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FRM Part I · FRM Exam Part I · Bond Yields and Return Calculations

The one-year spot rate is 3.00% and the two-year spot rate is 4.00%, both with annual compounding. What is the annual-pay par yield on a two-year bond?

The par yield is about 3.98%. It is the coupon that makes the bond price equal 100 when discounted at the spot rates, calculated as one minus the two-year discount factor divided by the sum of the two discount factors. It falls just below the 4% two-year spot rate.

  1. A3.50%
  2. B3.98%Correct
  3. C4.00%
  4. D4.50%

Explanation

Discount factors: d1 = 1/1.03 = 0.970874, d2 = 1/1.04^2 = 0.924556. Par coupon = (1 - d2)/(d1 + d2) = 0.075444/1.895430 = 3.98%. Check: 3.98/1.03 + 103.98/1.0816 = 3.86 + 96.14 = 100. Averaging the spots gives 3.50%, and using the two-year spot gives 4.00%, both wrong.

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