Summary Asset Pricing 4.1 2015

Week 2.1

Three Factor Model F&F 1992 Two easily measured variables, size and book-to-market equity, combine to capture the cross-sectional

variation in average stock returns associated with market beta, size, leverage, book-to-market equity,

and earnings-price ratios. Moreover, when the tests allow for variation in p that is unrelated to size, the

relation between market beta and average return is flat, even when beta is the only explanatory

variable.

Data

Nonfinancial firms only

o financial firms tend to have a higher leverage which has another meaning as for non-

financial firms where high leverage more likely indicates distress

Accounting data from June

o From this period is highly likely that all firms have filed their accounting data and made

it public. Normally this should be done within 3 months of the fiscal year end but this

does not always happen.

Two Methods

Sorting stocks on company characteristics in previous period and check the return in this period

o Easy, no need to assume linearity

o Non parametric test

o Do not assume a constant relation over time

o Hard to do multivariate analysis

o Exclusive focus on top-bottom deciles

o Not possible to do statistical inference

For each month run a cross-sectional regression with the returns of this period as a dependent

variable and company characteristics in previous period as explanatory variable.

Estimating Beta by Double Sorting

From portfolios on size, there is evidence that this produces a wide spread of average returns

and betas.

o Problem: Betas of size portfolios and size are highly correlated, so asset pricing tests

can’t efficiently separate size from beta effects in average returns.

o Solution: Estimate beta per stock for 2-5 prior years and divide each size decile into 10

portfolios on the basis of this pre-ranking Betas for individual stocks. This allows for

variation in Betas that is unrelated to size.

Calculate returns for the next 12 months

Redo each year

Allocate the full period post ranking beta of a size-beta portfolio to each stock in the portfolio

o These betas will be used in the FM cross sectional regression for individual stocks.

Double sorting

Advantage

o Magnifies the spread of betas

o Post ranking betas closely reproduce preranking beta orderings

o Allows for variation in beta unrelated to size

Disadvantage

o True betas are not the same for all stocks in a portfolio.

But precision of full period post ranking betas is higher than imprecise individual

stock estimates.

Outcomes

No relation between beta and return

Relation between size & book-to-market and returns

Three Factor Model F&F 1993

The paper identifies five common risk factors in the returns on stocks and bonds. Stock returns have

shared variation due to the stock market factors. The factors seem to explain average returns on stocks

and bonds.

Time series regression

Variables that are related to average returns must proxy for sensitivity to common risk factors in

returns

o If the factors capture all common variation the intercept should be zero

Test how different combinations of common factors capture the cross sectional returns.

Factor Mimicking Portfolios

SMB

o Sorts stock on size; ME

o Split at the median

o Go long in bottom half, go short in top half

HML

o Sort stocks on value; BM

o 3 blocks; 30/40/30 L/M/H

o Go long in top 30%, go short in bottom 30%

Market (RM-RF)

o RM: return on value weighted portfolio of stocks in 6 portfolios

o RF: 1-month treasury rate

Sorting

2 way sorts:

o 5 portfolios on size

o 5 portfolios on value

Total of 25 intersection portfolios

Outcomes

The 3 factors capture strong common variation in stock return

SMB stock slopes are related to size

HML stock slopes are related to BM

Size and value factors can explain the difference in average returns across stocks, but the

market factor is needed to explain why stocks returns are on average above the on month

treasury bill rate

Factor loadings

Applications

Portfolio selection

Performance evaluation

Measuring abnormal returns in event studies

Calculation of cost of capital

Risk or Characteristics?

Neoclassical:

o Premia associated with size and BM represent compensation or systematic risk

o With a 3 factor model, the issues largely disappear

o Because the factors are priced, they must be measuring risk because the market is

efficient

the factor loading is related to expected returns

Week 2.2

Short Run Momentum (Jegadeesh and Titman) The paper explains that strategies, which buy stocks that have performed will in the past an sell stocks

that have performed poor in the past, generates significant positive returns over 3 to 12 month holding

periods. The profitability of these strategies is not due to their systematic risk or to delayed stock price

reactions to common factors. The part of the abnormal returns generated in the first year after portfolio

formation disappears in the following two years.

