A local bank reviewed its credit card policy with the intention of recalling som

Question

A local bank reviewed its credit card policy with the intention of recalling some of its credit cards. In the past approximately 7% of cardholders defaulted, leaving the bank unable to collect the outstanding balance. Hence, management established a prior probability of .07 that any particular cardholder will default. The bank also found that the probability of missing a monthly payment is .20 for customers who do not default. Of course, the probability of missing a monthly payment for those who default is 1.

a. Given that a customer missed one or more monthly payments, compute the posterior probability that the customer will default (to 2 decimals).

b. The bank would like to recall its card if the probability that a customer will default is greater than . 2 0. Should the bank recall its card if the customer misses a monthly payment? Why or why not?

Explanation / Answer

1) Given P(default) = .07, thus, P(no default) = 0.93

P(missing a monthly payment / no default) = 0.20

P(missing a monthly payment / default) = 1.0

P(default/ missing a monthly payment = (1*0.07) / [(1*0.07) + (0.20*0.93) = 0.27344 or 27.34%

2) Yes, because from the computations above in Part-1, the probability of a customer may default is 27.34% if customer misses month payment for one month, however the bank can only afford having 20% of its customers default, then the bank would immediately stop providing the service to these customers in such a scenario.

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