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

Which statement about convexity in the context of Redington immunisation is correct?

The asset cashflows must be more spread about the discounted mean term than the liability cashflows, meaning asset convexity exceeds liability convexity. This is the second-order Redington condition that ensures the surplus is a local minimum, so small interest rate changes cannot cause a loss.

  1. AConvexity of assets must be less than convexity of liabilities, so that profits arise only for upward interest rate moves
  2. BConvexity of assets must be zero for the portfolio to be immunised
  3. CThe spread of the asset cashflows around the discounted mean term must be greater than the spread of the liability cashflowsCorrect
  4. DConvexity is irrelevant provided the present values and durations of assets and liabilities are equal
  5. Convexity of assets must equal convexity of liabilities exactly, and durations may differ

Explanation

Redington's third condition is that the asset convexity exceeds the liability convexity, equivalently the asset cashflows are more spread out about the discounted mean term. Equal convexities would give no guaranteed surplus, and ignoring convexity leaves only first-order protection.

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