Redington immunization

Redington immunization is the set of three conditions that make a balance sheet's net value insensitive to a small parallel shift in interest rates. Frank Redington, actuary at Britain's Prudential, framed the question in 1952 in terms actuaries still use: under what conditions does an insurer's net value stay put when rates move? His answer is three conditions, two equalities and one inequality. The present value of assets equals that of liabilities, without which the problem does not arise. Durations on both sides are equal, which cancels first-order sensitivity. And asset convexity is greater than or equal to liability convexity, which makes net value locally minimal as a function of yield, hence protected in both directions. Writing net value as S(i), the present value of assets minus the present value of liabilities, the Redington immunization conditions read S(i) equal to zero, S'(i) equal to zero and S''(i) positive. In practice the third condition asks that asset cash flows be more spread out in time around the duration than liability cash flows. Immunization is often mixed up with cash-flow matching, where every liability payment is met by an asset flow of the same date and amount. Exact matching protects against any change in the shape of the curve, immunization only against a small parallel shift, but it is far cheaper to maintain. The result comes with three caveats. Immunization is local: it holds for a small move and degrades beyond that. It assumes a parallel shift of the curve, and a non-parallel deformation defeats it, which is why asset-liability managers now track key rate durations. And it decays over time, since durations and convexities drift as cash flows approach, which requires periodic rebalancing and makes immunization an ongoing discipline rather than a one-off trade. In the ALM model of a life insurer or a pension fund, Redington's conditions are still the first check before any refinement.