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Annuitization and asset allocation with HARA utility

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  • KINGSTON, GEOFFREY
  • THORP, SUSAN

Abstract

A new explanation for the well-known reluctance of retirees to buy life annuities is due to Milevsky and Young (2002, 2003). Specifically, the decision to buy longevity insurance is largely irreversible, so that the real option to delay annuitization generally has value. Milevsky and Young analyticaly identify and numerically estimate the RODA in a setting of constant relative risk aversion (CRRA). This paper extends the analysis of Milevsky and Young to the case of hyperbolic absolute risk aversion (HARA),the simplest representation of a consumption habit.The formula for the optimal timing of annuitization ias surprisingly simple, but yields only a myopic solution, that is, the precise date of annuitization cannot be ascertained in advance. The effect of increasing the subsistence consumption rate on the timing of annuity purchase is similar to the effect of increasing the curvature function of the utility function. As in the CRRA case studied by Milevsky and Young, delayed annuitization is associated with optimistic forward-looking estimates of the Sharpe ratio.
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  • Kingston, Geoffrey & Thorp, Susan, 2005. "Annuitization and asset allocation with HARA utility," Journal of Pension Economics and Finance, Cambridge University Press, vol. 4(03), pages 225-248, November.
  • Handle: RePEc:cup:jpenef:v:4:y:2005:i:03:p:225-248_00
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    Cited by:

    1. Alexandra Spicer & Olena Stavrunova & Susan Thorp, 2016. "How Portfolios Evolve after Retirement: Evidence from Australia," The Economic Record, The Economic Society of Australia, vol. 92(297), pages 241-267, June.
    2. Hazel Bateman & Susan Thorp, 2008. "Choices and Constraints over Retirement Income Streams: Comparing Rules and Regulations," The Economic Record, The Economic Society of Australia, pages 17-31.
    3. Wolfram J. Horneff & Raimond H. Maurer, 2008. "Deferred Annuities and Strategic Asset Allocation," Working Papers wp178, University of Michigan, Michigan Retirement Research Center.
    4. Fedor Iskhakov & Susan Thorp & Hazel Bateman, 2015. "Optimal Annuity Purchases for Australian Retirees," The Economic Record, The Economic Society of Australia, vol. 91(293), pages 139-154, June.
    5. Horneff, Wolfram J. & Maurer, Raimond H. & Mitchell, Olivia S. & Dus, Ivica, 2008. "Following the rules: Integrating asset allocation and annuitization in retirement portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 396-408, February.
    6. Wolfram J. Horneff & Raimond H. Maurer & Olivia S. Mitchel & Michael Z. Stamos, 2008. "Asset Allocation and Location over the Life Cycle with Survival-Contingent Payouts," Working Papers wp177, University of Michigan, Michigan Retirement Research Center.
    7. 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, pages 163-183.
    8. Huaxiong Huang & Moshe A. Milevsky & Thomas S. Salisbury, 2012. "Valuation and hedging of the ruin-contingent life annuity (RCLA)," Papers 1205.3686, arXiv.org.
    9. Duxbury, Darren & Summers, Barbara & Hudson, Robert & Keasey, Kevin, 2013. "How people evaluate defined contribution, annuity-based pension arrangements: A behavioral exploration," Journal of Economic Psychology, Elsevier, vol. 34(C), pages 256-269.
    10. Wolfram Horneff & Raimond Maurer & Olivia Mitchell & Ivica Dus, 2006. "Optimizing the Retirement Portfolio: Asset Allocation, Annuitization, and Risk Aversion," Working Papers wp124, University of Michigan, Michigan Retirement Research Center.
    11. Milevsky, Moshe A. & Young, Virginia R., 2007. "The timing of annuitization: Investment dominance and mortality risk," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 135-144, January.
    12. Jinhui Zhang & Sachi Purcal & Jiaqin Wei, 2017. "Optimal Time to Enter a Retirement Village," Risks, MDPI, Open Access Journal, vol. 5(1), pages 1-20, March.
    13. Wolfram J. Horneff & Raimond H. Maurer & Michael Z. Stamos, 2008. "Optimal Gradual Annuitization: Quantifying the Costs of Switching to Annuities," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(4), pages 1019-1038.
    14. Wei-Ting Pan, 2016. "The Impact of Mandatory Savings on Life Cycle Consumption and Portfolio Choice," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 32.
    15. Huaxiong Huang & Moshe A. Milevsky & Thomas S. Salisbury, 2012. "Optimal retirement consumption with a stochastic force of mortality," Papers 1205.2295, arXiv.org.
    16. Wolfram Horneff & Raimond Maurer & Olivia Mitchell & Michael Stamos, 2007. "Money in Motion: Dynamic Portfolio Choice in Retirement," Working Papers wp152, University of Michigan, Michigan Retirement Research Center.
    17. Wolfram J. Horneff & Raimond H. Maurer & Olivia S. Mitchell & Michael Z. Stamos, 2008. "Asset Allocation and Location over the Life Cycle with Survival-Contingent Payouts," NBER Working Papers 14055, National Bureau of Economic Research, Inc.
    18. Milevsky, Moshe A. & Young, Virginia R., 2007. "Annuitization and asset allocation," Journal of Economic Dynamics and Control, Elsevier, vol. 31(9), pages 3138-3177, September.
    19. Zvi Bodie & Jérôme Detemple & Marcel Rindisbacher, 2009. "Life-Cycle Finance and the Design of Pension Plans," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 249-286, November.
    20. Horneff, Wolfram J. & Maurer, Raimond H. & Stamos, Michael Z., 2008. "Life-cycle asset allocation with annuity markets," Journal of Economic Dynamics and Control, Elsevier, vol. 32(11), pages 3590-3612, November.
    21. Huang, Huaxiong & Milevsky, Moshe A. & Salisbury, Thomas S., 2012. "Optimal retirement consumption with a stochastic force of mortality," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 282-291.

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    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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