Estimating Portfolio and Consumption Choice: A Conditional Euler Equations Approach

This paper develops a nonparametric approach to examine how portfolio and consumption choice depends on variables that forecast time-varying investment opportunities. I estimate single-period and multiperiod portfolio and consumption rules of an investor with constant relative risk aversion and a one-month to 20year horizon. The investor allocates wealth to the NYSE index and a 30-day Treasury bill. I find that the portfolio choice varies significantly with the dividend yield, default premium, term premium, and lagged excess return. Furthermore, the optimal decisions depend on the investor’s horizon and rebalancing frequency. HOW DOES PORTFOLIO AND CONSUMPTION CHOICE depend on variables that forecast time-varying investment opportunities? Prior studies that address this question assume a statistical model relating returns to forecasting variables and solve for an investor’s portfolio and consumption choice using estimates of the implied conditional distribution of returns. As a result, their answers are shaped as much by modeling assumptions as by the data. An incorrect model of how returns relate to forecasting variables can yield inconsistent portfolio and consumption choice estimates and invalid inferences. This paper develops and implements an econometric approach that is robust to such model misspecification. Sample analogues of the conditional Euler equations, the first-order conditions of the investor’s expected utility maximization, yield consistent estimates shaped by the data. I modify the method of moments approach of Hansen and Singleton ~1982!. I fix the parameters of an individual investor’s utility function and estimate the optimal wealth and consumption process, and thereby the investor’s portfolio and consumption rules, from sample analogues of the conditional Euler equations. In contrast, Hansen and Singleton use observations of the aggregate wealth and consumption process to estimate the parameters of the representative investor’s utility function from otherwise identical moment conditions. * The Wharton School, University of Pennsylvania. I thank Yacine Aït-Sahalia, George Constantinides, Lars Peter Hansen, Campell Harvey, and especially John Cochrane for their guidance and encouragement. I also thank Robert Hodrick, René Stulz ~the editor!, two anonymous referees, and seminar participants at the 1998 Western Finance Association conference, Columbia University, Duke University, MIT, Northwestern University, Ohio State University, Stanford University, the University of California at Berkeley and Los Angeles, the University of Chicago, the University of Pennsylvania, the University of Southern California, and Yale University for many helpful comments. I am responsible for any remaining errors. THE JOURNAL OF FINANCE • VOL. LIV, NO. 5 • OCTOBER 1999