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:
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:
are the losses of the subportfolio i
and the total portfolio respectively. ECAPT
are 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 CVaRα
of each sub-portfolio as a weight in the allocation of the total risk:3
3. Basel II. In this approach ...