Longevity hedge effectiveness: a decomposition

We use a case study of a pension plan wishing to hedge the longevity risk in its pension liabilities at a future date. The plan has the choice of using either a customised hedge or an index hedge, with the degree of hedge effectiveness being closely related to the correlation between the value of the hedge and the value of the pension liability. The key contribution of this paper is to show how correlation and, therefore, hedge effectiveness can be broken down into contributions from a number of distinct types of risk factor. Our decomposition of the correlation indicates that population basis risk has a significant influence on the correlation. But recalibration risk as well as the length of the recalibration window are also important, as is cohort effect uncertainty. Having accounted for recalibration risk, parameter uncertainty and Poisson risk have only a marginal impact on hedge effectiveness. Our case study shows that longevity risk can be substantially hedged using index hedges as an alternative to customised longevity hedges and that, as a consequence, index longevity hedges - in conjunction with the other components of an ALM strategy - can provide an effective and lower cost alternative to both a full buy-out of pension liabilities or even to a strategy using customised longevity hedges.