Other Applications 553tomer, the type and purpose of the loan, and forecasts of future economic con-
ditions, all of which influence or indicate the risk of default. Bank officers put
each loan into one of four categories on the basis of these scores. After a year’s
experience with the system, the bank is ready to assess its performance. In
doing so, it has constructed the data in Table 13.2a. The table shows the break-
down of “performing” (paying) loans in the four categories and defaulted loans
(also by category) over the past year.
Last year, the overall rate of default by the bank’s business customers was
1 in 10 loan accounts. The overall quality of business customers seeking loans
this year is expected to be unchanged from last (as is the general business cli-
mate). How should the bank use this information in making loan decisions?
Table 13.2b provides the answer. This table computes the joint probabilities of
all possible events by multiplying prior and conditional probabilities. For
example, the proportion of all loans that are designated in class A and that
default isThe other entries in the joint probability table are calculated in similar fashion.
The bank’s final step (Table 13.2c) is to compute revised probabilities:
the default risk for each designated loan category. These risks are approxi-
mately 5, 5, 13, and 25 percent for the respective categories. We can draw sev-
eral observations from these results. First, as we might expect, loans
identified as “high-risk” (class D) have by far the greatest probability of
default. Presumably these loans were extended under much stricter condi-
tions—higher interest rates, stiffer collateral conditions, lower loan
amounts—because of their risk. Still, it is natural to ask whether the bank’s
loan officers (at the time of granting) recognized exactly how risky class D
loans were. (Perhaps at the time they saw them as 15 to 20 percent risks.) In
light of the actual 25 percent default rate, the bank may be well advised to
stop making class D loans altogether (or make them under even more strin-
gent conditions).
A second observation is that the actual default risks for class A and class
B loans are indistinguishable. The scoring system seemingly does not work
very well in gauging small risks; that is, it makes a distinction when none
exists. This suggests taking a closer look at the class A (zero-risk) loans that
actually failed. Do these loans share common attributes? Could the scoring
system be modified to identify these loans as low-risk class B loans? To sum up,
the scoring system provides valuable information bearing on actual loan per-
formance. However, the bank probably has further work to do in refining the
system.(.1)(.1).01
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