-weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV, ARDL, and GARCH estimates. Hedge ratios utilizing rolling estimation windows are calculated using twenty tri-weekly spot and forward prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Naïve-

MV Naive-ARDL

Naive-MGA

Naive-GARCH

MV-ARDL

MV-MGA

MV-GARCH

ARDL-MGA

ARDL-GARCH

MGA- GARCH

0:00 1.29 1.02 1.26 1.57 -2.09 0.83 2.55 1.10 2.47 -0.40 1:00 -0.28 0.97 4.84 1.45 4.18 5.17 3.01 3.22 1.15 -1.47 2:00 0.91 0.76 2.10 1.15 -0.68 3.41 1.36 3.55 1.78 -4.18 3:00 0.06 1.49 3.51 -0.30 4.08 4.69 -0.80 2.94 -3.25 -4.27 4:00 -0.48 -0.31 -0.59 -0.82 -0.07 -0.59 -0.91 -0.91 -1.76 -0.15 5:00 -0.50 0.61 1.32 -1.36 1.63 1.46 -2.11 0.15 -3.67 -2.67 6:00 -3.28 -2.40 -2.57 -0.40 4.65 1.40 2.96 -0.47 1.98 1.67 7:00 0.36 1.14 1.93 1.64 3.54 2.22 1.84 0.79 0.81 0.39 8:00 -3.23 -1.92 0.46 -3.13 2.62 1.83 -0.54 0.90 -2.39 -1.98 9:00 1.14 1.75 0.59 -0.35 2.49 -0.25 -2.50 -0.63 -3.74 -0.92

10:00 1.16 1.85 0.75 1.13 3.75 0.09 0.68 -0.59 -0.13 1.09 11:00 0.76 1.39 0.55 -0.95 0.82 -0.40 -1.84 -0.67 -3.18 -1.33 12:00 -0.41 0.20 0.67 -0.08 3.31 2.76 2.73 1.94 -2.25 -2.20 13:00 -2.07 0.27 -2.18 -1.26 4.03 -0.52 3.87 -4.20 -2.99 2.79 14:00 1.60 2.32 2.24 0.69 1.72 2.96 -3.20 0.41 -2.74 -3.39 15:00 0.38 1.48 2.46 0.98 5.08 2.83 2.73 1.38 -2.33 -2.06 16:00 0.51 1.86 0.92 0.40 5.48 1.20 -1.54 -3.94 -5.62 -1.38 17:00 0.40 1.68 1.07 -0.80 3.28 2.50 -6.84 -1.14 -5.28 -4.68 18:00 1.50 1.90 1.47 1.07 0.83 0.41 -0.73 -0.39 -0.82 -1.15 19:00 2.14 2.90 1.85 1.51 -0.28 -0.03 -1.57 0.16 -0.43 -1.39

303

20:00 0.36 0.69 0.02 0.39 0.32 -1.03 -0.05 -0.66 -0.60 0.60 21:00 2.58 2.93 2.73 2.58 -0.85 1.95 1.86 1.79 1.51 -1.83 22:00 0.56 0.87 0.37 0.03 1.83 -0.06 -1.47 -0.40 -2.05 -0.53 23:00 1.92 2.27 1.78 2.34 1.26 -0.35 1.97 -2.28 -0.08 2.03



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



304


The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 29 tri-weekly, out-of-sample dollar returns between hedged and unhedged portfolios on the Michigan hub. MGA portfolios utilize twenty tri-weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV, ARDL, and GARCH estimates. Hedge ratios utilizing rolling estimation windows are calculated using twenty tri-weekly spot and forward prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Unhedged-

Naïve Unhedged-

MV Unhedged-

ARDL Unhedged-

MGA Unhedged-

GARCH

0:00 -1.32 -0.84 -0.94 -2.16 -0.59 1:00 -1.25 -1.57 -0.85 0.37 -1.13 2:00 -0.54 -0.31 -0.35 1.64 0.10 3:00 -2.33 -2.49 -1.64 -0.49 -2.51 4:00 1.20 1.22 1.59 2.47 1.38 5:00 0.74 0.21 0.76 0.66 0.08 6:00 0.09 -1.34 -0.84 0.20 0.52 7:00 -0.35 -0.22 0.15 0.45 0.15 8:00 0.45 -0.04 0.52 1.58 -0.08 9:00 -2.43 -1.58 -0.87 -2.58 -3.13

10:00 -1.51 -1.28 -0.16 -1.95 -1.26 11:00 -0.72 -2.90 -0.49 -1.81 -2.81 12:00 -0.83 -2.38 -1.91 -1.47 -2.15 13:00 0.60 -4.65 1.66 -4.60 -3.98 14:00 -2.13 -2.20 -0.92 -1.14 -2.04 15:00 -1.32 -3.89 -2.37 2.60 -3.78 16:00 -1.80 -0.85 1.59 -1.48 -0.93 17:00 -2.27 -1.98 -1.18 0.28 -3.18

305

18:00 -0.95 -0.48 1.13 0.69 -1.27 19:00 -1.86 -0.76 -0.47 -0.99 -0.80 20:00 -2.09 -1.52 -1.52 -1.04 -1.70 21:00 -3.91 -0.54 -2.97 0.89 -0.12 22:00 0.11 1.54 1.58 2.78 2.17 23:00 -1.98 -0.04 1.93 -2.35 0.85



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



306


The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 29 tri-weekly, out-of-sample dollar returns between hedged portfolios on the Michigan hub. MGA portfolios utilize twenty tri-weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV, ARDL, and GARCH estimates. Hedge ratios utilizing rolling estimation windows are calculated using twenty tri-weekly spot and forward prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Naïve-

MV Naive-ARDL

Naive-MGA

Naive-GARCH

MV-ARDL

MV-MGA

MV-GARCH

ARDL-MGA

ARDL-GARCH

MGA- GARCH

0:00 1.29 1.25 1.14 1.44 -1.13 0.53 1.94 0.65 1.57 -0.26 1:00 -0.57 1.49 2.33 0.69 3.47 3.20 1.57 2.70 -0.84 -2.43 2:00 0.74 0.67 1.06 0.96 -0.18 1.08 1.08 1.13 1.24 -0.95 3:00 0.31 2.37 2.98 0.37 4.03 3.26 0.34 2.33 -3.98 -3.29 4:00 -0.66 -0.22 -0.54 -0.67 0.12 -0.46 -0.56 -0.77 -1.07 0.12 5:00 -1.01 -0.32 -0.55 -1.29 0.82 1.07 -1.55 -0.02 -1.07 -1.38 6:00 -2.94 -2.19 1.57 1.12 3.73 2.92 3.16 2.22 2.47 0.89 7:00 0.44 0.95 1.32 1.10 2.45 3.64 1.18 3.08 0.09 -0.95 8:00 -1.77 0.04 0.50 -1.50 2.23 1.68 -0.22 0.64 -2.08 -1.99 9:00 2.12 2.70 1.43 -0.03 1.17 -0.32 -3.64 -0.53 -5.06 -1.62

10:00 1.33 1.92 0.62 1.28 3.98 -0.36 0.69 -1.01 -0.82 0.88 11:00 0.29 0.70 0.65 -0.09 0.90 2.32 -1.52 0.33 -1.51 -2.57 12:00 -0.26 0.16 0.64 -0.05 2.93 2.51 1.84 1.92 -1.75 -2.21 13:00 -2.66 -0.21 -2.26 -2.43 4.56 1.72 1.42 -3.95 -4.23 -0.50 14:00 1.39 2.03 1.81 1.17 1.30 2.40 -1.48 0.06 -1.43 -2.23 15:00 -0.41 0.36 1.63 -0.82 5.76 3.87 -1.33 2.62 -3.97 -3.93 16:00 1.13 2.01 1.27 1.09 2.54 0.22 -0.60 -3.81 -2.63 -0.37 17:00 1.20 1.97 2.45 0.58 1.45 1.71 -4.32 1.21 -3.13 -2.84 18:00 0.83 1.22 1.30 0.49 1.05 0.65 -1.59 -0.23 -1.48 -1.12 19:00 1.83 2.44 1.55 1.71 -0.23 -0.08 0.13 0.10 0.21 0.20

