Recovery Risk and Economic Capital

Jon Frye

Lenders know that any loan can default. They also know that the default rate of any portfolio can rise. If the default rate rises enough, the portfolio experiences loss. To absorb this possible loss, lenders must have capital.

A second effect can compound the loss. This is the variation in loss-given default (LGD). LGD is the fraction of exposure lost when a loan defaults. Lenders find that, when the default rate rises, the LGD rate tends to rise as well. When we think about possible loss, variation of the default rate is only half the picture. The variation of LGD can be just as important.

This chapter develops a framework for understanding the coordinated rise of the default rate and the LGD rate and their effect on economic capital. Both rates connect to an underlying systematic “risk factor”. As will be seen, this brings into being two distributions of LGD. These distributions play distinct roles in the analysis that leads back to economic capital. In this analysis, two pitfalls stem from themes developed earlier, and each leads to an understatement of risk. These pitfalls are to ignore a source of systematic risk while measuring LGD and to conflate the two distributions of