Asymmetric Volatility, Skewness, and Downside Risk in Different Asset Classes: Evidence from Futures Markets

Date01 February 2016
AuthorYiuman Tse
Published date01 February 2016
The Financial Review 51 (2016) 83–111
Asymmetric Volatility, Skewness, and
Downside Risk in Different Asset Classes:
Evidence from Futures Markets
Yiuman Tse
University of Missouri - St. Louis
This study examines the cross-sectional variation of futures returns from different asset
classes. The monthly returns are positively correlated with downside risk and negatively
correlated with coskewness. The asymmetric volatility effect generates negatively skewed
returns. Assets with high coskewness and low downside betas provide hedges against market
downside risk and offer low returns. The high returns offered by assets with low coskewness
and high downside betas are a risk premium for bearing downside risk. The asset pricing model
that incorporates downside risk partially explains the futures returns. The results indicate a
unified risk perspective to jointly price different asset classes.
Keywords: asymmetric volatility, skewness, coskewness, downside risk, international fu-
JEL Classifications: C22, G10, G13
Correspondingauthor: Department of Finance, College of Business Administration, University of Missouri
- St. Louis, St. Louis, One University Blvd., MO 63121; Phone: (314) 516-6828; Fax: (314) 516-6420;
I thank three anonymous reviewers and John Waldfor valuable comments.
C2016 The Eastern Finance Association 83
84 Y. Tse/The Financial Review 51 (2016) 83–111
1. Introduction
A stylized fact of stock markets is that volatility tends to be higher following
negative return shocks than it does following positive shocks, as first noted by Black
(1976) and Christie (1982). Engle (2004) points out that this asymmetric volatility
effect induces negatively skewed returns. Earlier work by Kraus and Litzenberger
(1976) and Rubinstein (1973) shows that investors dislikestocks with negative skew-
ness, and, therefore, they require higher returns on these assets. Harvey and Siddique
(2000) further show that coskewness with a U.S. stock market volatility portfolio ex-
plains the cross-sectional variation in expected returns. Stocks with low coskewness
(i.e., assets delivering low returns when market volatilityis high) earn higher average
Investors indicate a different level of concern about downside losses versus
upside gains. Ang, Chen and Xing (2006a) report that stocks with higher downside
betas have higher returns, indicating a premium for bearing downsiderisk in the cross-
section. Ang, Chen and Xing (2006b, p. 260) provide an intuitive description of how
market volatility risk is related to downside risk, coskewness, and asset returns:
Risk averse agents demand stocks that hedge against [market volatility] risk. Periods
of high volatility also tend to coincide with downward market movements. . . . As
Bakshi and Kapadia (2003) comment, assets with high sensitivities to market volatility
risk provide hedges against market downside risk. The higher demand for assets with
high systematic volatility loadings increases their price and lowers their average return.
Finally, stocks that do badly when volatility increases tend to have negatively skewed
returns over intermediate horizons, while stocks that do well when volatility rises tend
to have positively skewed returns. If investors have preferences over coskewness (see
Harvey and Siddique, 2000), stocks that have high sensitivitiesto innovations in market
volatility are attractive and have lowreturns.
I provide a systematic approach for describing these relations in diverse asset
classes, represented by 55 futures contracts, including indexes, bonds, commodities,
and currencies. I test two hypotheses: (1) asymmetric volatility results in negative
long-run skewness and (2) downside risk is priced in the cross-section of different
asset classes. I start with the relation between asymmetric volatility and long-run
skewness and then look at the relation among skewness, downside beta, and coskew-
ness. Finally, I examine the risk premium for downside risk. The results provide
insight into risk management with international multiple asset classes represented by
futures contracts.
Futures contracts with lower transaction costs facilitate an examination of the
relationship among asymmetric volatility, risks, and returns. The index and bond
futures comprise all the major international markets, including Germany, Japan, the
United Kingdom, and the United States. Although investors can take a long or short
position in futures, like Gorton and Rouwenhorst (2006) and Lettau, Maggiori and
Weber(2014) in commodities futures, this study examines returns on long positions in
futures contracts. Gorton and Rouwenhorst (2006) study the diversificationbenefits of

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