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FRM Part I · FRM Exam Part I · Applying Duration, Convexity, and DV01

A bond is priced at 100.00 at its current yield. If the yield falls by 10 basis points the price is 100.80, and if it rises by 10 basis points the price is 99.22. Using these finite-difference prices, what is the bond's convexity?

Convexity is 200. The sum of the shocked prices minus twice the base price is 0.02. Dividing by the base price times the squared yield change, 100 × 0.000001 = 0.0001, gives 200. The one-half factor is used only when applying convexity to estimate price changes.

  1. A100
  2. B200Correct
  3. C400
  4. D20

Explanation

Convexity = (P₋ + P₊ - 2P₀)/(P₀×Δy²) = (100.80 + 99.22 - 200)/(100×0.001²) = 0.02/0.0001 = 200. A result of 100 would wrongly apply a one-half factor, which belongs in the price approximation formula and not in the convexity definition. 400 doubles the result, and 20 comes from a scaling error.

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