IDEAS home Printed from https://ideas.repec.org/a/spr/cejnor/v20y2012i3p497-527.html
   My bibliography  Save this article

On the sub-optimality cost of immediate annuitization in DC pension funds

Author

Listed:
  • Marina Di Giacinto
  • Elena Vigna

Abstract

We consider the position of a member of a defined contribution (DC) pension scheme having the possibility of taking programmed withdrawals at retirement. According to this option, she can defer annuitization of her fund to a propitious future time, that can be found to be optimal according to some criteria. This option, that adds remarkable flexibility in the choice of pension benefits, is not available in many countries, where immediate annuitization is compulsory at retirement. In this paper, we address and try to answer the questions: “Is immediate annuitization optimal? If it is not, what is the cost to be paid by the retiree obliged to annuitize at retirement?”. In order to do this, we consider the model by Gerrard et al. in Quant Finance, ( 2011 ) and extend it in two different ways. In the first extension, we prove a theorem that provides necessary and sufficient conditions for immediate annuitization being always optimal. The not surprising result is that compulsory immediate annuitization turns out to be sub-optimal. We then quantify the extent of sub-optimality, by defining the sub-optimality cost as the loss of expected present value of consumption from retirement to death and measuring it in many typical situations. We find that it varies in relative terms between 6 and 40%, depending on the risk aversion of the member. In the second extension, we make extensive numerical investigations of the model and seek the optimal annuitization time. We find that the optimal annuitization time depends on personal factors such as the retiree’s risk aversion and her subjective perception of remaining lifetime. It also depends on the financial market, via the Sharpe ratio of the risky asset. Optimal annuitization should occur a few years after retirement with high risk aversion, low Sharpe ratio and/or short remaining lifetime, and many years after retirement with low risk aversion, high Sharpe ratio and/or long remaining lifetime. This paper supports the availability of programmed withdrawals as an option to retirees of DC pension schemes, by giving insight into the extent of loss in wealth suffered by a retiree who cannot choose programmed withdrawals, but is obliged to annuitize immediately on retirement. Copyright Springer-Verlag 2012

