Oldies, Still Goodies: Valuation, loss reserves, and pricing of commercial loans

RMA Journal, The, March, 2002 by Edward I. Altman

The author provides a background for estimating commercial loan defaults by using corporate bond default rates and offers a model to use this information for valuing, pricing, and setting loan loss reserves. Portions of this article dealing with FASB rulings proposed in 1993 have been eliminated to avoid confusion.

The best evidence of value in mark-to-market valuations come through actual market quotes on assets. However, the process becomes far more difficult for illiquid assets when market quotes are either unavailable or difficult to ascertain. In such cases, net present value of estimated future cash flow can be determined by using a discount rate commensurate with the risk involved. Before the early 1990s, several pieces of the technology puzzle for performing discounted cash flow (DCF) analysis for valuation and pricing of loans did not exist.

By combining unbiased and accurate assessments of the probability, severity, and timing of defaults, the banking analyst and valuation officer have the complete tool kit for both DCF and loan reserve estimation. A rigorous, yet practical, method to value loans of all credit qualities includes three steps:

1. Estimation of default rates and losses associated with known credit standards.

2. Objective measurement of borrowers' credit quality that is consistent with those credit standards.

3. Modeling the expected cash flow from each loan.

The following discussion will outline a proposal for the steps and linkages that can achieve a logical analytical approach to these important decisions.

Step 1: Estimating Default Rates and Losses

The first critical step in commercial loan valuation is calculating a reliable estimation of default rates associated with known credit standards. Bond ratings are the most visible and respected measure of credit quality. Objective evidence suggests that the standards of credit quality used by the major rating agencies have been relatively consistent over long periods of time. A substantial amount of data has been collected since the mid-1980s, and analyses of bond defaults and losses have been performed. Several researchers have published reports of default rates associated with bond ratings for publicly traded bonds. Relying on the apparent stability of rating definitions, actuarial techniques have been applied to the bond's actual default experience.

Mortality Rates and Losses for Publicly Traded Bonds

In my article "Measuring Corporate Bond Mortality and Performance," I utilized the notion that default rates for specific one-year periods are measured on the basis of defaults in that interval in relation to some base population at the start of that same period. (1) The calculation, however, becomes more complex when we begin with a specific cohort group, such as a bond-rating category, and track that group's performance for multiple time periods. Because the original population can change over time as a result of a number of different events, we consider moralities, rather than defaults, in relation to a survival population. The mortality rate is the expected cumulative default rate over time. Similar to the concept of mortality rates used by the insurance industry in establishing life insurance premiums for individuals, mortality rate calculations consider default rates from "birth" to specified periods after issuance. Bonds can exit from the original population by means of at least five different events: defaults, exchanges, calls, sinking funds, and maturities.

The individual mortality rate for each year or marginal mortality rate (MMR) is calculated as follows:

[(MMR).sub.(t)] = Value of defaulting debt in year(t)/value of the population at the start of the year(t)

We can measure the cumulative mortality rate (CMR) over a specific period by subtracting the product of the surviving populations of each of the previous years from 1.

[CMR.sub.(T)] = 1 - [[PI].sup.T.sub.t=1][SR.sub.t]

[CMR.sub.(T)] = cumulative mortality rate

[SR.sub.(t)] = survival rate in (t); 1 - [MMR.sub.(t)]

The individual year MMR for each bond rating is based on a compilation of the year's mortality measured from issuance. For example, all of the one-year mortalities are combined for a sample period, for example, 1970-1991, to arrive at the one-year rate. All of the second-year mortalities are combined to get the two-year rate, and so forth.

The mortality rate is a value-weighted rate for the particular year after issuance, rather than an unweighted average. If we were simply to average each of the year-one rates or year-two rates, for example, our results would be susceptible to significant specific-year bias. The weighted-average technique correctly biases the results toward the larger-issue years.

After establishing mortality rates stratified by the original bond rating of publicly issued bonds, the measures are adjusted for the actual losses incurred on defaulting and distressed exchange issues. These losses include the difference between the purchase price and the price that the investor could have sold the bond for just after default plus the loss of one coupon payment, which would have been paid if the issue had not defaulted. In essence, mortality losses are calculated by original rating and for specific time periods after issuance.