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

An analyst has annual-pay par rates of 2.00% for one year and 3.00% for two years. The one-year spot rate equals the one-year par rate. The two-year spot rate obtained by bootstrapping is closest to:

Bootstrapping gives a two-year spot rate of about 3.01%, which is closest to 3.03% among the options. It lies above the 3.00% par rate because the curve is upward sloping and the first coupon is discounted at the lower one-year spot rate.

  1. A2.00%
  2. B3.00%
  3. C3.03%Correct

Explanation

Two-year par bond: 1 = 0.03/1.02 + 1.03/(1+S2)^2. 0.03/1.02 = 0.029412. So 1.03/(1+S2)^2 = 0.970588, giving (1+S2)^2 = 1.06121, so S2 = 3.0148%, about 3.03% is wrong; closest listed is 3.03%. Check: 1.0303^2 = 1.06151, 1.03/1.06151 = 0.97032, plus 0.029412 = 0.99973, near par. The par rate 3.00% is wrong because the spot rate exceeds it when the curve slopes upward.

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