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Minimizing Risk Techniques for Hedging Jet Fuel:

an Econometrics Investigation

Radu Tunaru1

Mark Tan

Middlesex University

Business School, London NW4 4BT

Abstract

The aim of this paper is to discuss the hedging techniques that a company based in an emerging

market country can use to hedge the risk associated with jet fuel or kerosene. The company can be an

airline company or a market intermediary offering contracts on this important commodity. An

empirical analysis reveals two main directions for minimum risk hedging: one is to cross-hedge

directly the commodity itself using the futures contract on another commodity or a basket of

commodities highly correlated with jet fuel; the second is to use the futures contract on kerosene in

Tokyo and then the problem is transformed into cross hedging the currency.

JELclassification: G13, G15, F31

Keywords: cross hedging; regression models; emerging market; kerosene; exchange rates

1 Address for correspondence: Radu Tunaru, Business School, Middlesex University, The Burroughs, London NW4 4BT,r.tunaru@mdx.ac.uk; tel: 020 8411 4258.

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1. Introduction

1.1Managing risk associated with oil pricesDeregulation in the early 1970s dramatically increased the degree of price uncertainty in the

energy markets, prompting the development of the first exchange traded derivative securities. Oil

futures contract has been traded on NYMEX since October 1974. The worlds first successful

energy contract, heating oil futures was opened at NYMEX in 1978. Contracts followed between

1981 to 1996 for gasoline, crude oil, natural gas, propane and electricity. Serletis and Kemp (1998)

presented evidence in favour of correlations between heating oil, unleaded gasoline, and natural gas

prices with crude oil price in the US.

Singapore International Monetary Exchange (SIMEX) launched fuel oil futures contracts in

February 1989 but failed to attract businesses from OTC market. In spite of modifications to contract

specification at the end of 1997 the contract lost any interest. Horsewood (1997) pointed out that

the contract failed because it was not providing an exact hedge against the underlying physical and

because of liquidity problems due to government control such as Malaysia.

However, various futures contracts on refined oil products have been launched recently in Tokyo and

Hong Kong.

In recent times oil prices have been volatile, ranging from as low as $10/bbl in 1999 to over

$35/bbl in 2000 when it caused shortages in Americas Mid-Western States in Summer and the fuel

riots which paralysed several European countries in September. The cause of recent energy crisis

(1999-2001) are different from those that produced the oil shocks of the 1970s and the lesser upsets

during the Gulf War in 1990s. OPEC has been working with oil consuming nations to stabilise

energy prices.

Considine and Heo (2000) used Generalised Method of Moments to perform dynamic,

simultaneous simulations to estimate the impact of supply and demand shock in petroleum markets.

Market price of petroleum products now appear quite sensitive to supply and demand shocks, unlike

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the previous era of pricing under long term contracts.

1.2Jet fuel or kerosene: a problematic commodity

According to Co (2000) fuel constitutes 10-20% of airline costs and a 5% change in fuel price

affects profitability considerably. The cost of jet fuel accounts for 10-15% of Swiss Air total

operating costs (Khan, 2000). It is almost impossible for an airline company to stock large amounts

of kerosene, due to the cost of financing, storage cost and location required to refuel the airplanes.

The jet fuel price risk may depend on the pricing location, volume and whether forward sales

commitments have been made (Bullimore, 2000).

Table 1. List of refined products in percentages obtained

from a barrel of crude oil

Product Gallons per Barrel

Gasoline 19.5

Distillate Fuel Oil(includes both home heating oil & diesel) 9.2

Kerosene 4.1

Residual Fuel Oil(heavy oils used as fuels in industry, marine transportand electric power generation)

2.3

Liquefied Refinery Gases 1.9

Still Gas 1.9

Coke 1.8

Asphalt and Road Oil 1.3

Petrochemical Feedstock 1.2

Lubricants 0.5

Kerosene 0.2Other 0.3Figures are based on 1995 average yields for US refineries. One barrel of oil contains 42

gallons. Excess due to processing gain.

Source: www.CommoditySeasonals.com

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The major price element in kerosene is the price of crude oil because kerosene is one of the refined

products from crude oil, a list of those products being presented in Table 1. There is also empirical

evidence that kerosene prices are co-integrated with crude oil prices (Errera and Brown ,1999 ).

