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

Annual-pay par yields are 2.00% for 1 year and 3.00% for 2 years. Using bootstrapping, what is the 2-year spot rate, annually compounded?

The 2-year spot rate is about 3.01%. Pricing the 3% par bond at 100 and discounting its first coupon at the 2% one-year spot leaves 97.06 as the present value of the final 103. That implies a two-year growth factor of 1.0612, or about 3.01% per year.

  1. A3.00%
  2. B2.50%
  3. C4.01%
  4. D3.01%Correct

Explanation

The 1-year spot is 2.00%. A 2-year par bond gives 100 = 3/1.02 + 103/(1+s)^2. The first term is 2.9412, so 103/(1+s)^2 = 97.0588 and (1+s)^2 = 1.06116. Then 1+s = 1.03013, so s is about 3.01%. The 3.00% option wrongly treats the par yield as the spot rate, because the first coupon is discounted at the lower 1-year rate.

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