A Copula-GARCH Model for Macro Asset Allocation of a Portfolio with Commodities: an Out-of-Sample Analysis

Many authors have suggested that the mean-variance criterion, conceived by Markowitz (1952), is not optimal for asset allocation, because the investor expected utility function is better proxied by a function that uses higher moments and because returns are distributed in a non-Normal way, being asymmetric and/or leptokurtic, so the mean-variance criterion can not correctly proxy the expected utility with non-Normal returns. In Riccetti (2010) I apply a simple GARCH-copula model and I find that copulas are not useful for choosing among stock indices, but they can be useful in a macro asset allocation model, that is, for choosing the stock and the bond composition of portfolios. In this paper I apply that GARCH-copula model for the macro asset allocation of portfolios containing a commodity component. I find that the copula model appears useful and better than the mean-variance one for the macro asset allocation also in presence of a commodity index, even if it is not better than GARCH models on independent univariate series, probably because of the low correlation of the commodity index returns to the stock, the bond and the exchange rate returns.