Question

Assume the risk free rate is 7% and a person wants to borrow $200 from a risk neutral investor Assume: With prob. 80%, the borrower repays loan + promised interest With prob. 19%, the borrower repays $100 With prob. 1%, the borrower repays $0 Q: What is the default premium?

Select one:

a. The default premium is 13.87%

b. The default premium is 14.88%

c. The default premium is 16.88%

d. The default premium is 15.88%

Answer 1

Risk Free rate = 7%

Principal amount = $200

If investment is made in risk free asset, future value = principal + interest

If investment is made in risk free asset, future value = 200 + 200 x7%

If investment is made in risk free asset, future value = 214.

Risk neutral investor is neutral between risky asset and risk free asset.

Therefore expected future value from risky asset = 214

Let the interest amount for loan to be provided be I

Expected future value from loan = 0.8 x (principal + interest) + 0.19 x 100 + 0.01 x 0

214 = 0.8 x (200 + I) + 0.19 x 100 + 0.01 x 0

214 = 160 + 0.8I + 19 +0

0.8I = 35

I = $43.75

Therefore Interest rate on loan = $43.75 / $200

Therefore Interest rate on loan = 21.88%

Risk free rate = 7%

Therefore Default Risk Premium = 21.88% - 7% = 14.88%

Therefore option b is correct