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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: This article examined whether a corporate disclosure practice is a reason for the forecast dispersion anomaly and found that firms with higher dispersion in analysts' earnings forecasts are more likely to experience poor earnings in subsequent quarters.
Abstract: This paper examines whether a corporate disclosure practice is a reason for the forecast dispersion anomaly -- the negative relation between analyst forecast dispersion and future stock returns. Prior studies have shown that firms tend to disclose good news in a timely manner and delay the disclosure of bad news, and that withholding of news leads to greater dispersion in analysts’ forecasts. Accordingly, we predict that firms with higher dispersion in analysts’ earnings forecasts are more likely to experience poor earnings in subsequent quarters, and find evidence consistent with this prediction. After controlling for the relation between forecast dispersion and future earnings, we find that forecast dispersion is no longer negatively related to future stock returns. These results suggest that firms’ tendency to withhold bad news increases forecast dispersion as well as causes the market to temporarily overvalue stocks until the bad news is publicly released.
12 citations
TL;DR: In this paper, the authors discuss when and why custom multi-factor risk models are warranted and give source code for computing some risk factors, and discuss various aspects of custom risk model building.
Abstract: We discuss when and why custom multi-factor risk models are warranted and give source code for computing some risk factors. Pension/mutual funds do not require customization but standardization. However, using standardized risk models in quant trading with much shorter holding horizons is suboptimal: 1) longer horizon risk factors (value, growth, etc.) increase noise trades and trading costs; 2) arbitrary risk factors can neutralize alpha; 3) "standardized" industries are artificial and insufficiently granular; 4) normalization of style risk factors is lost for the trading universe; 5) diversifying risk models lowers P&L correlations, reduces turnover and market impact, and increases capacity. We discuss various aspects of custom risk model building.
11 citations
TL;DR: In this paper, the authors study the perception of dependence between asset returns and its impact on investment decisions, and they find that while changes in dependence are not neglected, correlation does not properly capture investors' perception of dependency.
Abstract: We study the perception of dependence between asset returns and its impact on investment decisions. Our findings suggest that, while changes in dependence are not neglected, correlation does not properly capture investors' perception of dependence. In several laboratory experiments we vary dependence between two assets. When dependence is linear, participants understand it and consistently diversify less at higher correlations. However, when we vary non-linear dependence -- increasing dependence in extreme returns while decreasing dependence in moderate returns -- most participants do not understand dependence in extreme returns. Consequently, they diversify less when dependence in moderate returns increases, even if overall correlation decreases due to less dependence in extreme returns. This finding suggests that investors could improve portfolio selection by taking into account biased beliefs about dependence.
11 citations
TL;DR: The authors hypothesize that if the negative relationship between asset growth and stock returns is due to mispricing, it should be more pronounced and more persistent when there are more severe limits to arbitrage.
Abstract: In this paper, we hypothesize that if the negative relationship between asset growth and stock returns is due to mispricing, it should be more pronounced and more persistent when there are more severe limits to arbitrage. The empirical evidence supports our hypothesis. Our findings are not due to conventional risks, firm characteristics, equity issuance, or idiosyncratic risk. In addition, the role of limits to arbitrage in the asset growth anomaly is not a manifestation of liquidity risk and is not simply ex-post justified by trading expenses. Our results appear to support the limits-to-arbitrage argument proposed by Shleifer and Vishny (1997).
11 citations
TL;DR: In this paper, the authors examine the relation between return R2 and expected stock returns and find that stocks with lower R2 earn higher future returns, while stocks with higher R2 are more difficult to value, tend to be affected by investor sentiment, attract retail investors, and are avoided by institutional investors.
Abstract: Return R2 is the statistic obtained by regressing individual stock returns on return factors. We find that stocks with lower R2 are more difficult to value, tend to be affected by investor sentiment, attract retail investors, and are avoided by institutional investors. We examine the relation between R2 and expected stock returns, and find that stocks with lower R2 earn higher future returns. From July 1966 through June 2008, the average return on low R2 stocks exceeds that on high R2 stocks by 0.39% per month, after adjusting for the market return as well as size, value, momentum, and liquidity factors. These results are consistent with the conjecture that stocks with lower R2 have poor information quality and are more likely to be subject to noise trading. According to DeLong, Shleifer, Summers and Waldmann (1990), such stocks assume higher noise trader risk and hence command higher expected returns. Based on R2, we form a noise trader risk factor by constructing a factor mimicking portfolio that goes long on stocks with low R2 and short on stocks with high R2. We find that the sensitivities of stocks to this factor could explain the cross-section of stock returns, even when their sensitivities to other conventional return factors are controlled. The results suggest that the trading activities of noise traders are correlated and affect stock returns in a systematic way.
11 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