Imagine a lender facing a choice between one of two strategies: high-risk strategy or moderate-risk strategy. For simplicity, there is only two dates in this example (today and tomorrow). The lender chooses its strategy today and the return on this strategy is delivered tomorrow (cash flows only take place tomorrow). The bank has $270M in funds (total funding raised) and 90% of the funds raised by the lender were deposits paying no interest. In the high-risk strategy, the assets (loans) generate a return equal to 7% with probability 90% and there is a 10% chance that the assets generate a return equal to -40%. On the other hand, in the moderate-risk strategy, the assets (loans) generate a return equal to 5% with probability 95% and there is a 5% chance that the assets generate a return equal to -20%. Deposits are fully insured. The lender (and the government/ deposit insurance fund) discount tomorrows cash flows using a 3% discount rate (independently of their risk).

(a) Suppose that the deposit insurance premium paid by the bank equals zero. Compute the value of the implicit subsidy (or implicit transfer) provided by the deposit insurance fund to the bank under the two strategies. (b) Suppose now that the government wants to set this implicit subsidy equal to zero by asking the bank to pay a deposit insurance premium today. What should be the value of this premium (paid only today) under each of the two strategies? (c) How would your answer to parts (a) and (b) change if only 60% of the deposits from the bank were covered by deposit insurance?