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

An asset portfolio is valued at Rs 2,00,000 at an effective annual interest rate of 8% and has a discounted mean term of 6.48 years. Using the first-order (volatility) approximation, by roughly how much does the asset value change if the effective annual interest rate immediately rises to 8.5%?

The asset value falls by about Rs 6,000. Volatility is the discounted mean term divided by one plus the interest rate, 6.48 divided by 1.08, which is 6. Multiplying 2,00,000 by 6 and by the 0.5% rise gives the fall.

  1. AIncrease of Rs 6,000
  2. BFall of Rs 6,480
  3. CFall of Rs 5,555.56
  4. DFall of Rs 6,000Correct
  5. Fall of Rs 3,000

Explanation

Volatility = DMT/(1+i) = 6.48/1.08 = 6.00. Change ≈ -V × volatility × Δi = -2,00,000 × 6 × 0.005 = -Rs 6,000. Rs 6,480 forgets to divide by (1+i); Rs 5,555.56 divides by 1.08 twice.

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