Mean-CVaR portfolio selection: A nonparametric estimation framework

Authors:
Haixiang Yao;Zhongfei Li;Yongzeng Lai
Affiliations:
School of Informatics, Guangdong University of Foreign Studies, Guangzhou 510006, China;Sun Yat-sen Business School, Sun Yat-sen University, Guangzhou 510275, China and Lingnan College, Sun Yat-sen University, Guangzhou 510275, China;Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada N2L 3C5
Venue:
Computers and Operations Research
Year:
2013

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Abstract

In this paper, we use Conditional Value-at-Risk (CVaR) to measure risk and adopt the methodology of nonparametric estimation to explore the mean-CVaR portfolio selection problem. First, we obtain the estimated calculation formula of CVaR by using the nonparametric estimation of the density of the loss function, and formulate two nonparametric mean-CVaR portfolio selection models based on two methods of bandwidth selection. Second, in both cases when short-selling is allowed and forbidden, we prove that the two nonparametric mean-CVaR models are convex optimization problems. Third, we show that when CVaR is solved for, the corresponding VaR can also be obtained as a by-product. Finally, we present a numerical example with Monte Carlo simulations to demonstrate the usefulness and effectiveness of our results, and compare our nonparametric method with the popular linear programming method.