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The Cross-Section of Volatility and Expected Returns
TL;DR: This paper examined the pricing of aggregate volatility risk in the cross-section of stock returns and found that stocks with high sensitivities to innovations in aggregate volatility have low average returns, and that stock with high idiosyncratic volatility relative to the Fama and French (1993) model have abysmally low return.
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 In addition, we find that stocks with high idiosyncratic volatility relative to the Fama and French (1993) 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
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TL;DR: The authors examined the relation between expected returns and idiosyncratic risk across 44 countries from 1980 to 2007 and found that the typical investor holds an under-diversified portfolio, and that such risk premiums are larger in markets with lower investor wealth and higher investor risk tolerance.
Abstract: We examine the relation between expected returns and idiosyncratic risk across 44 countries from 1980 to 2007. Theory suggests that expected returns are unrelated to idiosyncratic risk if investors hold fully-diversified portfolios, and positively related if investors hold under-diversified portfolios. The empirical evidence to date has been decidedly mixed. In this study, we apply Fu’s (2009) EGARCH model to an international setting and provide supportive evidence for a positive and significant relation between expected returns and idiosyncratic risk – suggesting that the typical investor holds an under-diversified portfolio. Our international dataset also allows us to examine the relation between country-level determinants of investor under diversification and idiosyncratic risk premiums. We find that such risk premiums are larger in markets with lower investor wealth and higher investor risk tolerance. We also find that investor characteristics are more important determinants of the size of the idiosyncratic risk premium than are information and transaction costs. Our study makes two primary contributions. First, we verify the existence of a positive risk premium for idiosyncratic volatility using over seven million observations from 58,000 stocks across 44 markets. Second, and perhaps more important, we show that idiosyncratic risk premiums are directly attributable to investor under-diversification.
42 citations
TL;DR: The authors compare two versions of the market Variance Risk Premium (VRP) measured in the equity and option markets, and find that their difference is strongly related to measures of the financial standing of intermediaries.
Abstract: We formally compare two versions of the market Variance Risk Premium (VRP) measured in the equity and option markets. Both VRPs follow common patterns and respond similarly to changes in volatility and economic conditions. However, we reject the null hypothesis that they are identical and find that their difference is strongly related to measures of the financial standing of intermediaries. These results shed new light on the information content of the VRP, suggest the presence of market frictions between the two markets, and are consistent with the key role played by intermediaries in setting option prices.
42 citations
TL;DR: This article proposed an empirical framework of disaster concerns to explain cross-sectional return variation both within and across asset classes, using a large set of out-of-the-money options on international equity indices, foreign currencies, and global government bonds.
Abstract: We propose an empirical framework of disaster concerns to explain cross-sectional return variation both within and across asset classes. Using a large set of out-of-the-money options on international equity indices, foreign currencies, and global government bonds, we measure the global …nancial market’s rare disaster concerns under only no-arbitrage conditions. Assets that have low return covariations with such concerns earn high excess returns in the future. The return predictability driven by rare disaster concerns is distinct from that driven by exposures to realized disaster shocks such as macroeconomic downturns and liquidity crunches, and is not
41 citations
TL;DR: In this article, the authors examined whether stock return dispersion (RD) provides useful information about future stock returns and found that RD consistently forecasts a decline in the excess market return at multiple horizons, and compares favorably with alternative predictors used in the literature.
Abstract: In this paper, I examine whether stock return dispersion (RD) provides useful information about future stock returns. RD consistently forecasts a decline in the excess market return at multiple horizons, and compares favorably with alternative predictors used in the literature. The out-of-sample performance of RD tends to beat the alternative predictors, and is economically significant as indicated by the certainty equivalent gain associated with a trading investment strategy. RD has greater forecasting power for big and growth stocks compared to small and value stocks, respectively. I discuss a theoretical mechanism giving rise to the negative correlation between RD and the equity premium.
41 citations
TL;DR: In this article, the authors show that an equity pairs trading strategy generates large and significant abnormal returns, and that this return is not driven purely by the short-term reversal of returns.
Abstract: We show that an equity pairs trading strategy generates large and significant abnormal returns We find that this return is not driven purely by the short-term reversal of returns The evidence related to the cross-sectional variation, the time-series variation, and the persistence of the pairs trading profits, and the determinants of return correlations is consistent with the delay in information diffusion as the driver for the pairs trading strategy Evidence from the liquidity factor and the recent financial crisis suggests that the short-term liquidity provision is not the main cause of the pairs trading strategy
40 citations
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TL;DR: In this paper, the authors present some additional tests of the mean-variance formulation of the asset pricing model, which avoid some of the problems of earlier studies and provide additional insights into the nature of the structure of security returns.
