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Zbl 0902.90003
Balvers, Ronald J.; Mitchell, Douglas W.
Autocorrelated returns and optimal intertemporal portfolio choice.
(English)
[J] Manage. Sci. 43, No.11, 1537-1551 (1997). ISSN 0025-1909; ISSN 1526-5501/e

Summary: In recent years it has been shown empirically that stock returns exhibit positive or negative autocorrelation, depending on observation frequency. In this context of autocorrelated returns, the present paper is the first to derive an explicit analytical solution to the dynamic portfolio problem of an individual agent saving for retirement (or other change of status, like the purchase of a house or starting college). Using a normal $\text{ARMA}(1, 1)$ process, dynamic programming techniques combined with the use of Stein's lemma are employed to examine dollar-cost-averaging'' and age effects'' in intertemporal portfolio choice with CARA preferences. We show that with a positive moving average parameter and positive riskfree rates, if first-order serial correlation is nonnegative, then the expected value of the optimal risky investment is increasing over time, while if first-order serial correlation is negative this path can be increasing or decreasing over time. Thus a necessary but not sufficient condition to obtain the conventional age effect of increasing conservatism over time is that first-order serial correlation be negative. Further, dollar-cost averaging in the general sense of gradual entry into the risky asset does not emerge as an optimal policy. Simulation results for U.S. data are used to illustrate optimal portfolio paths.
MSC 2000:
*91B28 Finance etc.

Keywords: dynamic portfolio problem; intertemporal portfolio choice

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