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

Annually compounded spot rates are 2% for 1 year, 3% for 2 years and 4% for 3 years. What is the 2-year par yield (annual coupon, par value 100), closest to?

The 2-year par yield is about 2.99%. It is calculated as one minus the 2-year discount factor, divided by the sum of the 1-year and 2-year discount factors. With an upward-sloping curve, the par yield lies slightly below the 2-year spot rate of 3%.

  1. A2.99%Correct
  2. B3.00%
  3. C3.50%
  4. D2.50%

Explanation

Discount factors: d1 = 1/1.02 = 0.980392; d2 = 1/1.0609 = 0.942596. Par yield = (1 - d2)/(d1 + d2) = 0.057404/1.922988 = 2.985%, about 2.99%. The 3.00% option is the 2-year spot rate, and 3.5% would be an incorrect average with the 3-year rate. Par yield is below the spot rate when the curve slopes upward.

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