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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 paper, the authors examine country-level parallels to the stock-level low-risk anomaly and find that the inter-market variation in returns do not follow the intra-market patterns, although the effect is largely explained by cross-national value, size and momentum effects.
Abstract: The aim of this paper is to examine country-level parallels to the stock-level low-risk anomaly. The inter-market variation in returns do not follow the intra-market patterns. The country-level returns are positively related to standard deviation, value at risk, and idiosyncratic volatility, although the effect is largely explained by cross-national value, size and momentum effects. The risk-return links seem stronger for idiosyncratic risk and almost non-existent for systematic risk (market beta). Furthermore, an additional sorting on value at risk can markedly improve the performance of country-level size and value strategies. The investigations are based on a cross-section of 78 national stock markets for years 1999-2014.
23 citations
TL;DR: In this article, the authors conduct comprehensive analyses of the return characteristics of stock portfolios sorted by idiosyncratic volatility and show that the relationship between idiosyncratic variance and expected stock returns depends on whether the portfolio is composed of stocks with extreme performance and whether the returns are computed over January and non-January months.
Abstract: We conduct comprehensive analyses of the return characteristics of stock portfolios sorted by idiosyncratic volatility. We show that the relationship between idiosyncratic volatility and expected stock returns depends on whether the portfolio is composed of stocks with extreme performance and whether the returns are computed over January and non-January months. The dominance of loser stocks in December and a reversal effect in the subsequent month lead to a positive relation between idiosyncratic volatility and portfolio returns in January. Whereas for other months, the impact of past winner stocks dominates and a negative relation is observed due to the return reversal of these winner stocks. Our study contributes to the understanding of how January effect and short-term return reversal can lead to different relation between idiosyncratic volatility and expected returns.
23 citations
TL;DR: In this paper, a significant and robust connection between firm-level asset changes and return momentum was found, and the effect of aggregate asset growth is stronger than that of variables related to business cycles and investor sentiment.
Abstract: We document a significant and robust connection between firm-level asset changes and return momentum. Momentum profits are large and significant for firms that have experienced large asset expansions or contractions, whereas they otherwise are small and often insignificant. The interaction pattern is not subsumed by previously documented drivers of momentum and shows up in market states where prior literature has documented an absence of momentum profits. Furthermore, we find a positive time-series relationship between aggregate asset growth and return momentum, and the effect of aggregate asset growth is stronger than that of variables related to business cycles and investor sentiment. While most existing models of firm investment and momentum cannot explain our results, recent real options models appear to hold the most promise.
23 citations
TL;DR: In this article, the authors investigate whether corporate insiders trade when asymmetric information is high, using data on U.S. corporate insider transactions between 1986 and 2012, and find that profits are significantly higher when insiders buy during periods of high relivol, but not when they sell shares.
Abstract: This paper investigates whether corporate insiders trade when asymmetric information is high, using data on U.S. corporate insider transactions between 1986 and 2012. The key innovation of this paper is our proxy for asymmetric information relivol which measures deviations of idiosyncratic volatility from a firm's normal level. Our findings indicate that relivol positively predicts insider purchases, which indicates that insiders buy shares when their informational advantage is high. However, insiders appear to sell less if relivol is high, which is consistent with existing evidence on sales being driven by alternative, non-information related trading motives such as liquidity or diversification needs. Further, we find that profits are significantly higher when insiders buy during periods of high relivol, but not when they sell shares.
23 citations
TL;DR: In this paper, the authors give a complete algorithm and source code for constructing what they refer to as heterotic risk models (for equities), which combine granularity of an industry classification, diagonality of the principal component factor covariance matrix for any sub-cluster of stocks, and dramatic reduction of the factor matrix size in the Russian-doll risk model construction.
Abstract: We give a complete algorithm and source code for constructing what we refer to as heterotic risk models (for equities), which combine: i) granularity of an industry classification; ii) diagonality of the principal component factor covariance matrix for any sub-cluster of stocks; and iii) dramatic reduction of the factor covariance matrix size in the Russian-doll risk model construction. This appears to prove a powerful approach for constructing out-of-sample stable short-lookback risk models. Thus, for intraday mean-reversion alphas based on overnight returns, Sharpe ratio optimization using our heterotic risk models sizably improves the performance characteristics compared to weighted regressions based on principal components or industry classification. We also give source code for: a) building statistical risk models; and ii) Sharpe ratio optimization with homogeneous linear constraints and position bounds.
23 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