307

20:00 0.95 1.09 1.12 0.82 -0.06 1.05 -0.65 0.40 -0.20 -1.36 21:00 3.00 3.49 3.32 2.85 -0.73 2.77 0.61 1.78 0.73 -2.65 22:00 0.52 0.68 0.84 0.59 1.30 1.90 0.59 0.94 -0.11 -1.12 23:00 2.03 2.48 1.67 2.17 1.65 -1.06 0.97 -2.23 -1.35 1.74



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



308


The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 29 tri-weekly, out-of-sample dollar returns between hedged and unhedged portfolios on the Minnesota hub. MGA portfolios utilize twenty tri-weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV, ARDL, and GARCH estimates. Hedge ratios utilizing rolling estimation windows are calculated using twenty tri-weekly spot and forward prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Unhedged-

Naïve Unhedged-

MV Unhedged-

ARDL Unhedged-

MGA Unhedged-

GARCH

0:00 0.56 1.49 -0.13 -0.44 1.27 1:00 0.13 -0.86 -0.65 0.09 -0.84 2:00 0.65 0.14 0.01 0.57 -0.55 3:00 3.98 1.64 2.78 4.46 0.90 4:00 1.23 0.69 0.57 1.61 0.59 5:00 1.07 1.00 0.75 1.29 0.76 6:00 -0.14 -2.20 -1.96 1.16 -1.99 7:00 1.03 1.17 1.39 2.34 0.87 8:00 1.83 1.06 1.37 2.57 1.58 9:00 1.90 1.75 1.97 3.61 1.61

10:00 -0.06 -0.30 -0.38 1.04 -0.30 11:00 -0.41 -0.84 -1.30 1.09 -1.53 12:00 -0.15 -1.61 0.55 -2.07 -1.82 13:00 1.93 2.21 2.30 3.04 2.30 14:00 2.60 2.21 2.38 3.18 1.39 15:00 2.32 2.48 2.31 2.50 1.94 16:00 -0.13 -0.41 0.96 0.76 -0.16 17:00 -0.03 -0.49 -0.06 0.77 0.04

309

18:00 0.79 1.52 1.24 1.57 1.93 19:00 0.79 -0.21 0.10 0.53 0.00 20:00 -0.12 0.19 0.13 0.70 -1.51 21:00 0.67 1.08 0.69 1.24 -1.43 22:00 2.48 2.30 2.20 2.91 2.31 23:00 1.59 2.12 1.75 2.20 1.46



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



310


The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 29 tri-weekly, out-of-sample dollar returns between hedged portfolios on the Minnesota hub. MGA portfolios utilize twenty tri-weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV, ARDL, and GARCH estimates. Hedge ratios utilizing rolling estimation windows are calculated using twenty tri-weekly spot and forward prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Naïve-

MV Naive-ARDL

Naive-MGA

Naive-GARCH

MV-ARDL

MV- MGA

MV-GARCH

ARDL-MGA

ARDL-GARCH

MGA-GARCH

0:00 1.02 -1.93 -3.10 0.60 -1.99 -2.07 -0.61 -0.97 1.65 1.74 1:00 -1.33 -1.30 -0.53 -1.46 0.17 1.11 -0.11 1.09 -0.45 -1.22 2:00 -1.18 -1.43 -0.03 -1.63 -0.19 0.94 -1.50 1.37 -0.91 -1.43 3:00 -2.64 -0.82 -3.19 -3.36 3.99 0.66 -3.41 -1.17 -4.20 -1.70 4:00 -1.45 -1.45 -0.88 -1.48 0.15 0.48 -0.79 0.25 -0.43 -0.84 5:00 -0.78 -1.25 -0.31 -0.87 -1.55 0.59 -0.91 1.04 -0.23 -0.88 6:00 -0.93 -0.58 0.16 -0.71 1.98 2.19 1.61 1.96 -1.42 -1.99 7:00 -0.74 -0.63 -0.97 -0.90 1.08 -1.03 -1.48 -1.28 -1.66 0.66 8:00 -1.38 -1.09 -1.44 -1.02 1.41 0.01 1.29 -0.69 -0.58 0.44 9:00 -1.39 -1.29 -1.75 -1.35 1.46 -1.38 0.09 -1.72 -1.27 1.26

10:00 -0.23 -0.83 0.42 -0.23 -0.48 1.25 -0.08 0.99 0.31 -1.04 11:00 0.14 -1.31 0.54 -0.93 -1.59 1.33 -1.95 1.55 0.03 -1.85 12:00 -0.26 0.55 -0.66 -0.75 1.05 -1.68 -1.04 -1.48 -1.52 0.12 13:00 -1.37 -1.16 -1.73 -1.20 1.55 -1.28 1.57 -2.02 -0.97 1.79 14:00 -2.16 -1.74 -1.79 -2.59 0.89 -0.07 -0.94 -0.33 -1.03 -0.48 15:00 -1.38 -1.59 -0.86 -2.03 -1.59 1.47 -2.00 1.71 -0.58 -2.25 16:00 0.07 0.71 0.40 0.11 1.19 0.81 0.39 -0.76 -1.18 -0.75

311

17:00 -0.55 -0.01 0.29 0.13 1.44 1.31 2.48 0.55 0.43 -0.47 18:00 -0.24 -0.43 -0.25 -0.23 -0.81 -0.16 -0.15 0.67 0.87 -0.09 19:00 -2.37 -2.32 -0.95 -1.83 1.97 2.39 1.27 1.78 -0.54 -1.50 20:00 0.16 1.06 0.86 -0.28 0.10 0.72 -1.76 0.62 -0.55 -1.15 21:00 -0.07 -0.41 0.26 -1.24 -0.81 1.16 -2.02 1.18 -1.63 -1.98 22:00 -1.27 0.03 -0.88 -0.74 0.68 -0.21 0.54 -0.52 -0.56 0.35 23:00 -0.43 0.03 -0.04 -1.08 0.60 1.25 -1.63 -0.08 -1.31 -1.70



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



312


The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 29 tri-weekly, out-of-sample dollar returns between hedged and unhedged portfolios on the First Energy hub. MGA portfolios utilize twenty tri-weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV, ARDL, and GARCH estimates. Hedge ratios utilizing rolling estimation windows are calculated using twenty tri-weekly spot and forward prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Unhedged-

Naïve Unhedged-

MV Unhedged-

ARDL Unhedged-

MGA Unhedged-

GARCH

0:00 -2.86 -2.76 -2.68 -0.89 -2.46 1:00 -1.74 -1.04 -0.24 -0.63 -1.40 2:00 -0.98 -0.84 -0.85 1.04 -0.30 3:00 -2.77 -2.78 -2.99 0.03 -2.13 4:00 0.11 0.63 0.89 2.46 0.80 5:00 -0.69 0.25 0.15 0.18 -0.06 6:00 -0.43 -1.25 -0.78 -1.11 0.12 7:00 -1.91 -1.84 -1.45 -0.92 -2.04 8:00 0.13 -0.54 0.04 1.09 -0.69 9:00 -3.85 -3.25 -2.54 -0.11 -2.59

10:00 -1.69 -1.66 -0.41 0.77 -2.17 11:00 -1.82 -1.77 -1.51 -1.11 -2.54 12:00 -1.70 -1.35 -0.80 -0.70 -1.34 13:00 -1.21 -2.93 -3.02 -0.87 -0.93 14:00 -3.79 -1.71 -1.67 -0.65 -1.93 15:00 -3.56 -2.45 -2.40 -2.11 -2.76 16:00 -2.64 -0.11 1.96 -0.87 0.39 17:00 -3.70 -2.33 -1.83 -1.33 -2.53

313

18:00 -2.46 -1.58 -1.23 0.18 0.04 19:00 -2.40 -1.24 -1.74 -0.08 -1.16 20:00 -2.99 -1.98 -2.90 0.18 -3.31 21:00 -4.01 -4.49 -4.02 1.49 -4.66 22:00 -0.04 0.55 0.46 2.74 0.83 23:00 -3.12 -1.72 0.85 -0.86 -0.43



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



314


The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 29 tri-weekly, out-of-sample dollar returns between hedged portfolios on the First Energy hub. MGA portfolios utilize twenty tri-weekly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV, ARDL, and GARCH estimates. Hedge ratios utilizing rolling estimation windows are calculated using twenty tri-weekly spot and forward prices. These hedge ratios are updated every three weeks by dropping the oldest spot and forward price in the estimation window and replacing them with the current tri-weekly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Naïve-

