Bank A has 100 worth of assets (only loans for simplicity): L = 100, capital K = 60 and liabilities (only deposits for simplicity) D = 40. Similarly, Bank B has 100 worth of assets (only loans for simplicity): L = 100, but its capital is K = 40 and its liabilities (only deposits for simplicity) are D = 60. The interest rates on deposits is iliabilities = 0.01. The interest rates on assets is: iassets = 0.05. There are two possible outcomes for the banks loans, good or bad. In the good outcome, no loan defaults. Thus the interest payments on a banks assets are=i_assets L. In the bad outcome, 50% of loans defaults. Thus the interest payments on a banks assets are=0.5 i_assets L. Each outcome is equally likely (that is the probability of each outcome is 0.5). In any case, the interest payments on a banks liabilities are=i_liabilities D.

(a) Compute bank As ROE in the good outcome.

(b) Compute bank As ROE in the bad outcome.

(c) Compute the expected value of bank As ROE.

(d) Compute bank Bs ROE in the good outcome.

(e) Compute bank Bs ROE in the bad outcome.

(f) Compute the expected value of bank Bs ROE.

(g) Which bank has higher expected ROE?

(h) What is the probability Bank A is insolvent?

(i) What is the probability Bank B is insolvent?

(j) Which bank has higher insolvency risk?