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Valuing variable annuities with guaranteed minimum lifetime withdrawal benefits

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  • Steinorth, Petra
  • Mitchell, Olivia S.

Abstract

Variable annuities with guaranteed minimum lifetime withdrawal benefits (VA/GLWB) offer retirees longevity protection, exposure to equity markets, and access to flexible withdrawals in emergencies. We model how risk-averse retirees optimally withdraw from the products, balancing returns and the embedded longevity protection. Assuming reasonable individual preferences, the resulting cash flow generates a Money’s Worth Ratio of around 0.9 for our stylized VA/GLWB in the post-crisis product, considerably lower than what was offered prior to 2008. Sensitivity analyses with respect to portfolio choice, mortality, fees, and guaranteed withdrawal rates show that MWRs range from 0.80 to 1.0, with the portfolio choice making the biggest difference. For most parameter choices, the utility value of the VA/GLWB exceeds that of a similar mutual fund, but it is less than for a fixed annuity. Interestingly, VA/GLWB withdrawals in early retirement can optimally exceed contract maximum withdrawals, despite the fact that this reduces future withdrawal guarantees.

Suggested Citation

  • Steinorth, Petra & Mitchell, Olivia S., 2015. "Valuing variable annuities with guaranteed minimum lifetime withdrawal benefits," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 246-258.
    • Handle: RePEc:eee:insuma:v:64:y:2015:i:c:p:246-258
    DOI: 10.1016/j.insmatheco.2015.04.001
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    1. Suzanne Doyle & Olivia S. Mitchell & John Piggott, 2004. "Annuity Values in Defined Contribution Retirement Systems: Australia and Singapore Compared," Australian Economic Review, The University of Melbourne, Melbourne Institute of Applied Economic and Social Research, vol. 37(4), pages 402-416, December.
    2. Raimond Maurer & Olivia S. Mitchell & Ralph Rogalla, 2010. "The Effect of Uncertain Labor Income and Social Security on Life-cycle Portfolios," NBER Working Papers 15682, National Bureau of Economic Research, Inc.
    3. Bacinello, Anna Rita & Millossovich, Pietro & Olivieri, Annamaria & Pitacco, Ermanno, 2011. "Variable annuities: A unifying valuation approach," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 285-297.
    4. James M. Poterba & Steven F. Venti & David A. Wise, 2011. "Were They Prepared for Retirement? Financial Status at Advanced Ages in the HRS and AHEAD Cohorts," NBER Chapters, in: Investigations in the Economics of Aging, pages 21-69, National Bureau of Economic Research, Inc.
    5. 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.
    6. Francisco Gomes & Alexander Michaelides, 2005. "Optimal Life‐Cycle Asset Allocation: Understanding the Empirical Evidence," Journal of Finance, American Finance Association, vol. 60(2), pages 869-904, April.
    7. Joelle H. Y. Fong & Olivia S. Mitchell & Benedict S. K. Koh, 2011. "Longevity Risk Management in Singapore's National Pension System," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 78(4), pages 961-982, December.
    8. Gabriella Piscopo & Steven Haberman, 2011. "The Valuation of Guaranteed Lifelong Withdrawal Benefit Options in Variable Annuity Contracts and the Impact of Mortality Risk," North American Actuarial Journal, Taylor & Francis Journals, vol. 15(1), pages 59-76.
    9. Thomas Davidoff, 2009. "Housing, Health, and Annuities," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(1), pages 31-52, March.
    10. Jingjing Chai & Wolfram Horneff & Raimond Maurer & Olivia S. Mitchell, 2011. "Optimal Portfolio Choice over the Life Cycle with Flexible Work, Endogenous Retirement, and Lifetime Payouts," Review of Finance, European Finance Association, vol. 15(4), pages 875-907.
    11. Horneff, Wolfram J. & Maurer, Raimond H. & Mitchell, Olivia S. & Stamos, Michael Z., 2010. "Variable payout annuities and dynamic portfolio choice in retirement," Journal of Pension Economics and Finance, Cambridge University Press, vol. 9(2), pages 163-183, April.
    12. Huang, H. & Milevsky, M.A. & Salisbury, T.S., 2014. "Optimal initiation of a GLWB in a variable annuity: No Arbitrage approach," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 102-111.
    13. Jeffrey R. Brown & James M. Poterba, 2006. "Household Ownership of Variable Annuities," NBER Chapters, in: Tax Policy and the Economy, Volume 20, pages 163-191, National Bureau of Economic Research, Inc.
    14. Eric Ulm, 2010. "The Effect of Policyholder Transfer Behavior on the Value of Guaranteed Minimum Death Benefits," North American Actuarial Journal, Taylor & Francis Journals, vol. 14(1), pages 16-37.
