Optimal Asset Allocation Strategy for Defined-Contribution Pension Plans with Different Power Utility Functions


The relationship between the optimal asset allocation and the functional form of power utility is investigated for defined-contribution (DC) pension plans. The horizon dependence of optimal pension portfolios is determined by the argument of the power utility function. The optimal composition of pension portfolios is horizon independent when terminal utility is a power function of wealth-to-wage ratio, and deterministically horizon dependent when terminal utility is a function of terminal wealth or replacement ratio (the pension-to-final wage ratio). The optimal portfolios all contain a speculative component to satisfy the risk appetite of DC plan members, which is dominated by bonds under usual market assumptions. The optimal compositions of financial wealth on hand (the sum of pension portfolio and the short-sold wage replicating portfolio) are stochastically horizon dependent when wages are fully hedgeable and stochastic. The optimal pension portfolios also have a preference free component to hedge wage risk, when terminal utility is a function of wealth-to-wage ratio or replacement ratio. A state variable dependent component in optimal pension portfolios exists when terminal utility is a function of terminal wealth or replacement ratio, but it disappears when terminal utility is a function of terminal wealth-to-wage ratio and the risk premium is constant.

Share and Cite:

Ma, Q. (2014) Optimal Asset Allocation Strategy for Defined-Contribution Pension Plans with Different Power Utility Functions. Open Access Library Journal, 1, 1-17. doi: 10.4236/oalib.1100754.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Merton, R.C. (1969) Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case. Review of Economics and Statistics, 51, 247-57.
[2] Sørensen, C. (1999) Dynamic Allocation and Fixed Income Management. Journal of Financial and Quantitative Analysis, 34, 513-532.
[3] Campbell, J.Y. and Viceira, L.M. (2002) Strategic Asset Allocation: Portfolio Choice for Long-Term Investors. Oxford University Press, Oxford.
[4] Liu, J. (2007) Portfolio Selection in Stochastic Environments. Review of Financial Studies, 20, 1-39.
[5] Kim, T.S. and Omberg, E. (1996) Dynamic Nonmyopic Portfolio Behavior. Review of Financial Studies, 9, 141-161.
[6] Vigna, E. and Haberman, S. (2001) Optimal Investment Strategy for Defined Contribution Pension Schemes. Insurance: Mathematics and Economics, 28, 233-262.
[7] Boulier, J.F., Huang, S.J. andTaillard, G. (2001) Optimal Management under Stochastic Interest Rates: The Case of a Protected Defined Contribution Pension Fund. Insurance: Mathematics and Economics, 28, 173-189.
[8] Deelstra, G., Grasselli, M. and Koehl, P.F. (2003) Optimal Investment Strategies in the Presence of a Minimum Guarantee. Insurance: Mathematics and Economics, 33, 189-207.
[9] Battocchio, P. and Menoncin, F. (2004) Optimal Pension Management in a Stochastic Framework. Insurance: Mathematics and Economics, 34, 79-95.
[10] Cairns, A.J.G., Blake, D. and Dowd, K. (2006) Stochastic Lifestyling: Optimal Dynamic Asset Allocation for Defined Contribution Pension Plans. Journal of Economic Dynamics and Control, 30, 843-877.
[11] Vasicek, O.E. (1977) An Equilibrium Characterization of the Term Structure. Journal of Financial Economics, 5, 177-188.
[12] Øksendal, B. (2000) Stochastic Differential Equation—An Introduction with Applications. 5th Edition, Springer, Berlin.
[13] Duffie, D. (2001) Dynamic Asset Pricing Theory. 3rd Edition, Princeton University Press, Princeton and Oxford.
[14] Bodie, Z., Merton, R.C. and Samuelson, W. (1992) Labor Supply Flexibility and Portfolio Choice in a Lifecycle Model. Journal of Economic Dynamics and Control, 16, 427-449.

Copyright © 2023 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.