Introduction to Mortgage Mathematics and Mortgage-Backed Securities
1. (Level-Payment Mortgages) Compute the monthly payment on a 30-year level payment mortgage assuming an annual mortgage rate of 5% and an initial mortgage principal of $400,000. Submission Guideline: Give your answer rounded to two decimal places. For example, if you compute the answer to be $73.2367, submit 73.24.
2. (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 what is the total amount of interest paid to the pass-through investors? Submission Guideline: Give your answer in millions rounded to two decimal places. For example, if you compute the answer to be $123,456,789,12, submit 123.46.
3. (Mortgage-Pass Throughs) Referring to the same mortgage pass-through of the previous question, what is the total amount of the prepayments? Submission Guideline: Give your answer in millions rounded to two decimal places. For example, if you compute the answer to be $123,456,789,12, submit 123.46.
4. (Mortgage-Pass Throughs) Referring to the same mortgage pass-through of the previous question, what is the total amount of the prepayments if the rate of prepayments increases to 200 PSA? Submission Guideline: Give your answer in millions rounded to two decimal places. For example, if you compute the answer to be $123,456,789,12, submit 123.46.
5. (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? Submission Guideline: Give your answer in millions rounded to two decimal places. For example, if you compute the answer to be $123,456,789,12, submit 123.46.
6. (Principal-Only MBS and Interest-Only MBS) Referring to the previous question, what is the value of the IO MBS? Submission Guideline: Give your answer in millions rounded to two decimal places. For example, if you compute the answer to be $123,456,789,12, submit 123.46.
7. (Principal-Only MBS and Interest-Only MBS) Referring to the previous question, what is the average life of the IO MBS? Submission Guideline: Give your answer in years rounded to two decimal places. For example, if you compute the answer to be 12.1234 years, submit 12.12.
8. (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? Submission Guideline: Give your answer in millions rounded to two decimal places. For example, if you compute the answer to be $123,456,789,12, submit 123.46.
9. (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% and that 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 in millions rounded to two decimal places. For example, if you compute the answer to be $123,456,789,12, submit 123.46.