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

A three-year annual-pay bond with a 5% coupon and par value of 100 is priced at a yield to maturity of 6%, giving a price of 97.33. If the yield rises by 100 bps to 7%, the percentage change in the bond's price is closest to:

The price change is about -2.65%. At a 7% yield the bond is worth about 94.75, versus 97.33 at 6%. Dividing the 2.58 decline by the starting price of 97.33 gives -2.65%, smaller in size than the +2.75% gain from an equal yield fall.

  1. A-2.75%
  2. B-2.65%Correct
  3. C-2.58%

Explanation

At 7%: 5/1.07 + 5/1.07^2 + 105/1.07^3 = 4.673 + 4.367 + 85.713 = 94.75. Change = (94.75 - 97.33)/97.33 = -2.65%. The -2.75% figure is the gain when yield falls 100 bps to 5% (price 100), which is larger because of convexity. The -2.58% figure wrongly divides the price change by par instead of the starting price.

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