Minimizing CVaR and VaR for a portfolio of derivatives |
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| Institution: | 1. School of Management, Hefei University of Technology, Hefei 230009, Anhui, PR China;2. Key Laboratory of Process Optimization and Intelligent Decision-making, Ministry of Education, Hefei 230009, Anhui, PR China;3. Department of Mathematics, Brunel University, Uxbridge UB8 3PH, UK;4. Department of Statistics, Florida State University, Tallahassee 32304, USA;1. Department of Automation, Shanghai Jiao Tong University, China;2. Department of Systems Engineering & Engineering management, The Chinese University of Hong Kong, Shatin, NT, Hong Kong |
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| Abstract: | Value at risk (VaR) and conditional value at risk (CVaR) are frequently used as risk measures in risk management. Compared to VaR, CVaR is attractive since it is a coherent risk measure. We analyze the problem of computing the optimal VaR and CVaR portfolios. We illustrate that VaR and CVaR minimization problems for derivatives portfolios are typically ill-posed. We propose to include cost as an additional preference criterion for the CVaR optimization problem. We demonstrate that, with the addition of a proportional cost, it is possible to compute an optimal CVaR derivative investment portfolio with significantly fewer instruments and comparable CVaR and VaR. A computational method based on a smoothing technique is proposed to solve a simulation based CVaR optimization problem efficiently. Comparison is made with the linear programming approach for solving the simulation based CVaR optimization problem. |
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