IDEAS home Printed from https://ideas.repec.org/a/ibg/eajour/v40y2007i3-4p87-118.html
   My bibliography  Save this article

Joined-Up Pensions Policy in the UK: An Asset-Liability Model for Simultaneously Determining the Asset Allocation and Contribution Rate

Author

Listed:
  • John Board

    (University of Reading, The ICMA Centre)

  • Charles Sutcliffe

    (University of Reading, The ICMA Centre)

Abstract

The trustees of funded defined benefit pension schemes must make two vital and interrelated decisions - setting the asset allocation and the contribution rate. While these decisions are usually taken separately, it is argued that they are intimately related and should be taken jointly. The objective of funded pension schemes is taken to be the minimization of both the mean and the variance of the contribution rate, where the asset allocation decision is designed to achieve this objective. This is done by splitting the problem into two main steps. First, the Markowitz mean-variance model is generalised to include three types of pension scheme liabilities (actives, deferreds and pensioners), and this model is used to generate the efficient set of asset allocations. Second, for each point on the risk-return efficient set of the asset-liability portfolio model, the mathematical model of Haberman (1992) is used to compute the corresponding mean and variance of the contribution rate and funding ratio. Since the Haberman model assumes that the discount rate for computing the present value of liabilities equals the investment return, it is generalised to avoid this restriction. This generalisation removes the trade-off between contribution rate risk and funding ratio risk for a fixed spread period. Pension schemes need to choose a spread period, and it is shown how this can be set to minimise the variance of the contribution rate. Finally, using the result that the funding ratio follows an inverted gamma distribution, shortfall risk and expected tail loss are computed for funding below the minimum funding requirement, and funding above the taxation limit. This model is then applied to one of the largest UK pension schemes - the Universities Superannuation Scheme.

Suggested Citation

  • John Board & Charles Sutcliffe, 2007. "Joined-Up Pensions Policy in the UK: An Asset-Liability Model for Simultaneously Determining the Asset Allocation and Contribution Rate," Economic Analysis, Institute of Economic Sciences, vol. 40(3-4), pages 87-118.
  • Handle: RePEc:ibg:eajour:v:40:y:2007:i:3-4:p:87-118
    as

