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

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*10 22 . We also find that the minimum guarantee that will accrue to the PPM at retirement to be N3.05*10 8 . 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