Department of Applied Mathematics & Physics, Kyoto University

Technical Report 2011-008 (March 16, 2011)

Robust Portfolio Selection with a Combined WCVaR and Factor Model
by Ke Ruan and Masao Fukushima

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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 in Japan 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.