# A sensitivity analysis of the alpha factor

## Michael Einemann and Michael Kalkbrener

#### Need to know

• Identification of the key model parameters driving the internal alpha factor.
• Analytical formulae for the alpha factor of infinitely granular portfolios.
• Stabilizing alternative alpha definition based on expected shortfall.

#### Abstract

In the credit risk weighted assets formula for derivatives, the exposure-at-default is scaled by a multiplier: the so-called internal alpha factor. This has been introduced by the Basel Committee to offset the model or estimation error arising from the usage of a constant exposure amount and should account for the uncertainty of counterparty exposure, the correlation between exposures and the correlation between exposure and default. In this paper, we investigate the alpha factor’s sensitivity to key model parameters under stylized portfolio assumptions in order to better understand its complex characteristics. Our analysis is based on the numerical simulation of alpha sensitivities as well as the derivation of analytical formulas under the assumption of infinitely granular portfolios. We show that the relative exposure volatility and parameters that specify the link between the underlying credit portfolio model and the exposure variables (wrong-way/right-way risk parameters) have a particularly significant impact on the alpha factor. For small homogeneous portfolios the alpha factor is rather unstable with respect to the number of counterparties. We investigate an alternative definition based on the coherent risk measure expected shortfall, which reduces the alpha instability quite significantly.