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

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  • Leora Friedberg
  • Anthony Webb

Abstract

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%u2019 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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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 11984.

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Date of creation: Jan 2006
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Publication status: published as Friedberg Leora & Webb Anthony, 2007. "Life Is Cheap: Using Mortality Bonds to Hedge Aggregate Mortality Risk," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 7(1), pages 1-33, July.
Handle: RePEc:nbr:nberwo:11984

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References

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  1. 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.
  2. Mehra, Rajnish & Prescott, Edward C., 2003. "The equity premium in retrospect," Handbook of the Economics of Finance, Elsevier, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 14, pages 889-938 Elsevier.
  3. Shenyi Jiang & Wei Sun & Anthony Webb, 2011. "Did the Housing Boom Increase Household Spending?," Issues in Brief ib2011-10, Center for Retirement Research, revised Aug 2011.
  4. Olivia S. Mitchell, 1999. "New Evidence on the Money's Worth of Individual Annuities," American Economic Review, American Economic Association, American Economic Association, vol. 89(5), pages 1299-1318, December.
  5. 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.
  6. Thomas Davidoff & Jeffrey R. Brown & Peter A. Diamond, 2005. "Annuities and Individual Welfare," American Economic Review, American Economic Association, American Economic Association, vol. 95(5), pages 1573-1590, December.
  7. 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, The American Risk and Insurance Association, vol. 73(4), pages 687-718.
  8. Brown, Jeffrey R. & Cummins, J. David & Lewis, Christopher M. & Wei, Ran, 2004. "An empirical analysis of the economic impact of federal terrorism reinsurance," Journal of Monetary Economics, Elsevier, Elsevier, vol. 51(5), pages 861-898, July.
  9. 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.
  10. 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.
  11. 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.
  12. Kevin Dowd, 2003. "Survivor Bonds: A Comment on Blake and Burrows," Journal of Risk & Insurance, The American Risk and Insurance Association, The American Risk and Insurance Association, vol. 70(2), pages 339-348.
  13. Ronald Lee & Timothy Miller, 2001. "Evaluating the performance of the lee-carter method for forecasting mortality," Demography, Springer, Springer, vol. 38(4), pages 537-549, November.
  14. 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.
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Cited by:
  1. Olivia S Mitchell & John Piggott & Michael Sherris & Shaun Yow, 2006. "Financial Innovation for an Ageing World," RBA Annual Conference Volume, Reserve Bank of Australia, in: Christopher Kent & Anna Park & Daniel Rees (ed.), Demography and Financial Markets Reserve Bank of Australia.
  2. Jeffrey R. Brown & Amy Finkelstein, 2007. "Why is the market for long-term care insurance so small?," NBER Chapters, in: Trans-Atlantic Public Economics Seminar (TAPES), Public Policy and Retirement, pages 1967-1991 National Bureau of Economic Research, Inc.
  3. 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.
  4. 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.
  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. 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.
  7. Blake, David & Courbage, Christophe & MacMinn, Richard & Sherris, Michael, 2011. "Longevity risks and capital markets: The 2010-2011 update," MPRA Paper 34279, University Library of Munich, Germany.
  8. 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.
  9. Justin van de Ven & Martin Weale, 2007. "Annuities and Aggregate Mortality Uncertainty," WEF Working Papers, ESRC World Economy and Finance Research Programme, Birkbeck, University of London 0027, ESRC World Economy and Finance Research Programme, Birkbeck, University of London.

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