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

Which of the following is a genuine practical limitation of Redington immunisation as applied by a life insurer?

The key limitation is that Redington immunisation protects only against small changes in interest rates and assumes a parallel shift of a flat yield curve. Non-parallel or large movements can still produce losses, and the portfolio also needs regular rebalancing as durations drift apart.

  1. ANo portfolio of bonds can ever have greater convexity than a single liability cashflow
  2. BThe method protects only against small changes in interest rates and is derived assuming all rates move by the same amount, so a non-parallel shift in the yield curve can still cause lossesCorrect
  3. COnce immunised, the portfolio stays immunised indefinitely without any trading as time passes
  4. DThe method requires the present value of assets to exceed the present value of liabilities by the full convexity margin
  5. The method cannot be used when the liabilities are payable in rupees

Explanation

Redington's conditions are local: they assume a small change in a flat force of interest and a parallel shift. Non-parallel shifts or large changes may produce a loss. Option C is wrong because durations of assets and liabilities change at different rates over time, so rebalancing is needed. Option A is false since a spread-out portfolio easily exceeds the convexity of a single payment.

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