Short run

Lagged returns between J=1 to 4 quarters

Holding period between K=1 to 4 quarters

Methods

Calculate returns over all stocks in past J months

Rank them in ascending order

Create 10 equally weighted deciles, top=loser, bottom=winner

Buy winners, sell losers

Repeat every month

Outcomes

Momentum effect is not driven by size effect

Stocks with higher beta have a higher momentum

There is a book to market effect

o This indicates that relative strength portfolios are not primarily due to cross sectional

differences in systematic risk. Profits are due to serial correlation in the firm specific

component but not confined to any particular subsample of stocks.

Seasonal Effects

Negative returns in January

Even excluding January, returns are seasonal

Results are consistent for different subsamples

Strength over time

Positive for the first 12 months

Could be temporary

o This indicates that the strategy does not tend to pick stocks that have high unconditional

expected returns.

Interpretations

Transactions by investors that buy past winners and sell past losers move prices away from their

long run values temporarily and thereby cause prices to overreact.

The market underreacts to information about the short term prospects. This is plausible given

the nature of the information available about a firms short term prospects differs from the

nature of more ambiguous information that is used by investors to asses a firms long term

prospects.

Four factor model

Momentum is the fourth factor MOMt

based on return from month -12 to -2

long in top 30%, short in bottom 30%

Long run mean reversion (DeBondt, Thaler) This study of market efficiency investigates whether overreaction affects stock prices. The empirical

evidence is consistent with the overreaction hypothesis. Substantial weak form market inefficiencies are

discovered. The results also shed new light on the January returns earned by prior "winners" and

"losers". Portfolios of losers experience exceptionally large January returns as late as five years after

portfolio formation

Long run mean reversion

Test if overreaction hypothesis is predictive

If stock prices systematically overshoot, there their reversal should be predictable from past

return data alone, with no use of any accounting data like earnings

Hypothesis

o Extreme movements are followed by movements in opposite direction

o The more extreme the movement, the more extreme the adjustment

This implies a violation of weak form market efficiency

Method

Monthly returns of all stocks

Take excess returns

Compute cumulative returns for 16 non overlapping 3 year past periods per stock

Rank from low to high, top decile=winner, bottom decile =loser

Calculate cumulative excess returns for next 16 non overlapping 3 year periods for both

portfolios

Calculate average return over 16 periods of each portfolio and check for significance using a t-

test

Outcomes

Consistent with overreaction hypotheses

Effect is asymmetric; Loser effect > Winner effect

Most excess returns are realized in January

Overreaction occurs in 2nd and 3rd year, 1st is insignificant

Effect is qualitatively different from January effect and seasonality of stock prices

Implications

Effect losers > effect winners

o Average winner beta > average loser beta > 1

loser portfolios are less risky

o the excess return calculations assume the CAPM beta =1

this systematic bias may be responsible for asymmetry

January drives results

o Investors may wait for years before realizing loses and the observed seasonality of the

market as a whole

P/E effect

o Result support price-ratio hypothesis

High P/E-stocks are overvalued, low ones are undervalued

o But P/E is also a January driven phenomena

No practical application of this strategy today!

Explaining Patters (Barberis, Shleifer, Vishny) Recent empirical research in finance has uncovered two families of pervasive regularities: underreaction

of stock prices to news such as earnings announcements, and overreaction of stock prices to a series of

good or bad news. In his paper they propose a model of investor sentiment, or of how investors form

beliefs, which is consistent with the empirical findings.