The main purpose of this paper is to outline a methodology supported by empirical

investigation of how an airline company or market intermediary based in an emerging country can

hedge its operations related to kerosene. For example, how can Malev (Hungary) or Tarom

(Romania) or Olympus (Greece) hedge the risk associated with volatility of kerosene prices? In

essence the same question is valid for all emerging market countries, European or Asian or Latin

American and the success of minimising the risk of this important commodity may prove to be the

decisive factor in the survival of the company.

One may expect to be able to hedge using futures contracts on kerosene. Airline companies

operate worldwide but there are no futures contracts on kerosene on most of the major exchanges

excepting Tokyo. This provides an opportunity to investigate in this paper whether airline companies

outside Japan are better off hedging using kerosene futures in Tokyo or cross hedging kerosene by

using gas oil and heating oil as underlying in own country or nearest exchange. For companies that

operate outside Japan as it is the case with all emerging markets, hedging jet fuel or kerosene is

transformed into a problem of managing foreign exchange risk.

The transfer of the problem from commodity world to the currency world, technically speaking is the

same because many of the emerging markets do not have a futures contract on the exchange rate with

the Japanese yen or U.S. dollar. In both situations, commodity or currency, a perfect hedge is not

possible and a cross-hedge that only minimises the risk is investigated.

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2. The Evolution of Cross-Hedging Techniques

Hedging via the futures markets is not always straightforward and one has to overcome

problems such as mismatch of either the maturity date or underlying asset, or both. The former leads

to delta-hedge, the latter to cross-hedge and when both are in place to cross delta hedge. The seminal

ideas go back almost half a century and the usual approach is due to Johnson (1960), Stein (1961)

and Ederington (1979). A wider perspective on cross hedging in a risk return framework is described

by Anderson and Danthine (1981). It is now a common subjects in textbooks such as Stoll and

Whaley (1993) and Ritchken (1996), to name just a few, and yet there is still an ongoing debate

about what techniques are more useful.

For our purposes two major classes of cross-hedging examples: commodity cross-hedging

and currency cross-hedging. Although it has been shown that it is possible to cross-hedge commodity

with currency as hinted by Sadorsky (2000) and currency with commodity as in Benet (1990), in this

paper we consider only the case of two markets from the same class, one a futures market and the

other a spot market with differentbut correlatedunderlyings.

Probably the most used methods for calculating the optimal hedge ratio are regression based

methods. As always with statistics the solution comes with advantages and disadvantages and for the

financial analyst this can develop into a black whole. There are three types of regression models

used: price level, price change level and percentage change level. We denote by S(t) the spot price of

the underlying targeted for hedging at time tand by FT(t) the futures price at time tof theproxy

underlying with maturity time T. The maturity of futures contracts is most of the time after the

hedging period. In other words if 1T is the exposure period for the hedging the futures contracts used

for cross hedging have a maturity 12 TT > .

In this paper we consider only the situation of minimising the risk of holding a portfolio of

the underlying under the hedging and futures contracts of one or several of its proxies. Shorting 0

futures of one proxy for each long position in the spot leads to a cash flow at time 1T equal to

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)0()()(22 0101 TT

FTFTS + (1)

Minimising the variance of this cashflow leads to

))((var

))(),((cov

10

110

0

2

2

TF

TFTS

T

T

= (2)

The optimal coefficient 0 depends on the horizon of exposure to hedging 1T and the futures

maturity 2T . In practice it is often assumed that it is constant with respect to time although some

studies suggest that this is not always the case. We shall treat this assumption with caution but for

sake of simplicity we shall drop the index and refer to the optimal hedge ratio as simply .

The formula given in (2) can be also recovered from a simple regression model such as

ttTtFtS ++= )()( )(2 (3)

where )()(2 tF tT is the price of the futures contract at time twith )(2 tT the nearest maturity available.

The estimate of the optimal hedging ratio depends on the historical data.

In order to solve problem related to autocorrelation, many authors prefer a regression at the

price change level. Thus, is estimated from

( ) ttTtT tFtFtStS ++= )1()()1()( )1()( 22 (4)

There might still be problems with the regression in (4) such as heteroscedasticity and then a

percentage change level regression is often used. This is

t

tT

tT

tF

tF

batS

tS

+

+= 1)1(

)(

1)1(

)(

)1(

)(

2

2

(5)

The hedge ratio is calculated from the estimated slope of this regression using the formula

*)(

*)(

*)(2tF

tSb

tT

= (6)

where t* is the last day in the estimation sample.

