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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 showed that stocks with low book-to-market ratios, also known as glamour stocks, have significantly more positive skewness in their return distributions compared to the return distributions of value stocks with high book-tomarket ratios.
Abstract: This study demonstrates that stocks with low book-to-market ratios, also known as glamour stocks, have significantly more positive skewness in their return distributions compared to the return distributions of value stocks with high book-tomarket ratios. The premium (discount) investors apply to these glamour (value) stocks also correlates significantly with the difference in return skewness. These findings suggest that the value/glamour-stock puzzle is partially explained by investor preference for positive skewness in stock returns. Such preference for skewness, which is consistent with investors having inverse S-shaped utility functions, is observed in such consumer behaviors as lottery purchases and gambling. This paper further documents significant predictive power of accounting-based measures, such as the book rate of return, with respect to the skewness of stock returns.
23 citations
TL;DR: In this article, the authors examine the performance of the low-risk strategy previously considered in the literature and of a beta-neutral low risk strategy more relevant to practice and demonstrate that the historical performance of low risk investing, like any quantitative investment strategy, is time-varying.
Abstract: Research showing that the lowest risk stocks tend to outperform the highest risk stocks over time has led to rapid growth in so-called low-risk equity investing in recent years. We examine the performance of the low-risk strategy previously considered in the literature and of a beta-neutral low-risk strategy more relevant to practice. We demonstrate that the historical performance of low risk investing, like any quantitative investment strategy, is time-varying. We find that both of our low-risk strategies exhibit dynamic exposure to the well-known value, size, and momentum factors and appear to be influenced by the overall economic environment. Our results suggest time-variation in the performance of low-risk strategies is likely influenced by the approach to constructing the low-risk portfolio strategy and by the market environment and associated valuation premia.
23 citations
TL;DR: In this paper, the authors show that the prices of risk for factors that are nonlinear in the market return are readily obtained using index option prices, and that the new estimates of the price of risk improve the models' performance.
Abstract: We show that the prices of risk for factors that are nonlinear in the market return are readily obtained using index option prices. The price of co-skewness risk corresponds to the market variance risk premium, and the price of co-kurtosis risk corresponds to the market skewness risk premium. Option-based estimates of the prices of risk lead to reasonable values of the associated risk premia. An out-of-sample analysis of factor models with co-skewness and co-kurtosis risk indicates that the new estimates of the price of risk improve the models' performance.
22 citations
TL;DR: In this article, a simple short-term return reversal trading strategy designed to capture the residual component generates a highly significant risk-adjusted return three times the size of the standard reversal strategy during a 1982-2009 sampling period.
Abstract: The profit to a standard short-term return reversal strategy can be decomposed analytically into four components related to (1) across-industry return momentum; (2) within-industry variation in expected returns; (3) underreaction to within-industry cash flow news; (4) and a residual. Only the residual component, which isolates reaction to recent "non-fundamental" price changes, is significant and positive in the data. A simple short-term return reversal trading strategy designed to capture the residual component generates a highly significant risk-adjusted return three times the size of the standard reversal strategy during our 1982-2009 sampling period. Our decomposition suggests that short-term return reversal is pervasive, much greater than previously documented, and driven by investor sentiment on the short-side and liquidity shocks on the long-side.
22 citations
TL;DR: This paper found that adjusting CAPM for anchoring-influenced judgments provides a plausible unified framework for understanding almost all of the key cross-sectional anomalies facing CAPM, and the market equity premium is also larger with anchoring.
Abstract: Empirical evidence on the behavioral of professional stock analysts suggest that they form qualitatively correct judgments within the same sector, and that they spend most of their research time on sector leaders. This suggest a role for the anchoring and adjustment of Tversky and Kahneman (1974). The surprising finding is that adjusting CAPM for anchoring-influenced judgments provides a plausible unified framework for understanding almost all of the key cross-sectional anomalies facing CAPM. The market equity premium is also larger with anchoring.
22 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