Mean-variance inefficiency of CRRA and CARA utility functions for portfolio selection in defined contribution pension schemes
AbstractWe consider the portfolio selection problem in the accumulation phase of a defined contribution pension scheme in continuous time, and compare the mean-variance and the expected utility maximization approaches. Using the embedding technique pioneered by Zhou and Li (2000) we first find the efficient frontier of portfolios in the Black-Scholes financial market. Then, using standard stochastic optimal control we find the optimal portfolios derived via expected utility for popular utility functions. As a main result, we prove that the optimal portfolios derived with the CARA and CRRA utility functions are not mean-variance efficient. As a corollary, we prove that this holds also in the standard portfolio selection problem. We provide a natural measure of inefficiency based on the difference between optimal portfolio variance and minimal variance, and we show its dependence on risk aversion, Sharpe ratio of the risky asset, time horizon, initial wealth and contribution rate. Numerical examples illustrate the extent of inefficiency of CARA and CRRA utility functions in defined contribution pension schemes.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Center for Research on Pensions and Welfare Policies, Turin (Italy) in its series CeRP Working Papers with number 89.
Length: 40 pages
Date of creation: Sep 2009
Date of revision:
Mean-variance approach; efficient frontier; expected utility maximization; defined contribution pension scheme; portfolio selection; risk aversion; Sharpe ratio;
Find related papers by JEL classification:
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
- 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
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Hakansson, Nils H., 1971. "Capital Growth and the Mean-Variance Approach to Portfolio Selection," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 6(01), pages 517-557, January.
- 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.
- R. C. Merton, 1970. "Optimum Consumption and Portfolio Rules in a Continuous-time Model," Working papers 58, Massachusetts Institute of Technology (MIT), Department of Economics.
- Kahneman, Daniel & Tversky, Amos, 1979.
"Prospect Theory: An Analysis of Decision under Risk,"
Econometric Society, vol. 47(2), pages 263-91, March.
- Amos Tversky & Daniel Kahneman, 1979. "Prospect Theory: An Analysis of Decision under Risk," Levine's Working Paper Archive 7656, David K. Levine.
- 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.
- Devolder, Pierre & Bosch Princep, Manuela & Dominguez Fabian, Inmaculada, 2003. "Stochastic optimal control of annuity contracts," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 227-238, October.
- Luigi Guiso & Monica Paiella, 2007.
"Risk Aversion, Wealth, and Background Risk,"
Economics Working Papers
ECO2007/47, European University Institute.
- Luigi Guiso & Monica Paiella, 2003. "Risk Aversion, Wealth and Background Risk," Temi di discussione (Economic working papers) 483, Bank of Italy, Economic Research and International Relations Area.
- Guiso, Luigi & Paiella, Monica, 2001. "Risk Aversion, Wealth and Background Risk," CEPR Discussion Papers 2728, C.E.P.R. Discussion Papers.
- Monica Paiella & Luigi Guiso, 2004. "Risk Aversion, Wealth and Background Risk," 2004 Meeting Papers 525, Society for Economic Dynamics.
- Gao, Jianwei, 2008. "Stochastic optimal control of DC pension funds," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1159-1164, June.
- Robert Bordley & Marco LiCalzi, 2000. "Decision analysis using targets instead of utility functions," Decisions in Economics and Finance, Springer, vol. 23(1), pages 53-74.
- 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.
- Jorion, Philippe, 1985. "International Portfolio Diversification with Estimation Risk," The Journal of Business, University of Chicago Press, vol. 58(3), pages 259-78, July.
- Henry R. Richardson, 1989. "A Minimum Variance Result in Continuous Trading Portfolio Optimization," Management Science, INFORMS, vol. 35(9), pages 1045-1055, September.
- 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.
- Duan Li & Wan-Lung Ng, 2000. "Optimal Dynamic Portfolio Selection: Multiperiod Mean-Variance Formulation," Mathematical Finance, Wiley Blackwell, vol. 10(3), pages 387-406.
- Robert R. Grauer & Nils H. Hakansson, 1993. "On the Use of Mean-Variance and Quadratic Approximations in Implementing Dynamic Investment Strategies: A Comparison of Returns and Investment Policies," Management Science, INFORMS, vol. 39(7), pages 856-871, July.
- 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.
- Marina Di Giacinto & Salvatore Federico & Fausto Gozzi & Elena Vigna, 2010. "Constrained portfolio choices in the decumulation phase of a pension plan," Carlo Alberto Notebooks 155, Collegio Carlo Alberto.
- Battocchio, Paolo & Menoncin, Francesco, 2004. "Optimal pension management in a stochastic framework," Insurance: Mathematics and Economics, Elsevier, vol. 34(1), pages 79-95, February.
- Xiao, Jianwu & Hong, Zhai & Qin, Chenglin, 2007. "The constant elasticity of variance (CEV) model and the Legendre transform-dual solution for annuity contracts," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 302-310, March.
- 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.
- 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.
- Laura Schechter, 2007. "Risk aversion and expected-utility theory: A calibration exercise," Journal of Risk and Uncertainty, Springer, vol. 35(1), pages 67-76, August.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Silvia Maero).
If references are entirely missing, you can add them using this form.