Calculating the variancecovariance value at risk of a portfolio is great but being able to identify how much each component of the portfolio contributes to the total portfolio VaR is even better. The Component VaR is one way to achieve that analysis.
Calculation of Parametric VarianceCovariance Value at Risk
The VaR over d days at a confidence level c is calculated as
where
is a scaling factor
is the daily volatility
Note: can be scaled back from a weekly, monthly or annualised volatility by applying the following:
where are the weights of the securities in the portfolio,
and is the covariance matrix.
Component VaR
Concept
The idea behind Component VaR (CVaR) is to find a way of calculating the contribution to the total VaR of a portfolio of any subportfolios, including individual positions. Asusming is a partition of the total portfolio, i.e. the union of all the subportfolios is exactly equal to the total portfolio, the CVaR has the following properties:
 , the sum of the CVaRs is the total VaR
 , if a subportfolio is removed, the impact on total VaR is approximately its CVaR
 if a subportfolio is a hedge, its CVaR should be negative
Definition
VaRDelta is defined by [Garman] as
VaRDelta has the following interesting property:
The Component VaR of the security i is then defined as ,
where and is the kronecker symbol.
References
