Bayesian Dynamic Portfolio Allocation Methods

Abstract

In the portfolio allocation problem, the optimal weights assigned to a set of assets have traditionally been determined by the Markowitz mean-variance optimization criterion. Recently, Polson and Tew (2000) and Aguilar and West (2000) employed the Bayesian predictive approach to the optimization problem where the error distribution of the time series of the asset returns is assumed to be a multivariate normal or a Student-t distribution. However, it is known that the error distribution may be skewed or fat-tailed in real life data. In this talk, I will describe how we can extend the predictive approach to incorporating the skewed and the heavy-tailed error distribution in the stochastic volatility models. A hierarchical Bayesian approach using a Markov chain Monte Carlo method will be used for inference and prediction. Instead of the mean-variance Bayesian predictive optimization, we explore the use of the VAR (value-at-risk) as a measure of risk to obtain the optimal weighting. A real life data set will be used to illustrate the advantages of incorporating the skewed and fat-tailed error distributions. This talk is based on the joint work with Jun Ying.