MV Naive-ARDL

Naive-MGA

Naive-GARCH

MV-ARDL

MV- MGA

MV-GARCH

ARDL-MGA

ARDL-GARCH

MGA-GARCH

0:00 2.25 2.29 3.64 2.55 -0.50 5.30 3.00 5.00 2.34 -5.27 1:00 1.86 1.53 2.77 1.40 0.81 0.83 -1.89 -0.41 -1.14 -1.83 2:00 0.74 0.77 1.88 1.15 -0.19 2.68 1.79 2.70 1.32 -2.79 3:00 1.73 1.66 3.09 2.28 -0.75 3.53 2.92 3.88 2.46 -2.74 4:00 0.76 1.14 0.61 0.69 1.01 0.29 0.26 -0.05 -0.56 -0.26 5:00 1.59 1.68 2.17 1.80 -0.39 -0.10 -0.93 0.28 -0.86 -1.45 6:00 -1.77 -1.08 -2.98 1.04 2.47 0.43 2.51 -1.04 2.06 2.11 7:00 1.32 2.08 2.76 1.35 0.63 1.49 -0.70 2.27 -2.19 -4.67 8:00 -2.57 -0.70 0.96 -2.35 2.79 2.39 -0.81 1.35 -2.41 -2.83 9:00 2.93 3.70 3.63 3.61 5.29 2.80 1.92 2.15 -1.32 -2.24

10:00 1.03 2.40 1.85 0.25 3.61 1.91 -1.94 0.61 -4.01 -2.45 11:00 1.48 1.61 1.23 0.26 -0.37 0.46 -2.96 0.47 -3.05 -1.51 12:00 0.82 1.32 1.46 0.79 1.74 1.52 -0.22 0.69 -1.67 -1.45 13:00 -4.76 -4.74 3.29 1.23 -1.12 4.73 4.31 4.75 4.35 0.06 14:00 4.27 4.58 3.93 4.11 -0.47 1.89 -0.80 1.84 -0.06 -2.17 15:00 3.39 3.67 5.76 2.80 -0.41 -0.32 -2.52 -0.25 -2.23 -0.66 16:00 2.25 2.97 1.78 2.37 0.67 -1.71 1.00 -1.12 -0.17 2.09 17:00 3.59 4.24 4.12 3.53 -0.33 1.77 -2.39 2.56 -2.39 -2.89 18:00 2.26 2.34 2.07 2.15 0.02 0.93 1.18 0.81 0.98 -0.21 19:00 1.94 2.31 1.89 1.73 -0.50 0.83 -0.75 0.72 -0.16 -0.94

315

20:00 1.78 1.93 2.16 1.70 -0.82 2.23 -1.12 1.57 -0.01 -1.94 21:00 2.16 2.84 3.84 2.58 4.01 4.12 2.95 3.67 1.08 -4.24 22:00 0.76 1.00 0.43 0.83 -0.03 -0.01 0.77 -0.01 0.40 0.25 23:00 3.02 3.71 2.82 3.76 2.24 0.97 1.61 -0.97 -1.38 -0.12



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



316


The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 17 monthly, out-of-sample dollar returns between hedged and unhedged portfolios on the Illinois hub. MGA portfolios utilize twenty monthly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV, ARDL, and GARCH estimates. Hedge ratios utilizing rolling estimation windows are calculated using twenty monthly spot and forward prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Unhedged-

Naïve Unhedged-

MV Unhedged-

ARDL Unhedged-

MGA Unhedged-

GARCH

0:00 0.62 -0.30 0.90 0.04 0.53 1:00 -1.04 -0.53 -0.31 -0.34 -0.16 2:00 -1.36 -1.76 -0.89 -1.34 -0.81 3:00 -1.50 -1.00 -0.35 -0.95 0.02 4:00 -0.72 -0.89 -1.62 -0.65 -1.37 5:00 1.61 1.53 1.47 0.93 0.90 6:00 0.28 0.45 0.74 1.52 0.58 7:00 0.64 0.86 0.81 0.74 0.35 8:00 -0.32 -0.20 -0.33 -0.28 -0.78 9:00 0.26 0.02 0.89 -0.12 0.53

10:00 0.36 0.08 0.38 -0.20 0.38 11:00 -0.30 -0.12 0.27 -0.37 -0.34 12:00 0.85 0.48 0.04 0.96 -0.02 13:00 -0.88 -0.47 -0.81 -0.85 -0.79 14:00 -0.49 0.47 -0.14 -0.53 -4.38 15:00 -0.70 -0.94 -1.42 -1.09 -0.84 16:00 0.70 0.21 -0.21 0.07 0.67 17:00 -1.63 -2.55 -1.63 -1.49 -4.44 18:00 1.16 1.41 1.12 1.52 0.56 19:00 0.95 1.00 0.89 1.29 0.70

317

20:00 0.87 0.92 0.57 1.08 0.35 21:00 0.40 0.32 0.81 0.03 -0.08 22:00 1.50 1.42 1.88 1.46 1.47 23:00 0.99 0.89 1.87 1.04 0.77



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1

s ]. . Critical values are 1.74 .11, and .898 for


318


The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 17 monthly, out-of-sample dollar returns between hedged portfolios on the Illinois hub. MGA portfolios utilize twenty monthly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV, ARDL, and GARCH estimates. Hedge ratios utilizing rolling estimation windows are calculated using twenty monthly spot and forward prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Naïve-

MV Naive-ARDL

Naive-MGA

Naive-GARCH

MV- ARDL

MV- MGA

MV-GARCH

ARDL-MGA

ARDL-GARCH

MGA-GARCH

0:00 -1.49 1.49 -0.69 -0.45 1.93 0.88 1.14 -1.04 -1.28 0.49 1:00 1.28 1.90 1.60 1.23 0.06 0.43 0.65 0.16 0.35 0.38 2:00 -0.72 2.35 2.73 1.51 1.63 0.79 1.87 -2.27 0.85 1.49 3:00 1.39 2.24 2.75 1.71 1.06 -0.42 1.38 -1.65 0.50 1.15 4:00 -0.39 -2.09 1.11 -3.43 -1.45 0.62 -0.54 2.03 1.60 -3.19 5:00 -1.01 -1.31 -0.68 -1.72 -0.59 -0.04 -1.71 0.17 -1.59 -0.61 6:00 0.65 0.74 -0.04 0.45 0.16 -0.25 0.00 -0.50 -0.26 0.33 7:00 0.43 0.10 0.53 -0.99 -0.48 -0.31 -1.18 0.15 -1.36 -1.28 8:00 0.98 0.20 1.07 -0.63 -0.77 -0.81 -1.36 0.06 -1.35 -0.86 9:00 -0.34 0.31 -2.86 0.05 1.68 -0.18 0.49 -0.75 -0.57 0.50

10:00 -0.77 -0.22 -1.14 -0.24 0.92 -0.43 0.63 -0.67 -0.16 0.54 11:00 0.27 0.63 -1.00 0.06 0.52 -0.37 -0.52 -0.69 -0.72 0.16 12:00 -0.78 -0.89 -0.55 -0.89 -0.73 0.83 -0.71 1.00 -0.09 -0.97 13:00 0.32 0.39 1.55 0.04 -0.02 -0.28 -1.40 -0.34 -0.64 -0.01 14:00 0.85 1.17 -1.48 -2.28 -0.49 -0.88 -4.42 -1.23 -3.16 -2.17 15:00 0.35 -3.08 -2.45 0.33 -1.40 -0.96 -0.16 2.83 1.52 1.03 16:00 -3.06 -1.57 -1.36 -0.35 -0.97 -0.39 0.57 1.88 0.88 0.56 17:00 -0.24 -0.58 2.31 -0.34 -0.03 1.22 -0.30 1.54 -0.19 -0.79 18:00 0.48 0.58 -0.50 -1.21 0.18 -0.95 -1.65 -0.58 -1.49 -0.65 19:00 -0.17 -0.42 -0.48 -1.31 -0.15 -0.49 -1.26 -0.33 -0.89 -0.32

319

20:00 -0.36 -1.45 -0.12 -1.68 -0.70 0.30 -1.63 0.83 -0.64 -1.65 21:00 -0.56 0.43 -0.94 -1.22 0.57 -0.69 -0.97 -0.73 -2.73 -0.14 22:00 -0.73 -0.29 0.30 -1.28 0.27 0.72 -0.49 0.30 -0.97 -1.13 23:00 -1.01 -0.21 0.01 -0.93 0.59 1.18 -0.76 0.23 -2.40 -1.00



