Robust Multi-Period Portfolio Selection with Asymmetrically Distributed Uncertainty Set and Return Predictability

Abstract

This paper considers a robust multi-period portfolio selection problem with asymmetrically distributed uncertainty set. We introduce the mean-LPM (lower partial moment) risk measure and establish a multi-period portfolio selection model, in which the mean-LPM is used to limit the loss of portfolio. To add practicality, we allow the uncertainty set to be asymmetric and include transaction cost in the model. A computationally tractable approximation approach based on second order cone optimization is used for solving the proposed model. Comprehensive numerical comparisons with simulated data and real market data are reported. The numerical results indicate that the proposed model can obtain better expected returns and Sharpe ratios, while reduce the standard deviation and turnover ratios, compared with some well-known models in the literature.