Suppose a representative bank like the one we studied in class. On the asset side of their T-account, the bank has loans for $100, government issued bonds (completely risk-free) for $20 and some cash reserves for $15. To finance these assets, on the liability side, the bank is considering three options: Option 1: Deposits for $100 and borrowing for $0 (leaving an equity of $35) Option 2: Deposits for $80, borrowings for $40 (leaving an equity of $15) Option 3: Deposits for $80, borrowing for $20 (leaving an equity of $35) loans Suppose further that the interest rate on loans is = 0.12, the interest rate on the government issued bonds is = 0.03. The deposits in turn, pay an interest of dep = 0.02 and debt finally the bank borrowed (from a larger financial institution) at an interest rate of 1. = 0.1. However, there is risk associated with the bank's assets. In particular, there is a probability p that 10% of the loans the bank made, will default. a. Incorporating the risk of default, write down the bank's expected profit as a function of p, for each of the three possible options. b. Assume now that p = 0.5. What is the bank's expected ROE for each of the three cases? If the bank's objective were to maximize expected ROE, which of the three options would the bank choose?