Optimization in an uncertain world

In this paper, we investigate the impact of uncertainty on portfolio allocation and how incorporating stochasticity in the investment strategy improves performance. We use both stochastic programming and robust optimization to maximize return with constrained risk measured by Conditional Value-at-Risk (CVaR), using scenarios generated via Filtered Historical Simulation (FHS). We compare the results based on return, risk, stability of the weights over time, and a newly introduced dispersion measure. We find that incorporating uncertainty only slightly enhances performance. In an expanding window estimation, the effect of incorporating uncertainty in returns disappears and the inclusion of parameter uncertainty has a negative impact. Also, managerial and legislative restrictions have much influence on the optimization outcomes and induce the stochasticity in the risk constraint to have little impact. When we exclude these supplementary restrictions, incorporating uncertainty becomes more effective.