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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Allowing for inflation

An index-linked bond of nominal Rs 100 pays an annual coupon of 3% of the indexed nominal and is redeemed at par, also indexed, after 3 years. Both payments are indexed to the price level from issue, with no indexation lag. An investor requires a real yield of 4% per year. What is the price per Rs 100 nominal at issue?

The price is Rs 97.22 per Rs 100 nominal. With full indexation and no lag, the cashflows are fixed in real terms, so they are discounted at the 4% real yield. That is 3 times a three-year annuity factor plus 100 times the three-year discount factor.

  1. ARs 94.55
  2. BRs 100.00
  3. CRs 112.55
  4. DRs 97.22Correct
  5. Rs 102.78

Explanation

Because the cashflows are indexed with no lag, they are fixed in real terms. The price is therefore 3·a3 + 100·v^3 at 4% real, which is 3 × 2.77509 + 100 × 0.88900 = 8.325 + 88.900 = 97.22. Discounting at 5% instead of 4% gives 94.55, and compounding the answer by inflation gives 112.55, both of which are wrong.

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