Risk Management of a Defined Benefit Pension Scheme: A Stochastic Programming Approach

Abstract

This study investigates how the investment returns of Social Security and Insurance Trust (SSNIT) of Ghana has performed over the years compared with the financial market and designs a method for the optimal asset mix strategy for the scheme under different risk preferences using stochastic linear programming approach. A time series of annual data on returns on equity and treasury bills from the year 2001 to 2013 were used to investigate the performance of the SSNIT investment compared with Ghana’s financial market using a trend analysis. A twenty-four annual market data of returns on equity and treasury and average wage growth rate spanning from 1990 to 2014 was used to simulate stochastic future wage growth and return on equity and Treasury bill using Vector Autoregressive model. The study found that the SSNIT investment returns on equity and treasury bills outperformed that of the financial market. The study also found that the optimal asset allocation for the risk adverse model has a higher allocation to treasury bills than equity. Again, it was found that the final wealth (i.e. the ratio of assets to liabilities) is greater than one with all the risk preference models. Also the asset composition of risk neutral models has a higher allocation to equity than treasury bills. It was also found that the optimal asset allocation and the final expected wealth are sensitive to changes in the transaction cost. The study then recommends that the SSNIT pension scheme should adapt stochastic programming model for the optimal asset allocation. Also the SSNIT pension scheme should trade with least transaction cost since higher transaction decreases the final expected wealth value.