The Art of Credit Derivatives: Demystifying the Black Swan

Appendix A

Economic Capital Allocation Approaches

Assume a loss distribution defined by L and a certain quantile α. The credit value at risk (CVaR) associated with the quantile is defined respectively as:

(A.1)

Below we will define approaches using standard risk measures that are largely used in practice for allocating economic capital. Assume the conglomerate is comprised of n subportfolios whose allocations we want to determine. Below we show some of the different approaches used for ECAP allocation with some comments on the differences:

1. VaR / Covar. Although largely used by practitioners, this approach is typical for Gaussian loss distribution. The allocated capital of a certain subportfolio is given by:

(A.2)

where L_i and L are the losses of the subportfolio i and the total portfolio respectively. ECAP_T(α) andare the total ECAP of the portfolio at the quantile α, and the total portfolio loss variance respectively.

2. Pro-rata CVaR. In this approach one uses the stand-alone CVaR_α of each sub-portfolio as a weight in the allocation of the total risk:³

(A.3)

3. Basel II. In this approach ...