Summary Asset Pricing 4
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Transcript of Summary Asset Pricing 4
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