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

A portfolio manager must meet a single liability due in 5 years and buys a bond with a Macaulay duration of 5.0 years but a maturity of 8 years. Immediately after purchase, yields fall by a small parallel amount. Compared with the original yield to maturity, the manager's value at year 5 is most likely:

The year-5 value is approximately equal to the target based on the original yield. With the horizon matching Macaulay duration, the bond's higher sale price after yields fall offsets lower reinvestment income on coupons, so the liability is approximately immunized despite the longer maturity.

  1. Amaterially lower, because reinvestment income declines more than price rises
  2. Bapproximately equal, because the price gain offsets the lower reinvestment incomeCorrect
  3. Cmaterially higher, because the bond's remaining 3 years of maturity add price gains

Explanation

Because the horizon equals Macaulay duration, the higher bond price at year 5 offsets the lower reinvestment income on coupons after the yield decline. Maturity of 8 years is irrelevant to the offset; only duration matching the horizon matters. The first option overstates reinvestment loss, and the third double counts price gains.

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