sector concentration risk: a model for estimating capital requirements

the model only requires values for two variables: the probability of default and loss if default occurs. using a 99% likelihood and assuming that all sectors are equally correlated, the model estimates x through the cumulative distribution function for the gaussian distribution.

but many bank portfolios do not fit these hypotheses, and therefore the asrf model underestimates actual capital requirements. thus, a surcharge for concentration risk is required.

there are two kinds of concentration risk (sector and name concentration risk), each one corresponding to the violation of one of the above mentioned hypotheses. supervisory authorities are currently developing models to incorporate this surcharge into banking solvency rules. in spain, the spanish central bank bases its surcharge proposal for sectorial concentration on the herfindahl–hirschman index (hhi). in this paper we show that hhi treats all sectors as equally risky and propose an alternative index (ci) in which sectors are weighted according to risk. moreover, our index also incorporates the relations between each pair of sectors (in the hhi framework no sectorial relationship is considered). our proposal is based on an adjusted variance–covariance matrix, in which negative covariances have been equalled to 0. we demonstrate the hhi is a particular case of our proposed index, by means of simplifying hypotheses.

as we will show, the proposed index has two fundamental properties: it is lower and upper bounded; and it decreases as concentration and/or risk decreases. these properties allow the index to be incorporated into bank risk management models. in this way bank estimations can improve upon those based on the supervisory model and, according to banking rules, can also be used for determining the capital surcharge for sectorial concentration.