Robust portfolio selection with a combined WCVaR and factor model

Ke Ruan; Masao Fukushima

doi:10.3934/jimo.2012.8.343

Article Contents

2012, Volume 8, Issue 2: 343-362. Doi: 10.3934/jimo.2012.8.343

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Robust portfolio selection with a combined WCVaR and factor model

Ke Ruan^1, and
Masao Fukushima^1,

1.
Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501

Received: February 28, 2011

Revised: July 31, 2011

Published: March 2012

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Abstract

In this paper, a portfolio selection model with a combined Worst-Case Conditional Value-at-Risk (WCVaR) and Multi-Factor Model is proposed. It is shown that the probability distributions in the definition of WCVaR can be determined by specifying the mean vectors under the assumption of multivariate normal distribution with a fixed variance-covariance matrix. The WCVaR minimization problem is then reformulated as a linear programming problem. In our numerical experiments, to compare the proposed model with the traditional mean variance model, we solve the two models using the real market data and present the efficient frontiers to illustrate the difference. The comparison reveals that the WCVaR minimization model is more robust than the traditional one in a market recession period and it can be used in a long-term investment.

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Mathematics Subject Classification: Primary: 90B50, 90C05; Secondary: 90C90, 91G10.

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