Benchmarking the loss given default parameter for mortgage loan portfolios under stress

Christian Greve and Lutz Hahnenstein

Abstract

ABSTRACT

In this paper, we analyze the impact of a decline in property prices that leads to stressed recovery rates for collateral on the loss given default (LGD) parameter in portfolios of mortgage loans. After discussing the shape of a portfolio's loan-to value (LTV) distribution, we prove that the average LGD's stress sensitivity depends on the LTV distribution, and we derive a closed-form solution for portfolio LGD under the assumption of beta-distributed LTV ratios. Further, we present numerical evidence that the relationship between LTV distribution and portfolio LGD is crucial for understanding the stress resilience of banks involved in the mortgage business. Our formula appears to be a meaningful starting point for benchmarking analyses by regulators, rating agencies and risk managers.