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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
Citations
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TL;DR: In this paper, the authors investigated the variance risk premium in an international setting and provided empirical evidence that the US variance premium outperforms that of all other countries in predicting local and foreign equity returns.
Abstract: This paper investigates the variance risk premium in an international setting. First, I provide new evidence on the basic stylized facts traditionally documented for the US. I show that while the variance premiums in several other countries are, on average, positive and display signi…cant time variation, they do not predict local equity returns. Then, I extend the domestic model in Bollerslev, Tauchen and Zhou (2009) to an international setting. In light of the qualitative implications of my model, I provide empirical evidence that the US variance premium outperforms that of all other countries in predicting local and foreign equity returns.

52 citations

Journal ArticleDOI
TL;DR: In this paper, the authors show that a stock's expected return is decreasing in factor-loading uncertainty, controlling for the average level of its factor loading, and they estimate that average annual returns of a firm with the median level of factorloading uncertainty are 400 to 525 basis points lower than a comparable firm without factor loading uncertainty.
Abstract: Firm-specific information can affect expected returns if it affects investor uncertainty about risk-factor loadings. We show that a stock's expected return is decreasing in factor-loading uncertainty, controlling for the average level of its factor loading. When loadings are persistent, learning by investors can induce time-series variation in price-dividend ratios, expected returns, and idiosyncratic volatility, even when the aggregate risk-premium is constant and fundamental shocks are homoscedastic. Consistent with our predictions, we estimate that average annual returns of a firm with the median level of factor-loading uncertainty are 400 to 525 basis points lower than a comparable firm without factor-loading uncertainty.

52 citations

Journal ArticleDOI
TL;DR: The authors show that the average market beta of actively managed mutual funds captures their desire for leverage and thus the tightness of constraints, and they propose a measure for this leverage constraint tightness by inverting the argument that constrained investors tilt their portfolios to riskier assets.
Abstract: Prior theory suggests that time variation in the degree to which leverage constraints bind affects the pricing kernel. We propose a measure for this leverage constraint tightness by inverting the argument that constrained investors tilt their portfolios to riskier assets. We show that the average market beta of actively managed mutual funds -- intermediaries facing leverage restrictions -- captures their desire for leverage and thus the tightness of constraints. Consistent with theory, it strongly predicts returns of the betting-against-beta portfolio, and is a priced risk factor in the cross-section of mutual funds and stocks. Funds with low exposure to the factor outperform high-exposure funds by 5% annually, and for stocks this difference exceeds 8%. Our results show that the tightness of leverage constraints has important implications for asset prices.

51 citations

Journal ArticleDOI
TL;DR: In this article, the authors extend the accounting-based valuation framework of Ohlson (1995) and Feltham and Ohlsen (1999) to incorporate dynamic expectations about the level of systematic risk in the economy, which explains recent empirical findings documenting a strong negative association between changes in economywide risk and future stock returns.
Abstract: This study extends the accounting-based valuation framework of Ohlson (1995) and Feltham and Ohlson (1999) to incorporate dynamic expectations about the level of systematic risk in the economy. Our model explains recent empirical findings documenting a strong negative association between changes in economy-wide risk and future stock returns. Importantly, the model also generates costs of capital that are solely a linear function of accounting variables and other firm fundamentals including the book-to-market ratio, the earnings-to-price ratio, the forward earnings-to-price ratio, size and the dividend yield. This result provides a theoretical rationale for the inclusion of these popular variables in cost of capital (expected return) computations by the accounting and finance literatures and obviates the need to estimate costs of capital from unobservable (future) covariances. The model also generates an accounting return decomposition in the spirit of Vuolteenaho (2002). Empirically, we find that costs of capital generated by our model are significantly associated with future returns both in and out of sample in contrast to standard benchmark models. We further obtain significantly lower valuation errors in out-of-sample tests than traditional models that ignore dynamic risk expectations.

50 citations

Journal ArticleDOI
TL;DR: In this paper, the authors show theoretically and empirically that low risk anomalies are driven by return skewness, and that the profitability of betting against beta/volatility increases with firms' downside risk.
Abstract: This paper shows theoretically and empirically that beta- and volatility-based low risk anomalies are driven by return skewness. The empirical patterns concisely match the predictions of our model which generates skewness of stock returns via default risk. With increasing downside risk, the standard capital asset pricing model increasingly overestimates required equity returns relative to firms' true (skew-adjusted) market risk. Empirically, the profitability of betting against beta/volatility increases with firms' downside risk. Our results suggest that the returns to betting against beta/volatility do not necessarily pose asset pricing puzzles but rather that such strategies collect premia that compensate for skew risk.

50 citations

References
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Posted Content
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

Posted Content
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

Journal ArticleDOI
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

Posted Content
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

Journal ArticleDOI
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