Underreaction

The expected return of a next period after good news is higher than the expected return of a

next period after bad news

If the price underreacts, then it must be corrected in a following period

People do not fully incorporate the news at the time it occurs

Overreaction

The expected return of a next period after stream of good news is lower than the expected

return of a next period after a stream of bad news

News is being extrapolated too far

Model

A representative, risk neutral investor; reflecting consensus

1 security that pays 100% of earnings as dividend

o So that the equilibrium price of the security equals the NPV of future earnings, as

forecasted by the investor

No information in prices over and above the information already contained in earnings

Earnings follow a random walk

Investor does not know about the random walk properties and things there are 2 options,

o The price will do down with a (relative) high possibility

o The price will go down with a (relative) low possibility

Model 1

Mean reverting model

Conservatism

o Investor tends to underreact to the importance of the news

Mean reverting earnings expectations

o If there is positive news today, investor believes it will be negative tomorrow and vice

versa

On average the price is too low, so the average post earnings announcement is high

o This is consistent with momentum and post earnings announcement drift

Model 2

Representativeness

o After a string of negative news, the investor extrapolates the performance too far

Trending in terms of earnings expectations

Price is too high on average, future returns are low

o Consistent with overreaction

Choose model

If a shock t+1 is positive after a positive shock the investor will put more weight on model 2

If a shock t+1 is positive after a negative shock the investor will put more weight on model 1

Week 3.1

Limits to arbitrage (Shleifer, Vishny) The model also suggests where anomalies in financial markets are likely to appear, and why arbitrage

fails to eliminate them.

Arbitrage

Theory

o Infinite small risk neutral arbitrageurs

o Direct price adjustment

o Zero risk

o No investment needed

Reality

o Small number of specialized institutions

o Slower price adjustment

o Capital needed

o Risky

o Arbitrageurs may avoid extreme volatile arbitrage positions

Although this position offers attractive returns, it also has a high exposure to

risk of loses and the need to liquidate the portfolio under pressure from the

investor

Fama vs. Shleifer/Vishny

Fama:

o High BM stocks results in high returns because they have a high loading on a different

risk factor then the market. The portfolio itself is a proxy for such a distress factor.

But no macroeconomic factor which explains this is given by Fama...

Shleifer and Vishny:

o Result of investor sentiment and cost of arbitrage

Growth/value stocks is consistent with representativeness and leads to mean

reversion

Very volatile value portfolio on short term

Likely to be avoided by arbitrageurs

Limits to arbitrage

Implementation cost

o Transaction cost

Bid/ask spread, direct transaction cost

Liquidity

o Capital needed for marginal requirements

Short selling

Derivatives

o Arbitrage might not be complete

Arbitrageurs stay our because of cost

Fundamental risk

o Market can move against position of arbitrageur

Noise trader risk

o Prices diverge more in short term

Short run loss for arbitrageur

Margin call for short end

Noise Trader Risk (DeLong, Shleifer, Summers, Waldman) They present a simple overlapping generation’s model of an asset market in which noise traders both

affect prices and earn higher expected returns. The unpredictability of noise traders' beliefs creates a

risk in the price of the asset that prevents rational arbitrageurs from aggressively betting against them.

As a result, prices can diverge significantly from fundamental values even in the absence of fundamental

risk. Moreover, bearing a disproportionate amount of risk that they themselves create enables noise

traders to earn a higher expected return than rational investors do.

Noise trader risk

The risk of a further change of noise traders’ opinion away from its mean

Arbitrage dos not eliminate effect of noise because noise itself creates risk

Model

2 periods, Young and Old

Labor income when your, consumption when old

Investment decision when young

o S; safe asset with fixed dividends r

Perfectly elastic supply

Similar to riskless short term bond

o U; unsafe asses with fixed dividends r

Fixed supply

Similar to equity

2 agents

o Rational

o Noise traders

When old, agents sell S and U for the current price and consumption

Variance

The variance of prices is derived solely from noise trader’s risk. Both agents limit their demand

for asset U because the price they can sell it for when old depends on the uncertain beliefs of

the next period noise traders.

o This limits the extent to which they are willing to bet against each other

o Keeps arbitrageurs from driving prices to fundamental values

Return differences

When the relative amount of noise traders is small:

o This will result in an enormous opposite sign positions because small noise trader risk

makes groups think an almost riskless opportunity exists.

