Concentration Risk in the Credit Portfolio

The essay provides a complete framework – based on the works by Gordy, Pykhtin, Martin and Wilde and others – to bridge the gap between Pillar 1 capital against credit risk and the true amount of economic capital that a bank needs when the actual characteristics of its loan portfolio (in terms of correlation, name concentration, industry concentration, etc.) are measured and accounted for. In fact, while it is comparatively easy for a bank to set up a VaR model on its credit portfolio and to estimate the losses associated with some worst-case scenario (in order to decide how much capital has to be held), a much more difficult step is to reconcile this economic capital with the regulatory capital dictated by Pillar 1. The essay, using a step by step example, shows how the gap between those two measures of capital can be quantified and explained; the last paragraph also shows how this methodology can be used to spot “regulatory arbitrages” based on name and industry correlation, that would otherwise go unnoticed if banks and supervisors were to rely exclusively on Pillar 1 capital requirements.