Optimal Variational Portfolios with Inflation Protection Strategy and Efficient Frontier of Expected Value of Wealth for a Defined Contributory Pension Scheme

Abstract

This paper examines optimal variational Merton portfolios (OVMP) with inflation protection strategy for a defined contribution (DC) Pension scheme. The mean and variance of the expected value of wealth for a pension plan member (PPM) are also considered in this paper. The financial market is composed of a cash account, inflation-linked bond and stock. The effective salary of the plan member is assumed to be stochastic. It was assumed that the growth rate of PPM’s salary depends on some macroeconomic factors over time. The present value of PPM’s future contribution was obtained. The sensitivity analysis of the present value of the contribution was established. The OVMP processes with inter-temporal hedging terms and inflation protection that offset any shocks to the stochastic salary of a PPM were established. The expected values of PPM’s terminal wealth, variance and efficient frontier of the three classes of assets are obtained. The efficient frontier was found to be nonlinear and parabolic in shape. In this paper, we allow the stock price to be correlated to inflation risk index, and the effective salary of the PPM is correlated to inflation and stock risks. This will enable PPMs to determine extents of the stock market returns and risks, which can influence their contributions to the scheme.