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

Annual-pay discount factors are 0.9700 for 1 year, 0.9300 for 2 years and 0.8900 for 3 years. What is the 3-year par yield with annual coupons?

The 3-year par yield is 3.94%. A par bond's coupon equals one minus the final discount factor, 0.11, divided by the sum of the discount factors, 2.79. The result differs from the 3.96% zero rate because coupons are received before maturity.

  1. A3.94%Correct
  2. B3.96%
  3. C3.67%
  4. D4.12%

Explanation

The par yield is (1 - DF3) / (DF1 + DF2 + DF3) = 0.11 / 2.79 = 3.94%. The 3.96% option is the 3-year zero rate, (1/0.89)^(1/3) - 1, which is not a coupon-bond yield. The 3.67% option divides 0.11 by 3, as if every discount factor were 1.

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