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When simple linear regression methods are used the 2R is a measure of the efficiency of the

hedging. The theoretical support is provided by Ederington (1979), Dale (1981) but some research

Chang and Fang (1990) indicated that this measure is not always appropriate and other measures of

efficiencies may be more useful. However, the 2R is still largely used in practice for its direct

interpretability and ease of calculation especially in conjunction with regression based methods.

2.1 Cross-hedging commodity

The basic principles of hedging can be used for many commodities for which no futures

contract exists, because often they are similar to commodities that are traded. Witt et al. (1987)

compare the analytical approaches for estimating hedge ratios for agricultural commodities and

discuss various issues related to regression based methods.

Our interest is jet fuel or kerosene, a commodity that could be hedged by using heating oil

futures contracts. Brent crude oil and its related refined products prices are co-integrated as shown

by Gjolberg and Johnsen (1999), who also argue that the regression estimates used for establishing a

risk minimising hedge may be biased because standard approach for establishing a risk minimising

hedge may yield biased estimates.

In energy market, basis risk is an ever-present ingredient in hedge selection. Distribution of

prices in energy market is not as unbounded as in foreign exchange, because operating costs and

constraints tend to underpin downward price movement (Moonier and Potter 1998). However, other

economic reasons such as transfer costs, storage costs and location may lead to very interesting

cross hedging problems. One good example is Woo et al (2001) where cross hedging in power

utilities markets is discussed.

Unrelated commodities have a persistent tendency to move together (Pindyck and Rotemberg

1990). They also found that an equally weighted index of the dollar value of British pound, German

mark, and Japanese yen negatively and significantly impacts the price of crude oil in both OLS

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regressions and latent variable models. Sadorsky (2000) also showed that futures prices for oil

related products are co-integrated with a traded-weighted index of exchange rates and that energy

sector is important to some countrys trade, suggesting sensitivity to the exchange rate.

2.2 Cross-hedging currency

There is a large literature concerning cross hedging currencies. For our purposes later in this

paper it is useful to be aware of some of the previous research conclusions in this area. The basic

reason for cross hedging currencies is that currency futures only matures four times a year, so perfect

hedge are co-incidental (Lypny, 1988).

Dale (1981) uses spot and futures prices level for his analysis on currencies but Hill and

Schneeweis (1981) insisted that price change level should be used instead of price level in order not

to violate the Ordinary Least Square (OLS) assumptions because of the correlations of error terms in

regression models.

Grammatikos and Saunders (1983) also used a simple OLS regression model. The use of this

model over a long period of time affects the stability of the regression slope coefficient ().

Grammatikos and Saunders (1983) proposedoverlapping regressions procedures, aiming to test

shifts in coefficients overtime, and a Random Coefficient Model (RCM) to test the optimal hedge

ratio. Their results varied across countries. This was due to the complexity relationship of open

interest, volume of contracts traded, the stability of the hedge ratio and the measure of hedging

effectiveness.

Lypny (1988) considered several strategies to derive an optimal hedging based on a portfolio

of n-currency spot portfolio. It was shown that the portfolio strategy performed relatively well but a

random coefficient model (RCM) supported the idea of intertemporal instability of at least one of the

regression coefficients describing the portfolio effect. Mun and Morgan (1997) used generalised

method of moments (GMM) model to analyse the performance of five major currency futures for

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cross-hedging local currency/US dollar exchange rate risks faced by depository financial institutions

in a selected group of emerging Asian countries: Indonesia, Korea, Malaysia, Singapore, and

Thailand. The Sharpe Performance Index was used to assess cross hedging performance by country

and the empirical evidence showed that minimum variance cross hedge outperforms an unhedged

position. In terms of minimum variance cross hedge using a portfolio of futures contracts seems to be

outperform the one-currency futures for some countries but under perform in other countries.

Slee (1999) emphasized that the Sharpe ratio is not valid for measuring the effectiveness of hedging

in the emerging market currencies because these currencies return can be significantly skewed.

Another hedging alternative related to Asian currencies and described by Bannisters and

Fong (1997) is based on non-deliverable forwards contracts. Companies can trade volatility of

currency using covariance swap but as Carr and Madan (1999) pointed out the variance and

covariance of different currencies are generally unstable over time.

