A copula–GARCH model for macro asset allocation of a portfolio with commodities

Many authors have suggested that the mean-variance criterion, conceived by Markowitz (The Journal of Finance 7(1):77–91, 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 cannot correctly proxy the expected utility with non-Normal returns. In Riccetti (The use of copulas in asset allocation: when and how a copula model can be useful? LAP Lambert, Saarbrücken 2010), a copula–GARCH model is applied and it is found that copulas are not useful for choosing among stock indices, but can be useful in a macro asset allocation model, that is, for choosing stock and bond composition of portfolios. In this paper I apply that copula–GARCH model for the macro asset allocation of portfolios containing a commodity component. I find that the copula model appears to be 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.