Language models (LMs) have exhibited exceptional versatility in reasoning and in-depth financial analysis through their proprietary information processing capabilities. Previous research focused on evaluating classification performance while often overlooking explainability or pre-conceived that refined explanation corresponds to higher classification accuracy. Using a public dataset in finance domain, we quantitatively evaluated self-explanations by LMs, focusing on their factuality and causality. We identified the statistically significant relationship between the accuracy of classifications and the factuality or causality of self-explanations. Our study built an empirical foundation for approximating classification confidence through self-explanations and for optimizing classification via proprietary reasoning.