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Stochastic lifestyling: optimal dynamic asset allocation for defined contribution pension plans

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Listed author(s):
  • Andrew J. G. Cairns
  • David Blake
  • Kevin Dowd

Abstract

This paper considers the asset-allocation strategies open to members of defined- contribution pension plans. We investigate a model that incorporates three sources of risk: asset risk and salary (or labour-income) risk in the accumulation phase; and interest-rate risk at the point of retirement. We propose a new form of terminal utility function, incorporating habit formation, that uses the plan member's final salary as a numeraire. The paper discusses various properties and characteristics of the optimal stochastic asset-allocation strategy (which we call stochastic lifestyling) both with and without the presence of non-hedgeable salary risk. We compare the performance of stochastic lifestlying with some popular strategies used by pension providers, including deterministic lifestyling (which involves a gradual switch from equities to bonds according to preset rules) and static strategies that invest in benchmark mixed funds. We find that the use of stochastic lifestyling significantly enhances the welfare of a wide range of potential plan members relative to these other strategies.

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File URL: http://eprints.lse.ac.uk/24831/
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Paper provided by London School of Economics and Political Science, LSE Library in its series LSE Research Online Documents on Economics with number 24831.

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Length: 41 pages
Date of creation: 13 Sep 2004
Handle: RePEc:ehl:lserod:24831
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Keywords: Stochastic control; Optimal asset allocation; Stochastic lifestyling; Utility numeraire; Habit formation; Non-hedgeable salary risk; HJB equation;

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Find related papers by 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
  • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth

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  1. Kimball, Miles S, 1993. "Standard Risk Aversion," Econometrica, Econometric Society, vol. 61(3), pages 589-611, May.
  2. Sundaresan, Suresh M, 1989. "Intertemporally Dependent Preferences and the Volatility of Consumption and Wealth," Review of Financial Studies, Society for Financial Studies, vol. 2(1), pages 73-89.
  3. 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.
  4. Epstein, Larry G & Zin, Stanley E, 1989. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework," Econometrica, Econometric Society, vol. 57(4), pages 937-969, July.
  5. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
  6. Cairns, Andrew, 2000. "Some Notes on the Dynamics and Optimal Control of Stochastic Pension Fund Models in Continuous Time," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 30(01), pages 19-55, May.
  7. Constantinides, George M, 1990. "Habit Formation: A Resolution of the Equity Premium Puzzle," Journal of Political Economy, University of Chicago Press, vol. 98(3), pages 519-543, June.
  8. Pratt, John W & Zeckhauser, Richard J, 1987. "Proper Risk Aversion," Econometrica, Econometric Society, vol. 55(1), pages 143-154, January.
  9. Sundaresan, Suresh & Zapatero, Fernando, 1997. "Valuation, Optimal Asset Allocation and Retirement Incentives of Pension Plans," Review of Financial Studies, Society for Financial Studies, vol. 10(3), pages 631-660.
  10. Gollier, Christian & Pratt, John W, 1996. "Risk Vulnerability and the Tempering Effect of Background Risk," Econometrica, Econometric Society, vol. 64(5), pages 1109-1123, September.
  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. Black, Fischer & Perold, AndreF., 1992. "Theory of constant proportion portfolio insurance," Journal of Economic Dynamics and Control, Elsevier, vol. 16(3-4), pages 403-426.
  13. Duffie, Darrell & Fleming, Wendell & Soner, H. Mete & Zariphopoulou, Thaleia, 1997. "Hedging in incomplete markets with HARA utility," Journal of Economic Dynamics and Control, Elsevier, vol. 21(4-5), pages 753-782, May.
  14. Griselda Deelstra & Martino Grasselli & Pierre-François Koehl, 2000. "Optimal investment strategies in a CIR framework," ULB Institutional Repository 2013/7594, ULB -- Universite Libre de Bruxelles.
  15. Cox, John C. & Huang, Chi-fu, 1991. "A variational problem arising in financial economics," Journal of Mathematical Economics, Elsevier, vol. 20(5), pages 465-487.
  16. Boulier, Jean-Francois & Huang, ShaoJuan & Taillard, Gregory, 2001. "Optimal management under stochastic interest rates: the case of a protected defined contribution pension fund," Insurance: Mathematics and Economics, Elsevier, vol. 28(2), pages 173-189, April.
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