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



320


The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 17 monthly, out-of-sample dollar returns between hedged and unhedged portfolios on the Cinergy hub. MGA portfolios utilize twenty monthly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV, ARDL, and GARCH estimates. Hedge ratios utilizing rolling estimation windows are calculated using twenty monthly spot and forward prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Unhedged-

Naïve Unhedged-

MV Unhedged-

ARDL Unhedged-

MGA Unhedged-

GARCH

0:00 -0.21 -0.89 -0.05 -0.57 -0.66 1:00 -1.39 -0.76 -0.64 -0.86 -0.61 2:00 -1.67 -2.11 -1.19 -1.86 -1.15 3:00 -1.82 -1.29 -0.76 -1.42 -0.52 4:00 -1.02 -0.95 -1.99 -0.94 -2.09 5:00 0.93 1.15 0.95 0.11 1.77 6:00 0.00 -0.61 -0.10 0.39 -0.10 7:00 -0.59 -0.54 -0.40 -0.47 -0.87 8:00 -0.11 0.07 -0.03 0.17 0.13 9:00 0.10 1.17 1.50 1.44 1.59

10:00 0.96 0.89 0.55 0.97 0.58 11:00 1.25 1.26 0.68 1.36 1.30 12:00 1.22 1.05 1.03 1.38 0.94 13:00 0.32 0.29 -0.16 0.47 0.23 14:00 0.83 0.63 0.43 0.63 -0.31 15:00 -0.01 -0.22 -0.44 0.03 -1.18 16:00 1.23 0.16 0.72 1.13 0.57 17:00 -1.39 -2.80 -1.74 -1.47 -4.17

321

18:00 1.30 0.44 0.50 0.96 0.81 19:00 1.52 1.00 1.18 1.88 1.31 20:00 0.82 0.86 0.69 1.11 0.71 21:00 0.16 -0.14 0.49 0.36 0.21 22:00 1.30 1.49 1.59 1.55 1.13 23:00 0.78 0.88 1.37 0.93 1.42



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



322

Table A225 4 Week Hedging Effectiveness (Price Differences): Cinergy Hub (Comparisons of Hedging Techniques) The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 17 monthly, out-of-sample dollar returns between hedged portfolios on the Cinergy hub. MGA portfolios utilize twenty monthly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV, ARDL, and GARCH estimates. Hedge ratios utilizing rolling estimation windows are calculated using twenty monthly spot and forward prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Naïve-

MV Naive-ARDL

Naive-MGA

Naive-GARCH

MV-ARDL

MV- MGA

MV-GARCH

ARDL-MGA

ARDL-GARCH

MGA-GARCH

0:00 -1.90 0.94 -1.30 -2.83 1.99 0.98 1.11 -1.34 -3.41 0.29 1:00 1.66 2.20 2.17 1.54 -0.05 -0.73 0.66 -1.61 0.57 0.90 2:00 -1.12 2.71 -3.32 1.89 2.77 0.29 2.54 -3.09 1.10 2.14 3:00 1.72 2.46 3.37 2.44 1.80 -0.93 2.19 -1.99 1.16 2.03 4:00 -0.07 -2.77 1.38 -2.26 -2.17 0.44 -0.91 2.60 1.62 -3.34 5:00 0.13 -0.63 -1.66 -0.18 -0.88 -1.18 -0.33 -0.65 0.45 0.66 6:00 -3.23 -0.39 0.59 -0.38 1.73 1.64 2.85 1.13 -0.05 -0.59 7:00 0.57 1.15 1.85 -0.99 0.83 0.15 -1.28 -0.49 -2.12 -1.60 8:00 0.34 0.25 0.53 0.53 -0.50 0.38 0.27 0.82 0.68 -0.10 9:00 0.53 0.72 0.58 0.50 0.78 0.22 0.09 -0.87 -0.63 -0.13

10:00 -0.85 -1.45 -0.26 -1.00 -1.59 0.88 -0.96 1.50 -0.12 -1.02 11:00 -1.10 -1.94 -0.90 -0.43 -0.87 1.18 0.62 2.74 0.81 -0.13 12:00 -1.40 -1.28 -1.01 -0.99 -0.81 -0.09 -0.42 0.79 0.09 -0.30 13:00 -0.29 -0.82 0.01 -0.22 -1.07 0.52 -0.09 1.21 0.38 -0.30 14:00 0.15 -0.17 -0.08 -1.62 -0.47 -0.45 -2.86 0.21 -1.79 -2.13 15:00 -0.61 -1.58 0.86 -1.07 -0.69 0.92 -1.04 1.52 -0.39 -1.15 16:00 -1.44 -0.44 -0.13 -1.10 2.36 1.63 1.67 0.50 -0.80 -1.31 17:00 -4.24 -1.64 -2.20 -5.09 3.57 4.34 -1.30 1.17 -3.45 -4.76 18:00 -0.18 -0.17 0.16 -0.34 0.11 0.31 0.07 0.33 0.03 -0.50 19:00 -0.73 0.36 -1.22 -1.10 1.14 -0.51 -0.26 -0.85 -0.79 0.60

323

20:00 -0.48 -1.63 -0.22 -0.46 -0.42 0.20 -0.09 0.46 0.18 -0.16 21:00 -2.76 0.38 0.64 -0.04 1.12 2.58 0.87 -0.13 -0.76 -0.76 22:00 -0.45 -0.40 -0.19 -1.16 -0.12 0.87 -1.46 0.73 -1.11 -1.60 23:00 -0.57 -0.22 0.12 -0.40 0.70 0.96 -0.13 0.35 -0.98 -0.54



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



324


The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 17 monthly, out-of-sample dollar returns between hedged and unhedged portfolios on the Michigan hub. MGA portfolios utilize twenty monthly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV, ARDL, and GARCH estimates. Hedge ratios utilizing rolling estimation windows are calculated using twenty monthly spot and forward prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Unhedged-

Naïve Unhedged-

MV Unhedged-

ARDL Unhedged-

MGA Unhedged-

GARCH

0:00 -0.09 -0.99 0.24 -0.75 0.29 1:00 -0.63 -0.38 -0.19 -0.18 0.96 2:00 -1.48 -1.86 -1.19 -1.65 -0.60 3:00 -1.09 -0.89 -0.40 -0.91 -0.36 4:00 -1.02 -0.78 -2.15 -0.87 -1.89 5:00 0.64 0.71 0.68 0.21 0.97 6:00 0.05 -0.30 0.02 0.59 0.05 7:00 -0.41 -0.34 -0.49 -0.69 -1.05 8:00 0.21 0.28 0.37 0.42 0.35 9:00 -0.71 -0.58 -0.16 -0.45 -0.65

10:00 0.47 0.65 0.74 0.20 0.71 11:00 -0.46 0.49 0.37 -0.22 0.28 12:00 0.30 0.68 0.50 0.38 0.11 13:00 -0.84 0.91 0.02 -0.70 -0.25 14:00 -0.76 -0.24 -0.74 -0.86 -0.76 15:00 -0.74 -0.89 -1.02 -1.03 -1.51 16:00 0.48 -0.34 0.19 0.12 0.01 17:00 -1.82 -3.44 -2.07 -2.30 -2.60 18:00 1.32 0.62 0.60 1.12 0.86 19:00 0.91 0.79 0.75 1.45 0.97

325

20:00 1.18 1.33 1.24 1.55 1.35 21:00 -0.10 -0.49 0.38 -0.24 -0.22 22:00 1.51 1.68 1.77 1.74 1.14 23:00 0.85 0.86 1.49 1.02 0.97



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



326


The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 17 monthly, out-of-sample dollar returns between hedged portfolios on the Michigan hub. MGA portfolios utilize twenty monthly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV, ARDL, and GARCH estimates. Hedge ratios utilizing rolling estimation windows are calculated using twenty monthly spot and forward prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Naïve-

