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

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Author Info

  • 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.

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Bibliographic Info

Article provided by Institute of Economic Sciences in its journal Economic Analysis.

Volume (Year): 40 (2007)
Issue (Month): 3-4 ()
Pages: 87-118

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Handle: RePEc:ibg:eajour:v:40:y:2007:i:3-4:p:87-118

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Keywords: Pension scheme; portfolio theory; asset-liability; modelling; contribution rate risk; solvency risk;

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References

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  1. Ederington, Louis H, 1979. "The Hedging Performance of the New Futures Markets," Journal of Finance, American Finance Association, vol. 34(1), pages 157-70, March.
  2. 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.
  3. 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(01), pages 57-85, March.
  4. Rudolf, Markus & Ziemba, William T., 2004. "Intertemporal surplus management," Journal of Economic Dynamics and Control, Elsevier, vol. 28(5), pages 975-990, February.
  5. 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.
  6. Haberman, Steven, 1992. "Pension funding with time delays : A stochastic approach," Insurance: Mathematics and Economics, Elsevier, vol. 11(3), pages 179-189, October.
  7. 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.
  8. 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.
  9. 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 429-61, October.
  10. Kingsland, Louis, 1982. " Projecting the Financial Condition of a Pension Plan Using Simulation Analysis," Journal of Finance, American Finance Association, vol. 37(2), pages 577-84, May.
  11. 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.
  12. 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.
  13. 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 324-34, July.
  14. 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.
  15. 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.
  16. 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.
  17. 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(04), pages 533-555, November.
  18. Tepper, Irwin, 1974. "Optimal Financial Strategies for Trusteed Pension Plans," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 9(03), pages 357-376, June.
  19. 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.
  20. 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.
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