Suggested Citation

  • Marina Di Giacinto & Elena Vigna, 2012. "On the sub-optimality cost of immediate annuitization in DC pension funds," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 20(3), pages 497-527, September.
    • Handle: RePEc:spr:cejnor:v:20:y:2012:i:3:p:497-527
    DOI: 10.1007/s10100-011-0221-8
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10100-011-0221-8
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10100-011-0221-8?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Marina Di Giacinto & Salvatore Federico & Fausto Gozzi, 2011. "Pension funds with a minimum guarantee: a stochastic control approach," Finance and Stochastics, Springer, vol. 15(2), pages 297-342, June.
    2. Cairns, Andrew J.G. & Blake, David & Dowd, Kevin, 2006. "Stochastic lifestyling: Optimal dynamic asset allocation for defined contribution pension plans," Journal of Economic Dynamics and Control, Elsevier, vol. 30(5), pages 843-877, May.
    3. Moshe A. Milevsky & Kristen S. Moore & Virginia R. Young, 2006. "Asset Allocation And Annuity‐Purchase Strategies To Minimize The Probability Of Financial Ruin," Mathematical Finance, Wiley Blackwell, vol. 16(4), pages 647-671, October.
    4. Gabriele Stabile, 2006. "Optimal Timing Of The Annuity Purchase: Combined Stochastic Control And Optimal Stopping Problem," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(02), pages 151-170.
    5. Blake, David & Cairns, Andrew J. G. & Dowd, Kevin, 2003. "Pensionmetrics 2: stochastic pension plan design during the distribution phase," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 29-47, August.
    6. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    7. Griselda Deelstra & Martino Grasselli & Pierre-François Koehl, 2003. "Optimal investment strategies in the presence of a minimum guarantee," ULB Institutional Repository 2013/7598, ULB -- Universite Libre de Bruxelles.
    8. 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.
    9. 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.
    10. 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.
    11. Blake, David & Cairns, Andrew J. G. & Dowd, Kevin, 2001. "Pensionmetrics: stochastic pension plan design and value-at-risk during the accumulation phase," Insurance: Mathematics and Economics, Elsevier, vol. 29(2), pages 187-215, October.
    12. Pablo Antolín & Colin Pugh & Fiona Stewart, 2008. "Forms of Benefit Payment at Retirement," OECD Working Papers on Insurance and Private Pensions 26, OECD Publishing.
    13. Deelstra, Griselda & Grasselli, Martino & Koehl, Pierre-Francois, 2003. "Optimal investment strategies in the presence of a minimum guarantee," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 189-207, August.
    14. 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.
    15. Gerrard, Russell & Haberman, Steven & Vigna, Elena, 2004. "Optimal investment choices post-retirement in a defined contribution pension scheme," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 321-342, October.
    16. Albrecht, Peter & Maurer, Raimond, 2002. "Self-Annuitization, Consumption Shortfall in Retirement and Asset Allocation: The Annuity Benchmark," Journal of Pension Economics and Finance, Cambridge University Press, vol. 1(3), pages 269-288, November.
    17. Moshe Milevsky & Chris Robinson, 2000. "Self-Annuitization and Ruin in Retirement," North American Actuarial Journal, Taylor & Francis Journals, vol. 4(4), pages 112-124.
    18. Steven Haberman & Elena Vigna, 2002. "Optimal investment strategies and risk measures in defined contribution pension schemes," ICER Working Papers - Applied Mathematics Series 09-2002, ICER - International Centre for Economic Research.
    19. Haberman, Steven & Vigna, Elena, 2002. "Optimal investment strategies and risk measures in defined contribution pension schemes," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 35-69, August.
    20. Battocchio, Paolo & Menoncin, Francesco, 2004. "Optimal pension management in a stochastic framework," Insurance: Mathematics and Economics, Elsevier, vol. 34(1), pages 79-95, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lambregts, Timo R. & Schut, Frederik T., 2020. "Displaced, disliked and misunderstood: A systematic review of the reasons for low uptake of long-term care insurance and life annuities," The Journal of the Economics of Ageing, Elsevier, vol. 17(C).
    2. Yao, Haixiang & Yang, Zhou & Chen, Ping, 2013. "Markowitz’s mean–variance defined contribution pension fund management under inflation: A continuous-time model," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 851-863.
    3. Di Giacinto, Marina & Federico, Salvatore & Gozzi, Fausto & Vigna, Elena, 2014. "Income drawdown option with minimum guarantee," European Journal of Operational Research, Elsevier, vol. 234(3), pages 610-624.
    4. Bernhardt, Thomas & Donnelly, Catherine, 2019. "Modern tontine with bequest: Innovation in pooled annuity products," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 168-188.
    5. Hainaut, Donatien & Deelstra, Griselda, 2014. "Optimal timing for annuitization, based on jump diffusion fund and stochastic mortality," Journal of Economic Dynamics and Control, Elsevier, vol. 44(C), pages 124-146.
    6. Wu, Huiling & Zhang, Ling & Chen, Hua, 2015. "Nash equilibrium strategies for a defined contribution pension management," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 202-214.
    7. Zhang, Ling & Zhang, Hao & Yao, Haixiang, 2018. "Optimal investment management for a defined contribution pension fund under imperfect information," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 210-224.
    8. Thomas Bernhardt & Catherine Donnelly, 2019. "Modern tontine with bequest: innovation in pooled annuity products," Papers 1903.05990, arXiv.org.
    9. Francesco Menoncin & Elena Vigna, 2013. "Mean-variance target-based optimisation in DC plan with stochastic interest rate," Carlo Alberto Notebooks 337, Collegio Carlo Alberto.

