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CFA Level I · CFA Level I Exam · Interest Rate Risk and Return

A 3-year, 6% annual-pay bond with a par value of 100 trades at par, so its yield to maturity is 6.00%. Its Macaulay duration is closest to:

Macaulay duration is the present-value-weighted average time to receipt of cash flows. For this par bond, the weighted times sum to 283.34 and the price is 100, giving about 2.83 years. It is below the 3-year maturity because coupons arrive earlier.

  1. A2.67 yearsCorrect
  2. B2.83 years
  3. C3.00 years

Explanation

PV of cash flows at 6%: 5.660, 5.340, 89.000 (CF 6, 6, 106). Weighted time: 1(5.660)+2(5.340)+3(89.000)=5.660+10.680+267.0=283.34. Divide by price 100 to get 2.83. The 2.67 option results from using only the time-weighted coupons and a wrong base; 3.00 is the maturity, which only a zero-coupon bond has.

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