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

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  • Li, Jing
  • Xu, Mingxin

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.

Suggested Citation

  • Li, Jing & Xu, Mingxin, 2009. "Minimizing Conditional Value-at-Risk under Constraint on Expected Value," MPRA Paper 26342, University Library of Munich, Germany, revised 25 Oct 2010.
    • Handle: RePEc:pra:mprapa:26342
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    References listed on IDEAS

    as
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Conditional Value-at-Risk; Portfolio optimization; Risk minimization; Neyman-Pearson problem;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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