Robust Scenario Optimization based on Downside-Risk Measure for Multi-Period Portfolio Selection

We develop and test multistage portfolio selection models maximizing expected end-of-horizon return while minimizing one-sided deviation from a target return level. The trade-o between two objectives is controlled by means of a non-negative parameter as in Markowitz Mean-Variance portfolio theory. We use a piecewise-linear penalty function, leading to linear programming mod-els and ensuring optimality of subsequent stage decisions. We adopt a simulated market model to randomly generate scenarios approximating the market stochasticity. We report results of rolling horizon simulation with two variants of the proposed models depending on the inclusion of trans-action costs, and under dierent simulated stock market conditions. We compare our results with the usual expected return-based stochastic programming models. The results indicate that the ro-bust investment policies are indeed quite stable in the face of market risk while ensuring expected return levels quite similar to the competing expected-return maximizing stochastic programming model at the expense of solving larger linear programs