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

A zero-coupon bond pays 1,000 in exactly four years and trades at 790.00. Using annual compounding, the four-year spot rate is closest to:

The four-year spot rate is about 6.1%. It is found by taking the fourth root of the ratio of face value to price (1,000/790 = 1.2658) and subtracting one, which gives roughly 1.0607 minus one under annual compounding.

  1. A5.2%
  2. B6.1%Correct
  3. C7.1%

Explanation

Spot rate = (1,000/790)^(1/4) - 1. 1,000/790 = 1.26582; the square root is 1.12508 and its square root is 1.06070, so the rate is about 6.1%. Using 1/4 of the total return (26.6%/4 = 6.6%) would overstate the rate, and 5.2% results from ignoring compounding in the wrong direction.

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