Robust portfolio selection under downside risk measures

Abstract

We investigate a robust version of the portfolio selection problem under a risk measure based on the lower-partial moment (LPM), where uncertainty exists in the underlying distribution. We demonstrate that the problem formulations for robust portfolio selection based on the worst-case LPMs of degree 0, 1 and 2 under various structures of uncertainty can be cast as mathematically tractable optimization problems, such as linear programs, second-order cone programs or semidefinite programs. We perform extensive numerical studies using real market data to reveal important properties of several aspects of robust portfolio selection. We can conclude from our results that robustness does not necessarily imply a conservative policy and is indeed indispensable and valuable in portfolio selection.

Keywords:

• Portfolio selection
• Downside risk
• Lower-partial moment
• Robust optimization

Acknowledgements

This research is partially supported by National Science Foundation of China under No. 70401009 and No. 70518001 and by Research Grants Council, Hong Kong, under . The authors are grateful to two anonymous referees for their helpful suggestions and comments.