## Term Glossary

### 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. $$CVaR_{\alpha}=-E(r|r\leq-VaR_{\alpha})$$ $$CVaR_{\alpha}=\frac{1}{\alpha}\int_{0}^{\alpha}VaR_{\gamma}(r)d\gamma=\frac{1}{\alpha}\int_{-\infty}^{-VaR_{\alpha}}rF(r)dr$$

$r_i$
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