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Answer: $29,703 and 1,004,878
**Explanation:** To map the bond to standard positions in zero-coupon bonds, we need to calculate the present value of each cash flow using the respective zero-coupon rates: 1. **First coupon payment (6 months):** - Coupon amount = $1,000,000 × 6% × 0.5 = $30,000 - Present value using 6-month rate (2% annual, 1% semi-annual): PV = $30,000 / (1 + 0.01) = $29,703 2. **Second coupon + principal payment (12 months):** - Total payment = $30,000 (coupon) + $1,000,000 (principal) = $1,030,000 - Present value using 12-month rate (2.5% annual): PV = $1,030,000 / (1 + 0.025) = $1,004,878 Therefore, the mapped positions are $29,703 in the 6-month zero and $1,004,878 in the 12-month zero.
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Q-47. An analyst is using the delta-normal method to determine the VaR of a fixed income portfolio. The portfolio contains a long position in 1-year bonds with a $1 million face value and a 6% coupon that is paid semi-annually. The interest rates on six-month and twelve-month maturity zero-coupon bonds are, respectively, 2% and 2.5%. Mapping the long position to standard positions in the six-month and twelve-month zeros, respectively, provides which of the following mapped positions?
A
$30,000 and 1,030,000
B
$29,500 and 975,610
C
$29,703 and 1,004,878
D
$30,300 and 1,035,000
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