Imagine a lender that can choose between one of two strategies: high-risk strategy or low-risk strategy. The

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Question:

Imagine a lender that can choose between one of two strategies: high-risk strategy or low-risk strategy. The bank has $500M in funds (total funding raised) and has to choose between investing this entire amount in one of the two strategies. In both cases, the investment includes only loans, but the risk of the loans is different across strategies. In the low-risk scenario, the assets (loans) always generate a return equal to 5%. In the high-risk strategy, the assets (loans) generate a return equal to 9% with a probability of 90% and there is a 10% chance that the assets generate a return equal to -50%. 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 lender discounts tomorrow’s cash flows using a 3% discount rate (independently of their risk). The lender wants to maximize the (expected) value of is equity (shareholder value).

(a) Suppose the lender only raised equity financing. Show the value of the lender’s equity under the high- and low-risk strategies and determine the strategy chosen by the lender.

(b) Suppose now that 90% of the funds raised by the lender were deposited paying no interest. The deposits are insured by the deposit insurance fund. Show the value of the lender’s equity under the high- and low-risk strategies and determine the strategy chosen by the lender.

(c) In the context of part (b), suppose now that there is no deposit insurance. We still have that 90% of the banks’ funds are deposited, but depositors will demand higher rates if they expect greater potential losses (they are not insured). Explain in words, without calculations, if you expect the high-risk strategy to become more or less attractive to the bank (when compared to the low-risk strategy). Why would you expect this to be the case?