A simulation comparison of risk measures for portfolio optimization

In this paper, we compare risk measures regarding performance of optimal portfolio strategies. We consider eleven risk measures from different classes. In particular, we propose a formulation that generates from any loss measure, a deviation based on the dispersion of results worse than it, which leads to very interesting risk measures. We consider 198,000 portfolios composed by stocks of the U.S. equity market, considering different scenarios in a simulation framework. Results indicate there is no clearly dominant risk measure. Despite this lack of dominance, including deviation terms consistently exhibits advantages regarding performance.