Skip to content

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

A portfolio is worth USD 2,000,000 and has a modified duration of 5.0 and a convexity of 40. Yields fall by 50 basis points. Using the second-order approximation, what is the estimated change in portfolio value?

The portfolio gains about USD 51,000. Duration contributes 2.5% (USD 50,000) and convexity adds 0.5 × 40 × (0.005)² = 0.05% (USD 1,000), because convexity adds value for a yield move in either direction.

  1. A+USD 50,000
  2. B+USD 51,000Correct
  3. C+USD 49,000
  4. D+USD 52,000

Explanation

ΔP/P = -5×(-0.005) + 0.5×40×(0.005)² = 0.025 + 0.0005 = 0.0255. Multiplied by 2,000,000 this gives +51,000. Duration alone gives +50,000. Subtracting the convexity term gives 49,000. Dropping the 0.5 factor gives 52,000.

Did you get it right without looking?

One question tells you little. A timed set on Applying Duration, Convexity, and DV01 shows your real accuracy, how long you take and where you lose marks.

Practise Applying Duration, Convexity, and DV01Free diagnostic mock

More Applying Duration, Convexity, and DV01 questions