Aggregating Economic Capital

Abstract

In this paper we analyze and evaluate a standard approach financial institutions use to calculate their so-called total economic capital.

If we consider a business that faces a total random loss S over a given one-year horizon then economic capital is traditionally defined as the difference between the 99.97% percentile of S and its expectation. The standard approach essentially assumes that the different components (risks) of S are multivariate normally distributed and this highly facilitates the computation of the total aggregated economic capital.

In this paper we show that this approach also holds for a more general framework which encompasses as a special case the multivariate normal (and elliptical) setting. We question also the assumption of multivariate normality since for many risks one often assumes other than normal distributions (e.g. a lognormal distribution for insurance risk). Assuming that risks are either normal or lognormal distributed we propose, using the concept of comonotonicity, an alternative aggregation approach.

Keywords: economic capital, aggregation, Solvency II, Basel II, VaR