MV Naive-ARDL

Naive-MGA

Naive-GARCH

MV- ARDL

MV- MGA

MV-GARCH

ARDL-MGA

ARDL-GARCH

MGA-GARCH

0:00 -2.03 0.92 -1.48 1.02 1.96 0.41 2.79 -1.42 0.29 1.71 1:00 0.72 1.42 1.26 1.05 0.15 0.28 1.32 0.20 0.72 0.77 2:00 -0.75 2.11 -3.02 1.82 1.81 0.13 2.28 -2.69 1.44 1.99 3:00 0.94 1.53 2.14 1.31 1.36 -0.54 1.21 -1.31 0.41 1.11 4:00 0.56 -3.02 1.32 -1.90 -2.32 0.06 -1.32 2.67 2.09 -3.90 5:00 0.50 -0.31 -1.39 -0.21 -0.48 -1.72 -0.34 -0.57 -0.09 0.34 6:00 -0.93 -0.24 0.35 0.00 0.92 1.17 0.51 0.45 0.08 -0.31 7:00 0.44 -0.42 -1.86 -2.64 -0.71 -1.50 -2.60 -1.13 -2.20 -2.81 8:00 -0.03 0.21 0.35 0.07 0.63 0.56 0.26 0.20 -0.25 -0.51 9:00 0.53 0.87 2.38 0.47 1.00 0.02 0.23 -0.53 -1.59 0.11

10:00 0.21 0.08 -0.80 0.27 -0.09 -0.54 0.17 -0.40 0.26 0.55 11:00 1.38 1.46 0.89 1.20 -0.46 -1.14 -0.17 -1.58 0.12 0.68 12:00 0.34 -0.01 0.06 -0.22 -0.84 -0.38 -0.79 0.03 -0.32 -0.24 13:00 1.53 1.22 1.46 0.83 -2.04 -1.44 -2.03 -1.01 -0.31 0.65 14:00 1.38 -0.37 -1.62 -0.25 -1.47 -1.62 -1.37 -0.47 -0.05 0.15 15:00 0.06 -1.92 -2.27 -3.01 -1.01 -1.04 -2.92 -0.40 -1.05 -0.73 16:00 -2.77 -0.90 -1.19 -2.15 2.88 4.29 2.54 -0.59 -0.96 -0.65 17:00 -4.88 -1.17 -3.15 -0.65 4.36 2.86 1.53 -1.49 -0.29 0.36 18:00 -0.23 -0.30 0.13 -0.09 -0.21 0.32 0.36 0.43 0.50 -0.20 19:00 -1.00 -0.35 -0.63 -0.64 0.32 -0.45 -0.33 -0.46 -0.37 0.49

327

20:00 -0.57 -0.84 -0.51 -0.49 -0.36 -0.25 0.05 0.02 0.26 0.25 21:00 -2.79 0.66 -1.35 -0.12 1.47 0.87 0.80 -0.82 -1.54 0.21 22:00 -0.60 -0.52 -0.36 -2.07 0.02 0.76 -1.60 0.73 -1.57 -2.28 23:00 -0.75 -0.30 0.09 -0.68 0.82 1.28 -0.49 0.46 -1.64 -0.91



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



328


The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 17 monthly, out-of-sample dollar returns between hedged and unhedged portfolios on the Minnesota hub. MGA portfolios utilize twenty monthly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV, ARDL, and GARCH estimates. Hedge ratios utilizing rolling estimation windows are calculated using twenty monthly spot and forward prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Unhedged-

Naïve Unhedged-

MV Unhedged-

ARDL Unhedged-

MGA Unhedged-

GARCH

0:00 -0.90 0.83 -0.58 -0.08 -0.58 1:00 -0.85 -1.61 -1.61 -1.21 -0.90 2:00 -0.42 -0.68 -0.41 -0.41 -0.75 3:00 -0.05 0.14 0.46 0.37 0.42 4:00 -0.77 -1.90 -1.16 -0.47 -0.96 5:00 0.18 0.22 0.55 0.52 -0.29 6:00 0.10 -0.25 0.17 -0.17 -0.42 7:00 0.19 -0.06 0.28 -0.46 0.08 8:00 1.08 1.22 1.55 1.30 1.58 9:00 1.94 1.66 1.69 2.48 1.96

10:00 0.47 0.65 -1.96 -1.66 -1.74 11:00 1.07 1.53 1.16 1.61 0.99 12:00 1.24 -3.10 1.50 1.78 1.02 13:00 1.73 -0.49 0.77 2.19 -0.96 14:00 2.04 -0.31 1.22 2.62 1.59 15:00 2.11 3.15 1.62 2.84 2.08 16:00 0.98 1.66 1.05 1.58 1.60 17:00 0.30 0.48 0.32 0.57 0.34 18:00 2.37 3.28 3.29 2.80 2.60 19:00 2.61 3.05 3.21 2.99 3.03

329

20:00 0.91 0.63 0.44 1.55 1.33 21:00 -1.32 -1.35 -0.56 -0.75 -1.12 22:00 1.88 2.94 2.86 3.68 3.25 23:00 0.99 2.42 1.38 1.70 1.62



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



330


The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 17 monthly, out-of-sample dollar returns between hedged portfolios on the Minnesota hub. MGA portfolios utilize twenty monthly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV, ARDL, and GARCH estimates. Hedge ratios utilizing rolling estimation windows are calculated using twenty monthly spot and forward prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Naïve-

MV Naive-ARDL

Naive-MGA

Naive-GARCH

MV- ARDL

MV- MGA

MV-GARCH

ARDL-MGA

ARDL-GARCH

MGA-GARCH

0:00 1.52 1.10 1.10 1.09 -2.17 -2.27 -1.73 0.94 -0.21 -0.85 1:00 -3.19 -3.92 -2.58 0.40 -0.38 1.31 2.55 2.31 2.57 1.42 2:00 -1.51 -0.10 1.51 -0.03 1.07 1.54 0.40 0.13 -0.01 -0.03 3:00 0.26 0.70 0.71 0.25 2.02 1.38 0.22 -0.47 -0.48 -0.31 4:00 0.01 -0.45 0.99 0.38 -0.20 1.45 1.14 2.11 0.64 -0.35 5:00 -0.11 0.16 0.36 -0.31 1.19 1.14 -0.58 0.38 -1.05 -0.86 6:00 -1.46 0.09 -1.12 -1.29 1.13 0.19 -0.69 -0.61 -1.33 -0.59 7:00 -1.45 0.28 -1.73 -0.99 1.40 -1.23 1.65 -1.40 -0.82 1.57 8:00 -0.79 -0.25 -0.72 -0.48 2.82 0.33 0.49 -2.55 -0.85 0.29 9:00 -1.97 -2.03 -1.47 -1.79 1.26 2.45 -0.21 0.56 -0.99 -2.52

10:00 0.21 -2.40 -2.10 -2.20 -2.37 -2.07 -2.15 2.15 1.06 -1.24 11:00 -0.34 -0.81 -0.75 -0.94 -1.59 -1.05 -1.58 -0.15 -0.32 0.00 12:00 -1.60 -1.13 -1.17 -1.23 2.36 2.75 1.96 -1.04 -0.24 0.52 13:00 -1.97 -2.21 -1.58 -2.28 1.12 2.60 -0.93 0.36 -1.89 -2.39 14:00 -2.16 0.27 -1.71 -0.65 1.29 2.59 1.75 -0.88 -0.63 0.90 15:00 -1.57 0.06 -1.64 -0.46 1.12 0.60 1.42 -1.10 -0.42 1.30 16:00 -0.62 -0.29 -0.80 -0.40 0.67 -1.57 1.18 -0.87 -0.41 1.53 17:00 0.47 0.45 -0.02 0.14 -0.31 -0.32 -0.53 -0.09 -0.04 0.08 18:00 0.39 -0.33 -1.98 -0.68 -1.82 -3.35 -2.23 -3.15 -0.58 1.94 19:00 -0.23 -0.30 -2.15 2.12 -0.03 -2.37 2.25 -2.91 2.34 2.73

331

20:00 -0.86 -0.94 -0.46 -0.44 -0.07 1.55 1.28 1.73 1.51 0.05 21:00 0.34 1.70 1.68 0.65 1.78 1.74 0.51 -0.46 -1.44 -1.27 22:00 0.04 -0.40 -1.29 -0.02 -1.20 -2.22 -0.16 -2.12 1.92 2.71 23:00 0.54 -0.32 -0.37 -0.59 -1.68 -2.28 -2.10 -0.30 -0.84 -1.00



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



332


The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 17 monthly, out-of-sample dollar returns between hedged and unhedged portfolios on the First Energy hub. MGA portfolios utilize twenty monthly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV, ARDL, and GARCH estimates. Hedge ratios utilizing rolling estimation windows are calculated using twenty monthly spot and forward prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Unhedged-