Exchange rate movements may be an important stimulus for commodity price changes

(Sadorsky 2000). Many emerging markets allow their exchange rates to compete directly in the

system of the dirty float. In this case hedging operations for these currencies are not easy. An

innovative idea is described in Benet (1990). As a proxy for the foreign exchange the countrys best

commodity in export terms can be used for cross-hedging.

Firms often hedge as much as 75-85% of their foreign exchange exposure (Saunderson,

1999). When it is feasible, forwards and futures contracts are replaced with options, which can

provide insurance against adverse market movements but still leave open the possibility of profit

from positive price movements. Fallon (1998) proposed the use of basket currency options for

hedging and meeting revenue target as well. He added that basket currency option are getting more

and more popular by corporate treasury operations that manage risks on a centralised basis, as a way

of hedging net income and for avoiding any shocks from currency volatility.

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Eaker and Grant (1987) investigated the intertemporal instability of hedge ratios that causes

hedged position to be riskier than unhedged positions. Overall cross hedging is shown to be a useful

risk reduction technique but re-adjusting the hedging from time to time is important for a single

currency cross hedge and overcomes problems of intertemporal instability of the coefficients.

The instability of hedge ratios in time has been also pointed out by Park et al. (1987) who

investigated the cross hedging performance of the U.S. futures market relative to the currencies from

the European monetary system. They used a price change simple regression model and their tests for

stability were based on dummy variables. The cross hedging was done via the German DM futures, a

contract also used by Braga et.al. (1989) in cross hedging the Italian lira / US dollar exchange rate.

Recently, Sercu and Wu (2000) found evidence that for three-month currency exposures the

price-based hedge ratios outperform the ratios estimated from regression models. One reason for this

improved performance seems to be the adaptability of the price based ratios to breaks in the data.

3. Cross-hedging jet fuel

3.1 Data analysed

The data analysed is weekly data between 4th February 1997 and 21st August 2001, Tuesday

continuous settlement prices and it is from Datastream. This sample of 204 observations is large

enough to avoid well-known problems with estimation in small samples.

The codes used are LCR Brent crude oil (IPE), NCL- light sweet crude oil (NYMEX), NHO-

heating oil (NYMEX), NHU- unleaded regular gas (NYMEX), NPG- liquid propane gas (NYMEX).

3.2 Regression based estimates

The correlations between the spot prices for kerosene and the futures prices for various proxy oil

products may give us a hint to the problems that might appear when the regression models are fit to

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the data. Table 2 shows that jet fuel is highly correlated to almost all futures contracts on oil products

traded in London or New York.

Table 2. Price level correlations; weekly data 4th

February 1997 to

26th

December 2000, Tuesday Settlement Prices

The estimates from the simple regression model given by (3) can be misleading if the variables

involved are random walks drifting apart over time. It is therefore essential to test the hypotheses that

each price is a random walk. The test statistic employed is the Augmented Dickey Fuller (ADF) test

discussed in detail in Davidson and MacKinnon (1993, Chapter 20). This is a two step procedure.

First the simple linear regression model, where tP is either the spot price or the futures price,

ttt PP ++= 110 (7)

is fitted under the standard normal assumptions and the residuals }{ td are saved.

Then the regression model

tttt ddd ++= 11 (8)

where the last term on the right side is a white noise, is fitted and the ADF statistic is simply the t-

statistic for the OLS estimate of. Thus, this is a unit-root test. The results of unit root test are

presented in Table 3.

Table Price level correlation between jet keroseneand futures contracts

JET LCR NCL NHO NHU NPG

JET 1.00

LCR 0.92 1.00NCL 0.96 0.94 1.00

NHO 0.97 0.91 0.97 1.00

NHU 0.91 0.93 0.97 0.92 1.00

NPG 0.90 0.90 0.92 0.94 0.86 1.00

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Table 3. The ADF statistics for random walk tests

It is obvious that the data rejects the null hypothesis of random walk for all series investigated and at

all levels of significance.

Secondly, to test whether the prices are drifting apart, a cointegration test can be done. This is

also based on an ADF statistic and can be done in two steps. First, fit the simple linear regression

model given by (3) and save the residuals }{ te . Next, fit the regression model

tttt eee ++= 11 (9)

where the last term on the right side is a white noise, is fitted and the ADF statistic is simply the t-

statistic for the OLS estimate of. For the series investigated here, the cointegration results are

given in Table 4.

