Long, Kete, "The Fallacy of an Overly Simpliﬁed Asymptotic Single-risk-factor Model", Journal of Risk Model Validation, Vol. 5, No. 4, (Winter 2011/12), pp. 27-48.
Abstract: Factor models are mathematical constructs for capturing the joint default of obligors and, in this way, are essential to most portfolio credit risk models. This paper explains the potential flaws of overly simplified factor models. The asymptotic single-risk-factor (ASRF) model fails to capture the underlying correlation structure. With empirical evidence, we demonstrate how inaccurate the model can be. Dimension reduction imposes too many limitations and severely compromises model performance. This paper presents empirical tests that quantify error propagation by using a portfolio credit risk modeling process to measure economic capital. Test results reveal that overly simplified ASRFs can be inaccurate in some situations, with the errors occurring in the case of large portfolios. The law of large numbers does not apply effectively in real-world portfolios.