Assets Selection and Portfolio Optimization in a Developing Economy Using Linear Programming

Abstract

Portfolio construction in developing economies such as Nigeria is often complicated by market inefficiencies, high volatility, limited diversification opportunities, and inadequate analytical approaches for optimal asset allocation. This study develops an optimal investment portfolio model using Linear Programming (LP) to support rational asset selection and fund allocation in the Nigerian stock market. The model seeks to maximize portfolio performance by simultaneously considering return, liquidity, and risk. Financial data were obtained from the annual reports of five selected companies listed on the Nigerian Exchange Group, namely Zenith Bank Plc, United Bank for Africa (UBA), TotalEnergies Marketing Nigeria Plc, Fidelity Bank Plc, and Nigerian Breweries Plc. The objective function was formulated as the ratio of the product of return and liquidity to risk, while the constraints were specified using the relative proportions of each firm’s return, liquidity, and risk. The resulting LP model was solved using the simplex algorithm implemented in LINGO 17.0 (64-bit) software. The results identified United Bank for Africa and Nigerian Breweries as the constituents of the optimal portfolio, with Nigerian Breweries accounting for the larger allocation and providing the greatest contribution to portfolio performance. Sensitivity analysis was subsequently performed to assess the robustness and stability of the optimal solution under possible changes in investment parameters. The analysis of reduced costs indicated that the assets excluded from the optimal portfolio would require sufficiently favorable changes in their performance coefficients before becoming economically attractive for inclusion in the portfolio. Furthermore, the shadow prices associated with the right-hand-side constraints provided information on the marginal effect of changes in the available investment resources and model constraints on the optimal objective value. The sensitivity results demonstrated that the optimal portfolio remained stable within specified ranges of variation in the objective coefficients and constraint values, implying that moderate fluctuations in market conditions would not alter the composition of the portfolio. This robustness highlights the ability of the proposed model to provide reliable investment decisions even under uncertain and dynamic market environments.