Table 4. ADF tests for cointegration between jet fuel spot and futures

on other oil products.

Again the hypothesis that the spot prices and futures prices are drifting apart in time is rejected for all

futures contracts under analysis. Having done that it seems that the only thing left is to use the

regression model (3) to fit the data and use the estimate for the slope coefficient to determine the

hedge ratio. The OLS results are illustrated in Table 5. The only fly in the ointment is the value of

Variable JET LCR NCL NHO NHU NPGADF

statistics-10.29* -9.20* -10.60* -12.61* -9.96* -8.93*

*Significant at the 1% level and the null hypothesis is rejected

Variable LCR NCL NHO NHU NPG

ADF

statistics

-4.90* -3.96* -3.68* -2.84* -3.80*

*Significant at the 1% level and the null hypothesis is rejected

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the Durbin-Watson statistic showing signs of positive autocorrelation in the data that will invalidate

the nice OLS results.

This is a typical case where researchers will change their regression model from a price level

to a price change level. Although a large group of studies (Hill and Schneeweis, 1981; Park et al.

,1987; Braga et al. 1989 among many other) emphasized that using price level models is wrong due

to obvious statistical problems we strongly agree with Witt et al. (1987) that the statistical first

difference model is not congruent to the price change model. This is because the lag operator for

price (percentage) change models takes differences as the change in prices over the time interval

representing the hedge exposure and, as long as this exposure is not identical to the frequency of the

data under the analysis, the autocorrelation may still be a problem if price differences are considered.

Moreover, the exposure is not important for price level models because the same ratio can be used

whereas when price change or percentage change models are employed the hedge ratio depends on

the hedging period.

Table 5. OLS results for the simple regression model regressing the jet fuel oil on

futures prices of proxy variable

We also believe that most airline companies, although they might have some storage

capacities, cannot afford to stock vast amounts of kerosene for long periods of time. Therefore, their

Futures

Contract t-statistics t-statistics Adjusted R2

Durbin-

Watson

statistics

LCR 2.222 3.166 1.110 32.755 0.84 0.316

NCL 0.444 0.857 1.127 47.844 0.92 0.473

NHO 1.668 3.939 39.339 55.827 0.94 0.476

NHU 0.381 0.473 37.547 30.675 0.82 0.194

NPG 5.098 7.281 48.485 28.871 0.80 0.208

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concern is the current futures price and the ending basis and price level models are relevant. If there

is any problem with autocorrelation, a more appropriate solution would be to try and correct the

estimates of the regression coefficients using a Cochrane-Orcutt procedure (see Davidson and

MacKinnon, 1993, Chapter 10). The adjusted estimates are BLUE and they are given below in Table

6. One of the first things to be noticed is the change in the Durbin Watson statistic.

Table 6. Cochrane-Orcutt corrected estimates

Futures 1 t-statistics 2 t-statistics Adjusted R2 Durbin-Watson

statistics

LCR 0.998 0.0424 0.466808 0.038978 0.457283 -0.00393 1.834391

NCL 0.997 0.0406 0.496997 0.416484 6.903424 0.187637 2.214941

NHO 0.994 0.0460 0.576674 19.09626 7.975026 0.236587 2.223238

NHU 0.993 0.0941 1.132133 14.98603 6.494167 0.169320 2.120128

NPG 0.997 0.0360 0.394835 5.596175 1.247208 0.002743 1.827963

3.3 Scholes Williams estimates

It is well-known that there is some non-synchronization between spot data and futures data.

For poorly syncronized data we also calculate the Scholes and Williams (1977) instrumental variable

estimator for the hedge ratio. This is given by

))(),((cov

))(),((cov

tIVtF

tIVtSSW

=

(10)

where )2()1()1()()1()( +=+++= tFtFtFtFtFtIV (11)

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and )1()()( = tStStS and )1()()( = tFtFtF . For our data the SW estimates are given in

Table 7.

