Answer all questions, and show your work.
Mr. Smith borrows $400,000 from a bank to buy a $400,000 house. He has to pay back principal plus interest next period.
1. The price of the house at the time of payback is uncertain. Suppose the mortgage interest rate is 10%. What is the price below which Smith will in fact default?
2. Suppose that all prices between $300,000 and $600,000 are equally likely. What is the probability of default in that case?
3. Now suppose that Jones makes a 20% down payment. Redo (1) for Mr. Jones.
4. And (2)
5. Suppose there are three mortgages that are exactly like Mr. Jones. Design a set of three mortgage backed pass through securities that use these three mortgages in a pool. What are the possible payoffs, and the probability of each payoff. What is the expected value of the security?
6. Now design a second set of securities, again referencing each of these identical mortgages, in which the highest tranche gets paid after one mortgage fulfillment, the next tranche gets paid off after the second fulfillment and the third gets paid off after the third fulfillment. What are the default probabilities for each of these three tranches?
7. Redo (6) but using three borrowers identical to Mr. Smith (i.e. only 10% down). Comment on the differences in default probabilities between (6) and this scenario.