Portfolio Selection with Probabilistic Utility, Bayesian Statistics, and Markov Chain Monte Carlo

We propose a novel portfolio selection approach that manages to ease some of the problems that characterise standard expected utility maximisation. The optimal portfolio is no longer defined as the extremum of a suitably chosen utility function: the latter, instead, is reinterpreted as the logarithm of a probability distribution for optimal portfolios and the selected portfolio is defined as the expected value with respect to this distribution. A further theoretical aspect is the adoption of a Bayesian inference framework. We find that this approach has several attractive features, when comparing it to the standard maximisation of expected utility. We remove the over-pronounced sensitivity on external parameters that plague optimisation procedures and obtain a natural and self consistent way to account for uncertainty in knowledge and for personal views. We test the proposed method against traditional expected utility maximisation, using artificial data to simulate finite-sample behaviour, and find superior performance of our procedure. All numerical integrals are carried out by using Markov Chain Monte Carlo, where the chains are generated by an adapted version of Hybrid Monte Carlo. We present numerical results for a portfolio of eight assets using historical time series running from January 1988 to January 2002.