(Mortgage Pass-Throughs) Consider a $400 million pass-through MBS that has just been created (so the 'seasoning' of the pass-through is equal to 0). The underlying pool of mortgages each has a maturity of 20 years and an annual mortgage coupon rate of 6%. The pass-through rate of the mortgage pool is 5%. Assuming a prepayment multiplier of 100 PSA , Suppose we construct principal-only (PO) and interest-only (IO) mortgage-backed securities (MBS) using the mortgage pass-through of the previous questions. Assume a prepayment multiplier of 100 PSA. if we use an annual risk-free rate of 4.5% to value the cash-flows

Q1)what is the value of the IO MBS?

Q2)Referring to the previous question, what is the average life of the IO MBS?

Q3) (Principal-Only MBS and Interest-Only MBS) Suppose now that you purchased the IO MBS of the previous question and that the price you paid was the same price that you calculated in the previous question. The risk-free interest rate suddenly changes from 4.5% to 3.5%. Everything else stays the same. How much money have you made or lost on your investment?

*In each of the following questions monthly mortgage coupon rates should be calculated by simply dividing the annual rate by 12. You should also assume that all of the securities pay monthly. You should also divide annual interest rates by 12 to get the corresponding monthly rate and assume monthly compounding when computing present values.*