Product Diversity and Return on Equity with Kernel Density Approach in Petrochemical Companies

Abstract

This study aimed to investigate the effect of product diversification on return on equity (ROE) in petrochemical companies listed on the Tehran Stock Exchange using kernel density estimation and linear/nonlinear regression approaches during the 2011–2021 period. This applied descriptive-correlational study employed an ex-post facto research design. The statistical population consisted of firms listed on the Tehran Stock Exchange, and the sample included companies that continuously operated in the market between 2011 and 2021. Return on equity was considered the dependent variable, while product diversification measured through a kernel density-based index was the primary independent variable. Linear regression, nonlinear regression, analysis of variance, and model fit statistics were utilized to test the study hypotheses. The linear regression model was statistically significant (F = 2.422, p = 0.017) with an R² value of 0.097. Firm size (β = 0.214, p = 0.024), EBIT-to-total-assets ratio (β = -0.508, p = 0.048), retained earnings-to-assets ratio (β = 0.695, p = 0.008), and net earnings-to-sales ratio (β = -1.415, p = 0.050) significantly influenced ROE. However, the product diversification index (KDR) did not exhibit a significant direct effect on ROE (β = 0.003, p = 0.972). The nonlinear kernel density model revealed a significant nonlinear association between product diversification and ROE, characterized by an inverted U-shaped relationship, indicating that moderate diversification enhances shareholder returns while excessive diversification may reduce financial performance. The findings suggest that product diversification alone is not a dominant determinant of shareholder returns in petrochemical firms. Financial efficiency and internal organizational factors play a more substantial role in explaining variations in ROE. Nevertheless, the identified inverted U-shaped relationship indicates that diversification can improve financial performance up to an optimal level, beyond which additional diversification may impose managerial and operational costs that outweigh its benefits. Therefore, managers should pursue balanced diversification strategies to maximize shareholder value and sustain long-term performance.