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Why is CVaR Superior to VaR?: A Unified Framework for MeanRisk Portfolio Optimization,Used
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Until recently, ValueatRisk (VaR) has been a widely used risk measure in portfolio optimization. The recently frequent bank failures show that VaR fail to account for losses caused by rare events such as the global financial crisis, thereby questioning its reliability and credibility as a measure of risk. Alternatively, previous work concurs that Conditional ValueatRisk (CVaR) is a coherent tail risk measure, and has established the superiority of CVaR over traditional measures of risk from a theoretical standpoint. This book investigates the reasons that render CVaR superior to other risk measures from an empirical perspective. We develop a theoretical model that solves the meanrisk portfolio optimization problem within a unified framework for all three risk measures variance, VaR and CVaR. We test our model empirically using financial data on return indices over a period covering the financial crisis. Our results support the theoretical predictions. The meanCVAR framework respects diversification and can be applied to multimodel returns, unlike meanvariance and meanVaR which are only valid when returns are normal. CVaR is the most conservative measure of risk.
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