Term Glossary

Metrics, Models & Concepts

Component Conditional Value-at-Risk

Component Condiational Value-at-Risk (also, Component Expected Tail Loss, Component Expected Shortfall) is the contribution of a specific position to the entire portfolio’s CVaR. If this position were removed, then the portfolio CVaR would drop by the component asset CVaR. Thus, portfolio CVaR is the sum of all component CVaRs. \begin{equation} \text{Component CVaR}_{\alpha}=-E(r_{i}\omega_{i}|r_{i}\omega_{i}\leq-VaR_{i,\alpha}) \end{equation}

return of i-th asset
expected return of i-th asset
portfolio weight of i-th asset
market beta of i-th asset
confidence level, \(\alpha \in (0, 1)\)
Value-at-Risk of i-th asset at \(\alpha\)-quantile