Credit Risk Measurement: Avoiding Unintended Results: Part 3: Discount Rates and Loss Given Default
Davis, Peter O., The RMA Journal
Loss given default is the measure of economic loss on a defaulted financial obligation. The discount rate selected to calculate economic loss, collections, and costs related to the defaulted asset could affect the interpretation and application of this fundamental credit metric. This article explores common discounting approaches and their potential impact on the meaning of the resulting LGD metric.
Metrics calculated for one purpose may have limitations for broader application or they may generate certain unintended theoretical interpretations when used for other purposes. This article focuses on the relatively fine point of the discount rate used to calculate loss given default (LGD). There are a number of options for choosing an "appropriate" discount rate, and mach helps answer a slightly different question. The discount rate selected affects how an LGD should be interpreted and applied in other calculations.
Modeling Loss Given Default
As discussed in Part 1, the art/science of measuring LGD is far less mature than default risk modeling or grading methodologies. As institutions continue to collect more data on default events and the reasons for default losses, LGD models and grading frameworks will likely become increasingly sophisticated. Rather than focusing on LGD, this third article in the series looks at discounting post-default cash flows.
LGD represents the net present value of the cash flow stream related to a given exposure following the default event. Using a loan as an example, LGD would include all collections made on the loan, plus direct and indirect costs. (In practice, most institutions have not allocated indirect costs to individual loans.) Discounting each cash flow to the point of default provides the economic recovery on the defaulted loan. Expressing this recovery amount as a percent of the loan balance at default provides the recovery rate. The reciprocal of the recovery rate is the LGD. For example, if the balance at default were $100, and $80 were recovered over time, representing $75 on a present-value basis, then the loss given default would be 25%. How much the economic recovery rate differs from the cash recovery rate is driven by both the amount of time it took to collect on the defaulted loan and the discount rate applied.
Understanding the length of time to recover is important to understanding the significance of the discount rate. For products where recoveries are collected relatively quickly, such as credit cards, differences in discount rates will have little impact on the resulting LGD. Where collection efforts may be protracted, such as large corporate bankruptcies, the discount rate can have a significant impact on the calculated loss given default.
Selecting a Discount Rate
Selecting a discount rate should be driven by the question one is looking to answer. As shown in Exhibit 1, this article outlines two common discounting approaches and the answers that they appear to offer.
While these two options are perhaps the most common approaches to calculating LGD, a number of other approaches are used as well. In some cases, institutions do not take the net present value of cash flows at all, but instead rely on net principal charge-offs as a rough proxy for LGD. In other cases, conceptually similar approaches to the current comparable market rate are employed. For example, an institution's cost of funds is used as the discount rate in all LGD calculations.
Borrower Interest Rate at Default
This is the approach described in FAS No. 114, the accounting standard that governs accounting for impaired loans. Under this approach, the discount rate is based on the borrower's interest rate at the time of default. For fixed-rate loans, neither changes in interest rates nor changes in credit pricing since loan origination affect the calculated net present value of the recoveries. In other words, this approach to LGD effectively ignores the pricing decision made at the time of loan origination and subsequent changes in interest rates. …