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Until recently, Value-at-Risk (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 Value-at-Risk (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 mean-risk 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 mean-CVAR framework respects diversification and can be applied to multi-model returns, unlike mean-variance and mean-VaR which are only valid when returns are normal. CVaR is the most conservative measure of risk.