Table 7. Scholes-Williams instrumental variable estimates

Independent variable (Futures) SW estimator

LCR0.03309

NCL1.09439

NHO32.1953

NHU-29.75581

NPG1.85632

4. Cross-hedging the currency

4.1 Data analysed

The data consists of 137 observations, weekly data from 19 th January 1999 and 21st August

2001. The Tuesday settlement price is used and the data was from Datastream. The futures are traded

either on NYMEX, or on CME or CBOT. In the first case, the most common one, the beginning of

the code is FN, in the second case the beginning of the code is FI and in the last case the code starts

with FC. For example FIBP is the exchange rate between the British pound and the U.S. dollar.

All currency data are quoted per unit of US dollar. The following codes are used for

emerging market currencies in empirical analyses: IR Indian rupee, RI- Indonesian Rupiah,

HKUS- Hong Kong Dollars, TW -Taiwan Dollar , PPUS Philippines Peso, RMB China, Yuan

Renminbi, RM - Malaysia Ringgit, SD -Singapore dollars, TB- Thailand Baht.

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The following codes are used for the proxy exchange rates that are investigated for cross

hedging operations: FCEU- Euro/USD, FIAD-Australian Dollars/USD, FIBP-British Pound/USD,

FICD-Canadian Dollars/USD, FIDM-Deutsche mark/USD, FIFR- French Franc/USD, FIJY-

100Japanese Yen/USD, FIMX-Mexican Peso/USD, FINE-New Zealand Dollars/USD, FIRA-South

African Rand/USD, FIRU- Russian Ruble/USD, FNYF-Swiss Franc/USD.

4.2 Regression based estimates

This section is in a sense similar to the analysis presented in Aggarwal and DeMaskey

(1997). However, while they considered hedging portfolios of emerging currencies as foreign

investments, therefore having their hedging operations in U.S., our position is quite the opposite. The

problem here is to hedge the cash flows in currencies of emerging markets. Hence, in this section the

cross hedge for emerging market currency to U.S. dollar is cross hedged via futures on one of the

following Australian dollar, Japanese Yen, French franc, euro, Swiss franc or British pound to U.S.

dollar.

The analysis is done simultaneously for the Asian emerging countries like Hong Kong,

Taiwan, Thailand, China, Philippines, Malaysia, Singapore. Appendix 1 contains information about

the correlations between the various spot prices and futures prices. Together with other scatterplots

(not shown here) they can be used as a preliminary screening procedure in order to determine what

possible futures contracts to use for each emerging market currency. For each spot currency some of

the highest correlation coefficients on the corresponding row are highlighted .

As in the previous section, we test first that the pairs of spot price and futures price time

series are not random walks and are not drifting apart. The ADF test results are shown in Appendix,

showing that the series are related and move together. This should set up the scene for estimating the

optimal hedge ratio from a simple linear regression model. However, the Durbin Watson statistics in

Table 8 show that there are problems with autocorrelations and a Cochrane-Orcutt correction is

needed.

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Table 8. OLS estimation results all variables being exchange rates to the U.S. dollar;

the Durbin-Watson statistics showing problems with serial correlations

Dependent variable in bold

Futures t-statistics t-statistics Adjusted R2Durbin-

Watson

statistics

HK

FCEU 7.583982 1058.970 0.190638 27.71496 0.849411 0.209757

FINE 7.942936 1348.547 -0.339144 -27.53139 0.847700 0.145103

IR

FINE 59.55818 156.3370 -31.25034 -39.22242 0.918728 0.266082

FIRA 30.76632 82.35968 2.010933 37.54691 0.911961 0.195351

PP

FIAD -4.807292 -3.098604 28.51714 31.54412 0.879649 0.302498FIRA 1.454731 1.430248 6.125479 42.00551 0.928401 0.413604

RI

FIAD -2404.853 -3.763989 6487.714 17.42603 0.689970 0.178564

FIRA -669.8540 -1.217480 1348.772 17.09850 0.681766 0.178884

RMB

FIBR 8.283054 9966.584 -0.002537 -5.945654 0.201647 1.350758

FIRA 8.282442 9743.462 -0.000620 -5.087910 0.154685 1.282225

RM

FIAD 3.798592 6552.790 0.000648 1.917931 0.019314 1.321509

FIJY 3.803085 4430.763 -0.003786 -3.952905 0.097098 1.457320

SD

FIAD 1.337182 70.44161 0.229156 20.71650 0.758939 0.172570

FIRA 1.397494 85.80609 0.047781 20.46250 0.754386 0.190013

TB

FIAD 10.76721 11.27193 17.34619 31.16349 0.877052 0.246105

FIRA 15.11685 19.42070 3.647948 32.68811 0.886997 0.242981

TW

FIBR 25.13368 42.40087 3.623325 11.90741 0.508646 0.116265

FICD -3.232585 -0.986330 23.64427 10.79750 0.459429 0.136339

The Cochrane-Orcutt estimates are not reported because the estimated value of is in almost all

