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

A bond has a modified duration of 8.00 and a convexity of 90.0. Yield-to-maturity falls by 50 bps. The estimated percentage price change using duration and convexity is closest to:

The estimated price increase is about +4.11%. Duration contributes +4.00% (8.00 x 0.5%), and convexity adds 0.5 x 90 x 0.005 squared, about 0.11%. Convexity always adds to the price estimate regardless of the direction of the yield change.

  1. A+4.00%
  2. B+4.11%Correct
  3. C+4.23%

Explanation

Duration effect = -8.00 x (-0.005) = +4.00%. Convexity effect = 0.5 x 90 x (0.005)^2 = 0.1125%. Total = +4.11%. Using +4.00% omits convexity; +4.23% would result from adding the convexity effect twice or an arithmetic error.

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