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

The one-year and two-year spot rates are 2.00% and 3.00%, annually compounded. What is the par yield (annual coupon rate) on a two-year bond priced at par that pays annual coupons?

The par yield is about 2.99%. It is the coupon that makes the discounted value of the two coupons and the principal equal to 100 using the spot-rate discount factors, which is (1 minus d2) divided by (d1 plus d2). It is slightly below the 3% two-year spot rate.

  1. A2.99%Correct
  2. B2.50%
  3. C3.00%
  4. D2.00%

Explanation

Discount factors are d1 = 1/1.02 = 0.98039 and d2 = 1/1.0609 = 0.94260. Par coupon c = (1 − d2)/(d1 + d2) = 0.05740/1.92299 = 2.985%, or about 2.99%. Check: 2.985/1.02 + 102.985/1.0609 = 100. The 3.00% option wrongly uses the two-year spot rate as the par yield. The 2.50% option is a simple average of the spots.

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