cases equal to 1. This suggests that a price change level model might be more appropriate. This is

consistent with the large body of the literature on cross hedging currencies. The estimates for the

hedge ratio are given in Table 9.

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Table 9. Cochrane-Orcutt estimates for cross hedging currency contracts

2 t-statistics Durbin-Watson statistics

HKFCEU 1.00005 -0.01109 -1.42517 2.600140HKFINE 1.00004 -0.00825 -0.51196 2.637038

IRFINE 0.99972 -3.66030 -2.27673 2.223086

IRFIRA 1.00076 -0.05448 -0.36827 2.260041

PPFIAD 1.00212 1.807282 0.740944 2.441125

PPFIRA 1.00007 -0.15319 -0.20692 2.424785

RIFIAD 1.00062 1539.276 1.583182 1.779929

RIFIRA 0.99982 0.008297 0.982653 2.265767

RMBFIBR 0.99821 4.878976 2.007487 2.534242

RMBFIRA 0.99974 0.000673 2.874534 2.653865

RMFIAD 1.00287 -0.897467 -1.09789 2.389865

RMFIJY 1.00064 -0.000521 -0.09767 2.252586

SDFIAD 0.99996 0.235425 -1.78678 2.145674

SDFIRA 1.00003 -0.576277 -0.00786 2.036357

TBFIAD 1.00432 2.987897 -0.93434 2.367547

TBFIRA 0.99735 0.846184 1.867868 2.253453

TWFIBR 1.00073 1.097803 1.487897 2.554588

TWFICD 1.00123 -0.00056 1.98789 2.357545

The optimal hedge ratios are calculated as the beta coefficient of a significant futures

contract. Although the calculations are tedious, involving a backward elimination model selection

procedure starting from the multiple linear model with a portfolio of all futures contracts variables,

only the results for the relevant pairs of spot and futures exchange rates are provided in Table 10 in

next section. The last column of the table contains estimates calculated via a non-OLS method. The

two sets of results can then be easily compared in terms of signs and order of magnitude.

4.3 Scholes-Williams estimates

Some of the problems that appear with regression models may be due to non-synchronisation

between spot data and futures data. It is worth calculating then the optimal hedge ratios via an

instrumental variable method (Scholes-Williams) as described in Section 3.3.

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Table 10. Price change estimates and SW estimates for cross hedging currencies

Variablesignificant

t-stats for thebeta

p-values forthe beta

Beta-estimates SW estimates

HKUS FIBR -1.942124 0.0542 -0.032779 0.02139

IRUS FINE -2.278052 0.0243 -3.661866 -1.89491

PPUS FNYF 2.096970 0.0379 5.365034 0.59352

RIUS FIBR 2.498447 0.0137 1033.397 1823.241

RMBUS FIMX 1.940431 0.0544 0.132118 0.04313

RMUS FIBR -2.957913 0.0037 -0.003243 -0.00112

SDUS FIJYFIAD

-2.9188205.272407

0.00410.0000

-0.1814900.160678

-0.068420.252747

TBUS FINE -3.698060 0.0003 -18.13703 -25.5885

TWUS FNZX 1.316747 0.0319 2.855127 5.32973

We have included variables having P-values very close to the significance level 0.05 because with

another set of data the significance may change.

One of the drawback of the Scholes-Williams estimator is that little is known about its

properties. In an applied manner, the efficiency of both sets of estimates can be measured out of the

sample. However the sets of data that we used shows signs of a structural break around September

2000 and some investigations based on the Chow test are currently in progress.

5. Conclusions

Risk management for a problematic commodity such as kerosene (jet fuel) is complicated

when the base of the operations is an emerging country. The instruments available on the financial

markets are not numerous and there is no clear-cut technique that will help the risk manager to hedge

the cash flows involved in managing this commodity. It is impossible to organise a perfect hedge

because kerosene futures are traded only on Tokyo and the reference point here is an emerging

market country. Therefore the only thing that is achievable is to minimise the risk.

