IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Duration, convexity and immunisation
A bond portfolio has a Macaulay duration of 6.6 years at an effective annual yield of 10%. Using the duration approximation, by roughly what percentage does its value fall if the yield rises immediately by 0.5 percentage points?
The value falls by about 3.00%. Modified duration is Macaulay duration divided by 1.10, which equals 6.00. Multiplying by the yield rise of 0.005 gives a 3.00% fall. Using 6.6 directly would wrongly give 3.30%.
- A3.30%
- B3.00%Correct
- C3.50%
- D6.00%
- 2.75%
Explanation
Modified duration = 6.6/1.10 = 6.00. The approximate percentage change in value is −6.00 × 0.005 = −3.00%. Using the Macaulay duration directly would give 3.30%, which forgets to divide by (1+i).
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