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149
Option pricing when underlying stock returns are discontinuous
 Journal of Financial Economics
, 1976
"... The validity of the classic BlackScholes option pricing formula dcpcnds on the capability of investors to follow a dynamic portfolio strategy in the stock that replicates the payoff structure to the option. The critical assumption required for such a strategy to be feasible, is that the underlying ..."
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Cited by 512 (1 self)
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The validity of the classic BlackScholes option pricing formula dcpcnds on the capability of investors to follow a dynamic portfolio strategy in the stock that replicates the payoff structure to the option. The critical assumption required for such a strategy to be feasible, is that the underlying stock return dynamics can be described by a stochastic process with a continuous sample path. In this paper, an option pricing formula is derived for the moregeneral cast when the underlying stock returns are gcncrated by a mixture of both continuous and jump processes. The derived formula has most of the attractive features of the original Black&holes formula in that it does not dcpcnd on investor prcfcrenccs or knowledge of the expcctsd return on the underlying stock. Morcovcr, the same analysis applied to the options can bc extcndcd to the pricingofcorporatc liabilities. 1. Intruduction In their classic paper on the theory of option pricing, Black and Scholcs (1973) prcscnt a mode of an:llysis that has rcvolutionizcd the theory of corporate liability pricing. In part, their approach was a breakthrough because it leads to pricing formulas using. for the most part, only obscrvablc variables. In particular,
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 340 (8 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.
On estimating the expected return on the market  an exploratory investigation
 Journal of Financial Economics
, 1980
"... The expected market return is a number frequently required for the solution of many investment and corporate tinance problems, but by comparison with other tinancial variables, there has been little research on estimating this expected return. Current practice for estimating the expected market retu ..."
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Cited by 249 (1 self)
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The expected market return is a number frequently required for the solution of many investment and corporate tinance problems, but by comparison with other tinancial variables, there has been little research on estimating this expected return. Current practice for estimating the expected market return adds the historical average realized excess market returns to the current observed interest rate. While this model explicitly reflects the dependence of the market return on the interest rate, it fails to account for the effect of changes in the level of market risk. Three models of equilibrium expected market returns which reflect this dependence are analyzed in this paper. Estimation procedures which incorporate the prior restriction that equilibrium expected excess returns on the market must be positive are derived and applied to return data for the period 19261978. The principal conclusions from this exploratory investigation are: (1) in estimating models of the expected market return, the nonnegativity restriction of the expected excess return should be explicitly included as part of the specification; (2) estimators which use realized returns should be adjusted for heteroscedasticity. 1.
Resurrecting the (C)CAPM: A CrossSectional Test When Risk Premia Are TimeVarying
 Journal of Political Economy
, 2001
"... This paper explores the ability of conditional versions of the CAPM and the consumption CAPM—jointly the (C)CAPM—to explain the cross section of average stock returns. Central to our approach is the use of the log consumption–wealth ratio as a conditioning variable. We demonstrate that such conditio ..."
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Cited by 141 (4 self)
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This paper explores the ability of conditional versions of the CAPM and the consumption CAPM—jointly the (C)CAPM—to explain the cross section of average stock returns. Central to our approach is the use of the log consumption–wealth ratio as a conditioning variable. We demonstrate that such conditional models perform far better than unconditional specifications and about as well as the FamaFrench threefactor model on portfolios sorted by size and booktomarket characteristics. The conditional consumption CAPM can account for the difference in returns between lowbooktomarket and highbooktomarket portfolios and exhibits little evidence of residual size or booktomarket effects. We are grateful to Eugene Fama and Kenneth French for graciously providing the
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 127 (3 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
Characteristics, Covariances, And Average Returns: 1929 To 1997
, 1999
"... The value premium in U.S. stock returns is robust. The positive relation between average return and booktomarket equity is as strong for 1929 to 1963 as for the subsequent period studied in previous papers. A threefactor risk model explains the value premium better than the hypothesis that the bo ..."
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Cited by 104 (6 self)
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The value premium in U.S. stock returns is robust. The positive relation between average return and booktomarket equity is as strong for 1929 to 1963 as for the subsequent period studied in previous papers. A threefactor risk model explains the value premium better than the hypothesis that the booktomarket characteristic is compensated irrespective of risk loadings. Firms with high ratios of book value to the market value of common equity have higher average returns than firms with low booktomarket ratios (Rosenberg, Reid, and Lanstein (1985)). Because the capital asset pricing model (CAPM) of Sharpe (1964) and Lintner (1965) does not explain this pattern in average returns, it is typically called an anomaly. There are four common explanations for the booktomarket (BE/ME) anomaly. One says that the positive relation between BE/ME and average return (the socalled value premium) is a chance result unlikely to be observed out of sample (Black (1993), MacKinlay (1995)). Outofs...
The CrossSection of Volatility and Expected Returns
 Journal of Finance
, 2006
"... We especially thank an anonymous referee and Rob Stambaugh, the editor, for helpful suggestions that greatly improved the article. Andrew Ang and Bob Hodrick both acknowledge support from the NSF. ..."
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Cited by 87 (6 self)
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We especially thank an anonymous referee and Rob Stambaugh, the editor, for helpful suggestions that greatly improved the article. Andrew Ang and Bob Hodrick both acknowledge support from the NSF.
Conditioning manager alphas on economic information: Another look at the persistence of performance
 Review of Financial Studies
, 1998
"... This article presents evidence on persistence in the relative investment performance of large, institutional equity managers. Similar to existing evidence for mutual funds, we find persistent performance concentrated in the managers with poor priorperiod performance measures. A conditional approach ..."
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Cited by 69 (11 self)
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This article presents evidence on persistence in the relative investment performance of large, institutional equity managers. Similar to existing evidence for mutual funds, we find persistent performance concentrated in the managers with poor priorperiod performance measures. A conditional approach, using timevarying measures of risk and abnormal performance, is better able to detect this persistence and to predict the future performance of the funds than are traditional methods.
Trading Activity and Expected Stock Returns
 Journal of Financial Economics
, 2001
"... Trading Activity and Expected Stock Returns Given the evidence that the level of liquidity aects asset returns, a reasonable hypothesis is that the second moment of liquidity should be positively related to asset returns, provided agents care about the risk associated with uctuations in liquidity. ..."
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Cited by 52 (8 self)
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Trading Activity and Expected Stock Returns Given the evidence that the level of liquidity aects asset returns, a reasonable hypothesis is that the second moment of liquidity should be positively related to asset returns, provided agents care about the risk associated with uctuations in liquidity. Motivated by this observation, we analyze the relation between expected equity returns and the level as well as the volatility of trading activity (a proxy for liquidity) . We document a result contrary to our initial hypothesis, namely, a negative and surprisingly strong crosssectional relationship between stock returns and the variability of dollar trading volume and share turnover, after controlling for size, bookto market, momentum, and the level of dollar volume or share turnover. This eect survives a number of robustness checks and is statistically and economically signi# cant. Our analysis demonstrates the importance of trading activityrelated variables in the crosssection of ex...