Effects

Hold more effect

o Noise traders’ returns relative to those of sophisticated investors are increased when

noise traders on average hold more of the risky asset and earn a larger share of the

reward to risk bearing. When the expected average price of noise traders is negative,

noise trader’s misperceptions still make riskless asses U risky and still push up the

expected return on asset U. However, the rewards are disproportionally accrued to

sophisticated individuals who hold more of the risky asses then the noise traders.

Price pressure effect

o As noise traders become more bullish, their demand more of the risky asset on average

and drive up tis price. They reduce the return/risk bearing and therefore the differential

between their and sophisticated returns.

Friedmann effect

o Misperceptions are stochastic; they have the worst possible timing. They but most of

risky assets U, just when other noise traders are buying it, which is when they are most

likely to suffer capital loss. The more variable noise traders are, the more damage their

prior market riming does to their returns.

Create space effect

o To take advantage of noise trader’s misperceptions, rational investors must bear this

noise traders risk. Since they are risk averse, they reduce the extent to which they bet

against noise traders.

Utility

Utility of rational traders is higher by definitions. Since they maximize the true utility, every

strategy that earns a higher mean return must have a higher variance which makes it

unattractive.

Higher expected returns does not compensate for extra risk for noise traders

o It comes at the cost of holding portfolios that give a lower expected utility due to the

higher variance

Rational traders always have a higher utility with noise traders present

o Their trading option expands from safe assets to safe and unsafe assets

o This is not valid when stock of risky asset is endogenous, noise traders can then reduce

price of risk and make capital more riskier

Imitation of beliefs

Based on returns

o If the expected difference return is positive then the expected fraction of noise traders

at time t is higher than the expected fraction of noise traders at the point of no

difference in expected returns.

Create space effect causes the fraction of noise traders to approach 1

Based on utility

o The fraction of noise traders always approaches 0, as an increase in returns is a decrease

in utility by the noise traders utility function

Implications explanation

Possible explanation of excess volatility

o No changes in fundamentals, jet volatility rises when noise traders enter the market

Mean reversion

o If asses prices respond to noise traders and if the errors of noise traders are temporary,

then asset prices revert to the mean

Equity premium puzzle

o If equity trades below fundamental value, which is the only way for noise traders to

have higher expected returns, as a result of noise trader risk, equities yield a higher

return then the bond market

Week 3.2

Market Liquidity (Pastor, Stambaugh) Investigate if market wide liquidity is a state variable important for asset pricing. They find that expected

stock returns are related cross sectional to the sensitivities of returns to fluctuations in aggregate

liquidity. The liquidity measure relies on the principle that order flow (volume) induces greater return

reversals when liquidity is lower. A liquidity risk factor accounts for half of the profits to a momentum

strategy.

Liquidity

The degree to which an asset or security can be bought or sold in the market without affecting

the asset's price (/ depth).

The ability to convert an asset to cash quickly

Liquidity is characterized by a high level of trading activity

Sources of illiquidity

Exogenous trading costs

o Just think of broker/exchange commissions. Remuneration for setting up a trading

system

Private information

o If there is a probability of trading against an informed trader, the market maker will

require a compensation in the form of bid-ask spread (Adverse Selection)

Search costs

o Especially in OTC markets finding a counterparty may require time, which is costly

because of the uncertainty on the price at which the trade is executed

Inventory risk for the market maker

o Market maker intermediates between sellers and buyers. Needs to carry inventory. He

bears a risk that fundamentals change in the meantime. Bid-ask spread compensates

market-maker for inventory risk

Measuring liquidity is hard (slides)

The bid-ask spread, typically as a fraction of the price (relative spread)

Volume (shares or dollars traded over some interval of time) or turnover (volume divided by

capitalization)

Amihud‘s ratio on daily data for day t is ILLIQt = |R| / Vol

The fraction of days with zero returns within a month

Measuring liquidity (pastor and Stambaugh)

Market level liquidity per month as the average of stock lever liquidity

Order flow should be accompanied by a return that is expected to be partially reversed in the

future if the stock is not perfectly liquid

There is a negative relation between the expected reversal, given a volume and the stocks

liquidity.