Naïve Unhedged-

MV Unhedged-

ARDL Unhedged-

MGA Unhedged-

GARCH

0:00 0.16 -0.72 0.45 -0.26 0.54 1:00 -1.65 -1.11 -1.25 -1.32 -2.26 2:00 -2.30 -2.07 -2.05 -2.35 -1.94 3:00 -2.14 -1.19 -1.23 -1.82 -0.84 4:00 -1.33 -1.45 -2.25 -1.22 -2.08 5:00 0.13 0.25 0.31 -0.25 -0.31 6:00 0.21 -0.08 0.09 0.95 0.14 7:00 0.06 0.13 0.07 -0.04 -0.26 8:00 0.25 0.49 0.51 0.45 0.34 9:00 -0.06 0.85 0.99 0.81 0.95

10:00 0.89 1.03 0.95 0.78 0.93 11:00 0.46 0.37 0.74 0.76 -0.19 12:00 0.84 0.81 1.04 1.20 -0.51 13:00 -0.33 0.21 -0.39 -0.04 -1.17 14:00 -0.63 -0.05 -0.51 -0.86 -2.96 15:00 -0.17 -0.32 -0.74 -0.31 -0.88 16:00 0.42 -0.21 0.17 0.16 -0.08 17:00 -1.61 -3.03 -1.96 -2.00 -4.05

333

18:00 1.35 -0.20 -0.29 0.84 0.58 19:00 0.64 0.95 0.57 1.24 0.72 20:00 0.58 0.73 0.53 0.84 0.66 21:00 0.10 -0.03 0.39 0.14 0.16 22:00 1.28 1.59 1.48 1.78 1.24 23:00 0.17 0.17 0.54 0.29 0.21



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



334


The following table shows t-statistics from Morgan’s test for differences between variances. Each column represents a comparison of the variance of 17 monthly, out-of-sample dollar returns between hedged portfolios on the First Energy hub. MGA portfolios utilize twenty monthly spot and forward observations to estimate a static hedge ratio, while a rolling windows estimation period is used for MV, ARDL, and GARCH estimates. Hedge ratios utilizing rolling estimation windows are calculated using twenty monthly spot and forward prices. These hedge ratios are updated every month by dropping the oldest spot and forward price in the estimation window and replacing them with the current monthly day-ahead and real-time price. A positive, significant t-statistic indicates that the first hedging strategy listed in the column produces a higher variance than the second. A negative, significant t-statistic means that the first hedging strategy listed in the column has a lower variance than the second. The last row indicates the number of negative, statistically significant t-statistics found in each column.

Hour Naïve-

MV Naive-ARDL

Naive-MGA

Naive-GARCH

MV- ARDL

MV- MGA

MV-GARCH

ARDL-MGA

ARDL-GARCH

MGA-GARCH

0:00 -2.08 1.01 -1.04 1.17 2.00 1.16 2.26 -1.11 0.59 1.18 1:00 1.83 2.28 2.14 1.10 -0.87 -0.94 -0.18 0.65 0.43 0.31 2:00 0.37 2.38 -3.66 1.76 0.71 -0.52 1.73 -2.55 1.38 1.84 3:00 2.10 2.73 3.36 2.50 0.21 -1.55 1.34 -2.38 1.60 2.18 4:00 0.18 -3.04 1.75 -0.79 -1.81 0.21 -0.50 2.84 2.08 -2.52 5:00 0.64 0.59 -1.68 -0.89 -0.01 -2.04 -0.94 -1.23 -1.76 0.11 6:00 -1.42 -1.02 -0.12 -0.10 1.30 0.19 0.83 0.01 0.24 0.07 7:00 0.45 0.02 -1.14 -1.62 -0.36 -0.80 -1.27 -0.46 -1.11 -1.73 8:00 0.19 0.49 0.22 -0.05 0.46 -0.06 -1.20 -0.43 -0.85 -0.48 9:00 0.81 1.14 0.96 0.88 1.01 0.18 0.41 -1.34 -0.70 0.17

10:00 -0.38 -0.47 -0.02 -0.61 -0.11 0.24 -0.50 0.30 -0.32 -0.41 11:00 -0.42 -0.20 -0.13 -0.59 0.68 0.75 -0.77 0.44 -0.89 -0.86 12:00 -0.77 -0.68 -0.72 -1.01 0.30 0.08 -1.12 -0.22 -1.27 -0.98 13:00 0.37 0.24 0.79 -0.37 -0.64 -0.12 -1.41 0.24 -0.97 -0.77 14:00 1.23 0.53 -1.80 -2.13 -0.91 -1.48 -5.39 -1.55 -2.30 -1.18 15:00 -0.12 -2.47 -1.49 -2.05 -1.03 -0.23 -1.52 2.82 0.12 -1.34 16:00 -2.62 -0.71 -0.89 -4.63 1.47 2.93 0.69 -0.05 -0.94 -1.07 17:00 -4.37 -1.81 -2.80 -1.40 2.86 2.82 0.75 -0.89 -0.76 -0.30 18:00 -1.13 -1.32 -0.16 -1.10 -0.37 1.45 0.82 1.81 1.04 -0.84 19:00 -0.30 -0.05 -0.60 -0.40 0.23 -0.90 0.07 -0.53 -0.28 0.66

335

20:00 -0.23 -0.69 0.13 -0.37 -0.11 1.17 -0.50 0.90 -0.22 -0.81 21:00 -0.48 0.30 1.01 0.04 0.83 0.71 0.78 -0.24 -0.65 -0.07 22:00 -0.27 -0.30 -0.46 -0.54 0.10 -0.71 0.00 -0.55 -0.05 0.30 23:00 -0.15 0.38 0.39 -0.13 1.27 0.63 -0.09 -0.36 -0.99 -0.34



.

(1-R ). , where R

s1 -s

[(s1 s

) -4r s1



336

Table A232 Weekly Day-Ahead (1,25) Moving Average Trading Rule: Morning Hours

The table below shows profits, in terms of dollars per megawatt hour ($/MWh), that are achieved from implementing a (1,25) weekly moving average trading rule on day-ahead electricity delivered in the morning hours for each MISO hub. The trading rule used can be expressed as follows: Rt Rule t. The weekly dollar return (Rt) is expressed as a function of an indicator variable (Rule). The indicator variable is equal to one if the short term moving average (defined as a 1 week) is below the long run (25 week) moving average. The indicator variable is set to negative one if the opposite occurs. Estimated t-statistics appear in italics.

Hour IL CINERGY MI MN FE 0:00 3.73 4.01 1.21 3.19 4.23

3.58 3.48 3.46 2.05 3.39

1:00 2.07 2.06 0.85 1.99 2.71

2.81 2.55 2.49 1.84 3.13

2:00 1.24 1.70 0.80 1.13 2.38

1.56 2.18 2.22 1.14 2.94

3:00 1.13 1.41 0.76 1.08 2.05

1.53 1.93 2.14 1.17 2.57

4:00 1.27 1.65 0.77 1.16 2.27

1.69 2.22 2.27 1.25 2.79

5:00 1.07 1.64 0.84 1.17 2.52

1.38 2.01 2.31 1.23 2.95

6:00 2.24 3.39 1.29 2.12 4.34

2.08 2.65 3.73 1.89 3.22

7:00 2.10 3.46 1.88 2.00 3.97

1.45 1.93 1.82 1.22 2.02

8:00 3.11 5.04 2.23 2.54 4.50

1.77 2.37 2.39 1.11 2.06

9:00 4.74 5.63 2.38 3.69 5.86

2.72 2.56 3.01 1.51 2.47

10:00 4.10 4.78 2.26 3.59 6.21 2.24 2.19 2.53 1.49 2.71

11:00 4.55 6.71 2.06 6.70 7.45 2.26 3.23 3.0 9 2.80 3.58

337


Note: The test statistic for this analysis is t=

SE( ). Critical values are 1.64 1.96, and . 76 for

significance levels of 10%, 5%, and 1% respectively. 149 weekly day-ahead prices from 6/1/2006-4/11/2009 are used in this analysis.

