
Explanation:
To replicate a 1-year 5% semiannual coupon bond, which pays USD 2.50 in 6 months and USD 102.50 in 1 year, we can construct a portfolio using the 1-year zero-coupon bond (Bond 1) and the 1-year 7% semiannual coupon bond (Bond 2). Bond 1 pays USD 0 in 6 months and USD 100 in 1 year. Its price is USD 90. Bond 2 pays USD 3.50 in 6 months and USD 103.50 in 1 year. Its price is USD 110.
Let be the number of units of Bond 1 and be the number of units of Bond 2.
Matching the 6-month cash flow:
$3.50 \times w_2 = 2.50 \Rightarrow w_2 = \frac{2.5}{3.5} = \frac{5}{7} \approx 0.7143$
Matching the 1-year cash flow:
$100 \times w_1 + 103.50 \times w_2 = 102.50100\times w_1 + 103.50 \times \left(\frac{5}{7}\right) = 102.50$
The price of the replicated bond should be the cost of this portfolio:
Rounding to two decimal places, the price is USD 104.29.
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Q.45 A bond portfolio manager is interested in checking for arbitrage opportunities in the Treasury bond market. Suppose that two bonds are available for trading: a 1-year zero-coupon bond selling at USD 90 and a 1-year bond paying a 7% coupon semiannually, selling at USD 110. By applying a replication approach, what should be the price of a 1-year Treasury bond paying a 5% coupon semiannually?
A
95.71.
B
104.29.
C
78.57.
D
71.43.