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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: In this article, the authors test whether expected idiosyncratic volatility is related to the cross-section of asset returns and find that, contrary to several recent papers, the expected volatility has no reliable relationship to expected returns.
Abstract: We test whether expected idiosyncratic volatility is related to the cross section of asset returns. We find that, contrary to several recent papers, expected idiosyncratic volatility has no reliable relationship to expected returns. Further, realized contemporaneous idiosyncratic volatility does have a positive relationship with expected returns - this relationship is driven by unexpected idiosyncratic volatility. A look-ahead bias that has been present in recent papers has led to false conclusions about the relationship between expected idiosyncratic volatility and expected return. Our findings are robust to several choices of volatility forecasting models and systematic factor models.
20 citations
TL;DR: This article showed that the CAPM fails to explain the predictability of stock market returns because covariances with the forecasting variables are also important determinants of the stock market return, and that changing investment opportunities have important effects on stock prices.
Abstract: Fama and French (2003), among many others, show that the capital asset pricing model (CAPM) does not explain stock returns. These results should not be a surprise because the model has some strong assumptions, and the failure of any one of them may cause the model to fail. In particular, the CAPM is a static model in which expected stock returns are assumed to be constant. However, if expected returns are time-varying, Merton (1973) and Campbell (1993), among others, show that the return on an asset is determined not only by its covariance with stock market returns, as in the CAPM, but also by its covariance with variables that forecast stock market returns. In this article, I estimate a variant of Campbell’s intertemporal CAPM (ICAPM), using forecasting variables advocated in recent research. I find that the CAPM fails to explain the predictability of stock market returns because covariances with the forecasting variables are also important determinants of stock market returns. Therefore, consistent with some recent authors, for example, Brennan, Wang, and Xia (forthcoming) and Campbell and Vuolteenaho (2002), the failure of the CAPM is related to timevarying expected returns. The remainder of the article is organized as follows. I first briefly summarize the recent developments of the asset pricing literature and then present evidence that stock market returns and volatility are predictable. For illustration, I discuss and estimate a variant of Campbell’s ICAPM and show that changing investment opportunities have important effects on stock prices. 1 A BRIEF REVIEW OF THE LITERATURE In the past two decades, financial economists have documented many anomalies in financial
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TL;DR: In this paper, the authors review the evidence on cross-sectional return predictability and the failure of standard consumption CAPM models and their conditional versions to explain these predictability patterns.
Abstract: I review recent research efforts in the area of empirical cross-sectional asset pricing. I start by summarizing the evidence on cross-sectional return predictability and the failure of standard (consumption) CAPM models and their conditional versions to explain these predictability patterns. One response in part of the recent literature is to focus on ad-hoc factor models, which summarize the cross-section of expected returns in parsimonious form, or on production-based approaches, which suggest links between firm characteristics and expected returns. Without imposing restrictions on investor preferences and beliefs, neither one of these two approaches can answer the question why investors price assets the way they do. Within the rational expectations paradigm, recent research that imposes such restrictions has focused on the ICAPM, long-run risks models, as well as frictions and liquidity risk. Approaches based on investor sentiment have focused on the development of empirical proxies for sentiment and for the limits to arbitrage that allow sentiment to affect prices. Empirical work that considers learning and adaptation of investors has worked with out-of-sample tests of cross-sectional predictability.
20 citations
TL;DR: In this article, the authors compare the information content of quarterly earnings guidance and quarterly earnings by examining their associations with current and future stock returns when the two signals are bundled at earnings announcements and find a significantly stronger association between announcement returns and guidance news.
Abstract: I compare the information content of quarterly earnings guidance and quarterly earnings by examining their associations with current and future stock returns when the two signals are bundled at earnings announcements. At the bundled announcement, I find a significantly stronger association between announcement returns and guidance news. From the day after the bundled announcement through the next earnings announcement, both signals generate abnormal return drifts of about 200 basis points. However, the timing of the post-announcement returns differs considerably. For guidance, about 50% of the post-announcement drift occurs at the next earnings announcement. In contrast, for earnings, about 20% of the preceding drift reverses at the next earnings announcement. Investor ignorance of the drift following guidance news coupled with a fixation on post-earnings announcement drift potentially explains this surprising difference in the timing of the post-announcement returns. Overall, this study indicates that bundled quarterly earnings guidance contains more information than quarterly earnings and that investors incorrectly overweight the earnings news and underweight the guidance news during the post-announcement period until the next earnings announcement.
19 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