Part 2: Introduction to Mortgage Mathematics and Mortgage-Backed Securities

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.

30-year level payment mortgage assuming an annual mortgage rate of 5% and an initial mortgage principal of $400,000.

(Principal-Only MBS and Interest-Only MBS)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. What is the present value of the PO MBS if we use an annual risk-free rate of 4.5% to value the cash-flows?

Ans is 280.10 million

Q (Principal-Only MBS and Interest-Only MBS)Referring to the previous question, suppose the risk-free interest rate suddenly changes from 4.5% to 3.5%andthat the pre-payment multiplier changes from 100 PSA to 150 PSA. How much money have you made or lost on your investment in the IO MBS?

Submission Guideline:Give your answer inmillionsrounded to two decimal places. For example, if you compute the answer to be $123,456,789,12, submit 123.46.