Determining Optimal Portfolio in a Three-Asset Portfolio Mix in Nigeria

Abstract

This study is aimed at determining the optimal portfolio in a three-asset portfolio mix in Nigeria. The research employed majorly two empirical methodologies which were Matrix algebra and Lagrangian method of optimization. Matrix algebra was used to compute the various portfolio weights. Lagrangian method of optimization was useful in obtaining the global minimum variance and the efficient frontier of the portfolio. In order to arrive at the best asset in the portfolio that is expected to yield maximum expected return, the study employed the utility function test. The data used for the study were daily stock prices for First Bank Nigeria Plc, Guinness Nigeria Plc and Cadbury Nigeria Plc obtained from the Nigerian Stock Exchange for the period of January 2010 to December 2013 The result obtained from the analysis indicated that among the three assets chosen in the study, Guinness has the highest utility value of 0.031 with lowest risk of 4.268 and the investment opportunity point ( μ, σ ) which is (0.169, 2.065) lies on the Capital Market Line. The assets of Guinness and First Bank are located above the Global Minimum at point ( μ, σ ) which is (0.10, 1.84) and are said to be efficient assets with high expected returns and low risk. The study therefore concluded that First Bank and Guinness were the only efficient optimal assets in the three asset-portfolio mix and therefore, the preferred choice for every investor since they yielded a high return with minimum variance.