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CFA Level I · CFA Level I Exam · The Term Structure of Interest Rates: Spot, Par, and Forward Curves

An analyst observes annual-pay par rates of 2.00% for a one-year bond and 3.00% for a two-year bond. The one-year spot rate equals the one-year par rate. The two-year spot rate is closest to:

The two-year spot rate is about 3.02%. Discounting the first coupon at the 2.00% one-year spot rate and solving for the rate that prices the final 103 cash flow so the bond equals 100 gives a two-year spot rate slightly above the 3.00% par rate.

  1. A2.50%
  2. B3.02%Correct
  3. C3.51%

Explanation

Set 100 = 3/1.02 + 103/(1+S2)^2. Then 3/1.02 = 2.9412, so 103/(1+S2)^2 = 97.0588 and (1+S2)^2 = 1.06121, giving S2 = 3.02%. The 2.50% option wrongly averages the one-year spot rate and the two-year par rate.

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