Optimal Investment and Portfolio Strategies with Minimum Guarantee and Inflation Protection for a Defined Contribution Pension Scheme

Chukwuma R. Nwozo, Charles I. Nkeki

Abstract


Abstract: We study the optimal investment and optimal portfolio strategies with minimum guarantee and inflation protection in a defined contribution (DC) pension scheme. We assume a market structure that is characterized by a cash account, an indexed bond (i.e., inflation-linked bond) and stock. We obtain optimal share of portfolio values (that depend on the minimum guarantee) in the indexed bond and stock for the pension plan member (PPM) at time t. We find that in the presence of indexed bond in the investment strategy, the inflation risk that is associated with the PPM’s contributions and minimum guarantee is hedged. Hence, indexed bond can be used to hedge inflation risk that is associated with a contributory pension funds scheme. We also find in our numerical result that, with effective management of the pension funds by pension fund administrators (PFAs), PPMs will have high returns from their investment. From our results, we find that the optimal terminal wealth that will accrue to the PPM and PFA to be N1.97*1022 . We also find that the minimum guarantee that will accrue to the PPM at retirement to be N3.05*108 . The portfolio values in stock, indexed bond and cash account are 0.5, 3.1, and -2.6, respectively. Therefore, more investment should go to indexed bond and stock since they yield positive portfolio value.
Key words: Optimal Investment; Portfolio Strategies; Minimum Guarantee; Defined Contribution

Keywords


Optimal Investment; Portfolio Strategies; Minimum Guarantee; Defined Contribution

Full Text:

PDF

References


Basak, S. (2002). A Comparative Study of Portfolio Insurance. Journal of Economic Dynamics and Control, 26, 1217-1241.

Deelstra, G., Grasselli, M. and Koehl, P. (2003). Optimal Investment Strategies in the Presence of a Minimum Guarantee. Insurance: Mathematics and Economics, 33, 189-207.

Grossman, S. J. and Zhou, J. (1996). Equilibrium Analysis of Portfolio Insurance. Journal of Finance, 51, 1379-1403.

Hojgaard, B. and Vigna, E. (2007). Mean-variance Portfolio Selection and Efficient Frontier for Defined Contribution Pension Schemes. Collegio Carlo Alberto.

Nkeki, C. I. and Nwozo, C. R. (2011). Optimal Portfolio Strategies with Minimum Guarantee Maximizing the Expected Utility of Terminal Surplus for a Defined Contribution Pension Plan. Int. J. Appl. Math. Stat., 20, 60-72.

Rudolf, M. and Ziemba, W. T. (2004). Intertemporal Surplus Management. Journal of Economic Dynamics and Control, 28, 975-990.

Tepla, L. (2001). Optimal Investment with Minimum Performance Constraints. Journal of Economic Dynamics and Control, 25, 1629-1645.

Vigna, E. (2010). On Efficiency of Mean-Variance based Portfolio Selection in DC Pension Schemes. Collegio Carlo Alberto.

Zhang, A., Korn, R. and Ewald, C. O. (2007). Optimal Management and Inflation Protection for Defined Contribution Pension Plan. MPRA paper.




DOI: http://dx.doi.org/10.3968/j.sms.1923845220120202.007

DOI (PDF): http://dx.doi.org/10.3968/g1585

Refbacks

  • There are currently no refbacks.


Copyright (c)



Share us to:   

Reminder

If you have already registered in Journal A and plan to submit article(s) to Journal B, please click the CATEGORIES, or JOURNALS A-Z on the right side of the "HOME".


We only use three mailboxes as follows to deal with issues about paper acceptance, payment and submission of electronic versions of our journals to databases:
[email protected]; [email protected]; [email protected]

 Articles published in Studies in Mathematical Sciences are licensed under Creative Commons Attribution 4.0 (CC-BY).

 STUDIES IN MATHEMATICAL SCIENCES Editorial Office

Address: 1055 Rue Lucien-L'Allier, Unit #772, Montreal, QC H3G 3C4, Canada.

Telephone: 1-514-558 6138

Http://www.cscanada.net
Http://www.cscanada.org
E-mail:[email protected]

Copyright © 2010 Canadian Research & Development Centre of Sciences and Cultures