On the Effect of Inflation and Impact of Hedging on Pension Wealth Generation Strategies under the Geometric Brownian Motion Model

Bright O Osu,Kevin N C Njoku,Ben I Oruh

doi:10.34198/ejms.1219.119142

Abstract

This work investigates the effect of Inflation and the impact of hedging on the optimal investment strategies for a prospective investor in a DC pension scheme, using inflation-indexed bond and inflation-linked stock. The model used here permits the plan member to make a defined contribution, as provided in the Nigerian Pension Reform Act of 2004. The pension plan member is allowed to invest in risk-free asset (cash), and two risky assets (i.e., the inflation-indexed bond and inflation-linked stock). A stochastic differential equation of the pension wealth that takes into account certain agreed proportions of the plan member’s salary, paid as contribution towards the pension fund, is constructed and presented. The Hamilton-Jacobi-Bellman (H-J-B) equation, Legendre transformation, and dual theory are used to obtain the explicit solution of the optimal investment strategies for CRRA utility function. Our investigation reveals that the inflation have significant negative effect on wealth investment strategies, particularly, the RRA(w) is not constant with the investment strategy, since the inflation parameters and coefficient of CRRA utility function have insignificant input on the investment strategies, and also the inflation-indexed bond and inflation-linked stock has a positive damping effect (hedging) on the severe effect of inflation.

Highlights

There are two major designs of pension plan, namely, the defined benefit (DB) pension, and the defined contribution (DC) pension plan
The models we used is that of Othusite and Xue [13], though, we considered inflation of globally competing goods, and some real life assumptions are made to buttress this fact
From Remark 5.1, we discovered that the constant relative risk aversion (CRRA) utility function does not have much effect on inflation and its effect on wealth investment, whereas, the inflation linked bond and stock serves as a hedging mechanism against adverse effect of Inflation on the optimization of pension wealth

Summary

Introduction

There are two major designs of pension plan, namely, the defined benefit (DB) pension, and the defined contribution (DC) pension plan. In that of the DB, the benefits of the plan member are defined, and the sponsor bears the financial risk. In the DC pension plan, the contributions are defined, the retirement benefits depends on the contributions and the investment returns, and the contributors (the plan members) bears the financial risk. Investment strategies of the contributions, which in turn is a strong determinant of the investment returns vis-a-vis the benefits of the contributors at retirement must be given optimum attention. Cairns et al [3], did a work on, “stochastic life styling: optimal dynamic asset allocation for defined contribution pension plans. Various properties and characteristics of the optimal asset allocation strategy, both with and without the presence of non-hedge able salary risk were discussed. The significance of alternative optimal strategy by pension providers was established

Methods

Discussion

Conclusion