Explanation:
To solve this, we first need to determine the Single Monthly Mortality (SMM) from the given Conditional Prepayment Rate (CPR) using the formula provided. Re-arranging the formula, we find:
1` - \text{CPR} = (1 - \text{SMM})^{12}
\Rightarrow (1 - \text{CPR})^{\frac{1}{12}} = 1 - \text{SMM}
\Rightarrow \text{SMM} = 1 - (1 - \text{CPR})^{\frac{1}{12}}
\text{SMM} = 1 - (1 - 0.03)^{\frac{1}{12}} \ = 1 - (0.97)^{\frac{1}{12}} \ \approx 0.002535
\text{Principal Prepayment} = \text{SMM} \times \text{Current Balance} \ = 0.002535 \times 15,000,000 \ \approx \text{USD } 38,025
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Q.13 A hedge fund manager purchases a seasoned 4.5% agency MBS with a weighted average loan age of 48 months. The current balance on the loans at the beginning of this month is USD 15 million, and the conditional prepayment rate is assumed to be constant at 3% per year. What is the closest to the expected principal prepayment this month?
A
USD 42,200
B
USD 91,667
C
USD 38,025
D
USD 90,000
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