Abstract:
Until recently, value-at-risk (VaR) has been a widely used risk measure in portfolio optimization.
The large number of recent bank failures shows that VaR failed to account for the expected
losses which resulted from the outburst of a rare event 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 (variance and VaR) from a theoretical
standpoint. This study aims at investigating the reasons that render CVaR superior to other
traditional 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
different measures of risk (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 regarding the superiority of CVaR. We find that the mean-CVAR
framework can be applied to multi-model returns, unlike mean-variance (where variance is a
dispersion measure) and mean-VaR (where VaR is anon-coherent risk measure) which are only
valid when returns are normal. The mean-CVaR framework respects diversification, and we find
that CVaR is the most conservative measure of risk.
