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The Simple Analytics of a Pooled Annuity Fund

Author

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  • John Piggott
  • Emiliano A. Valdez
  • Bettina Detzel

Abstract

This article provides a formal analysis of payout adjustments from a longevity risk-pooling fund, an arrangement we refer to as group self-annuitization (GSA). The distinguishing risk diffusion characteristic of GSAs in the family of longevity insurance instruments is that the annuitants bear their systematic risk, but the pool shares idiosyncratic risk. This obviates the need for an insurance company, although such instruments could be sold through a corporate insurer. We begin by deriving the payout adjustment for a single entry group with a single annuity factor and constant expectations. We then show that under weak requirements a unique solution to payout paths exists when multiple cohorts combine into a single pool. This relies on the harmonic mean of the ratio of realized to expected survivorship rates across cohorts. The case of evolving expectations is also analyzed. In all cases, we demonstrate that the periodic-benefit payment in a pooled annuity fund is determined based on the previous payment adjusted for any deviations in mortality and interest from expectations. GSA may have considerable appeal in countries which have adopted national defined contribution schemes and/or in which the life insurance industry is noncompetitive or poorly developed. Copyright The Journal of Risk and Insurance.

Suggested Citation

  • John Piggott & Emiliano A. Valdez & Bettina Detzel, 2005. "The Simple Analytics of a Pooled Annuity Fund," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 72(3), pages 497-520.
    • Handle: RePEc:bla:jrinsu:v:72:y:2005:i:3:p:497-520
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    References listed on IDEAS

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    1. Brown, Jeffrey R. & Mitchell, Olivia S. & Poterba, James M. & Warshawsky, Mark J., 2001. "The Role of Annuity Markets in Financing Retirement," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262529130, January.
    2. Albrecht, Peter & Maurer, Raimond, 2001. "Self-Annuitization, Ruin Risk in Retirement and Asset Allocation: The Annuity Benchmark," Sonderforschungsbereich 504 Publications 01-35, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
    3. Suzanne Doyle & Olivia S. Mitchell & John Piggott, 2001. "Annuity Values in Defined Contribution Retirement Systems: The Case of Singapore and Australia," NBER Working Papers 8091, National Bureau of Economic Research, Inc.
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    Cited by:

    1. Maurer, Raimond & Mitchell, Olivia S. & Rogalla, Ralph & Siegelin, Ivonne, 2016. "Accounting and actuarial smoothing of retirement payouts in participating life annuities," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 268-283.
    2. Eduardo Roca & Victor Wong, 2008. "An analysis of the sensitivity of Australian superannuation funds to market movements: a Markov regime switching approach," Applied Financial Economics, Taylor & Francis Journals, vol. 18(7), pages 583-597.
    3. Milevsky, Moshe A. & Salisbury, Thomas S., 2015. "Optimal retirement income tontines," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 91-105.
    4. Donnelly, Catherine & Guillén, Montserrat & Nielsen, Jens Perch, 2014. "Bringing cost transparency to the life annuity market," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 14-27.
    5. repec:eee:hapoch:v1_865 is not listed on IDEAS
    6. Palmer, Edward, 2011. "Generic NDC - Equilibrium, Valuation and Risk Sharing with and without NDC Bonds," Working Paper Series 2011:3, Uppsala University, Department of Economics.
    7. Chao Qiao & Michael Sherris, 2011. "Managing Systematic Mortality Risk with Group Self Pooling and Annuitisation Schemes," Working Papers 201104, ARC Centre of Excellence in Population Ageing Research (CEPAR), Australian School of Business, University of New South Wales.
    8. Dr Justin van de Ven & Dr Martin Weale, 2008. "Mortality Risk and Pricing of Annuities," National Institute of Economic and Social Research (NIESR) Discussion Papers 322, National Institute of Economic and Social Research.
    9. Kam Ki Tang & Jie Zhang, 2007. "Morbidity, Mortality, Health Expenditures and Annuitization," CESifo Working Paper Series 2086, CESifo Group Munich.
    10. Raimond Maurer & Olivia S. Mitchell & Ralph Rogalla & Vasily Kartashov, 2013. "Lifecycle Portfolio Choice With Systematic Longevity Risk and Variable Investment—Linked Deferred Annuities," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(3), pages 649-676, September.
    11. Donnelly, Catherine & Guillén, Montserrat & Nielsen, Jens Perch, 2013. "Exchanging uncertain mortality for a cost," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 65-76.
    12. repec:pal:gpprii:v:42:y:2017:i:3:d:10.1057_s41288-017-0056-1 is not listed on IDEAS
    13. Moshe A. Milevsky & Thomas S. Salisbury, 2016. "Optimal retirement income tontines," Papers 1610.10078, arXiv.org.
    14. Hanewald, Katja & Piggott, John & Sherris, Michael, 2013. "Individual post-retirement longevity risk management under systematic mortality risk," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 87-97.
    15. Catherine Donnelly, 2013. "Actuarial fairness and solidarity in pooled annuity funds," Papers 1311.5120, arXiv.org, revised Jul 2014.
    16. repec:gam:jrisks:v:5:y:2017:i:2:p:32-:d:102044 is not listed on IDEAS
    17. repec:bla:ausecr:v:49:y:2016:i:4:p:483-493 is not listed on IDEAS
    18. Maurer, Raimond & Mitchell, Olivia S. & Rogalla, Ralph & Siegelin, Ivonne, 2015. "Accounting-based asset return smoothing in participating life annuities: Implications for annuitants, insurers, and policymakers," CFS Working Paper Series 518, Center for Financial Studies (CFS).
    19. Valdez, Emiliano A. & Piggott, John & Wang, Liang, 2006. "Demand and adverse selection in a pooled annuity fund," Insurance: Mathematics and Economics, Elsevier, vol. 39(2), pages 251-266, October.
    20. M. A. Milevsky & T. S. Salisbury, 2016. "Equitable retirement income tontines: Mixing cohorts without discriminating," Papers 1610.09384, arXiv.org.
    21. Chao Qiao & Michael Sherris, 2013. "Managing Systematic Mortality Risk With Group Self-Pooling and Annuitization Schemes," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(4), pages 949-974, December.

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