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

Annual-pay zero-coupon bonds trade at 95.00 (1-year) and 88.00 (2-year) per 100 face. A 2-year bond with a 5% annual coupon and face value 100 trades at 100.50. Ignoring transaction costs, what is the riskless arbitrage profit per 100 face value from the best strategy?

The arbitrage profit is 3.35 per 100 face. The coupon bond's cash flows can be replicated with zeros costing 5 × 0.95 + 105 × 0.88 = 97.15. Since the bond trades at 100.50, selling it and buying the replicating portfolio locks in the 3.35 difference.

  1. A0.50
  2. B3.35Correct
  3. C3.65
  4. D5.35

Explanation

Replicating cash flows of 5 at year 1 and 105 at year 2 costs 5 × 0.95 + 105 × 0.88 = 4.75 + 92.40 = 97.15. The coupon bond at 100.50 is overpriced, so sell it and buy the zero-coupon replication, earning 100.50 − 97.15 = 3.35. The 0.50 option compares only with par, which is irrelevant, and 3.65 results from swapping the discount factors.

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