    Download full text from publisher

    File URL: http://www.ien.bg.ac.rs/index.php/en/2007/2007-34
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Nijman, T.E. & Swinkels, L.A.P., 2003. "Strategic and Tactical Allocation to Commodities for Retirement Savings Schemes," Other publications TiSEM a09c2c88-4f10-4624-b3e0-d, Tilburg University, School of Economics and Management.
    2. Haberman, S., 1994. "Autoregressive rates of return and the variability of pension contributions and fund levels for a defined benefit pension scheme," Insurance: Mathematics and Economics, Elsevier, vol. 14(3), pages 219-240, July.
    3. Gregory H. Chun & Brian A. Ciochetti & James D. Shilling, 2000. "Pension-Plan Real Estate Investment in an Asset-Liability Framework," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 28(3), pages 467-491.
    4. Haberman, Steven, 1995. "Pension Funding With Time Delays and the Optimal Spread Period," ASTIN Bulletin, Cambridge University Press, vol. 25(2), pages 177-187, November.
    5. Haberman, S. & Day, C. & Fogarty, D. & Khorasanee, M. Z. & McWhirter, M. & Nash, N. & Ngwira, B. & Wright, I. D. & Yakoubov, Y., 2003. "A Stochastic Approach to Risk Management and Decision Making in Defined Benefit Pension Schemes," British Actuarial Journal, Cambridge University Press, vol. 9(3), pages 493-586, August.
    6. Zimbidis, Alexandros & Haberman, Steven, 1993. "Delay, feedback and variability of pension contributions and fund levels," Insurance: Mathematics and Economics, Elsevier, vol. 13(3), pages 271-285, December.
    7. Haberman, Steven & Butt, Zoltan & Megaloudi, Chryssoula, 2000. "Contribution and solvency risk in a defined benefit pension scheme," Insurance: Mathematics and Economics, Elsevier, vol. 27(2), pages 237-259, October.
    8. Dufresne, Daniel, 1989. "Stability of pension systems when rates of return are random," Insurance: Mathematics and Economics, Elsevier, vol. 8(1), pages 71-76, March.
    9. Haberman, Steven, 1992. "Pension funding with time delays : A stochastic approach," Insurance: Mathematics and Economics, Elsevier, vol. 11(3), pages 179-189, October.
    10. Kouwenberg, Roy, 2001. "Scenario generation and stochastic programming models for asset liability management," European Journal of Operational Research, Elsevier, vol. 134(2), pages 279-292, October.
    11. Cairns, Andrew J. G. & Parker, Gary, 1997. "Stochastic pension fund modelling," Insurance: Mathematics and Economics, Elsevier, vol. 21(1), pages 43-79, October.
    12. Blake, David & Lehmann, Bruce N & Timmermann, Allan, 1999. "Asset Allocation Dynamics and Pension Fund Performance," The Journal of Business, University of Chicago Press, vol. 72(4), pages 429-461, October.
    13. M. Iqbal Owadally & Steven Haberman, 1999. "Pension Fund Dynamics and Gains/Losses Due to Random Rates of Investment Return," North American Actuarial Journal, Taylor & Francis Journals, vol. 3(3), pages 105-117.
    14. John L. G. Board & Charles M. S. Sutcliffe, 1994. "Estimation Methods in Portfolio Selection and the Effectiveness of Short Sales Restrictions: UK Evidence," Management Science, INFORMS, vol. 40(4), pages 516-534, April.
    15. Hakansson, Nils H, 1971. "On Optimal Myopic Portfolio Policies, With and Without Serial Correlation of Yields," The Journal of Business, University of Chicago Press, vol. 44(3), pages 324-334, July.
    16. Haberman, Steven & Lam, Yuk Patrick & Wong, 1997. "Moving average rates of return and the variability of pension contributions and fund levels for a defined benefit pension scheme," Insurance: Mathematics and Economics, Elsevier, vol. 20(2), pages 115-135, September.
    17. Wright, I.D., 1998. "Traditional Pension Fund Valuation in a Stochastic Asset and Liability Environment," British Actuarial Journal, Cambridge University Press, vol. 4(4), pages 865-901, October.
    18. Ederington, Louis H, 1979. "The Hedging Performance of the New Futures Markets," Journal of Finance, American Finance Association, vol. 34(1), pages 157-170, March.
    19. M. I. Kusy & W. T. Ziemba, 1986. "A Bank Asset and Liability Management Model," Operations Research, INFORMS, vol. 34(3), pages 356-376, June.
    20. Haberman, Steven, 1993. "Pension funding with time delays and autoregressive rates of investment return," Insurance: Mathematics and Economics, Elsevier, vol. 13(1), pages 45-56, September.
    21. Tongxuan Yang, 2003. "Defined Benefit Pension Plan Liabilities and International Asset Allocation," Working Papers wp058, University of Michigan, Michigan Retirement Research Center.
    22. Jan Folkmann Wright, 2019. "Decision-making in Risk Management," Chapters, in: Ali G. Hessami (ed.), Perspectives on Risk, Assessment and Management Paradigms, IntechOpen.
    23. Exley, C.J. & Mehta, S.J.B. & Smith, A.D., 1997. "The Financial Theory of Defined Benefit Pension Schemes," British Actuarial Journal, Cambridge University Press, vol. 3(4), pages 835-966, October.
    24. Hakansson, Nils H, 1970. "Optimal Investment and Consumption Strategies Under Risk for a Class of Utility Functions," Econometrica, Econometric Society, vol. 38(5), pages 587-607, September.
    25. Rudolf, Markus & Ziemba, William T., 2004. "Intertemporal surplus management," Journal of Economic Dynamics and Control, Elsevier, vol. 28(5), pages 975-990, February.
    26. Campbell, John Y. & Viceira, Luis M., 2002. "Strategic Asset Allocation: Portfolio Choice for Long-Term Investors," OUP Catalogue, Oxford University Press, number 9780198296942.
    27. Cairns, Andrew, 2000. "Some Notes on the Dynamics and Optimal Control of Stochastic Pension Fund Models in Continuous Time," ASTIN Bulletin, Cambridge University Press, vol. 30(1), pages 19-55, May.
    28. Drijver, Sibrand J. & Klein Haneveld, Willem K. & Vlerk, Maarten H. van der, 2002. "ALM model for pension funds : numerical results for a prototype model," Research Report 02A44, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    29. repec:dgr:rugsom:02a44 is not listed on IDEAS
    30. Jacek Gondzio & Roy Kouwenberg, 2001. "High-Performance Computing for Asset-Liability Management," Operations Research, INFORMS, vol. 49(6), pages 879-891, December.
    31. Frankfurter, George M. & Hill, Joanne M., 1981. "A Normative Approach to Pension Fund Management," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 16(4), pages 533-555, November.
    32. Chang, Shih-Chieh & Chen, Chiang-Chu, 2002. "Allocating unfunded liability in pension valuation under uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 30(3), pages 371-387, June.
    33. Haberman, Steven, 1997. "Stochastic investment returns and contribution rate risk in a defined benefit pension scheme," Insurance: Mathematics and Economics, Elsevier, vol. 19(2), pages 127-139, April.
    34. John M. Mulvey & Gordon Gould & Clive Morgan, 2000. "An Asset and Liability Management System for Towers Perrin-Tillinghast," Interfaces, INFORMS, vol. 30(1), pages 96-114, February.
    35. Sutcliffe, Charles, 2005. "The cult of the equity for pension funds: should it get the boot?," Journal of Pension Economics and Finance, Cambridge University Press, vol. 4(1), pages 57-85, March.
    36. Kingsland, Louis, 1982. "Projecting the Financial Condition of a Pension Plan Using Simulation Analysis," Journal of Finance, American Finance Association, vol. 37(2), pages 577-584, May.
    37. Tepper, Irwin, 1974. "Optimal Financial Strategies for Trusteed Pension Plans," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 9(3), pages 357-376, June.
    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. Platanakis, Emmanouil & Sutcliffe, Charles, 2016. "Pension scheme redesign and wealth redistribution between the members and sponsor: The USS rule change in October 2011," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 14-28.

