AUTOCORRELATED RETURNS AND OPTIMAL INTERTEMPORAL PORTFOLIO CHOICE

In recent years it has been shown empirically that stock returns exhib it positive or negative autocorrelation, depending on observation freq uency. In this context of autocorrelated returns the present paper is the first to derive an explicit analytical solution to the dynamic por tfolio problem of an individual agent saving for retirement (or other change of status, like the purchase of a house or starting college). U sing a normal ARMA(1, 1) process, dynamic programming techniques combi ned with the use of Stein's Lemma are employed to examine ''dollar-cos t-averaging'' and ''age effects'' in intertemporal portfolio choice wi th CARA preferences. We show that with a positive moving average param eter and positive risk free rates, if first-order serial correlation i s nonnegative, then the expected value of the optimal risky investment is increasing over time, while if first-order serial correlation is n egative this path can be increasing or decreasing over time. Thus a ne cessary but not sufficient condition to obtain the conventional age ef fect of increasing conservatism over time is that first-order serial c orrelation be negative. Further, dollar-cost averaging in the general sense of gradual entry into the risky asset does not emerge as an opti mal policy. Simulation results for U.S. data are used to illustrate op timal portfolio paths.