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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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Journal ArticleDOI
TL;DR: In this paper, the role of volatility in tail risk reduction and in particular in tail-risk reduction is discussed. But the focus of this paper is on the effect of volatility on the performance of the portfolio optimization problem.
Abstract: As a consequence of recent market conditions an increasing number of investors are realizing the importance of controlling tail risk to reduce drawdowns thus increasing possibilities of achieving long-term objectives. Recently, so called volatility control strategies and volatility target approaches to investment have gained a lot of interest as strategies able to mitigate tail risk and produce better risk-adjusted returns. Essentially these are rule-based backward looking strategies in which no optimization is considered. In this contribution we focus on the role of volatility in downside risk reduction and, in particular, in tail risk reduction. The first contribution of our paper is to provide a viable way to integrate a target volatility approach, into a multiperiod portfolio optimization model, through the introduction of a local volatility control approach. Our optimized volatility control is contrasted with existing rule-based target volatility strategies, in an out-of sample simulation on real data, to assess the improvement that can be obtained from the optimization process. A second contribution of this work is to study the interaction between volatility control and downside risk control. We show that combining the two tools we can enhance the possibility of achieving the desired performance objectives and, simultaneously, we reduce the cost of hedging. The multiperiod portfolio optimization problem is formulated in a stochastic programming framework that provides the necessary flexibility for dealing with different constraints and multiple sources of risk.

1 citations

Journal ArticleDOI
TL;DR: In this paper, the authors conduct a comprehensive analysis of the rationales proposed in prior studies to explain several well-known characteristic anomalies, recognizing that only a minority of firms drive these anomalies, run a statistical leverage analysis to filter out these firms.
Abstract: We conduct a comprehensive analysis of the rationales proposed in prior studies to explain several well-known characteristic anomalies. Recognizing that only a minority of firms drive these anomalies, we run a statistical leverage analysis to filter out these firms. We then try to forecast the identity of these ‘high leverage firms’ using proxy variables related to the rationales. Our results indicate that traditionally-used risk factors hardly ever explain the anomalies, while idiosyncratic risk together with distress risk is of great importance for the size and the book-to-market anomalies. In contrast, no rationale seems entirely convincing in explaining the momentum anomaly.

1 citations

ReportDOI
TL;DR: In this article, the authors developed an assignment model of a labor market, where the value of a match between firms, that differ in multiple dimensions, and agents, that differed in precision, is endogenously generated from a stock-market equilibrium.
Abstract: Price efficiency plays an important role in financial markets. Firms influence it, particularly when they issue public equity. They can hire a reputable underwriter with a star analyst to generate public signals about profits to reduce uncertainty and increase valuations. We develop an assignment model of this labor market. The value of a match between firms, that differ in multiple dimensions, and agents, that differ in precision, is endogenously generated from a stock-market equilibrium. We characterize the multidimensional-to-one assignment and obtain testable predictions. Extensions allow firms to value efficiency for other reasons and apply to other labor markets like media-or-investor relations professionals.

1 citations

Journal ArticleDOI
TL;DR: In this paper, the authors used the new issues market to examine the impact of ambiguity and ambiguity aversion on the pricing of financial assets and found that the underwriter prices both the systematic and idiosyncratic components of ambiguity in the offer price while well diversified investors price only the systematic component in the aftermarket.
Abstract: The new issues market is used to examine the impact of ambiguity and ambiguity aversion on the pricing of financial assets. An IPO process is modeled assuming ambiguity regarding the returns on financial assets and risk and ambiguity aversion on the part of agents. Theoretically, the underwriter prices both the systematic and idiosyncratic components of ambiguity in the offer price while well diversified investors price only the systematic component in the aftermarket. This difference in pricing provides a novel explanation for IPO underpricing and highlights an observable impact of ambiguity on asset prices. Empirically, the results are consistent with the model's predictions.

1 citations

Posted Content
TL;DR: In this article, the authors test the predictability of eighteen stock return predictors, including classic factors such as firm size, book-to-market, and momentum, along with other proposed predictors from firm-specific, corporate investment, financing, and stock characteristic anomalies.
Abstract: We test the predictability of eighteen stock return predictors, including classic factors such as firm size, book-to-market, and momentum, along with other proposed predictors from firm-specific, corporate investment, financing, and stock characteristic anomalies. These predictors have power to predict raw returns and risk-adjusted returns (i.e., alpha) at the annual horizon during 1962 to 2008. However, since the Federal Reserve has distorted markets with its monetary policy responses to the financial crisis, none of these eighteen predictors can generate alpha.

1 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