From Moments, Co-Moments and Mean-Variance weights to Copula Portfolio Allocation

In Riccetti (2010) I find that the use of copulas can be useful in an asset allocation model for choosing the stock and the bond composition of portfolios (the macro asset allocation) or if the portfolio is composed by one bond index and some stock indices. Thus, in these cases, easy methods to reconstruct the copula allocation without estimating the copula, could be important for an asset manager/investor. In this paper I build a model that considers moments and co-moments of the returns till the fourth power (respectively the mean of the returns and the mean of the crossed products of the returns raised up to fourth power) in order to understand whether they can approximate the use of copulas to obtain optimal weights. I analyse two models: the first reconstructs the copula model's weights using only moments and co-moments, while the second models the weights using moments, co-moments and the mean-variance weights. I also use the moments and co-moments of the excess returns of the stock indices over the bond index return as independent variables. The in-sample and the out-of-sample analyses show that it is possible to have an approximation of the weights obtained by a copula model using moments and co-moments of returns. Even if these models are different for each asset, changeable in time, with explanatory variables and signs that are not predictable and with accuracy that is uncertain, both models appear useful: the first appears to be easier (because the weights of the Markowitz model are not needed), while the second is more accurate in-sample and out-of-sample. Moreover the regression with the excess returns of the stock indices over the less risky index seems to be useful: it is a bit less accurate, but it needs to calculate less combinations of moments and co-moments.