A Decision Theory Approach to Portfolio Selection

This paper starts with a brief summary of Harry Markowitz's portfolio selection model and proceeds to reformulate it within the framework of modern statistical decision theory. The future returns from securities are viewed as a function of the unknown state of nature. The investor has certain a priori probabilities for the different states of nature, which probabilities he later modifies in the light of new experimental information. Following the Bayesian strategy, the investor chooses that portfolio of securities which maximizes the weighted average of payoffs, using as weights the a posteriori probabilities of the states of nature. A computer program, based on the critical line method, is used to solve a simple illustrative problem.