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

Annual-coupon par bonds yield 2.0% at 1 year and 3.0% at 2 years. Bootstrapping from these par yields, what is the annually compounded 1-year forward rate starting one year from now?

The forward rate is 4.04%. Bootstrapping gives a 1-year discount factor of 0.980392 and a 2-year discount factor of 0.942318. Dividing the first by the second and subtracting one yields 4.04%. Treating par yields as zero rates gives the wrong 4.00%.

  1. A4.04%Correct
  2. B4.00%
  3. C3.02%
  4. D3.50%

Explanation

DF1 = 1/1.02 = 0.980392. For the 2-year par bond, 0.03 x DF1 + 1.03 x DF2 = 1, so DF2 = 0.970588/1.03 = 0.942318. The forward rate is DF1/DF2 - 1 = 4.04%. The 4.00% option applies 2 x 3% - 2% to par yields, which are not zero rates. The 3.02% option is the 2-year zero rate.

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