Abstract

Insurance companies, employer pension plans, and the U.S. government all provide annuities and therefore assume aggregate mortality risk. Using the widely-cited Lee-Carter mortality model, we quantify aggregate mortality risk as the risk that the average annuitant lives longer than is predicted by the model, and we determine that annuities expose providers to substantial risk. We also find that other recent actuarial forecasts lie at the edge or outside of Lee-Carter's 95% confidence interval, suggesting even more uncertainty about future mortality.We then evaluate the implications of aggregate mortality risk for insurance companies; this analysis can be extended to private pension providers and Social Security. Given the forecasts of the Lee-Carter model, we calculate that a markup of 3.9% on an annuity premium (or shareholders' capital equal to 3.9% of the expected present value of annuity payments) would be required to reduce the probability of insolvency resulting from aggregate mortality shocks to 5%, and a markup of 5.7% would reduce the probability of insolvency to 1%. Based on the same model, we find that a projection scale commonly referred to by the insurance industry underestimates aggregate mortality improvements and would leave annuities underpriced.Annuity providers could manage aggregate mortality risk more efficiently by transferring it to financial markets through mortality-contingent bonds. We calculate the returns that one recently proposed mortality bond would have paid had it been available over a long period. Using both the Capital and the Consumption Capital Asset Pricing Models, we determine the risk premium that investors would have required to hold the bond. At plausible coefficients of risk aversion, annuity providers should be able to hedge aggregate mortality risk via such bonds at very low cost.