A minimum Bayes risk approach to optimal portfolio choice

This paper presents a Bayes decision approach to optimal portfolio choice under uncertainty. The approach ties together the estimation and decision problems. It duly recognizes the uncertainty of estimation of unknown parameters of asset return distributions by postulating a posterior PDF. It differentiates between the true-optimal solution and a quasi-optimal solution and defines the difference between the realized utilities under these two different solutions as a loss. Then it treats the expected loss with respect to the posterior PDF as the Bayes risk. The optimal portfolio choice is formulated as a constrained optimization (nonlinear programming) problem. The Bayes solution is derived in general and is solved for diffuse and conjugate priors in particular. An illustrative example is provided. The numerical results are reported and compared to those obtained according to the traditional method that ignores estimation risk. To observe how estimation risk affects optimal portfolio decision, the Bayes expected portfolio return and Bayes portfolio risk are also computed.