338

Table A233 Weekly Day-Ahead (1,25) Moving Average Trading Rule: Evening Hours

The table below shows profits, in terms of dollars per megawatt hour ($/MWh), that are achieved from implementing a (1,25) weekly moving average trading rule on day-ahead electricity delivered in the evening hours for each MISO hub. The trading rule used can be expressed as follows: Rt Rule t. The weekly dollar return (Rt) is expressed as a function of an indicator variable (Rule). The indicator variable is equal to one if the short term moving average (defined as a 1 week) is below the long run (25 week) moving average. The indicator variable is set to negative one if the opposite occurs. Estimated t-statistics appear in italics.


12:00 4.42 6.36 2.18 6.97 8.91

2.09 2.81 3.50 2.78 3.85

13:00 3.36 4.31 2.11 6.73 5.50

1.54 1.96 1.47 3.14 2.46

14:00 3.77 3.50 2.20 5.65 3.93

1.61 1.55 0.73 2.54 1.63

15:00 0.39 1.14 2.41 3.89 2.93

0.15 0.47 0.56 1.65 1.15

16:00 0.99 2.62 2.66 3.11 2.47

0.38 0.89 0.91 1.30 0.93

17:00 1.15 2.75 2.52 3.35 2.95

0.46 0.99 1.16 1.42 1.16

18:00 6.07 6.15 2.26 6.69 8.64

2.76 2.24 2.90 2.69 3.80

19:00 6.80 9.36 2.29 4.93 8.20

2.88 3.69 3.93 1.92 3.26

20:00 7.66 7.05 2.08 5.70 9.23

3.65 3.17 3.20 2.00 4.16

21:00 5.10 6.10 2.24 4.08 8.41

2.75 2.89 3.78 1.79 3.73

22:00 5.39 5.12 2.11 4.62 4.83

3.03 2.56 3.09 2.01 2.25

23:00 4.59 4.46 1.64 3.92 4.31

3.33 2.87 2.81 1.99 2.70

339





340

Table A234 Weekly Real-Time (1,25) Moving Average Trading Rule: Morning Hours

The table below shows profits, in terms of dollars per megawatt hour ($/MWh), that are achieved from implementing a (1,25) weekly moving average trading rule on real-time electricity delivered in the morning hours for each MISO hub. The trading rule used can be expressed as follows: Rt Rule t. The weekly dollar return (Rt) is expressed as a function of an indicator variable (Rule). The indicator variable is equal to one if the short term moving average (defined as a 1 week) is below the long run (25 week) moving average. The indicator variable is set to negative one if the opposite occurs. Estimated t-statistics appear in italics.


0:00 3.90 4.65 2.13 5.05 5.12

2.04 2.46 3.06 1.73 2.56

1:00 5.52 6.25 1.69 8.54 5.84

2.39 3.41 4.23 2.94 2.93

2:00 3.41 3.79 1.45 6.76 3.82

1.95 3.26 3.03 2.19 2.83

3:00 4.35 1.99 1.68 3.71 3.17

3.22 1.25 1.19 1.17 2.00

4:00 8.11 4.98 1.95 5.91 6.02

3.39 2.76 3.51 1.90 3.16

5:00 7.37 6.92 2.29 7.20 6.37

4.19 3.15 4.61 2.67 3.11

6:00 8.75 9.15 3.97 8.82 8.51

2.93 2.60 2.75 3.04 2.37

7:00 10.33 6.76 3.41 8.07 5.79

3.48 2.09 2.78 2.86 1.77

8:00 8.74 8.01 4.13 10.51 7.58

2.11 2.00 1.89 2.15 1.86

9:00 10.20 10.03 2.44 12.59 10.59

4.59 4.29 3.75 2.49 4.46

10:00 11.30 10.75 3.90 14.00 15.52

3.21 3.18 3.28 3.30 4.26

11:00 8.14 8.10 3.43 9.11 7.73 2.46 2.39 2.45 2.27 2.36

341





342

Table A235 Weekly Real-Time (1,25) Moving Average Trading Rule: Evening Hours

The table below shows profits, in terms of dollars per megawatt hour ($/MWh), that are achieved from implementing a (1,25) weekly moving average trading rule on real-time electricity delivered in the evening hours for each MISO hub. The trading rule used can be expressed as follows: Rt Rule t. The weekly dollar return (Rt) is expressed as a function of an indicator variable (Rule). The indicator variable is equal to one if the short term moving average (defined as a 1 week) is below the long run (25 week) moving average. The indicator variable is set to negative one if the opposite occurs. Estimated t-statistics appear in italics.


12:00 11.60 13.02 4.01 17.05 10.80

2.92 3.24 2.99 2.30 2.69

13:00 12.64 11.06 3.60 15.45 11.05

3.70 3.05 3.24 3.88 2.69

14:00 17.40 14.11 3.41 12.71 12.55

4.58 3.90 3.65 2.42 3.88

15:00 7.69 10.51 4.19 5.79 11.40

1.89 2.42 1.93 1.35 3.05

16:00 9.21 8.96 5.01 4.62 7.83

1.79 1.82 2.12 0.86 1.56

17:00 7.42 9.42 4.37 8.90 8.68

1.71 2.14 2.34 1.93 2.04

18:00 17.09 14.94 4.80 18.04 16.33

4.03 3.05 3.90 4.51 3.43

19:00 8.37 14.63 3.52 12.77 16.71

2.54 4.10 3.56 2.24 4.75

20:00 9.86 7.32 3.68 16.30 7.35

2.45 2.08 2.05 2.80 1.99

21:00 7.20 6.68 3.63 13.55 6.56

1.93 1.84 2.03 2.83 1.77

22:00 8.28 9.18 2.36 11.10 8.94

3.30 3.95 4.00 3.24 3.77

23:00 8.01 8.11 2.03 10.22 8.39 4.01 4.07 4.34 3.11 4.12

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REFERENCES

Adams, J. & Montesi, C. (1995). Major issues related to hedge accounts. Newark, Connecticut: Accounting Standard Board. Baillie, R. & Myers, R. (1991). Bivariate GARCH estimation of the optimal commodity futures hedge. Journal of Applied Econometrics, 6(2), 109-124. Banerjee, S. & Noe, T. (2006). Exotics and electrons: electric power crises and financial risk management. Journal of Business, 79(5), 2659-2696. Benartzi, S. & Thaler, R. (1995). Myopic loss aversion and the equity premium puzzle. Quarterly Journal of Economics, 110(1), 75-92. Bessembinder, H. & Lemmon, M. (2002). Equilibrium pricing and optimal hedging in electricity forward markets. Journal of Finance, 57(3), 1347-1382. Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31(3), 307-327. Borenstein, S., Bushnell, J., Knittel, C. & Wolfram, C. (2001). Inefficiencies and market power in financial arbitrage: a study of California’s electricity markets. CSEM Working Paper no. 138, University of California Energy Institute. Borenstein, S., Bushnell, J., & Wolak, F. ( ). Measuring market inefficiencies in California’s wholesale electricity market. The American Economic Review, 92(5), 1376-1405. Bowden, N., Hu, S. & Payne, J. (2009). Day-ahead premiums on the Midwest ISO. The Electricity Journal, 22(2), 64-73. Bowden, N. & Payne, J. (2008). Short term forecasting of electricity prices for MISO hubs: Evidence from ARIMA-EGARCH models. Energy Economics, 30(6), 3186-3197. Brennan, M. (1958). The supply of storage. American Economic Review, 48(1), 50-72. Bystrom, H. (2003). The hedging performance of electricity futures on the Nordic power exchange. Applied Economics, 35(1), 1-11. Brock, W., Lakonishok, J., & LeBaron, B. (1992). Simple trading rules and the stochastic properties of stock returns. Journal of Finance, 47(1) 1731-1764. Cecchetti, S., Cumby, R., & Figlewski, S. (1988). Estimation of the optimal futures hedge. Review of Economics and Statistics, 70(4), 623-630.

345

Chang, J. & Shanker, L. (1986). Hedging effectiveness of currency options and currency futures. Journal of Futures Markets, 6(2), 289-305. Chen , S., Lee, C., & Shrestha, K. (2001). On a mean-generalized semivariance approach to determining the hedge ratio. Journal of Futures Markets, 21(6), 581-598.