    15. Horneff, Wolfram J. & Maurer, Raimond H. & Mitchell, Olivia S. & Stamos, Michael Z., 2009. "Asset allocation and location over the life cycle with investment-linked survival-contingent payouts," Journal of Banking & Finance, Elsevier, vol. 33(9), pages 1688-1699, September.
    16. Eric R. Ulm, 2006. "The Effect of the Real Option to Transfer on the Value of Guaranteed Minimum Death Benefits," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(1), pages 43-69, March.
    17. Mahayni, Antje & Schneider, Judith C., 2012. "Variable annuities and the option to seek risk: Why should you diversify?," Journal of Banking & Finance, Elsevier, vol. 36(9), pages 2417-2428.
    18. Charupat, Narat & Milevsky, Moshe A., 2002. "Optimal asset allocation in life annuities: a note," Insurance: Mathematics and Economics, Elsevier, vol. 30(2), pages 199-209, April.
    19. 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.
    20. Clark, Robert L. & Mitchell, Olivia S. (ed.), 2010. "Reorienting Retirement Risk Management," OUP Catalogue, Oxford University Press, number 9780199592609.
    21. Yang, Sharon S. & Dai, Tian-Shyr, 2013. "A flexible tree for evaluating guaranteed minimum withdrawal benefits under deferred life annuity contracts with various provisions," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 231-242.
    22. Pang, Gaobo & Warshawsky, Mark, 2010. "Optimizing the equity-bond-annuity portfolio in retirement: The impact of uncertain health expenses," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 198-209, February.
    23. Menahem E. Yaari, 1965. "Uncertain Lifetime, Life Insurance, and the Theory of the Consumer," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(2), pages 137-150.
    24. Bernard, Carole & MacKay, Anne & Muehlbeyer, Max, 2014. "Optimal surrender policy for variable annuity guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 116-128.
    25. Feng, Runhuan & Volkmer, Hans W., 2012. "Analytical calculation of risk measures for variable annuity guaranteed benefits," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 636-648.
    26. Gao, Jin & Ulm, Eric R., 2012. "Optimal consumption and allocation in variable annuities with Guaranteed Minimum Death Benefits," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 586-598.
    27. Luis M. Viceira, 2001. "Optimal Portfolio Choice for Long‐Horizon Investors with Nontradable Labor Income," Journal of Finance, American Finance Association, vol. 56(2), pages 433-470, April.
    28. Bauer, Daniel & Kling, Alexander & Russ, Jochen, 2008. "A Universal Pricing Framework for Guaranteed Minimum Benefits in Variable Annuities1," ASTIN Bulletin, Cambridge University Press, vol. 38(2), pages 621-651, November.
    29. John Ameriks & Andrew Caplin & Steven Laufer & Stijn Van Nieuwerburgh, 2011. "The Joy of Giving or Assisted Living? Using Strategic Surveys to Separate Public Care Aversion from Bequest Motives," Journal of Finance, American Finance Association, vol. 66(2), pages 519-561, April.
    30. Chen, Z. & Vetzal, K. & Forsyth, P.A., 2008. "The effect of modelling parameters on the value of GMWB guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 165-173, August.
    31. Horneff, Wolfram & Maurer, Raimond & Rogalla, Ralph, 2010. "Dynamic portfolio choice with deferred annuities," Journal of Banking & Finance, Elsevier, vol. 34(11), pages 2652-2664, November.
    32. Min Dai & Yue Kuen Kwok & Jianping Zong, 2008. "Guaranteed Minimum Withdrawal Benefit In Variable Annuities," Mathematical Finance, Wiley Blackwell, vol. 18(4), pages 595-611, October.
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    4. Hsieh, Ming-hua & Wang, Jennifer L. & Chiu, Yu-Fen & Chen, Yen-Chih, 2018. "Valuation of variable long-term care Annuities with Guaranteed Lifetime Withdrawal Benefits: A variance reduction approach," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 246-254.
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    6. Maria Alexandrova & Nadine Gatzert, 2019. "What Do We Know About Annuitization Decisions?," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 22(1), pages 57-100, March.
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    8. Ankush Agarwal & Christian-Oliver Ewald & Yongjie Wang, 2023. "Hedging longevity risk in defined contribution pension schemes," Computational Management Science, Springer, vol. 20(1), pages 1-34, December.
    9. Pavel V. Shevchenko & Xiaolin Luo, 2016. "A unified pricing of variable annuity guarantees under the optimal stochastic control framework," Papers 1605.00339, arXiv.org.
    10. Balter, Anne G. & Kallestrup-Lamb, Malene & Rangvid, Jesper, 2021. "Macro longevity risk and the choice between annuity products: Evidence from Denmark," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 355-362.
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