Minimizing Conditional Value-at-Risk under Constraint on Expected Value

Jing Li and Mingxin Xu

MPRA Paper from University Library of Munich, Germany

Abstract: Conditional Value-at-Risk (CVaR) measures the expected loss amount beyond VaR. It has vast advantage over VaR because of its property of coherence. This paper gives an analytical solution in a complete market setting to the risk reward problem faced by a portfolio manager whose portfolio needs to be continuously rebalanced to minimize risk taken (measured by CVaR) while meeting the reward goal (measured by expected return). The optimal portfolio is identified whenever it exists, and the associated minimal risk is calculated. An example in the Black-Scholes framework is cited where dynamic hedging strategy is calculated and the efficient frontier is plotted.

Keywords: Conditional Value-at-Risk; Portfolio optimization; Risk minimization; Neyman-Pearson problem (search for similar items in EconPapers)
JEL-codes: C61 G11 G32 (search for similar items in EconPapers)
Date: 2009-02-22, Revised 2010-10-25
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