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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Duration, convexity and immunisation

A portfolio has present value V, and its volatility is ν = 6. Its convexity is 60. If the effective yield rises by 0.01 (one percentage point), what is the approximate percentage change in value using the second-order expansion ΔV/V ≈ −ν Δi + ½ c (Δi)²?

The value falls by about 5.70%. The duration term gives −6%, and the convexity term adds back 0.5×60×0.0001, which is 0.3%. Subtracting the convexity term would wrongly give −6.30%.

  1. A−5.70%Correct
  2. B−6.30%
  3. C−5.40%
  4. D−6.00%
  5. +0.30%

Explanation

ΔV/V ≈ −6×0.01 + 0.5×60×0.0001 = −0.06 + 0.003 = −0.057, i.e. −5.70%. Using −6.30% subtracts the convexity term instead of adding it, and −6.00% ignores convexity.

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