The Cross‐Section of Volatility and Expected Returns

Abstract

We examine the pricing of aggregate volatility risk in the cross-section of stock returns. Consistent with theory, we find that stocks with high sensitivities to innovations in aggregate volatility have low average returns. Stocks with high idiosyncratic volatility relative to the French (1993, Journal of Financial Economics 25, 2349) model have abysmally low average returns. This phenomenon cannot be explained by exposure to aggregate volatility risk. Size, book-to-market, momentum, and liquidity effects cannot account for either the low average returns earned by stocks with high exposure to systematic volatility risk or for the low average returns of stocks with high idiosyncratic volatility.IT IS WELL KNOWN THAT THE VOLATILITY OF STOCK RETURNS varies over time. While considerable research has examined the time-series relation between the volatility of the market and the expected return on the market (see, among others, Campbell and Hentschel (1992) and Glosten, Jagannathan, and Runkle (1993)), the question of how aggregate volatility affects the cross-section of expected stock returns has received less attention. Time-varying market volatility induces changes in the investment opportunity set by changing the expectation of future market returns, or by changing the risk-return trade-off. If the volatility of the market return is a systematic risk factor, the arbitrage pricing theory or a factor model predicts that aggregate volatility should also be priced in the cross-section of stocks. Hence, stocks with different sensitivities to innovations in aggregate volatility should have different expected returns.The first goal of this paper is to provide a systematic investigation of how the stochastic volatility of the market is priced in the cross-section of expected stock returns. We want to both determine whether the volatility of the market * Ang is with Columbia University and NBER. Hodrick is with Columbia University and NBER.Yuhang Xing is at Rice University. Xiaoyan Zhang is at Cornell University. We thank Joe Chen, Mike Chernov, Miguel Ferreira, Jeff Fleming, Chris Lamoureux, Jun Liu, Laurie Hodrick, Paul Hribar, Jun Pan, Matt Rhodes-Kropf, Steve Ross, David Weinbaum, and Lu Zhang for helpful discussions. We also received valuable comments from seminar participants at an NBER Asset Pricing meeting,

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“…In conclusion, from the above critical review , one can observe that at the level of the relationship between unsystematic risks fluctuations and stocks expected returns, the studies' results were subdivided into three different scenarios: first, studies proved negative relationship between unsystematic risks and returns, like study of Ang et al (2006) Second scenario is represented by some studies that proved a positive relationship between unsystematic risks and returns like, study of Goyal and Santa Clara (2003) jiang and Lee (2006) as both studies applied to the U.S , on the aggregate level,.Also the same results were reached by Fu (2009) and Malkiel and Xu (2003) but at the firm level. And finally studies proved non statistical significant relationship between unsystematic risks and returns, such as, study of Bali and Cakici (2008), applied to the U.S as different fluctuations scales were used by using daily and monthly data from July 1926 to December 2002.…”

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