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

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  • Friedberg Leora

    ()
    (University of Virginia)

  • Webb Anthony

    ()
    (Center for Retirement Research at Boston College)

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.

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Bibliographic Info

Article provided by De Gruyter in its journal The B.E. Journal of Economic Analysis & Policy.

Volume (Year): 7 (2007)
Issue (Month): 1 (July)
Pages: 1-33

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Handle: RePEc:bpj:bejeap:v:7:y:2007:i:1:n:31

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  1. Anthony Webb & Shenyi Jiang & Wei Sun, 2010. "Did the Housing Boom Increase Household Spending," Issues in Brief ib2010-10, Center for Retirement Research, revised Jul 2010.
  2. Thomas Davidoff & Jeffrey R. Brown & Peter A. Diamond, 2003. "Annuities and Individual Welfare," NBER Working Papers 9714, National Bureau of Economic Research, Inc.
  3. Dahl, Mikkel, 2004. "Stochastic mortality in life insurance: market reserves and mortality-linked insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 113-136, August.
  4. Olivia S. Mitchell & James M. Poterba & Mark J. Warshawsky, . "New Evidence on the Money's Worth of Individual Annuities," Pension Research Council Working Papers 97-9, Wharton School Pension Research Council, University of Pennsylvania.
  5. Kevin Dowd, 2003. "Survivor Bonds: A Comment on Blake and Burrows," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 70(2), pages 339-348.
  6. Jeffrey R. Brown & James M. Poterba, 1999. "Joint Life Annuities and Annuity Demand by Married Couples," NBER Working Papers 7199, National Bureau of Economic Research, Inc.
  7. Rajnish Mehra & Edward C. Prescott, 2003. "The Equity Premium in Retrospect," NBER Working Papers 9525, National Bureau of Economic Research, Inc.
  8. Ronald Lee & Timothy Miller, 2001. "Evaluating the performance of the lee-carter method for forecasting mortality," Demography, Springer, vol. 38(4), pages 537-549, November.
  9. Dowd, Kevin & Cairns, Andrew J.G. & Blake, David, 2006. "Mortality-dependent financial risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 427-440, June.
  10. Jeffrey R. Brown & Olivia S. Mitchell & James M. Poterba, 2000. "Mortality Risk, Inflation Risk, and Annuity Products," NBER Working Papers 7812, National Bureau of Economic Research, Inc.
  11. Andrew J. G. Cairns & David Blake & Kevin Dowd, 2006. "A Two-Factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(4), pages 687-718.
  12. Renshaw, A. E. & Haberman, S., 2003. "Lee-Carter mortality forecasting with age-specific enhancement," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 255-272, October.
  13. Jeffrey R. Brown & J. David Cummins & Christopher M. Lewis & Ran Wei, 2004. "An Empirical Analysis of the Economic Impact of Federal Terrorism Reinsurance," NBER Working Papers 10388, National Bureau of Economic Research, Inc.
  14. Brouhns, Natacha & Denuit, Michel & Vermunt, Jeroen K., 2002. "A Poisson log-bilinear regression approach to the construction of projected lifetables," Insurance: Mathematics and Economics, Elsevier, vol. 31(3), pages 373-393, December.
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Cited by:
  1. Brown, Jeffrey R. & Finkelstein, Amy, 2007. "Why is the market for long-term care insurance so small?," Journal of Public Economics, Elsevier, vol. 91(10), pages 1967-1991, November.
  2. David Blake & Christophe Courbage & Richard MacMinn & Michael Sherris, 2011. "Longevity Risk and Capital Markets: The 2010–2011 Update," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan, vol. 36(4), pages 489-500, October.
  3. Coughlan, Guy & Khalaf-Allah, Marwa & Ye, Yijing & Kumar, Sumit & Cairns, Andrew & Blake, David & Dowd, Kevin, 2011. "Longevity hedging 101: A framework for longevity basis risk analysis and hedge effectiveness," MPRA Paper 35743, University Library of Munich, Germany.
  4. Olivia S. Mitchell & John Piggott & Michael Sherris & Shaun Yow, 2006. "Financial Innovation for an Aging World," NBER Working Papers 12444, National Bureau of Economic Research, Inc.
  5. Bauer, Daniel & Börger, Matthias & Ruß, Jochen, 2010. "On the pricing of longevity-linked securities," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 139-149, February.
  6. Justin van de Ven & Martin Weale, 2007. "Annuities and Aggregate Mortality Uncertainty," WEF Working Papers 0027, ESRC World Economy and Finance Research Programme, Birkbeck, University of London.
  7. Guan Gong & Steven A. Sass, 2007. "Evaluating the Advanced Life Deferred Annuity - An Annuity People Might Actually Buy," Working Papers, Center for Retirement Research at Boston College wp2007-15, Center for Retirement Research, revised Sep 2007.
  8. Blake, David & Brockett, Patrick & Cox, Samuel & MacMinn, Richard, 2011. "Longevity risk and capital markets: The 2009-2010 update," MPRA Paper 28868, University Library of Munich, Germany.
  9. Chen, Bingzheng & Zhang, Lihong & Zhao, Lin, 2010. "On the robustness of longevity risk pricing," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 358-373, December.

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