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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 impact of expected price risk on the direct cost of issuing equity and found that companies with higher option implied volatilities raise less external equity capital and pay higher total investment bank fees in the stock market.
Abstract: The structure of a firm-commitment Seasoned Equity Offering (SEO) resembles a put option underwritten by an investment bank syndicate. Employing implied volatilities from issuers’ stock options as a direct forward-looking measure, this paper examines the impact of expected price risk on the direct cost of issuing equity. Using a comprehensive sample of 1,208 SEOs between 1996 and 2009, we find issuers with higher option implied volatilities raise less external equity capital and pay higher total investment bank fees in the stock market, ceteris paribus. The effect of implied volatility on the investment bank fees is incremental to the previously documented factors, stronger for larger issuers with lower pre-SEO realized stock volatilities, and for SEOs with higher expected price pressures around issue dates. These relationships are robust to adjustments for correlations among control variables, sample selection bias and also simultaneous determination of offer size and SEO fees.
TL;DR: In this paper, the authors show that market volatility affects stock returns both directly and indirectly through its impact on liquidity provision and the negative relation between market volatility and stock returns arises not only from greater risk premiums but also greater illiquidity premiums that are associated with higher market volatility.
Abstract: This study shows that market volatility affects stock returns both directly and indirectly through its impact on liquidity provision and the negative relation between market volatility and stock returns arises not only from greater risk premiums but also greater illiquidity premiums that are associated with higher market volatility. In particular, we show that a stock’s return is more sensitive to unexpected changes in market volatility when its liquidity disappears more in response to volatility shocks, which indicates that liquidity providers play an important role in determining the effect of market volatility on stock returns. Stock returns are more sensitive to volatility shocks in the high-frequency trading era, and after the regulatory changes in the US markets that increased competition between public traders and market makers, reduced the tick size, and decreased the role of market makers.
TL;DR: In this paper, the authors claim that short-term investors have a stronger preference for speculative stocks featuring high volatility and high skewness than longterm investors do, supported by both of the theoretical analysis using Ingersoll and Jin's (2013) realization utility model and the empirical analysis following Bali, Cakici and Whitelaw's (2011) methodology.
Abstract: Different investors have different time preferences, which lead to different investment horizons. We claim that short-term investors have a stronger preference for speculative stocks featuring high volatility and high skewness than long-term investors do. It is supported by both of the theoretical analysis using Ingersoll and Jin’s (2013) realization utility model and the empirical analysis following Bali, Cakici and Whitelaw's (2011) methodology.
TL;DR: In this paper, the authors explore a middle ground between common risk factors and idiosyncratic risks as an alternative to the traditional factor model and introduce partial factors as a third category of factors that only affect certain groups of stocks.
Abstract: Over the past half century, the explanatory power of any factor models has dropped by more than 50%. Under a conventional asset pricing framework, more than 80% of individual stocks' return variations are now considered as firm specific. In order to explain more return variations, we explore a middle ground between common risk factors and idiosyncratic risks as an alternative to the traditional factor model. Specifically, we introduce partial factors as a third category of factors that only affect certain groups of stocks. To demonstrate the existence of such factors and in order to be parsimonious, we present a simple iterative procedure both to extract partial factors from individual stock returns and to group stocks simultaneously. In contrast to a decreasing trend in the explanatory power of common factors, we show that partial factors not only are pervasive within their groups but also have played an increasing role in accounting for comovement among individual stocks over time. For example, a multifactor model with two common factors and two partial factors are able to provide an additional 10% explanatory power over popular factor models. Partial factors are also useful in explaining variations in government bond returns and characteristics sorted portfolio returns.
TL;DR: The authors proposed a parsimonious, comprehensive proxy for innovations in limited arbitrage: the divergence between the return of an ETF and the return on the underlying net asset value, constructed from return divergence spanning four asset classes and found that equity LAFs are negatively priced in the cross-section of stock returns.
Abstract: We propose a parsimonious, comprehensive proxy for innovations in limited arbitrage: the divergence between the return on an ETF and the return on the underlying net asset value. Consistent with a common component, we confirm limited arbitrage risk-factors, LAF, constructed from return divergence spanning four asset classes are correlated. Consistent with well-known factors that limit arbitrage, increased volatility and market illiquidity, we find that equity LAFs are negatively priced in the cross-section of stock returns. However, our pricing tests confirm that LAFs also provide pricing information beyond well-known limits to arbitrage. Overall, our findings suggest that limited arbitrage risk is priced and LAF is a relevant risk-factor.
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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