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

A zero-coupon bond pays a single sum on redemption exactly 8 years from now. Whatever the effective annual interest rate used to value it, what is its discounted mean term (Macaulay duration)?

The discounted mean term is 8.00 years. With only one cashflow, the present-value weighting puts all weight on the payment date, so the weighted average time equals the term of the bond regardless of the interest rate.

  1. A4.00 years
  2. B7.41 years
  3. C8.00 yearsCorrect
  4. DDepends on the interest rate, and is below 8 years
  5. Depends on the interest rate, and is above 8 years

Explanation

The discounted mean term is the PV-weighted average of payment times. With one payment, all the weight sits at t = 8, so the result is 8 whatever the interest rate. The value 7.41 is the modified duration at about 8% and is wrong because it divides by (1+i).

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