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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 examined the pricing of tail risk for 43,000 stocks from 46 countries between 1995 and 2013 and decompose tail risks into those with respect to local and global market returns and find that both risks are independently priced.
Abstract: We examine the pricing of tail risk for 43,000 stocks from 46 countries between 1995 and 2013. We decompose tail risks into those with respect to local and global market returns and find that both risks are independently priced. Due to the increased demand for hedging tail risks, the premia for both tail risks are positively related to globalization. For local tail risk, though not for global tail risk, the premium is high when investor sentiment is low and its sensitivity is limited by globalization, reflecting that investors can diversify away local tail risk, but not global tail risk, globally.

8 citations

Journal ArticleDOI
TL;DR: In this article, the authors identify the underlying determinants of target price implied return forecast errors and find that analysts make systematic errors with respect to their use of past accounting fundamentals and risk proxies.
Abstract: Our research focuses on identifying the underlying determinants of target price implied return forecast errors. We predict and find that analysts make systematic errors with respect to their use of past accounting fundamentals and risk proxies. We show that analysts appear to over-extrapolate past sales growth, overvalue loss firms, and overvalue volatile stocks. Additional tests reveal that analysts provide overly optimistic forecasts for firms raising financing and firms with high trading volume, suggesting that self-serving biases could influence valuations made by analysts. Our target price determinants model explains approximately 15 percent of the target price valuation errors. We show that adjusting implied return forecasts for these predictable biases improves the returns to target price based trading strategies.

8 citations

Journal ArticleDOI
TL;DR: In this article, the authors provide theoretical and empirical evidence for the economic benefits in exploiting the timing-gains that result from the time-varying relative performance of these characteristic-based portfolios.
Abstract: Many exchange traded funds track simple characteristic-based equity portfolios such as the market capitalization, the fundamental value or the inverse volatility portfolio. This paper provides theoretical and empirical evidence for the economic benefits in exploiting the timing-gains that result from the time-varying relative performance of these characteristic-based portfolios. Under a factor model for expected returns, we show that this dynamic portfolio allocation can be efficient across the low-dimensional set of characteristic-based portfolios. We assess the out-of-sample performance on the S&P 100 universe over the period 1990-2013 and show gains in stability and significant positive risk-adjusted returns for the dynamic style portfolio. We conduct several robustness tests and extensions confirming the benefits of dynamic style allocation across characteristic-based portfolios.

8 citations

Journal ArticleDOI
TL;DR: In this article, the authors provide theoretical and empirical arguments in favor of a diminishing marginal premium for market risk, and they estimate that the market risk premium is at least five to six percent per annum, substantially above traditional estimates.
Abstract: We provide theoretical and empirical arguments in favor of a diminishing marginal premium for market risk. In capital market equilibrium with binding portfolio restrictions, investors with different risk aversion levels generally hold different sets of risky securities. Whereas the traditional linear relation breaks down, equilibrium can be described or approximated by a concave relation between expected return and market beta, and a concave relationship between market alpha and market beta. An empirical analysis of U.S. stock market data confirms the existence of a significant concave cross-sectional relation between average return and estimated market beta. We estimate that the market risk premium is at least five to six percent per annum, substantially above traditional estimates. A practical implication for active portfolio managers is that the alpha of "betting against beta" strategies seems dominated by the medium-minus-high-beta spread rather than the low minus-medium-beta spread. The success of such strategies thus largely depends on underweighting or short selling high-beta stocks.

8 citations

Journal ArticleDOI
TL;DR: In this paper, the authors propose a diversified risk parity (DRP) strategy, which aims for maximum diversification along uncorrelated risk sources embedded in the underlying commodities.
Abstract: Pursuing risk-based allocation across a universe of commodity assets, we find diversified risk parity (DRP) strategies to provide convincing results. DRP strives for maximum diversification along uncorrelated risk sources embedded in the underlying commodities. A straight-forward way to derive uncorrelated risk sources relies on principal components analysis (PCA). While the ensuing statistical factors can be associated with commodity sector bets, the corresponding DRP strategy entails excessive turnover because of the instability of the PCA factors. As an alternative, one may run the DRP strategy relative to common commodity risk factors that have been orthogonalized such that they exhibit a minimum tracking error to the original factors. The DRP strategy then builds on a more stable anchor that implicitly allows for a uniform exposure to commodity risk premia.

8 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