Term Glossary

Metrics, Models & Concepts

Conditional Value-at-Risk


Conditional Value-at-Risk (also, Expected Tail Loss, Expected Shortfall) is the negative of the expected value of the tail beyond the Value-at-Risk. Conditional Value-at-Risk is able to quantify dangers beyond Value-at-Risk, and moreover it is a coherent risk measure. \begin{equation} CVaR_{\alpha}=-E(r|r\leq-VaR_{\alpha}) \end{equation} \begin{equation} CVaR_{\alpha}=\frac{1}{\alpha}\int_{0}^{\alpha}VaR_{\gamma}(r)d\gamma=\frac{1}{\alpha}\int_{-\infty}^{-VaR_{\alpha}}rF(r)dr \end{equation}

\(r_i\)
i-th asset return
\(\alpha\)
confidence level, \(\alpha \in (0, 1)\)
\(F(r)\)
cumulative probability distribution function of asset returns
\(VaR_{\alpha}\)
Value-at-Risk of i-th asset at \(\alpha\)-quantile


Function Reference
portfolio_CVaR position_CVaR