Question

A loan buyer in a secondary market believes that x% of the loans are high quality, and the rest are low quality. The buyer values high quality loans at $90,000 and low quality at $70,000. Banks selling loans value high quality loans at $81,000 and low quality at $65,000. If the buyer cannot observe the bond's type, then the minimum x that will support trade in both types is?

45%

55%

61%

75%

Answer 1

Percentage of high quality loans = x %

Percentage of low quality loans = (100 - x) %

Value of high quality loans for buyer = $90000

Selling price of HQL (high quality loans) by banks = $81000

Expected profit = x.(90000 - 81000) / 100 = 90x

Value of low quality loans for buyer = $70000

Selling price of HQL (high quality loans) by banks = $65000

Expected profit = (100-x).(70000 - 65000) / 100 = 5000 - 50x

Minimum x that will support trade in both types is:

90x = 5000 - 50x => 140x = 5000 => x = 35.71%

Correct Ans - A