Using daily data within each month estimates

o For each month ad stock a liquidity-factor is obtained

If a stock is not perfectly liquid, then volume pushes up prices too much and therefor the next

period should be accompanied by reversal

Expect the liquidity-factor to be negative in general and larger in absolute magnitude when

liquidity is lower

Take the average of the liquidity factors for each month as a measure of market liquidity. Scale

this measure for the overall size of the stock market in each period.

Correlation in months with large liquidity drops

Flight to quality in months with exceptional low liquidity

o When liquidity drops, stocks and fixed income assets move in opposite direction

Is liquidity priced?

Check if a stocks expected return is related to the sensitivity of its returns restated to the

innovation in aggregate liquidity; L

Estimate time series factor model including L

At the end of each year sort stocks on their forecasted liquidity betas

Form 10 portfolios, calculate post formation returns, estimate 4-factor model on post ranking

portfolios

Sorting

Predicted values of beta-low used to sort stocks are obtained using 2 methods

1. Allows the predicted beta-low to depend on observable variables at the time of the sort

a. Large differences in expected returns that are unexplained by other factors

2. Using only historical betas to confirm that the 1st method and results are not driven solely by

sorting stocks on the other characteristics that help predict liquidity betas

a. Large significant differences in alphas on the beta-low sorted portfolios

b. Post ranking liquidity betas increase across deciles

Alphas and betas

o If liquidity risk factor is priced we see systematic differences in the average returns on

our beta sorted portfolios

o Premium is positive

o In stocks with higher sensitivity to aggregate liquidity stocks offer higher expected

returns

Consistent with the notion that in investor wants compensation for stocks with

greater exposure to this risk

Momentum and liquidity risk

The momentum strategy becomes less attractive when portfolio spreads based on liquidity are

also available

Funding liquidity (Brunnermeier, Peterson) Provide a model that links an asset’s market liquidity (i.e., the ease with which it is traded) and traders’

funding liquidity (i.e., the ease with which they can obtain funding). Traders provide market liquidity,

and their ability to do so depends on their availability of funding. Conversely, traders’ funding, i.e., their

capital and margin requirements, depends on the assets’ market liquidity. They show that margins are

destabilizing and market liquidity and funding liquidity are mutually reinforcing, leading to liquidity

spirals. The model explains the empirically documented features that market liquidity (i) can suddenly

dry up, (ii) has commonality across securities, (iii) is related to volatility, (iv) is subject to “flight to

quality,” and (v) co-moves with the market. The model provides new testable predictions, including that

speculators’ capital is a driver of market liquidity and risk premiums.

Funding liquidity

Model that links assets market liquidity and traders funding liquidity

Tight funding liquidity in traders become to take on positions, especially capital intensive

ones with high-margin securities lower market liquidity high volatility

Market liquidity

Can suddenly dry up

Has commonality across securities

Is related to volatility

Is subject to flight to quality

Co-moves with the market

Outcome

Destabilizing margins force speculators to de-lever their positions in times of crisis, leading to

pro-cyclical market liquidity provision:

o Margins can decrease with illiquidity and be stabilizing when financiers know the

illiquidity is temporary

As long as capital is abundant, liquidity is insensitive to change in margins

When speculators hit their constraints, they reduce positions and market liquidity declines:

o Now prices are more driven by funding liquidity then by fundamentals

There are multiple equilibria:

o Liquid favorable margin requirements helps speculators to make markets more

liquid

o Illiquid larger margin requirements restricting speculators from providing market

liquidity

Dry-up:

o If speculators capital is reduces enough, the market will eventually switch to low

liquidity/high margin

Margin spiral:

o Higher margins funding problems for speculators reduces positions prices move

away frown fundamentals, and so on…

Loss spiral:

o Large speculator position negatively correlated with costumers demand increase

market illiquidity speculator losses on initial positions reduce positions prices

move away from fundamentals, and so on…

Ratio of illiquidity is the same across all assets for which speculators provide liquidity:

o Speculators optimally invest in securities that have the greatest expected profit (i.e.

illiquidity) per capital use (determined by the assets dollar margin)

o Commonality of liquidity across assets

o Market liquidity is correlated across stocks

Market liquidity declines as fundamental volatility increases

o Flight to quality:

When speculators are induced to provide liquidity in securities that do not use

much capital(low vol/ low mag), thus the liquidity differential between high and

low volatility stocks increases

illiquid securities are predicted to have more liquidity risk

Risk that funding constraints become binding limits provision of market liquidity:

o Safety buffer affects initial prices increase of future prices covariance with future

shadow cost (funding liquidity).

Week 4.1

Investor Sentiment (Baker, Wurgler) Real investors and markets are too complicated to be neatly summarized by a few selected biases and

trading frictions. The “top down” approach to behavioral finance focuses on the measurement of

reduced form, aggregate sentiment and traces its effects to stock returns. It builds on the two broader

and more irrefutable assumptions of behavioral finance—sentiment and the limits to arbitrage—to

explain which stocks are likely to be most affected by sentiment. In particular, stocks of low

capitalization, younger, unprofitable, high volatility, non-dividend paying, growth companies, or stocks

of firms in financial distress, are likely to be disproportionately sensitive to broad waves of investor

sentiment.

Set of proxies

Closed end fund discounts

Turnover

Number of IPO’s

First-day IPO returns

Dividend premium

Equity share

Get away from fundamental news

Run Regression:

o SENT=α+β[Macro fundamentals]+ε

o Use residuals who are not orthogonal to the macro fundamentals

Method 1; in sample

Take all stocks

Sort on volatility over previous 12 months

Create 10 decile portfolios rom low to high volatility and calculate returns

Repeat this each month

Over the full sample estimate sentiment adjusted CAPM for each decile

Method 2; out of sample

Take all stocks

Sot on volatility over the previous 12 months

Split series into high and low sentiment periods using previous month measure of sentiment

Compute average return for each of the 10 portfolios:

o For the 2 separate periods

o For the whole period

Repeat this for each month

Outcomes

When sentiment is high (low), average future returns of speculative stocks are on average lower

(higher) then bond like stocks

o inconsistent with classical asset pricing

Socks that are difficult to arbitrage or to value are more effected by sentiment

Market Anomalies (Bouwman, Jacobsen) Model

Take stock market value weighted returns

Do a simple regression with a dummy variable for winter

Test if the coefficient of the dummy is significantly different from 0

Outcomes

There is an effect in period of countries at the 10% level

Results persistent over time?

o Take longer time series and redo regression until t=0 of last regression

o higher return in winter also or longer series

Compare with buy and hold strategy:

o For most countries the risk free rate and market index do not span the annual returns of

this trading strategy

Possible explanations

Economic significance

o The outcomes are economically significant, also with transaction cost taken into account

