Term Glossary

Metrics, Models & Concepts

Component Value-at-Risk


Component Value-at-Risk is the contribution of a specific position to the entire portfolio’s Value-at-Risk. If this position were removed, then the portfolio value at risk would drop by the component VaR. Thus, portfolio VaR is the sum of all component VaRs. Component VaR actually considers marginal VaR and incremental VaR in its calculation. \begin{equation} \text{Component VaR}_{i, \alpha}=\beta_{i}\omega_{i}VaR_{\alpha} \end{equation}

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