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342
Expected stock returns and volatility
 Journal of Financial Economics
, 1987
"... This paper examines the relation between stock returns and stock market volatility. We find evidence that the expected market risk premium (the expected return on a stock portfolio minus the Treasury bill yield) is positively related to the predictable volatility of stock returns. There is also evid ..."
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Cited by 472 (10 self)
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This paper examines the relation between stock returns and stock market volatility. We find evidence that the expected market risk premium (the expected return on a stock portfolio minus the Treasury bill yield) is positively related to the predictable volatility of stock returns. There is also evidence that unexpected stock market returns are negatively related to the unexpected change in the volatility of stock returns. This negative relation provides indirect evidence of a positive relation between expected risk premiums and volatility. 1.
Modeling and Forecasting Realized Volatility
, 2002
"... this paper is built. First, although raw returns are clearly leptokurtic, returns standardized by realized volatilities are approximately Gaussian. Second, although the distributions of realized volatilities are clearly rightskewed, the distributions of the logarithms of realized volatilities are a ..."
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Cited by 392 (41 self)
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this paper is built. First, although raw returns are clearly leptokurtic, returns standardized by realized volatilities are approximately Gaussian. Second, although the distributions of realized volatilities are clearly rightskewed, the distributions of the logarithms of realized volatilities are approximately Gaussian. Third, the longrun dynamics of realized logarithmic volatilities are well approximated by a fractionallyintegrated longmemory process. Motivated by the three ABDL empirical regularities, we proceed to estimate and evaluate a multivariate model for the logarithmic realized volatilities: a fractionallyintegrated Gaussian vector autoregression (VAR) . Importantly, our approach explicitly permits measurement errors in the realized volatilities. Comparing the resulting volatility forecasts to those obtained from currently popular daily volatility models and more complicated highfrequency models, we find that our simple Gaussian VAR forecasts generally produce superior forecasts. Furthermore, we show that, given the theoretically motivated and empirically plausible assumption of normally distributed returns conditional on the realized volatilities, the resulting lognormalnormal mixture forecast distribution provides conditionally wellcalibrated density forecasts of returns, from which we obtain accurate estimates of conditional return quantiles. In the remainder of this paper, we proceed as follows. We begin in section 2 by formally developing the relevant quadratic variation theory within a standard frictionless arbitragefree multivariate pricing environment. In section 3 we discuss the practical construction of realized volatilities from highfrequency foreign exchange returns. Next, in section 4 we summarize the salient distributional features of r...
Have Individual Stocks Become More Volatile? An Empirical Exploration of Idiosyncratic Risk
 THE JOURNAL OF FINANCE • VOL. LVI
, 2001
"... This paper uses a disaggregated approach to study the volatility of common stocks at the market, industry, and firm levels. Over the period 1962–1997 there has been a noticeable increase in firmlevel volatility relative to market volatility. Accordingly, correlations among individual stocks and the ..."
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Cited by 356 (14 self)
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This paper uses a disaggregated approach to study the volatility of common stocks at the market, industry, and firm levels. Over the period 1962–1997 there has been a noticeable increase in firmlevel volatility relative to market volatility. Accordingly, correlations among individual stocks and the explanatory power of the market model for a typical stock have declined, whereas the number of stocks needed to achieve a given level of diversification has increased. All the volatility measures move together countercyclically and help to predict GDP growth. Market volatility tends to lead the other volatility series. Factors that may be responsible for these findings are suggested.
Investing for the long run when returns are predictable
 Journal of Finance
, 2000
"... We examine how the evidence of predictability in asset returns affects optimal portfolio choice for investors with long horizons. Particular attention is paid to estimation risk, or uncertainty about the true values of model parameters. We find that even after incorporating parameter uncertainty, th ..."
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Cited by 351 (0 self)
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We examine how the evidence of predictability in asset returns affects optimal portfolio choice for investors with long horizons. Particular attention is paid to estimation risk, or uncertainty about the true values of model parameters. We find that even after incorporating parameter uncertainty, there is enough predictability in returns to make investors allocate substantially more to stocks, the longer their horizon. Moreover, the weak statistical significance of the evidence for predictability makes it important to take estimation risk into account; a longhorizon investor who ignores it may overallocate to stocks by a sizeable amount. ONE OF THE MORE STRIKING EMPIRICAL FINDINGS in recent financial research is the evidence of predictability in asset returns. 1 In this paper we examine the implications of this predictability for an investor seeking to make sensible portfolio allocation decisions. We approach this question from the perspective of horizon effects: Given the evidence of predictability in returns, should a longhorizon investor allocate his wealth differently from a shorthorizon investor? The motivation for thinking about the problem in these terms is the classic work of Samuelson ~1969! and Merton ~1969!. They show that if asset returns are i.i.d., an investor with power utility who rebalances his portfolio optimally should choose the same asset allocation, regardless of investment horizon. In light of the growing body of evidence that returns are predictable, the investor’s horizon may no longer be irrelevant. The extent to which the horizon does play a role serves as an interesting and convenient way of thinking about how predictability affects portfolio choice. Moreover, the results may shed light on the common but controversial advice that investors with long horizons should allocate more heavily to stocks. 2
Realized Variance and Market Microstructure Noise 161
, 2004
"... We study market microstructure noise in highfrequency data and analyze its implications for the realized variance (RV) under a general specification for the noise. We show that kernelbased estimators can unearth important characteristics of market microstructure noise and that a simple kernelbas ..."
