Extending the Basel II approach to estimate capital requirements for equity investments

Under the Basel II banking regulatory capital regime the capital requirements for credit exposures are calculated using the Asymptotic Single Risk Factor (ASRF) approach. The capital requirement is taken to be the contribution of an exposure to the unexpected loss on the bank's diversified portfolio. Here we extend this approach to calculate capital requirements for equity investments. We show that in the case when asset values have a normal distribution an analytical formula for the unexpected loss contribution may be developed. We show that the capital requirements for equity investments are quite different to those of credit exposures, since equity investments can suffer substantial loss of value even when the underlying company has not defaulted. Unexpected loss is commonly used as a measure of capital requirements, but it ignores the ability of earnings to absorb loss. We propose a definition of capital requirement that recognises the expected earnings on assets, and show how to combine the ASRF model and the Capital Asset Pricing Model to compute this quantity for credit and equity exposures.