1. Consider a pool of mortgages with balance at month 0 of $15,000,000 with interest rate of 10% and N=360.
a. What is the monthly payment?
b. Suppose 25% of the payment is interest in month 1, and 75% of the payment is principal. Also, suppose the actual payments received are $600,000. What is the Single Monthly Mortality Rate (SMM)?
c. What is the Constant Prepayment Rate (CPR)?
d. Assuming 100 PSA, what is the CPR and SMM for months 5, 20, and each month in the range of 31 through 360?
2. Suppose there is a nonagency pool with a 9% note rate and 300 months left to maturity, with a balance at time t of $10,000,000.
a. What is the pool's monthly payment, and how much of this is interest versus scheduled principal?
b. Suppose the pool receives $20,000 in voluntary prepayments and $18,000 in involuntary prepayments (due to defaults). What is the Monthly Default Rate (MDR)? What is the Conditional Default Rate (CDR)?
3. What is a major disadvantage of the Z-spread? What is an alternative measure of spread that we talked about in class, which overcomes this shortcoming of the Z-spread? In addition to stating the name of this alternative measure of spread, please explain it.
4. Suppose there are two securities, A and B. Security A is a 3 year security, interest only, coupon of 9 percent, par value of $10,000. Security B is also a 3 year security, priced at $10,000, and 3 payments of principal and interest of $3,950.55 are to be received annually at the end of each year.
a. What is the yield to maturity on each of these securities?
b. What is the duration (D) for each of these securities?
c. Which has a lower weighted average number of years to realize total cash flows from the investment?
5. Assume there is a security that is priced at par (i.e., 100). Its value is expected to rise to 100.50 if rates fall by 25 basis points, and expected to fall to 98 if rates rise by 25 basis points.
a. What is the effective duration of this security?
b. What is the convexity of this security?
c. Explain the meaning of the answers you got for a and b above - in other words, what is the relationship between duration and convexity?
6. Suppose $200 million of Mortgage Backed Bonds (MBB's) are issued against a $300 million pool of mortgages, in denominations of $10,000 for a period of 10 years. The bonds carry a coupon of 8% payable annually. Assume the securities receive the highest possible rating.
a. What is the price of the security, assuming the issuer and underwriter agree that the rate of return required to sell the bonds is 9% ?
b. At what percent of par value is the price of the security?
c. If the required rate of return is also 9% two years after the issue, what is the price of this security, and what is the percent of par value?
d. Answer parts a, b, c again, this time assuming the rate of return (i.e., yield to maturity) is 7%.