Chen , S., Lee, C., & Shrestha, K. (2004). An empirical analysis of the relationship between the hedge ratio and hedging horizon: a simultaneous estimation of the short- and long-run hedge ratios. Journal of Futures Markets, 24(4), 359-386. Christensen, T., Hurn, S., & Lindsay, K. (2009). It never rains but it pours: modeling the persistence of spikes in electricity prices. The Energy Journal, 30(1), 25-48. Cohen, K., Hawawini, G., Mayer, S., Schwartz, R., & Whitcomb, D. (1983). Estimating and adjusting for the intervaling effect bias in beta. Management Science, 29(1) 135-148. De Jong, A., De Roon, F., & Veld, C. (1997). Out-of-sample hedging effectiveness of currency futures for alternative models and hedging strategies. Journal of Futures Markets, 17(7), 817-837. De Jong, C. & Sewalt, M. (2003). Negative prices in electricity markets. Commodities Today, 1-4. Dickey, D. & Fuller, W. (1979). Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association, 74(366), 427-431. Dimson, E. (1979). Risk measurement when shares are subject to infrequent trading. Journal of Financial Economics, 7(2), 197-226. Ederington, L. (1979). The hedging performance of the new futures markets. Journal of Finance, 34(1), 157-170. Engle, R. & Granger, C. (1987). Co-integration and error correction: representation, estimation and testing. Econometrica, 55(2), 251-276. Fama, E. (1970). Efficient capital markets: a review of theory and empirical work. Journal of Finance, 25(2), 383-417. Federal Energy Regulatory Commission (1996). Order No. 888. Retrieved October 2011, from http://www.ferc.gov/legal/maj-ord-reg/land-docs/order888.asp. Federal Energy Regulatory Commission (1996). Order No. 889. Retrieved October 2011, from http://www.ferc.gov/legal/maj-ord-reg/land-docs/order889.asp.

346

http://www.ferc.gov/legal/maj-ord-reg/land-docs/order888.asp

http://www.ferc.gov/legal/maj-ord-reg/land-docs/order889.asp

Financial Accounting Standards Board. (1998). Statement of financial accounting standards No. 133: accounting for derivative instruments and hedging activities. Norwalk, CT: FASB. Finnerty, J. & Grant, D. (2002). Alternative approaches to testing hedge effectiveness under SFAS no. 133. Accounting Horizons, 16(2), 95-108. Fishburn, P. (1977). Mean-risk analysis with risk associated with below-target returns. American Economic Review, 67(2), 116-126. Genoese, F., Genoese, M., & Wietschel, M. (2010). Occurrence of negative prices on the

German spot market for electricity and their influence on balancing power markets. 7th International Conference of the European Energy Market, 1-6.

Giberson, M. (2008). Frequent negative prices in the west region of ERCOT result from

wasteful renewable power subsidies. Retrieved June 2010, from http://knowledgeproblem.com/2008/11/20/frequent_negati/.

Grant, S. & Kajii, A. (1998). ASUI expected utility: an anticipated utility theory of relative disappointment aversion. Journal of Economic Behavior and Organization, 37(3), 277-290. Greene, W., 2000, Econometric Analysis Upper Saddle River: Prentice-Hall. Gul, F. (1991). A theory of disappointment aversion. Econometrica, 59(3), 667-686. Hadsell, L. ( 7). The impact of virtual bidding on price volatility in New ork’s wholesale electricity market. Economics Letters, 95(1), 66-72. Hadsell, L. & Shawky, H. (2007). One day forward premiums and the impact of virtual bidding on the New York wholesale electricity market using hourly data. Journal of Futures Markets, 27(11), 1107-1125. Hakkio, C. & Rush, M. (1989). Market efficiency and cointegration: an application to the sterling

and deutschemark exchange markets. Journal of International Money and Finance, 8(1), 75-88.

Hartzmark, M. (1987). Returns to individual traders of futures: aggregate results. Journal of Political Economy, 95(6), 1292-1306. Howard, C. & D’Antonio, L. (1984). A risk-return measure of hedging effectiveness. Journal of Financial and Quantitative Analysis, 19(1), 101-112.

347

http://knowledgeproblem.com/2008/11/20/frequent_negati/

Huisman, R., Huurman, C., & Mahieu, R. (2007). Hourly electricity prices in day-ahead markets Energy Economics, 29(2), 240-248. Hsin, C., Kuo, J., & Lee, C. (1994). A new measure to compare the hedging effectiveness of foreign currency futures versus options. Journal of Futures Markets, 14(6), 685-707. Hsu, C., Tseng, C., & Wang, Y. (2008). Dynamic hedging with futures: a copula-based GARCH model. Journal of Futures Markets, 28(11), 1095-1116. Johnson, L. (1960). The theory of hedging and speculation in commodity futures. Review of Economic Studies, 27(3), 139-151. Kahneman, D. & Tversky, A. (1979). Prospect theory: an analysis of decision under risk. Econometrica, 47(2) 263-291. Kaldor, N. (1939). Speculation and economic stability. Review of Economic Studies, 7(1), 1-27. Kang, T., Brorsen, B., & Adam, B. (1996). A new efficiency criterion: the mean- separated target deviation risk model. Journal of Economics and Business, 48(1), 47-66. Keynes, J., 1930, Treatise on money London: Macmillan. Knittel, C. & Roberts, M. (2005). An empirical examination of restructured electricity prices. Energy Economics, 27(5), 791-817. Kolb, R. (1992). Is normal backwardation normal? Journal of Futures Markets, 12(1), 75-91. Krehbiel, T. & Adkins, L. (1993). Cointegration tests of the unbiased expectations hypothesis in metals markets. Journal of Futures Markets, 13(7) 753-763. Kroner, K. & Sultan, J. (1993). Time-varying distributions and dynamic hedging with foreign currency futures. Journal of Financial and Quantitative Analysis, 28(4) 535-551. LeBaron, B. (1999). Technical trading rule profitability and foreign exchange intervention. Journal of International Economics, 49(1), 125-143. Lien, D. (2005A). The use and abuse of the hedging effectiveness measure. International Review of Financial Analysis, 14(2), 277-282. Lien, D. (2005B). A note on the superiority of the OLS hedge ratio. Journal of Futures Markets, 25(11), 1121-1126.

348

Lien, D. (2008). A further note on the optimality of the OLS hedge strategy. Journal of Futures Markets, 28(3), 308-311. Lien, D. & Tse, Y. (2002). Some recent developments in futures hedging. Journal of Economic Surveys, 16(3), 357-396. Longstaff, F. & Wang, A. (2004). Electricity forward prices: a high-frequency empirical analysis. Journal of Finance, 59(4), 1877-1900. Luoma, M., Martikainen, T., & Perttunen, J. (1993). Thin trading and estimation of systematic

risk: an application of an error-correction model. Annals of Operations Research, 45 (1-4), 297-305.

Malliaris, A. & Urrutia, J. (1991). The impact of the lengths of estimation periods and hedging horizons on the effectiveness of a hedge: evidence from foreign currency futures. Journal of Futures Markets, 11(3), 271-289. Midwest ISO. (2009A). Historical LMPs. Retrieved April 2009, from https://www.midwestiso.org/Library/MarketReports/Pages/MarketReports.aspx Midwest ISO. (2009B). Midwest ISO business practice manual 002: Energy and operating

reserves markets . Retrieved April 2009, from https://www.midwestiso.org/Library/BusinessPracticesManuals/Pages/BusinessPracticesManuals.aspx

Midwest ISO. (2009C). Midwest ISO fact sheet. Retrieved April 2009, from https://www.midwestiso.org Morgan, W. (1939). A test for the significance of the difference between two variances in a sample from a normal bivariate population. Biometrika, 31(1), 13-19. Pesaran, M. (1997). The role of economic theory in modeling the long run. Economic Journal, 107(440), 178-191. Serletis, A.,& Herbert, J. (1999). The message in North American energy prices. Energy Economics, 21(1) 471-483. Shawky, H., Marathe, A., & Barrett, C. (2003). A first look at the relation between spot and and futures electricity prices in the United States. Journal of Futures Markets, 23(10) 931-955. U.S. House. 102nd Congress. “H.R.776.ENR: The Energy Policy Act of 199 .” (Version: 8; Version

Date: 10/24/92). Retrieved October 2011, from http://thomas.loc.gov/home/thomas.php#

349

https://www.midwestiso.org/Library/MarketReports/Pages/MarketReports.aspx

https://www.midwestiso.org/Library/BusinessPracticesManuals/Pages/BusinessPracticesManuals.aspx

https://www.midwestiso.org/Library/BusinessPracticesManuals/Pages/BusinessPracticesManuals.aspx

Working, H. (1948). Theory of the inverse carrying charge in futures markets. Journal of Farm Economics, 30(1), 1-28.

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