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}

\(r_i\)
return of i-th asset
\(E(r_i)\)
expected return of i-th asset
\(\omega_i\)
portfolio weight of i-th asset
\(\beta_i\)
market beta of i-th asset
\(\alpha\)
confidence level, \(\alpha \in (0, 1)\)
\(VaR_{i,\alpha}\)
Value-at-Risk of i-th asset at \(\alpha\)-quantile