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

Default-free zero-coupon discount factors are 0.95 for 1 year and 0.89 for 2 years. To rule out arbitrage, what is the implied 1-year rate that applies from year 1 to year 2, with annual compounding?

The no-arbitrage forward rate from year 1 to year 2 equals the 1-year discount factor divided by the 2-year discount factor, minus one. That is 0.95 / 0.89 - 1, or about 6.74%.

  1. A6.74%Correct
  2. B7.10%
  3. C6.00%
  4. D-6.32%

Explanation

Locking in a forward rate requires the ratio of discount factors: 0.95 / 0.89 = 1.06742, so the forward rate is 6.74%. Subtracting the two spot rates (12.36% - 5.26%) gives 7.10%, which is wrong. Taking the 2-year spot rate per year gives 6.00%. Inverting the ratio gives -6.32%.

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