Data mining

o Investors could have been aware of indicator

o It’s based on an old saying

o Out of sample test persistent also for different countries

o no data mining

Risk

o Risk measured as standard deviation tends to be similar in both periods

January effect

o New regression with January dummy

o Halloween effect still significant for some countries

Sector

o No evidence that the effect is related to the relative size of a specific sector in different

economies

Interest rates and trading volume

o Little evidence that this rates and volume differ during periods, all outcomes non-

significant

Vacations

o Significantly related to

Length and timing of vacation

Impact of vacation on trading activity

o But, arbitrage should bet against this

o But, no opposite effect for northern and southern hemisphere

News

o No seasonal factor in the news

Week 4.2

Prospect theory (Benazi, Thaler) The equity premium puzzle refers to the empirical fact that stocks have greatly outperformed bonds

over the last century. It appears difficult to explain the magnitude of the equity premium within the

usual economics paradigm because the level of risk aversion necessary to justify such a large premium is

implausibly large. They offer a new explanation which has two components. First, investors are assumed

to be 'loss averse meaning they are distinctly more sensitive to losses than to gains. Second, investors

are assumed to evaluate their portfolios frequently, even if they have long-term investment goals such

as saving for retirement or managing a pension plan. They call this 'myopic loss aversion'. Using

simulations they find that the size of the equity premium is consistent with the previously estimated

parameters of prospect theory if investors evaluate their portfolios annually. That is, investors appear to

choose portfolios as if they were operating with a time horizon of about one year. The same approach is

then used to study the size effect. Preliminary results suggest that myopic loss aversion may also have

some explanatory power for this anomaly.

1. What evaluation period would make investors indifferent between stocks and bonds?

2. Given a period, what is the optimal combination of stocks and bonds?

Method, simulations

Draw 100.000 n-month returns for various horizons

Generate artificial return series using the empirical observed distribution of returns

Rank from best to worse

Compare returns over 20 intervals

Now, compute prospect value of the given asset for the specific holding period

o For T-bills and bond returns

o For real and nominal terms

Result

1 year period is reasonable because:

o Valuation period is one year

o File taxes annually

o Receive feedback from broker, mutual fund, retirement yearly

o Asset managers are evaluated yearly

o 35%-50% in stocks is reasonable because:

o Pension funds invest 54%

o People choose 50/50

o

Size factor explanation

Or portfolios with more than 5 stocks

o Prospective utility of large and small stocks flat out while small stock returns are higher

than big stocks consistent with size effect

o Prospect utility of a single stock is virtually identical to the one od a portfolio of large

stocks:

Small stocks are held by individuals, the small premium depends on their

preferences, they tend to evaluate their purchases one stock at a time rather

than as a portfolio

Individuals compare the stock with large portfolio stock

Solution to puzzle

Combine a high sensitivity to losses with a tendency to frequently monitor wealth

The tendency shifts the utility domain form consumption to returns and makes people demand

large premium to accept return variability

Skewness preferences (Harvey, Siddique) If asset returns have systematic skewness, expected returns should include rewards for accepting this

risk. They formalize this intuition with an asset pricing model that incorporates conditional skewness.

Results show that conditional skewness helps explain the cross-sectional variation of expected returns

across assets and is significant even when factors based on size and book-to-market are included.

Systematic skewness is economically important and commands a risk premium, on average, of 3.60

percent per year. Results suggest that the momentum effect is related to systematic skewness. The low

expected return momentum portfolios have higher skewness than high expected return portfolios.

If assets have systematic Skewness, expected returns should have rewards for this risk included.

Coskewness: component of assets Skewness related to the market portfolios skewness.

Method

Rank stocks on their Coskewness from low to high

Create long-short portfolios with top/bottom 30% S- and S+

Calculate returns for 61 months

Compare 3 factor model with 3 factor model + S- factor

o Check if α=0

Estimate time series regressions and compare FM portfolio to FM+ skewness factor portfolio

Then compare the next month’s cross sectional regression with skewness factor

Outcomes

Inclusion of S- lowers the F-statistic on α drastically

Conditional skewness can explain a significant part of the variation in returns

Skewness improves the CAPM model a lot

Skewness captures something over and above the 3 factor model

Market risk premium is positive for all history lengths, but inconsistent for SMB and HML