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

Annually compounded spot rates are 2% for 1 year, 3% for 2 years and 4% for 3 years. What is the 3-year par yield for an annual-coupon bond, to two decimals?

The 3-year par yield is 3.95%. Convert the spot rates into discount factors, then divide one minus the 3-year discount factor by the sum of the three discount factors. Because the curve slopes upward, the par yield falls below the 3-year spot rate of 4%.

  1. A3.95%Correct
  2. B4.00%
  3. C3.00%
  4. D3.50%

Explanation

Discount factors: d1 = 1/1.02 = 0.98039, d2 = 1/1.03² = 0.94260, d3 = 1/1.04³ = 0.88900. Par yield = (1 − 0.88900)/(0.98039 + 0.94260 + 0.88900) = 0.11100/2.81199 = 3.95%. The 4.00% option wrongly uses the 3-year spot rate, and 3.00% is the average of the spot rates.

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