Risk forecasting models and optimal portfolio selection

This study analyses, from an investor's perspective, the performance of several risk forecasting models in obtaining optimal portfolios. The plausibility of the homoscedastic hypothesis implied in the classical Markowitz model is dicussed and more general models which take into account assymetry and time varying risk are analysed. Specifically, it studies whether ARCH-type based models obtain portfolios whose risk-adjusted returns exceed those of the classical Markowitz model. The same analysis is performed with models based on the Lower Partial Moment (LPM) which take into account the assymetry in the distribution of returns. The results suggest that none of the models achieve a clearly superior average performance. It is also found that models based on semivariance perform as well as those based on the variance, but not better than, even if the evaluation criterion is based on the Reward-to-Semivariance ratio. When attention turns to the analysis of worst case performance, the results are clearly different. Models which employ LPM with a high degree of risk aversion (n>2) as the risk measure are consistently superior to those which employ a symmetric measure, either homoscedastic or heteroscedastic.