Set of three conditions making a balance sheet's net value insensitive to a small parallel shift in rates, stated by Frank Redington in 1952 and the foundation of asset-liability management.
Frank Redington, actuary at the British Prudential, framed the question in 1952 in the terms that remain ours: under what conditions does an insurer's net value not move when rates move. His answer is three equalities. 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. Three caveats attend the result. Immunization is local, it holds for a small move and degrades beyond. It assumes a parallel shift of the curve, and a non-parallel deformation defeats it. And it decays over time, since durations and convexities drift as cash flows approach, which requires periodic rebalancing and makes immunization a discipline rather than an operation.
Frank Redington published Review of the Principles of Life Office Valuations in the Journal of the Institute of Actuaries in 1952. The British pension fund crisis of September and October 2022 illustrates the second caveat at the scale of a whole market: portfolios correctly immunized in duration ran into trouble not through a matching error, but because the hedge was leveraged and margin calls forced the sale of the very assets serving the hedge.
immunisation, immunization, trois conditions de Redington, couverture de duration