Explanation:
To identify if there is mispricing in the 2-year zero-coupon bond, back out its yield using your financial calculator. Using annual compounding: FV = 100; PV = −82.6446, N = 2; CPT I/Y = 10.00%.
Because its yield is too low (compared to the spot rate of 10.263%), this implies that its price is too high. So we will short this zero-coupon and buy the 2-year coupon bond. We would also short the 1-year zero-coupon bond because its principal repayment can be covered with the first-year coupon on the coupon bond.
The following calculations provide the arbitrage profit, assuming $1,000,000 of the coupon bond is bought.
The 1-year zero-coupon bond will be shorted in an amount corresponding to the first-year coupon on the coupon bond, which is 10% × $1,000,000 = $100,000. We will short the PV of this amount, which using the discount factor of 0.952381 (from the zero-coupon bond’s price) is $95,238.10.
The 2-year zero-coupon bond will be shorted in an amount corresponding to the second-year coupon and principal on the coupon bond, which is $1,100,000. We will short the PV of this amount, which using the discount factor of 0.826446 (from the zero-coupon bond’s price) is $909,090.60.
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Question 73
Given the information in the table below and given that the 2-year spot rate is 10.263%, what is the appropriate action of an arbitrageur? Assume annual coupons and compounding.
| Bond A | Bond B | Bond C | |
|---|---|---|---|
| Maturity in years | 1 | 2 | 2 |
| Coupon rate | 0% | 0% | 10% |
| Price | 95.2381 | 82.6446 | 100 |
A
The arbitrageur should short the 1- and 2-year zero-coupon bonds and buy the 2-year coupon bond.
B
The arbitrageur should buy the 1- and 2-year zero-coupon bonds and short the 2-year coupon bond.
C
The arbitrageur should buy the 1-year zero-coupon and 2-year coupon bond and short the 2-year zero-coupon bond.
D
The arbitrageur should short the 1-year zero-coupon and 2-year coupon bond and buy the 2-year zero-coupon bond.
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