Asset price bubbles and the quantification of credit risk capital with sensitivity analysis, empirical implementation and an application to stress testing

Michael Jacobs Jr.

Abstract

This paper presents an analysis of the impact of asset price bubbles on standard credit risk measures, extending research by Jacobs published in 2015 in which the author constructed a model, provided evidence that asset price bubbles understate economic credit capital and proposed a new credit risk measure that is robust to this bias (the expected holding period credit loss, or EHPCL). We perform a sensitivity analysis of the model parameters on the resulting credit risk measures as well as the changes in their relationship to the constant elasticity of variance (CEV) parameter; this controls the degree of market departure from fair value, illustrating an application of an important model validation procedure. We also perform an exercise in which we calibrate the model to historical equity prices and project credit losses on both baseline and stressed conditions for bubble and nonbubble parameter estimate settings. Through the estimation of the CEV model parameters from a long time series, we find statistically significant evidence that the historical Standard & Poor’s index exhibits only mild bubble behavior, but this translates into underestimation of potential extreme credit losses according to standard measures by an order of magnitude. However, while there is still some underestimation of unexpected credit losses under the EHPCL measure, it is of a much lower severity than in the case of traditional measures: it is on the order of 1.5% in the former, compared with tenfold in the latter. However, the degree of relative underestimation of risk due to asset price bubbles is significantly attenuated under stressed parameter settings in our model. The implication of these findings is that risk managers should be wary of measuring tail credit losses according to standard credit risk measures. Alternative measures, such as the EHPCL, should be considered, including benchmarking to stress testing generated credit losses.