Optimization with Tail-Dependence and Tail Risk: A Copula Based Approach for Strategic Asset Allocation

Abstract

This paper proposes a method to overcome the classical drawbacks of the Monte Carlo methods for the asset allocation, namely resampling, deeply dependent upon the multinormal assumption. The proposed approach allows to set a barrier against joint extreme negative returns (tail-dependence) and extreme (negative) returns (univariate tail risk) not included in the multivariate normal distribution. The dangerous tail-dependence between asset returns is considered by using a copula based approach instead of the multinormal Monte Carlo simulation. Then the proposed model has been applied on a sample of eleven euro-denominated asset classes with historical inputs and the consequent asset weights have been tested on multivariate Student's t returns and on a set of out-of-the sample real returns. The results of this model provide evidence of a barrier against extreme negative returns occurring simultaneously. The proposed model is distribution-free and therefore it does not involve any a priori decision on the marginal distributions for asset returns.