Abstract: Considerable attention has recently been given to general equilibrium models of the pricing of capital assets Of these, perhaps the best known is the mean-variance formulation originally developed by Sharpe (1964) and Treynor (1961), and extended and clarified by Lintner (1965a; 1965b), Mossin (1966), Fama (1968a; 1968b), and Long (1972) In addition Treynor (1965), Sharpe (1966), and Jensen (1968; 1969) have developed portfolio evaluation models which are either based on this asset pricing model or bear a close relation to it In the development of the asset pricing model it is assumed that (1) all investors are single period risk-averse utility of terminal wealth maximizers and can choose among portfolios solely on the basis of mean and variance, (2) there are no taxes or transactions costs, (3) all investors have homogeneous views regarding the parameters of the joint probability distribution of all security returns, and (4) all investors can borrow and lend at a given riskless rate of interest The main result of the model is a statement of the relation between the expected risk premiums on individual assets and their "systematic risk" Our main purpose is to present some additional tests of this asset pricing model which avoid some of the problems of earlier studies and which, we believe, provide additional insights into the nature of the structure of security returns The evidence presented in Section II indicates the expected excess return on an asset is not strictly proportional to its B, and we believe that this evidence, coupled with that given in Section IV, is sufficiently strong to warrant rejection of the traditional form of the model given by (1) We then show in Section III how the cross-sectional tests are subject to measurement error bias, provide a solution to this problem through grouping procedures, and show how cross-sectional methods are relevant to testing the expanded two-factor form of the model We show in Section IV that the mean of the beta factor has had a positive trend over the period 1931-65 and was on the order of 10 to 13% per month in the two sample intervals we examined in the period 1948-65 This seems to have been significantly different from the average risk-free rate and indeed is roughly the same size as the average market return of 13 and 12% per month over the two sample intervals in this period This evidence seems to be sufficiently strong enough to warrant rejection of the traditional form of the model given by (1) In addition, the standard deviation of the beta factor over these two sample intervals was 20 and 22% per month, as compared with the standard deviation of the market factor of 36 and 38% per month Thus the beta factor seems to be an important determinant of security returns
2,899 citations
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TL;DR: In this paper, the generalized autoregressive conditionally heteroskedastic (GARCH) model of returns is modified to allow for volatility feedback effect, which amplifies large negative stock returns and dampens large positive returns, making stock returns negatively skewed and increasing the potential for large crashes.
Abstract: It is sometimes argued that an increase in stock market volatility raises required stock returns, and thus lowers stock prices. This paper modifies the generalized autoregressive conditionally heteroskedastic (GARCH) model of returns to allow for this volatility feedback effect. The resulting model is asymmetric, because volatility feedback amplifies large negative stock returns and dampens large positive returns, making stock returns negatively skewed and increasing the potential for large crashes. The model also implies that volatility feedback is more important when volatility is high. In U.S. monthly and daily data in the period 1926-88, the asymmetric model fits the data better than the standard GARCH model, accounting for almost half the skewness and excess kurtosis of standard monthly GARCH residuals. Estimated volatility discounts on the stock market range from 1% in normal times to 13% after the stock market crash of October 1987 and 25% in the early 1930's. However volatility feedback has little effect on the unconditional variance of stock returns.
1,793 citations
TL;DR: In this article, the authors examined a class of continuous-time models that incorporate jumps in returns and volatility, in addition to diffusive stochastic volatility, and developed a likelihood-based estimation strategy and provided estimates of model parameters, spot volatility, jump times and jump sizes using both S&P 500 and Nasdaq 100 index returns.
Abstract: This paper examines a class of continuous-time models that incorporate jumps in returns and volatility, in addition to diffusive stochastic volatility. We develop a likelihood-based estimation strategy and provide estimates of model parameters, spot volatility, jump times and jump sizes using both S&P 500 and Nasdaq 100 index returns. Estimates of jumps times, jump sizes and volatility are particularly useful for disentangling the dynamic effects of these factors during periods of market stress, such as those in 1987, 1997 and 1998. Using both formal and informal diagnostics, we find strong evidence for jumps in volatility, even after accounting for jumps in returns. We use implied volatility curves computed from option prices to judge the economic differences between the models. Finally, we evaluate the impact of estimation risk on option prices and find that the uncertainty in estimating the parameters and the spot volatility has important, though very different, effects on option prices.
1,040 citations
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TL;DR: In this article, a new way to generalize the insights of static asset pricing theory to a multi-period setting is proposed, which uses a loglinear approximation to the budget constraint to substitute out consumption from a standard intertemporal asset pricing model.
Abstract: This paper proposes a new way to generalize the insights of static asset pricing theory to a multi-period setting. The paper uses a loglinear approximation to the budget constraint to substitute out consumption from a standard intertemporal asset pricing model. In a homoskedastic lognormal selling, the consumption-wealth ratio is shown to depend on the elasticity of intertemporal substitution in consumption, while asset risk premia are determined by the coefficient of relative risk aversion. Risk premia are related to the covariances of asset returns with the market return and with news about the discounted value of all future market returns.
805 citations
TL;DR: This article investigated whether market-wide liquidity is a state variable important for asset pricing and found that expected stock returns are related cross-sectionally to the sensitivities of returns to fluctuations in aggregate liquidity.
Abstract: This study investigates whether market-wide liquidity is a state variable important for asset pricing. We find that expected stock returns are related cross-sectionally to the sensitivities of returns to fluctuations in aggregate liquidity. Our monthly liquidity measure, an average of individual-stock measures estimated with daily data, relies on the principle that order flow induces greater return reversals when liquidity is lower. Over a 34-year period, the average return on stocks with high sensitivities to liquidity exceeds that for stocks with low sensitivities by 7.5% annually, adjusted for exposures to the market return as well as size, value, and momentum factors.
789 citations