CFA Level I · CFA Level I Exam · The Term Structure of Interest Rates: Spot, Par, and Forward Curves
The one-year, two-year and three-year discount factors are 0.9524, 0.9070 and 0.8638. An analyst wants the two-year spot rate, annual compounding. The rate is closest to:
The two-year spot rate is about 5.00%. Invert the two-year discount factor to get 1.1025 and take the square root, giving 1.05. The other discount factors are not needed for this calculation.
- A4.00%
- B5.00%Correct
- C5.50%
Explanation
Spot rate = (1/DF)^(1/2) − 1 = (1/0.9070)^0.5 − 1. 1/0.9070 = 1.10254, and its square root is 1.0500, so the rate is 5.00%. The 4.00% option wrongly takes the one-year rate or an average-type estimate.
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