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Cited by 166 (12 self)
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We study market microstructure noise in highfrequency data and analyze its implications for the realized variance (RV) under a general specification for the noise. We show that kernelbased estimators can unearth important characteristics of market microstructure noise and that a simple kernelbased estimator dominates the RV for the estimation of integrated variance (IV). An empirical analysis of the Dow Jones Industrial Average stocks reveals that market microstructure noise is timedependent and correlated with increments in the efficient price. This has important implications for volatility estimation based on highfrequency data. Finally, we apply cointegration techniques to decompose transaction prices and bid–ask quotes into an estimate of the efficient price and noise. This framework enables us to study the dynamic effects on transaction prices and quotes caused by changes in the efficient price.
Rangebased estimation of stochastic volatility models
, 2002
"... We propose using the price range in the estimation of stochastic volatility models. We show theoretically, numerically, and empirically that rangebased volatility proxies are not only highly efficient, but also approximately Gaussian and robust to microstructure noise. Hence rangebased Gaussian qu ..."
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Cited by 158 (13 self)
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We propose using the price range in the estimation of stochastic volatility models. We show theoretically, numerically, and empirically that rangebased volatility proxies are not only highly efficient, but also approximately Gaussian and robust to microstructure noise. Hence rangebased Gaussian quasimaximum likelihood estimation produces highly efficient estimates of stochastic volatility models and extractions of latent volatility. We use our method to examine the dynamics of daily exchange rate volatility and find the evidence points strongly toward twofactor models with one highly persistent factor and one quickly meanreverting factor. VOLATILITY IS A CENTRAL CONCEPT in finance, whether in asset pricing, portfolio choice, or risk management. Not long ago, theoretical models routinely assumed constant volatility ~e.g., Merton ~1969!, Black and Scholes ~1973!!. Today, however, we widely acknowledge that volatility is both time varying and predictable ~e.g., Andersen and Bollerslev ~1997!!, andstochastic volatility models are commonplace. Discrete and continuoustime stochastic volatility models are extensively used in theoretical finance, empirical finance, and financial econometrics, both in academe and industry ~e.g., Hull and
Asset pricing at the millennium
 Journal of Finance
"... This paper surveys the field of asset pricing. The emphasis is on the interplay between theory and empirical work and on the tradeoff between risk and return. Modern research seeks to understand the behavior of the stochastic discount factor ~SDF! that prices all assets in the economy. The behavior ..."
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Cited by 155 (2 self)
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This paper surveys the field of asset pricing. The emphasis is on the interplay between theory and empirical work and on the tradeoff between risk and return. Modern research seeks to understand the behavior of the stochastic discount factor ~SDF! that prices all assets in the economy. The behavior of the term structure of real interest rates restricts the conditional mean of the SDF, whereas patterns of risk premia restrict its conditional volatility and factor structure. Stylized facts about interest rates, aggregate stock prices, and crosssectional patterns in stock returns have stimulated new research on optimal portfolio choice, intertemporal equilibrium models, and behavioral finance. This paper surveys the field of asset pricing. The emphasis is on the interplay between theory and empirical work. Theorists develop models with testable predictions; empirical researchers document “puzzles”—stylized facts that fail to fit established theories—and this stimulates the development of new theories. Such a process is part of the normal development of any science. Asset pricing, like the rest of economics, faces the special challenge that data are generated naturally rather than experimentally, and so researchers cannot control the quantity of data or the random shocks that affect the data. A particularly interesting characteristic of the asset pricing field is that these random shocks are also the subject matter of the theory. As Campbell, Lo, and MacKinlay ~1997, Chap. 1, p. 3! put it: What distinguishes financial economics is the central role that uncertainty plays in both financial theory and its empirical implementation. The starting point for every financial model is the uncertainty facing investors, and the substance of every financial model involves the impact of uncertainty on the behavior of investors and, ultimately, on mar* Department of Economics, Harvard University, Cambridge, Massachusetts
Recovering Risk Aversion from Option Prices and Realized Returns. Manuscript
, 1998
"... A relationship exists between aggregate riskneutral and subjective probability distributions and risk aversion functions. Using a variation of the method developed by Jackwerth and Rubinstein (1996), we estimate riskneutral probabilities reliably from option prices. Subjective probabilities are es ..."
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Cited by 140 (7 self)
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A relationship exists between aggregate riskneutral and subjective probability distributions and risk aversion functions. Using a variation of the method developed by Jackwerth and Rubinstein (1996), we estimate riskneutral probabilities reliably from option prices. Subjective probabilities are estimated from realized returns. This paper then introduces a technique to empirically derive risk aversion functions implied by option prices and realized returns simultaneously. These risk aversion functions dramatically change shapes around the 1987 crash: Precrash, they are positive and decreasing in wealth and thus consistent with standard economic theory. Postcrash, they are partially negative and increasing and irreconcilable with the theory. Overpricing of outofthemoney puts is the most likely cause. A simulated trading strategy exploiting this overpricing shows excess returns even after accounting for the possibility of further crashes and transaction costs. * Jens Carsten Jackwerth is a visiting assistant professor at the London Business School. For helpful discussions I