Optimisation in the presence of tail-dependence and tail risk: A heuristic approach for strategic asset allocation

This paper presents a method to overcome the classical drawbacks of the Monte Carlo methods for the asset allocation, that is, resampling, deeply dependent on the multinormal assumption. This approach allows to set a derivative-free barrier against joint extreme negative returns (tail-dependence or contagion) and extreme (negative) returns (univariate tail risk) not considered in the multinormal framework. This barrier is set through an extensive use of copulas and Extreme Value Theory. The model has been applied on a sample of 11 euro-denominated asset classes with historical inputs. The weights have been tested on simulated (multivariate Student's t) returns and with real out-of-the sample returns. A comparison has been performed with the asset allocation given by the resampling method. The results provide evidence of a barrier against extreme negative returns occurring simultaneously. Furthermore, the model is totally distribution-free and therefore it does not involve any a priori decision on the marginal distributions for asset returns. The cost of this approach (loss of Sharpe ratio), in our example, is negligible.