Life is Cheap: Using Mortality Bonds to Hedge Aggregate Mortality Risk

Leora Friedberg and Anthony Webb

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 conclude that annuity business exposes

insurance companies to substantial mortality risk. We calculate that a markup

of 3.7% on an annuity premium (or else shareholders’ capital equal to 3.7%

of the expected present value of annuity payments) would reduce the

probability of insolvency resulting from uncertain aggregate mortality trends

to 5% and a markup of 5.4% would reduce the probability of insolvency to

1 %. Using the same model, we find that a projection scale commonly referred

to by the insurance industry underestimates aggregate mortality improvements.

Annuities that are priced on that projection scale without any conservative

margin appear to be substantially underpriced. Insurance companies could

deal with aggregate mortality risk by transferring it to financial markets

through mortality-contingent bonds, one of which has recently been offered.

We calculate the returns that investors would have obtained on such bonds

had they 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 on such bonds. At plausible coefficients of risk

aversion, annuity providers should be able to hedge aggregate mortality risk

via such bonds at a very low cost.