Natural hedge

Cox and Lin studied in 2007, in the North American Actuarial Journal ("Natural Hedging of Life and Annuity Mortality Risks"), the idea of a natural hedge. An insurer that holds both death cover, where it pays if the insured dies early, and annuities, where it pays as long as the annuitant lives, is partly immunized against demographic surprises. If lives get longer, what it loses on annuities it saves on death cover. This symmetry justifies the composite model and part of the capital requirement. Yet it rests on an unstated premise, that both books live in the same population. A selective therapy that reaches affluent annuitants first strikes hard where it costs and weakly where it would pay. The saving on death cover then offsets only a fraction of the loss on annuities, and the composite can end up with a net loss on a device meant to protect it.