IDEAS home Printed from https://ideas.repec.org/a/bpj/bejeap/v7y2007i1n31.html
   My bibliography  Save this article

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

Author

Listed:
  • 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.

Suggested Citation

  • 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:bpj:bejeap:v:7:y:2007:i:1:n:31
    DOI: 10.2202/1935-1682.1785
    as

    Download full text from publisher

    File URL: https://doi.org/10.2202/1935-1682.1785
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.

    File URL: https://libkey.io/10.2202/1935-1682.1785?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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, vol. 51(5), pages 861-898, July.
    2. 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.
    3. Amy Finkelstein & James Poterba, 2004. "Adverse Selection in Insurance Markets: Policyholder Evidence from the U.K. Annuity Market," Journal of Political Economy, University of Chicago Press, vol. 112(1), pages 183-208, February.
    4. Olivia S. Mitchell, 1999. "New Evidence on the Money's Worth of Individual Annuities," American Economic Review, American Economic Association, vol. 89(5), pages 1299-1318, December.
    5. Lori Achman & Marsha Gold, "undated". "Medicare Advantage 2004 Payment Increases Resulting from the Medicare Modernization Act," Mathematica Policy Research Reports 1ff74bd5eae84c7ebd2c29839, Mathematica Policy Research.
    6. Ronald Lee & Timothy Miller, 2001. "Evaluating the performance of the lee-carter method for forecasting mortality," Demography, Springer;Population Association of America (PAA), vol. 38(4), pages 537-549, November.
    7. Shripad Tuljapurkar & Nan Li & Carl Boe, 2000. "A universal pattern of mortality decline in the G7 countries," Nature, Nature, vol. 405(6788), pages 789-792, June.
    8. Carlos Wong-Fupuy & Steven Haberman, 2004. "Projecting Mortality Trends," North American Actuarial Journal, Taylor & Francis Journals, vol. 8(2), pages 56-83.
    9. Thomas Davidoff & Jeffrey R. Brown & Peter A. Diamond, 2005. "Annuities and Individual Welfare," American Economic Review, American Economic Association, vol. 95(5), pages 1573-1590, December.
    10. 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.
    11. 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.
    12. 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, June.
    13. Mehra, Rajnish & Prescott, Edward C., 2003. "The equity premium in retrospect," Handbook of the Economics of Finance, 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.
    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.
    15. 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.
    16. 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, December.
    17. 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.
    18. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bravo, Jorge Miguel & El Mekkaoui de Freitas, Najat, 2018. "Valuation of longevity-linked life annuities," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 212-229.
    2. David Blake & Marco Morales & Enrico Biffis & Yijia Lin & Andreas Milidonis, 2017. "Special Edition: Longevity 10 – The Tenth International Longevity Risk and Capital Markets Solutions Conference," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(S1), pages 515-532, April.
    3. Basellini, Ugofilippo & Camarda, Carlo Giovanni & Booth, Heather, 2023. "Thirty years on: A review of the Lee–Carter method for forecasting mortality," International Journal of Forecasting, Elsevier, vol. 39(3), pages 1033-1049.
    4. Carlos Vidal-Melia & Ana Lejárraga-García, 2004. "The Bequest Motive And Single People’S Demand For Life Annuities," Public Economics 0405005, University Library of Munich, Germany.
    5. Tsai, Jeffrey T. & Wang, Jennifer L. & Tzeng, Larry Y., 2010. "On the optimal product mix in life insurance companies using conditional value at risk," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 235-241, February.
    6. Rachel WINGENBACH & Jong-Min KIM & Hojin JUNG, 2020. "Living Longer in High Longevity Risk," JODE - Journal of Demographic Economics, Cambridge University Press, vol. 86(1), pages 47-86, March.
    7. Booth, Heather, 2006. "Demographic forecasting: 1980 to 2005 in review," International Journal of Forecasting, Elsevier, vol. 22(3), pages 547-581.
    8. Melnikov, Alexander & Romaniuk, Yulia, 2006. "Evaluating the performance of Gompertz, Makeham and Lee-Carter mortality models for risk management with unit-linked contracts," Insurance: Mathematics and Economics, Elsevier, vol. 39(3), pages 310-329, December.
    9. Amy Finkelstein & James Poterba, 2004. "Adverse Selection in Insurance Markets: Policyholder Evidence from the U.K. Annuity Market," Journal of Political Economy, University of Chicago Press, vol. 112(1), pages 183-208, February.
    10. Niels Haldrup & Carsten P. T. Rosenskjold, 2019. "A Parametric Factor Model of the Term Structure of Mortality," Econometrics, MDPI, vol. 7(1), pages 1-22, March.
    11. Heather Booth & Rob Hyndman & Leonie Tickle & Piet de Jong, 2006. "Lee-Carter mortality forecasting: a multi-country comparison of variants and extensions," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 15(9), pages 289-310.
    12. Rokas Gylys & Jonas Šiaulys, 2019. "Revisiting Calibration of the Solvency II Standard Formula for Mortality Risk: Does the Standard Stress Scenario Provide an Adequate Approximation of Value-at-Risk?," Risks, MDPI, vol. 7(2), pages 1-24, May.
    13. de Jong, Piet & Tickle, Leonie & Xu, Jianhui, 2020. "A more meaningful parameterization of the Lee–Carter model," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 1-8.
    14. Katja Hanewald & Thomas Post & Helmut Gründl, 2011. "Stochastic Mortality, Macroeconomic Risks and Life Insurer Solvency," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 36(3), pages 458-475, July.
    15. Blake, David & El Karoui, Nicole & Loisel, Stéphane & MacMinn, Richard, 2018. "Longevity risk and capital markets: The 2015–16 update," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 157-173.
    16. Blake, David & Cairns, Andrew J.G., 2021. "Longevity risk and capital markets: The 2019-20 update," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 395-439.
    17. Hyndman, Rob J. & Booth, Heather, 2008. "Stochastic population forecasts using functional data models for mortality, fertility and migration," International Journal of Forecasting, Elsevier, vol. 24(3), pages 323-342.
    18. Jorge Bravo, 2011. "Pricing Longevity Bonds Using Affine-Jump Diffusion Models," CEFAGE-UE Working Papers 2011_29, University of Evora, CEFAGE-UE (Portugal).
    19. Man Chung Fung & Gareth W. Peters & Pavel V. Shevchenko, 2016. "A unified approach to mortality modelling using state-space framework: characterisation, identification, estimation and forecasting," Papers 1605.09484, arXiv.org.
    20. David Atance & Ana Debón & Eliseo Navarro, 2020. "A Comparison of Forecasting Mortality Models Using Resampling Methods," Mathematics, MDPI, vol. 8(9), pages 1-21, September.

    More about this item

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G23 - Financial Economics - - Financial Institutions and Services - - - Non-bank Financial Institutions; Financial Instruments; Institutional Investors
    • J11 - Labor and Demographic Economics - - Demographic Economics - - - Demographic Trends, Macroeconomic Effects, and Forecasts
    • J14 - Labor and Demographic Economics - - Demographic Economics - - - Economics of the Elderly; Economics of the Handicapped; Non-Labor Market Discrimination

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bpj:bejeap:v:7:y:2007:i:1:n:31. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.