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

A bond with an embedded option trades at 100.00. If the yield curve shifts down 50 basis points, the model price is 102.60. If it shifts up 50 basis points, the model price is 97.60. What is the effective duration?

Effective duration equals the price when yields fall minus the price when yields rise, divided by twice the initial price times the yield shift. Here that is 5.00 / (2 × 100 × 0.005) = 5.0. One-sided or mis-scaled calculations give 5.2, 10.0 or 2.5.

  1. A2.5
  2. B5.0Correct
  3. C5.2
  4. D10.0

Explanation

Effective duration = (P- − P+) / (2 × P0 × Δy) = (102.60 − 97.60) / (2 × 100 × 0.005) = 5.00 / 1.00 = 5.0. Using one-sided change (2.60 / 0.5) gives 5.2. Omitting the factor of 2 gives 10.0, and using a 1% step in the denominator gives 2.5.

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