A BAYESIAN MODEL FOR PORTFOLIO SELECTION AND REVISION

Abstract

IN PORTFOLIO ANALYSIS, the basic setting is that of an individual or a group of individuals making inferences and decisions in the face of uncertainty about future security prices and related variables. Formal models for decision making under uncertainty require inputs such as probability distributions to reflect a decision maker's uncertainty about future events and utility functions to reflect a decision maker's preferences among possible consequences [30]. Moreover, when a series of interrelated decisions is to be made over time, the decision maker should (1) revise his probability distributions as new information is obtained and (2) take into account the effect of the current decision on future decisions. In terms of formal models of the decision-making process, probability revision can be accomplished by using Bayes' theorem and the interrelationships among the decisions can be taken into consideration by using dynamic programming to determine optimal decisions. Since portfolio selection and revision involves a series of interrelated decisions made over time, formal portfolio models should, insofar as possible, incorporate these features. A search of the extensive literature concerning portfolio models indicates, however, that such models have ignored one or both of these features. Since Markowitz [18] developed his original model of portfolio selection, a considerable amount of work has been conducted in the area of mathematical portfolio analysis, and much of this work is summarized by Sharpe [31] and Smith [33]. Although the emphasis in portfolio analysis has been primarily on single-period models and portfolio selection, multiperiod models and portfolio revision are investigated by Tobin [35], Smith [32], Mossin [21], Pogue [22], Chen, Jen, and Zionts [3], and Hakansson [13, 14]. In addition, general multiperiod models of consumption-investment decisions are developed by Hakansson [10, 11, 12], Merton [19], Samuelson [29], Fama [6], and Meyer [20]. However, it is generally assumed that the probability distributions of interest are completely specified and that they are unaffected by new information, implying that the portfolio revision models do not involve probability revision over time. Bayesian models have received virtually no attention in the portfolio literature. Mao and Siirndal [17] present a simple, discrete, single-period Bayesian model in which the returns from securities are related to the level of general business activity and information is obtained concerning business conditions. Kalymon [16] develops a model