Justify all answers.

A number of lending models covered in class predict how interest rates will vary with characteristics of the borrower or loan.

Do not answer part a. and b. Need answer for only parts c, d, e, f, g

Loan size:

a. First, assume loans are risk-free, but there is a fixed operating cost of making a loan of any size. How will the banks break-even interest rate vary with the size of the loan, all else equal? Why? Answer in 1-3 sentences.

b. As an example, imagine a bank that faces a $90 operating cost to process a loan of any size. If all loans are risk-free (i.e. are always repaid) and the bank aims to recover operating costs and in addition earn a 7% rate of return from each loan, what interest rate will it charge for a loan of $200? a loan of $700?

Borrower Risk:

c. Next, ignore operating costs, and assume borrowers projects are risky. If the bank can perfectly observe every borrowers project risk, how will the banks break-even interest rate vary with borrowers project risk, all else equal? Why? Answer in 1-3 sentences.

d. As an example, imagine a bank making a loan that is paid back in full with probability p and defaulted upon entirely with probability 1p. If the bank has no operating costs and targets a 7% expected rate of return on each loan, what interest rate will it charge for a loan that has a 93% chance of being paid back (p=0.93)? A 79% chance (p=0.79)?

e. The lending market may fall short of efficiency if the bank cannot observe and contract upon risk in the model of part d. If risk is a fixed characteristic of each borrower (not a choice), how might the market outcome fall short of the efficient outcome, and why? Answer in a few sentences.

For parts f. and g., consider group lending in the setting of part d.

f. Imagine the bank requires all borrowers to form groups of size two, charges all borrowers a direct interest rate of 18% (r = 18%), and requires a bailout payment from all successful borrowers of 85% of the principal of that borrowers partner when the partner fails (b = 85%). Calculate the effective interest rate for each of the two types of borrowers in part d., assuming borrowers match homogeneously. How does the effective interest rate vary by risk?

g. Explain in a few sentences how group lending is able to improve the risk-pricing ability of a bank that cannot observe project risk in this context. Explain in a few sentences how this improved risk-pricing can potentially improve the efficiency of the lending market outcome.