Variable Selection for Portfolio Choice

We study asset allocation when the conditional moments of returns are partly predictable. Rather than first model the return distribution and subsequently characterize the portfolio choice, we determine directly the dependence of the optimal portfolio weights on the predictive variables. We combine the predictors into a single index that best captures time variations in investment opportunities. This index helps investors determine which economic variables they should track and, more importantly, in what combination. We consider investors with both expected utility ~mean variance and CRRA! and nonexpected utility ~ambiguity aversion and prospect theory! objectives and characterize their market timing, horizon effects, and hedging demands. THERE IS BY NOW AMPLE EVIDENCE in the literature that the means, variances, covariances, and higher order moments of stock and bond returns are timevarying and predictable. However, it has proven difficult to translate this evidence of predictability into practical portfolio advice because the different moments of returns, which in turn determine the optimal portfolio weights, are typically predicted by different sets of economic variables. Perhaps because of this difficulty with modeling the conditional return distribution, most professional investment advice is given solely on the basis of variables that forecast expected returns, such as the dividend yield or the slope of the term structure. Looking beyond expected returns, it is difficult to decide which selection or combination of predictive variables the investor should focus on. ~As a result, the empirical literature on portfolio choice has relied on a predeter* Aït-Sahalia is with the Department of Economics, Princeton University, and NBER. Brandt is with the Wharton School, University of Pennsylvania, and NBER. We thank John Campbell, George Constantinides, David Chapman, Frank Diebold, Han Hong, Paul Pf leiderer, Jessica Wachter, and especially Anthony Lynch for their comments and suggestions. We also thank seminar participants at the 2001 Annual Meeting of the American Finance Association, Columbia University, Harvard University, MIT, NYU, Princeton University, Stanford University, and the University of Chicago. This research was conducted during the first author’s tenure as an Alfred P. Sloan Research Fellow. Financial support from the NSF under Grant SBR-9996023, the Bendheim Center for Finance at Princeton University, and the Rodney White Center at the Wharton School is gratefully acknowledged. 1 It is quite natural, of course, to focus on the first moment of the return distribution when making a conditional portfolio choice. First, expected returns are the most intuitive and arguably the most important input to the investor’s objective function; second, the dependence of the optimal portfolio choice on the first moment of the return distribution is monotonic for most preferences, unlike the dependence on higher order moments; and third, even with relatively simple preferences, the dependence of the optimal portfolio choice on the whole return distribution is so complex that it can usually only be solved numerically. THE JOURNAL OF FINANCE • VOL. LVI, NO. 4 • AUGUST 2001