On the Optimality of Some Multiperiod Portfolio Selection Criteria

Criteria for portfolio selection have received a great deal of attention in the recent economic literature. Modem portfolio analysis has its origin in the work of Markowitz, who specified the portfolio problem in terms of the one-period means and variances of returns.' However, most portfolio problems are multiperiod. The appropriateness of one-period analysis for this class of problems has been seriously questioned in recent years.2 As a result, several alternative decision rules and modification of the one-period analysis have been proposed. The purpose of this paper is to evaluate two proposals that have received wide attention in the economic literature. The first involves selecting portfolios on the basis of the geometric mean of future multiperiod returns. The second involves selecting portfolios on the basis of the expected utility of multiperiod returns.3 We shall show that, when the ability of the investor to revise his portfolio is considered, each of these rules is only appropriate under a very restrictive set of conditions. In order to evaluate any portfolio selection rule, it is necessary to establish a goal for portfolio management. In this paper, we will assume that the goal of portfolio managers is to maximize the expected utility of the investor's wealth at some terminal date. We have selected this goal because (1 ) the decision rules we will investigate were devised to achieve this goal, (2) the goal is appropriate for many real portfolio problems (such as retirement portfolios), and (3) this goal has been assumed by many other authors.4 Once this goal has been established, we can define the portfolio problem as the development of decision rules for selecting a sequence of