Blake, David and Wright, Douglas and Zhang, Yumeng (2011): Age dependent investing: Optimal funding and investment strategies in defined contribution pension plans when members are rational life cycle financial planners.
Download (624Kb) | Preview
A defined contribution pension plan allows consumption to be redistributed from the plan member’s working life to retirement in a manner that is consistent with the member’s personal preferences. The plan’s optimal funding and investment strategies therefore depend on the desired profile of consumption over the lifetime of the member. We investigate these strategies under the assumption that the member is a rational life cycle financial planner and has an Epstein-Zin utility function, which allows a separation between risk aversion and the elasticity of intertemporal substitution. We also take into account the member’s human capital during the accumulation phase of the plan and we allow the annuitisation decision to be endogenously determined during the decumulation phase.
We show that the optimal funding strategy involves a contribution rate that is not constant over the life of the plan but is age-dependent and reflects the trade-off between the desire for current versus future consumption, the desire for stable consumption over time, the member’s attitude to risk, and changes in the level of human capital over the life cycle. We also show that the optimal investment strategy during the accumulation phase of the plan is ‘stochastic lifestyling’, with an initial high weight in equity-type investments and a gradual switch into bond-type investments as the retirement date approaches in a way that depends on the realised outcomes for the stochastic processes driving the state variables. The optimal investment strategy during the decumulation phase of the plan is to exchange the bonds held at retirement for life annuities and then to gradually sell the remaining equities and buy more annuities, i.e., a strategy known as ‘phased annuitisation’.
|Item Type:||MPRA Paper|
|Original Title:||Age dependent investing: Optimal funding and investment strategies in defined contribution pension plans when members are rational life cycle financial planners|
|Keywords:||Defined Contribution Pension Plan; Funding Strategy; Investment Strategy; Epstein-Zin Utility; Stochastic Lifestyling; Phased Annuitisation; Dynamic Programming|
|Subjects:||G - Financial Economics > G1 - General Financial Markets > G11 - Portfolio Choice; Investment Decisions
G - Financial Economics > G2 - Financial Institutions and Services > G23 - Non-bank Financial Institutions; Financial Instruments; Institutional Investors
|Depositing User:||David Blake|
|Date Deposited:||07. Nov 2011 18:04|
|Last Modified:||16. Feb 2013 03:56|
Andersen, S., G. W. Harrison, M. I. Lau and E. E. Rutström (2008). ‘Eliciting Risk and Time Preferences’, Econometrica, 76, 583-618.
Blackburn, Douglas W. (2006). ‘Option Implied Risk Aversion and Elasticity of Intertemporal Substitution’, Indiana University working paper.
Blake, David (1996). ‘Efficiency, Risk Aversion and Portfolio Insurance: An Analysis of Financial Asset Portfolios Held by Investors in the United Kingdom’, Economic Journal, 106, 1175-1192.
Blake, David, Andrew J.G. Cairns and Kevin Dowd (2007). ‘The Impact of Occupation and Gender on Pensions from Defined Contribution Plans’, Geneva Papers on Risk & Insurance, 32, 458-82.
Boulier, Jean-Francois, ShaoJuan Huang and Gregory Taillard (2001). ‘Optimal Management under Stochastic Interest Rates: The Case of a Protected Defined Contribution Pension Fund’, Insurance: Mathematics and Economics, 28, 173-189.
Breeden, Douglas T. (1979). ‘An Intertemporal Asset Pricing Model with Stochastic Consumption and Investment Opportunities’, Journal of Financial Economics, 7, 265- 296.
Cairns, Andrew J.G, David Blake and Kevin Dowd (2006). ‘Stochastic Lifestyling: Optimal Dynamic Asset Allocation for Defined Contribution Pension Plans’, Journal of Economic Dynamics and Control, 30, 843-877.
Campbell, John Y., and Luis M. Viceira (2002). Strategic Asset Allocation: Portfolio Choice for Long-Term Investors, Oxford University Press, Oxford.
Cocco, João F., Francisco J. Gomes and Pascal J. Maenhout (2005). ‘Consumption and Portfolio Choice over the Life Cycle’, Review of Financial Studies, 18, 491-533.
Coller, M., and M. B. Williams (1999). ‘Eliciting Individual Discount Rates’, Experimental Economics, 2, 107-127.
Davidoff, Thomas, Jeffrey R. Brown and Peter A. Diamond (2005). ‘Annuities and Individual Welfare’, American Economic Review, 95, 1573-1590.
Epstein, L.G., and Stanley Zin (1989). ‘Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework’, Econometrica, 57, 937-969.
Fama, Eugene, and Kenneth French (2002). ‘The Equity Premium’, Journal of Finance, 57, 637-659.
Finkelstein, A., and J. M. Poterba (2002). ‘Selection Effects in the United Kingdom Individual Annuities Market’, Economic Journal, 112, 28–42.
Friedman, Benjamin, and Mark Warshawsky (1990). ‘The Cost of Annuities: Implications for Saving Behaviour and Bequests’, Quarterly Journal of Economics, 105, 135-154.
Gomes, F., L. Kotlikoff, and L.M. Viceira (2008). ‘Optimal Life-Cycle Investing with Flexible Labor Supply: A Welfare Analysis of Life-Cycle Funds’, American Economic Review: Papers & Proceedings, 98, 297-303.
