MATRIX ALGEBRA WITH STOCHASTIC TERMS FOR MODELING MARKET CAPITALIZATION TREND FUNCTIONS

Abstract

This paper explores the use of matrix algebra augmented with stochastic components to model market capitalization trends in investment planning. First, we derive mathematical formulations that express the stochastic rate of change in share prices under different trend structures such as quadratic, cubic, and seasonal models; which exert distinct effects on the share prices of Access Bank, Fidelity, and Merged Bank due to their individual characteristics. We also analyze how interest rate fluctuations influence the share prices of the three banks, finding that their share prices respond positively to rising interest rates, pointing to a potential opportunity for investors. We employ statistical metrics to evaluate how each trend model captures the characteristics of predicted share prices. Finally, we compare actual versus predicted share prices using Mean Squared Error (MSE) as the selection criterion. The results indicate that the seasonal trend model yields the most accurate predictions, with predicted values closely tracking actual ones. Graphical solutions were obtained to show the effectiveness of the fitted model. These findings carry important implications for investors, financial analysts, and policy makers, suggesting that the seasonal trend model can aid in investment decision-making and risk management.