Practical algorithms for value-at-risk portfolio optimization problems

Abstract

This article compares algorithms for solving portfolio optimization problems involving value-at-risk (VaR). These problems can be formulated as mixed integer programs (MIPs) or as chance-constrained mathematical programs (CCMPs). We propose improvements to their state-of-the-art MIP formulations. We also specialize an algorithm for solving general CCMPs, featuring practical interpretations. We present numerical experiments on practical-scale VaR problems using various algorithms and provide practical advice for solving these problems.

Keywords:

• value-at-risk
• portfolio optimization
• mixed integer programming
• mixed integer linear programming
• chance-constrained mathematical programs

JEL Classification:

• C02
• C61
• G11

Acknowledgments

The authors thank Dr James Luedtke and Dr Simge Küçükyavuz for offering insights into this work. Mingbin Feng and Andreas Wächter were supported partially by the NSF grant DMS-1216920.