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CFA Level I · CFA Level I Exam · Yield-Based Bond Duration Measures and Properties

A 3-year annual-pay bond has a 5% coupon, a par value of 100, and a yield to maturity of 5%, so it prices at 100. The Macaulay duration is closest to:

Macaulay duration is about 2.86 years. It is the present-value-weighted average time to receive the cash flows: the weighted sum of 285.94 divided by the price of 100. It is below the 3-year maturity because coupons are received earlier.

  1. A2.72 yearsCorrect
  2. B2.86 years
  3. C3.00 years

Explanation

PVs: 5/1.05=4.7619; 5/1.1025=4.5351; 105/1.157625=90.7029. Weighted times: 4.7619×1 + 4.5351×2 + 90.7029×3 = 4.7619+9.0703+272.1088=285.941. Divided by price 100 gives 2.86. 3.00 ignores coupons (zero-coupon duration); 2.72 is an arithmetic slip.

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