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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 liabilities = 0.01. The interest rates on assets are: assets = 0.05. There are two possible outcomes for the bank’s loans, good or bad. In the good outcome, no loan defaults. Thus the interest payments on a bank’s assets are=assets × L. In the bad outcome, 50% of loans default. Thus the interest payments on a bank’s assets are=0.5 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 bank’s liabilities are=liabilities × D.
(a) Compute bank A’s ROE in the good outcome.
(b) Compute bank A’s ROE in the bad outcome.
(c) Compute the expected value of bank A’s ROE.
(d) Compute bank B’s ROE in the good outcome.
(e) Compute bank B’s ROE in the bad outcome.
(f) Compute the expected value of bank B’s 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?
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