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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 184 (0 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
Intertemporally dependent preferences and the volatility of consumption and wealth
 Review of Financial Studies
, 1989
"... In this article we construct a model in which a consumer’s utility depends on the consumption history We describe a general equilibrium framework similar to Cox, Ingersoll, and Ross (1985a). A simple example is then solved in closedform in this general equilibrium setting to rationalize the observed ..."
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Cited by 165 (3 self)
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In this article we construct a model in which a consumer’s utility depends on the consumption history We describe a general equilibrium framework similar to Cox, Ingersoll, and Ross (1985a). A simple example is then solved in closedform in this general equilibrium setting to rationalize the observed stickiness of the consumption series relative to the fluctuations in stock market wealth. The sample paths of consumption generated from this model imply lower variability in consumption growth rates compared to those generated by models with separable utilizations. We then present a partial equilibrium model similar to Merton (1969, 1971) and extend Merton’s results on optimal consumption and portfolio rules to accommodate nonseparability in preferences. Asset pricing implications of our framework are briefly explored. The idea that a given bundle of consumption goods will provide the same level of satisfaction at any date regardless of one’s past consumption experience is implicit in models that use timeseparable utility functions to represent preferences. Separable utility functions have been the mainstay in much of the literature on asset pricing and optimal consumption and portfolio The results reported in this article were first presented at the EFA meetings in Bern, Switzerland, in 1985 [see Sundaresan (1984)]. Subsequently the article was presented at a number of universities and conferences. I thank the participants at those presentations for their feedback. I am especially thankful to Doug Breeden, Michael Brennan, John Cox, Chifu Huang, and Krishna Ramaswamy for their thoughtful comments and criticisms. I also thank Tongsheng Sun for explaining the simulation procedure for stochastic differential equations and for his comments and suggestions. I am responsible for any remaining errors. Correspondence should be sent to Suresh M. Sundaresan, Graduate
Portfolio and consumption decisions under meanreverting returns: An exact solution for complete markets
 Journal of Financial and Quantitative Analysis 37, 63–91. The Journal of Finance Wachter, Jessica A
, 2003
"... This paper solves, in closed form, the optimal portfolio choice problem for an investor with utility over consumption under meanreverting returns. Previous solutions either require approximations, numerical methods, or the assumption that the investor does not consume over his lifetime. This paper ..."
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Cited by 137 (8 self)
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This paper solves, in closed form, the optimal portfolio choice problem for an investor with utility over consumption under meanreverting returns. Previous solutions either require approximations, numerical methods, or the assumption that the investor does not consume over his lifetime. This paper breaks the impasse by assuming that markets are complete. The solution leads to a new understanding of hedging demand and of the behavior of the approximate loglinear solution. The portfolio allocation takes the form of a weighted average and is shown to be analogous to duration for coupon bonds. Through this analogy, the notion of investment horizon is extended to that of an investor who consumes at multiple points in time.
Dynamic consumption and portfolio choice with stochastic volatility in incomplete markets
, 2003
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Catching Up with the Joneses: Heterogeneous Preferences and the Dynamics of Asset Prices
, 2001
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A Simulation Approach to Dynamic Portfolio Choice with an Application to Learning About Return Predictability
, 2005
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Optimal Consumption and Portfolio Selection with Stochastic Differential Utility
, 1999
"... We develop the utility gradient (or martingale) approach for computing portfolio and consumption plans that maximize stochastic differential utility (SDU), a continuoustime version of recursive utility due to D. Duffie and L. Epstein (1992, Econometrica 60, 353 394). We characterize the firstorder ..."
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Cited by 89 (4 self)
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We develop the utility gradient (or martingale) approach for computing portfolio and consumption plans that maximize stochastic differential utility (SDU), a continuoustime version of recursive utility due to D. Duffie and L. Epstein (1992, Econometrica 60, 353 394). We characterize the firstorder conditions of optimality as a system of forward backward SDEs, which, in the Markovian case, reduces to a system of PDEs and forward only SDEs that is amenable to numerical computation. Another contribution is a proof of existence, uniqueness, and basic properties for a parametric class of homothetic SDUs that can be thought of as a continuoustime version of the CES Kreps Porteus utilities studied by L. Epstein and A. Zin (1989, Econometrica 57, 937 969). For this class, we derive closedform solutions in terms of a single backward SDE (without imposing a Markovian structure). We conclude with several tractable concrete examples involving the type of ``affine'' state price dynamics that are familiar from the term structure literature.
Dynamic Asset Allocation under Inflation
 Journal of Finance
, 2002
"... Wachter, two anonymous referees, and participants at the Brown Bag Micro Finance Lunch Seminar at the Wharton ..."
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Cited by 81 (2 self)
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Wachter, two anonymous referees, and participants at the Brown Bag Micro Finance Lunch Seminar at the Wharton
A variational problem arising in financial economics
, 1991
"... We provide sufficient conditions for a dynamic consumptionportfolio problem in continuous time to have a solution for a class of utility functions, when the price system follows a diffusion process and when the space of admissible policies is a linear space. Besides a regularity condition, it suffi ..."
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Cited by 72 (1 self)
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We provide sufficient conditions for a dynamic consumptionportfolio problem in continuous time to have a solution for a class of utility functions, when the price system follows a diffusion process and when the space of admissible policies is a linear space. Besides a regularity condition, it suffices to check whether a uniform growth and a local Lipschitz condition are satisfied by the parameters of a system of stochastic differential equations, which is completely derived from the price system. The class of utility functions includes concave functions that are, roughly, either bounded from below or strictly concave, and whose coefficients of relative risk aversion have nonzero limit infima as consumption/wealth goes to infinity. 'The authors would like to acknowledge helpful conversations with Sergiu Hart, Andreu Mas Colell, and HoMou Wu. The expositions of this paper were improved by comments from two anonymous referees. Various comments were made