Value-at-Risk vs. Conditional Value-at-Risk in Risk Management and Optimization

From the mathematical perspective considered in this tutorial, risk management is a procedure for shaping a risk distribution. Popular functions managing risk are valueat-risk (VaR) and conditional value-at-risk (CVaR). The problem of choice between VaR and CVaR, especially in financial risk management, has been quite popular in academic literature. Reasons affecting the choice between VaR and CVaR are based on the differences in mathematical properties, stability of statistical estimation, simplicity of optimization procedures, acceptance by regulators, etc. This tutorial presents our personal experience working with these key percentile risk measures. We try to explain strong and weak features of these risk measures and illustrate them with several examples. We demonstrate risk management/optimization case studies conducted with the Portfolio Safeguard package.