    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. Han, Nan-Wei & Hung, Mao-Wei, 2015. "The investment management for a downside-protected equity-linked annuity under interest rate risk," Finance Research Letters, Elsevier, vol. 13(C), pages 113-124.
    2. Marina Di Giacinto & Bjarne Højgaard & Elena Vigna, 2010. "Optimal time of annuitization in the decumulation phase of a defined contribution pension scheme," Working Papers 2010-08, Universita' di Cassino, Dipartimento di Economia e Giurisprudenza.
    3. Di Giacinto, Marina & Federico, Salvatore & Gozzi, Fausto & Vigna, Elena, 2014. "Income drawdown option with minimum guarantee," European Journal of Operational Research, Elsevier, vol. 234(3), pages 610-624.
    4. Russell Gerrard & Bjarne Højgaard & Elena Vigna, 2008. "Choosing the Optimal Annuitization Time Post Retirement," Carlo Alberto Notebooks 76, Collegio Carlo Alberto.
    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. Elena Vigna, 2009. "Mean-variance inefficiency of CRRA and CARA utility functions for portfolio selection in defined contribution pension schemes," CeRP Working Papers 89, Center for Research on Pensions and Welfare Policies, Turin (Italy).
    7. Elena Vigna, 2009. "Mean-variance inefficiency of CRRA and CARA utility functions for portfolio selection in defined contribution pension schemes," Carlo Alberto Notebooks 108, Collegio Carlo Alberto, revised 2009.
    8. Alessandro Milazzo & Elena Vigna, 2018. "The Italian Pension Gap: A Stochastic Optimal Control Approach," Risks, MDPI, vol. 6(2), pages 1-20, April.
    9. Yao, Haixiang & Lai, Yongzeng & Ma, Qinghua & Jian, Minjie, 2014. "Asset allocation for a DC pension fund with stochastic income and mortality risk: A multi-period mean–variance framework," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 84-92.
    10. Alessandro Milazzo & Elena Vigna, 2018. "“The Italian Pension Gap: a Stochastic Optimal Control Approach"," CeRP Working Papers 179, Center for Research on Pensions and Welfare Policies, Turin (Italy).
    11. Yao, Haixiang & Yang, Zhou & Chen, Ping, 2013. "Markowitz’s mean–variance defined contribution pension fund management under inflation: A continuous-time model," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 851-863.
    12. Gerrard, Russell & Haberman, Steven & Vigna, Elena, 2004. "Optimal investment choices post-retirement in a defined contribution pension scheme," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 321-342, October.
    13. Henrique Ferreira Morici & Elena Vigna, 2023. "Optimal additional voluntary contribution in DC pension schemes to manage inadequacy risk," Carlo Alberto Notebooks 699 JEL Classification: C, Collegio Carlo Alberto.
    14. Francesco Menoncin & Elena Vigna, 2013. "Mean-variance target-based optimisation in DC plan with stochastic interest rate," Carlo Alberto Notebooks 337, Collegio Carlo Alberto.
    15. Marina Di Giacinto & Salvatore Federico & Fausto Gozzi, 2011. "Pension funds with a minimum guarantee: a stochastic control approach," Finance and Stochastics, Springer, vol. 15(2), pages 297-342, June.
    16. Gao, Jianwei, 2009. "Optimal investment strategy for annuity contracts under the constant elasticity of variance (CEV) model," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 9-18, August.
    17. Dadashi, Hassan, 2020. "Optimal investment–consumption problem: Post-retirement with minimum guarantee," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 160-181.
    18. Stamos, Michael Z., 2008. "Optimal consumption and portfolio choice for pooled annuity funds," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 56-68, August.
    19. Zhiping Chen & Liyuan Wang & Ping Chen & Haixiang Yao, 2019. "Continuous-Time Mean–Variance Optimization For Defined Contribution Pension Funds With Regime-Switching," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(06), pages 1-33, September.
    20. He, Lin & Liang, Zongxia, 2013. "Optimal investment strategy for the DC plan with the return of premiums clauses in a mean–variance framework," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 643-649.

    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:spr:cejnor:v:20:y:2012:i:3:p:497-527. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.