Explanation:
D is true. For 100% PSA, the conditional prepayment rate (CPR) at month 30 is 6%. For 200% PSA, the CPR is 200% * 6% = 12%. The SMM is calculated as $1 - (1 - CPR)^{1/12}1` - (1 - 0.12)^{1/12} = 1.064%$.
A is false because the MBS is trading at a premium (value > principal). An increase in prepayment speed (higher PSA) means the principal is returned earlier at par, accelerating the loss of the premium and decreasing the security's value.
B and C are false because faster prepayments return principal sooner, which reduces both the duration and the weighted average life (WAL) of the security.
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612.2. Consider a mortgage-backed security (MBS) with a principal of $600.0 million. The original mortgage pool has a weighted average maturity (WAM) of 30.0 years, and weighted average coupon (WAC) equal to 6.50%. The pass-through security pays a coupon equal to 6.0%, i.e., lower than the average coupon rate of the mortgage pool, in order to ensure available cash flow for investors in addition to compensation for the issuer. If we assume a PSA rate of 200%, the value of the security is $634.76, and its duration is 5.83 years. Which of the following statements is TRUE?
A
An increase in the PSA rate assumption to 250% will increase the value of the security
B
An increase in the PSA rate assumption to 250% will increase the duration of the security
C
An increase in the PSA rate assumption to 250% will increase the weighted average life (WAL) of the security
D
On month 30, the single monthly mortality rate (SMM) is equal to about 1.06%, which equals $1 - (1 - 200% \times 6%)^{1/12}$
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