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

The 1-year spot rate is 2.0%, the 2-year spot rate is 3.0%, and the 3-year spot rate is 4.0%, all annual compounding. The 3-year par rate is closest to:

The 3-year par rate is about 3.94%. Compute discount factors from the spot rates, 0.9804, 0.9426 and 0.8890, sum them to 2.812, and apply par rate equals one minus the final discount factor divided by that sum. This gives roughly 3.94%, below the 4.00% spot rate.

  1. A3.00%
  2. B3.94%Correct
  3. C4.00%

Explanation

Discount factors: 1/1.02 = 0.98039; 1/1.0609 = 0.94260; 1/1.124864 = 0.88900. Sum = 2.81199. Par rate = (1 − 0.88900)/2.81199 = 0.11100/2.81199 = 3.947%, about 3.94%–3.95%. The 4.00% option wrongly uses the 3-year spot rate, and 3.00% is the simple average of the three spot rates.

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