Unveiling the optimal factor model in Pakistan : a machine learning approach using support vector regression and extreme gradient boosting algorithms

This study examines the explanatory power of Fama-French models to find the optimal model and pointing out the critical factors applying the grid search cross-validation (GridSearchCV)-based support vector regression (SVR) and extreme gradient boosting (XGBoost) in the Pakistani Stock Market. Data from 1990 to 2022 was collected from DataStream, and 100 test portfolios were formed, bivariate sorted on input factors to ensure accuracy and robustness. ANOVA and Diebold-Mariano tests were applied to pick the best model, while SHAP (SHapley Additive exPlanations) and TreeSHAP analyses identified the significant input factors by using the explainable artificial intelligence (ExP AI). Results reveal a six-factor model outperforms others, while market and size factors are the most influential factors. Opposing to Fama and French five-factor model, the value factor remains vital in the Pakistani equity market, like India and China, while investment factor is the least influential factor. Through the box-plot graphs, robustness was confirmed. The findings recommend investors should prioritize market and size risks, while policymakers should focus on growth of SME's (small- and medium-size enterprises) and macroeconomic stability to ensure and enhance market efficiency.