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

Two default-free zero-coupon bonds each pay exactly 100 in one year. Bond A trades at 95.00 and Bond B trades at 96.00. Assuming no transaction costs, which action locks in a riskless profit?

Buy the cheaper Bond A at 95 and short the dearer Bond B at 96. This gives a 1.00 inflow today, and the maturity payments cancel. The identical cash flows must trade at one price, so the gap is a riskless arbitrage.

  1. ABuy Bond A and sell short Bond B, earning 1.00 today with offsetting payoffs at maturityCorrect
  2. BBuy Bond B and sell short Bond A, earning 1.00 today with offsetting payoffs at maturity
  3. CBuy both bonds and hold them to maturity to earn the 5% yield
  4. DNo arbitrage exists because both bonds have the same maturity value

Explanation

The law of one price says identical cash flows must have the same price. Buying the cheaper bond (A at 95) and shorting the dearer one (B at 96) brings in 1.00 now. At maturity, A's 100 pays off the 100 owed on B, so there is no net liability. Buying B and shorting A would lock in a loss.

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