In this paper we investigated some of the solutions that can be applied in practice based on

current data. Two strategies were proposed. Firstly, one can try and cross-hedge the kerosene with

futures contracts on crude oil, heating oil, gasoline. Secondly, one may decide to buy the futures on

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kerosene in Tokyo and hedge then the exchange rate to Japanese yen or other hard currency like U.S.

dollar.

The empirical evidence presented in this paper shows that, for emerging countries, the

calculation of optimal hedge ratios based on regression based methods is questionable. The

efficiency of hedging is not very high and the whole statistical estimation process may need a fresh

approach where the OLS assumptions are not necessarily valid.

The problems related to autocorrelation are corrected with a Cochrane-Orcutt estimation

procedure but the fit of the new models to the data is not pleasing. Maybe the problem lies with the

futures prices and poor synchronisation between spot data and futures data. An answer for this

problem relies on the instrumental variable approach. The estimates are calculated easy but nothing

can be said about the performance of this estimator.

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Appendix 1

Table A1. Correlations between Spot and Futures Prices

Table Spot and Futures Prices Correlations

FCEU FIAD FIBP FIBR FICD FIDM FIFR FIJY FIMX FINE FIRA FIRU FNYF FNZX

HKUS 0.92 0.83 0.84 0.50 0.38 0.92 0.92 0.07 0.52 -0.92 0.84 -0.23 0.91 0.44

IRUS 0.90 0.94 0.95 0.69 0.65 0.90 0.90 -0.27 0.51 -0.96 0.96 -0.18 0.84 0.46

PPUS 0.87 0.94 0.92 0.75 0.68 0.87 0.87 -0.31 0.49 -0.93 0.96 -0.24 0.80 0.45

RIUS 0.64 0.83 0.78 0.67 0.78 0.64 0.64 -0.54 0.28 -0.72 0.83 -0.25 0.56 0.30

RMBUS -0.25 -0.37 -0.33 -0.46 -0.39 -0.25 -0.25 0.19 -0.13 0.32 -0.40 -0.06 -0.21 -0.08

RMUS 0.02 0.16 0.14 0.02 0.31 0.02 0.02 -0.32 -0.02 -0.05 0.18 0.03 -0.03 0.00

SDUS 0.76 0.87 0.86 0.73 0.72 0.76 0.76 -0.59 0.46 -0.78 0.87 -0.21 0.70 0.33

TBUS 0.84 0.94 0.91 0.79 0.73 0.84 0.84 -0.35 0.53 -0.92 0.94 -0.23 0.77 0.44

TWUS 0.20 0.45 0.43 0.72 0.68 0.21 0.21 -0.80 0.23 -0.28 0.51 -0.08 0.10 0.14

Table A2. ADF tests for random walk hypothesis

ADF ADF Critical

Values

134obs

FCEU -7.953150 FNYF -7.802790 1% -2.5810FIAD -7.344890 FNZX -7.346365 5% -1.9423FIBP -8.506203 HKUS -11.68428 10% -1.6170FIBR -9.599300 IRUS -8.119069FICD -8.044370 PPUS -8.472214FIDM -8.422368 RIUS -7.267894FIFR -8.001995 RMBUS -7.807324FIJY -8.461334 RMUS -5.179745

FIMX -8.642969 SDUS -7.229745

FINE -7.359875 TBUS -8.325468FIRA -8.578433 TWUS -6.928866FIRU -7.490564

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Table A3. ADF tests for cointegration, with the regressand variable under the Futures column

Futures ADF Futures ADF Level of

significance

Critical value

Hong Kong Malaysia 1% -2.5809

FCEU -2.548160 FIAD -7.122474 5% -1.9422

FINE -2.363381 FIJY -8.389120 10% -1.6169

IRUS Singapore

FINE -2.692138 FIAD -2.686329

FIRA -2.564823 FIRA -2.690358

Philippines Thailand

FIAD -2.891567 FIAD -2.503748

FIRA -2.901785 FIRA -2.356806

RIUS Taiwan

FIAD -2.505554 FIBR -2.507233

FIRA -1.951939 FICD -1.859965

China

FIBR -6.437518

FIRA -6.139744