Problem 3 There are two types of banks, A and B. Each bank has 20 loans. Each loan of type A bank generates $500 with probability 0.9 and $200 with probability 0.1, and these cash flows are independently distributed. Each loan of the type B bank generates $600 with probability 0.4 and $200 with probability 0.6, and these cash flows are independently distributed, too. Suppose that the bank XYZ is type A. However, the investors believe that XYZ is type A with probability 0.3 and type B with probability 0.7. Ignore investors’ opportunity cost of investment (or assume that that the risk-free interest rate is 0%.) The investors are risk neutral. Consider the following securitization options for the bank XYZ. 1. Suppose XYZ wants to securitize the portfolio of loans as a two-class bond. • If the class 1 bondholders would be promised certain payoff for sure, what is the amount the bank should promise? What is the market price of the class 1 bond? • If the class 2 bondholders are residual claimants, what is the true value of the class 2 bond? • Suppose the bank chooses to communicate the value of the class 2 bond, which costs 10% of the true value of the bond. What is the market value of this securitization (including both classes)? What is the net payoff to XYZ generated by this securitization?
Problem 3 There are two types of banks, A and B. Each bank has 20 loans. Each loan of type A bank generates $500 with probability 0.9 and $200 with probability 0.1, and these cash flows are independently distributed. Each loan of the type B bank generates $600 with probability 0.4 and $200 with probability 0.6, and these cash flows are independently distributed, too. Suppose that the bank XYZ is type A. However, the investors believe that XYZ is type A with probability 0.3 and type B with probability 0.7. Ignore investors’
1. Suppose XYZ wants to securitize the portfolio of loans as a two-class bond. • If the class 1 bondholders would be promised certain payoff for sure, what is the amount the bank should promise? What is the market price of the class 1 bond? • If the class 2 bondholders are residual claimants, what is the true value of the class 2 bond? • Suppose the bank chooses to communicate the value of the class 2 bond, which costs 10% of the true
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