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FRM Part I · FRM Exam Part I · Pricing Conventions, Discounting, and Arbitrage

A 1-year zero-coupon bond (face 100) trades at 95.00 and a 2-year zero-coupon bond (face 100) trades at 89.00. A 2-year bond with face 100 and a 6% annual coupon trades at 104.00. Which strategy captures an arbitrage profit per 100 face, ignoring transaction costs?

Sell the coupon bond and buy the replicating zero-coupon bonds for a profit of 3.96. The zeros reproducing the cash flows cost 0.06×95 + 1.06×89 per 100 face, which is 100.04, while the bond sells for 104.00. The overpriced bond should be shorted.

  1. ASell the coupon bond and buy the replicating zeros, locking in a profit of 3.96Correct
  2. BBuy the coupon bond and sell the replicating zeros, locking in a profit of 3.96
  3. CSell the coupon bond and buy the replicating zeros, locking in a profit of 4.00
  4. DNo arbitrage exists because the price is within one point of par

Explanation

The replicating zeros cost 6(0.95) + 106(0.89) = 5.70 + 94.34 = 100.04. The coupon bond at 104.00 is overpriced, so sell it and buy 6 face of the 1-year zero and 106 face of the 2-year zero. Profit is 104.00 - 100.04 = 3.96. Buying the bond reverses the direction, and 4.00 ignores the replication cost.

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