    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. Chang, Shih-Chieh & Chen, Chiang-Chu, 2002. "Allocating unfunded liability in pension valuation under uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 30(3), pages 371-387, June.
    2. Chang, S. C. & Tzeng, Larry Y. & Miao, Jerry C. Y., 2003. "Pension funding incorporating downside risks," Insurance: Mathematics and Economics, Elsevier, vol. 32(2), pages 217-228, April.
    3. Maurer, Raimond & Mitchell, Olivia S. & Rogalla, Ralph, 2009. "Managing contribution and capital market risk in a funded public defined benefit plan: Impact of CVaR cost constraints," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 25-34, August.
    4. Taylor, Greg, 2002. "Stochastic control of funding systems," Insurance: Mathematics and Economics, Elsevier, vol. 30(3), pages 323-350, June.
    5. Huang, Hong-Chih & Cairns, Andrew J.G., 2006. "On the control of defined-benefit pension plans," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 113-131, February.
    6. Cairns, Andrew J. G. & Parker, Gary, 1997. "Stochastic pension fund modelling," Insurance: Mathematics and Economics, Elsevier, vol. 21(1), pages 43-79, October.
    7. Miao Jerry C.Y. & Wang Jennifer L., 2006. "Intertemporal Stable Pension Funding," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 1(2), pages 1-15, February.
    8. Chang, Shih-Chieh, 1999. "Optimal pension funding through dynamic simulations: the case of Taiwan public employees retirement system," Insurance: Mathematics and Economics, Elsevier, vol. 24(3), pages 187-199, May.
    9. Dormidontova, Yulia & Nazarov, Vladimir & A. Tikhonova, 2014. "Analysis of Approaches of Participants of Pension Products Market to the Development of Optimal Investment Strategies of Pension Savings," Published Papers r90227, Russian Presidential Academy of National Economy and Public Administration.
    10. Christopher Bayliss & Marti Serra & Armando Nieto & Angel A. Juan, 2020. "Combining a Matheuristic with Simulation for Risk Management of Stochastic Assets and Liabilities," Risks, MDPI, vol. 8(4), pages 1-14, December.
    11. ManMohan S. Sodhi, 2005. "LP Modeling for Asset-Liability Management: A Survey of Choices and Simplifications," Operations Research, INFORMS, vol. 53(2), pages 181-196, April.
    12. Haberman, Steven & Sung, Joo-Ho, 2005. "Optimal pension funding dynamics over infinite control horizon when stochastic rates of return are stationary," Insurance: Mathematics and Economics, Elsevier, vol. 36(1), pages 103-116, February.
    13. Arjan Berkelaar & Roy Kouwenberg, 2011. "A Liability-Relative Drawdown Approach to Pension Asset Liability Management," Palgrave Macmillan Books, in: Gautam Mitra & Katharina Schwaiger (ed.), Asset and Liability Management Handbook, chapter 14, pages 352-382, Palgrave Macmillan.
    14. Streutker, Matthijs & van der Vlerk, Maarten & Klein Haneveld, Wim, 2007. "Implementation of new regulatory rules in a multistage ALM model for Dutch pension funds," Research Report 07005, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    15. Josa-Fombellida, Ricardo & Navas, Jorge, 2020. "Time consistent pension funding in a defined benefit pension plan with non-constant discounting," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 142-153.
    16. Josa-Fombellida, Ricardo & Rincón-Zapatero, Juan Pablo, 2012. "Stochastic pension funding when the benefit and the risky asset follow jump diffusion processes," European Journal of Operational Research, Elsevier, vol. 220(2), pages 404-413.
    17. Haberman, Steven, 1997. "Stochastic investment returns and contribution rate risk in a defined benefit pension scheme," Insurance: Mathematics and Economics, Elsevier, vol. 19(2), pages 127-139, April.
    18. Gabay, Daniel & Grasselli, Martino, 2012. "Fair demographic risk sharing in defined contribution pension systems," Journal of Economic Dynamics and Control, Elsevier, vol. 36(4), pages 657-669.
    19. repec:dgr:rugsom:07005 is not listed on IDEAS
    20. Khorasanee, Zaki, 2005. "Benefit uncertainty and default risk in pension plans," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 469-493, December.
    21. Libo Yin & Liyan Han, 2013. "Options strategies for international portfolios with overall risk management via multi-stage stochastic programming," Annals of Operations Research, Springer, vol. 206(1), pages 557-576, July.

    More about this item

    Keywords

    Pension scheme; portfolio theory; asset-liability; modelling; contribution rate risk; solvency risk;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G23 - Financial Economics - - Financial Institutions and Services - - - Non-bank Financial Institutions; Financial Instruments; Institutional Investors

    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:ibg:eajour:v:40:y:2007:i:3-4:p:87-118. 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: Zorica Bozic (email available below). General contact details of provider: https://edirc.repec.org/data/ienbgyu.html .

    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.