On Robust Multi-Period Pre-Commitment and Time-Consistent Mean-Variance Portfolio Optimization

Abstract

We consider robust pre-commitment and time-consistent mean-variance optimal asset allocation strategies, that are required to perform well also in a worst-case scenario regarding the development of the asset price. We show that worst-case scenarios for both strategies can be found by solving a specific equation each time step. In the unconstrained asset allocation case, the robust pre-commitment as well as the time-consistent strategy are identical to the corresponding robust myopic strategies, by which investors perform robust portfolio control only for one time step and conduct a risk-free strategy afterwards. In the experiments, the robustness of pre-commitment and time-consistent strategies is studied in detail. Our analysis and numerical results indicate that the time-consistent allocation strategy is more stable when possible incorrect assumptions regarding the future asset development are modeled and taken into account. In some situations, the time-consistent strategy can even generate higher efficient frontiers than the pre-commitment strategy (which is counter-intuitive), because the time-consistency restriction appears to protect an investor in such a situation.