Beyond Conditional Second Moments: Does Nonparametric Density Modelling Matter to Portfolio Allocation?

This paper investigates the economic importance of nonparametrically/semiparametrically modelling the shape and the change in the unknown distribution of returns in portfolio allocation problems from a Bayesian perspective. Besides parametric multivariate GARCH (MGARCH) benchmark models for returns, we consider an MGARCH with innovations following a Dirichlet process mixture and an infinite hidden Markov model (IHMM). We introduce a new Bayesian semiparametric model that combines the MGARCH component with the IHMM for innovations. This new model nonparametrically approximates both the shape and evolution through time of the unknown distribution of returns beyond that captured by the MGARCH part. The results show that the Bayesian nonparametric/semiparametric models lead to improved statistical forecast accuracy and economic gains for a quadratic utility and CRRA utility investor. The new model makes the greatest gains. Portfolio choice is improved by modelling beyond the conditional second moments.