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.

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