Gomes, Francisco, and Alexander Michaelides (2004). ‘A Human Capital Explanation for an Asset Allocation Puzzle’, UBS Pension Series 24, London School of Economics, http://fmg.lse.ac.uk/pdfs/dp491.pdf.
Gomes, Francisco, and Alexander Michaelides (2005). ‘Optimal Life-cycle Asset Allocation: Understanding the Empirical Evidence’, Journal of Finance, 60, 869-904.
Gourinchas, P. O., and J. Parker (2002). ‘Consumption over the Life Cycle’, Econometrica,70, 47–89.
GAD (2006). Occupational Pension Schemes 2005, Government Actuary’s Department,London.
Holt, C. A., and S. K. Laury (2002). ‘Risk Aversion and Incentive Effects’, American Economic Review, 92, 1644-1655.
Horneff, W. J., R. H. Maurer and M. Z. Stamos(2008). ‘Optimal Gradual Annuitization: Quantifying the Costs of Switching to Annuities’, Journal of Risk and Insurance, 75, 1019–38.
Howie, Robert, and Helen Davies (2002). ‘Setting Investment Strategy for the Long Term: A Closer Look at Defined Contribution Investment Strategy’, Faculty and Institute of Actuaries, Finance and Investment Conference 2002, http://www.actuaries.org.uk/files/pdf/library/proceedings/fin_inv/2002/Howie.pdf.
Inkmann, Joachim, Paula Lopes, and Alexander Michaelides, 2011. How Deep is the Annuity Market Participation Puzzle,? Review of Financial Studies, 24, 279-319.
Judd, Kenneth L. (1998). Numerical Methods in Economics, The MIT Press, Cambridge MA.
Kim, Myung Jig , Charles R. Nelson, and Richard Startz (1991). ‘Mean Reversion in Stock Prices? A Reappraisal of the Empirical Evidence’, Review of Economic Studies, 58, Special Issue: The Econometrics of Financial Markets, 515-528.
Laury, Susan K., Melayne Morgan McInnes, J. Todd Swarthout, and Erica Von Nessen(2011). ‘Avoiding the Curves: Direct Elicitation of Time Preferences’, Georgia State University, Andrew Young School of Policy Studies, Working Paper 11-07.
Merton, Robert C., 1969. ‘Lifetime Portfolio Selection under Uncertainty: The Continuous-time Case’, Review of Economics and Statistics, 51, 247-257.
Merton, Robert C., 1971. ‘Optimum Consumption and Portfolio Rules in a Continuoustime Model’, Journal of Economic Theory, 3, 373-413.
Merton, Robert C., 1973. ‘An Intertemporal Capital Asset Pricing Model’, Econometrica, 41, 867-887.
Milevsky, M. A., and V. Young (2007). ‘Annuitization and Asset Allocation’, Journal of Economic Dynamics & Control, 31, 3138–77.
Mitchell, Olivia S., James Poterba, Mark Warshawsky, and J. R. Brown (1999). ‘New Evidence on the Money’s Worth of Individual Annuities’, American Economic Review, 89, 1299-1318.
Mitchell, Olivia S., and Steve Utkus (eds) (2004) Pension Design and Structure: New Lessons from Behavioural Finance, Oxford University Press, Oxford.
Office for National Statistics (2005) Annual Survey of Hours and Earnings (ASHE), Office for National Statistics, London.
Panis, S. (2004) ‘Annuities and Retirement Satisfaction’, in Mitchell, O. and S. Utkus(2004).
Poterba, James M., and Lawrence H. Summers (1988). ‘Mean Reversion in Stock Prices: Evidence and Implications, Journal of Financial Economics, 22, 27-59.
Samuelson, P.A. (1989). ‘A Case at Last for Age-phased Reduction in Equity’, Proceedings of the National Academy of Sciences, 86(22), 9048–9051.
Schwartz, Eduardo, and Walter N. Torous (1999). ‘Can We Disentangle Risk Aversion from Intertemporal Substitution in Consumption’, Anderson School of Management, University of California, http://repositories.cdlib.org/anderson/fin/25-99.
Thaler, Richard, and Shlomo Bernartzi (2004). ‘Save More Tomorrow: Using Behavioural Economics to Increase Employee Saving’, Journal of Political Economy, 112, S164-S187.
Thaler, Richard, and Cass Sunstein (2008). Nudge: Improving Decisions about Health, Wealth and Happiness, Yale University Press, New Haven and London.
Viceira, Luis M. (2001). ‘Optimal Portfolio Choice for Long-horizon Investors with Nontradable Labor Income’, Journal of Finance, 56, 2, 433-470.
Vissing-Jørgensen, A. (2002). ‘Limited Asset Market Participation and the Elasticity of Intertemporal Substitution’. Journal of Political Economy, 110, 825–53.
Weil, Philippe (1990). ‘Non-expected Utility in Macroeconomics’, The Quarterly Journal of Economics, 105, 1, 29-42.
Yaari, M. (1965). ‘Uncertain Lifetime, Life insurance and the Theory of the Consumer’, Review of Economic Studies, 32, 137-150.