Explanation:
We need to compare the value of the bond using the yield to maturity (YTM) and using spot rates.
Step 1: Value the bond using the YTM.
$103.90Step 2: Value the bond using spot rates (discount each CF by its spot rate).
| Time | CF | DF | PV |
|---|---|---|---|
| 1 | 9 | $1/1.035$ | 8.696 |
| 2 | 9 | $1/1.07^2$ | 7.861 |
| 3 | 109 | $1/1.08^3$ | 86.528 |
Value $103.09 |
Step 3: Compare values.
As the values are different, an arbitrage opportunity exists. Remember to sell high and buy low. We therefore sell the bond and buy the strips and capture the difference between the prices (i.e., $103.90 - 103.09 = `).
(Book 4, Module 55.1, LO 55.c)
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Question 19
A three-year bond has an annual coupon of 9% and a yield of 7.5%. A one-year zero-coupon bond has a yield of 3.5%, a two-year zero-coupon bond has a yield of 7%, and a three-year zero-coupon bond has a yield of 8%. Which of the following is correct regarding an arbitrage opportunity?
A
Buy the bond and sell the strips for an arbitrage profit of more than $0.20.
B
Sell the bond and buy the strips for an arbitrage profit of less than $0.20.
C
Buy the bond and sell the strips for an arbitrage profit of less than $0.20.
D
Sell the bond and buy the strips for an arbitrage profit of more than $0.20.
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