This paper presents a framework called Summarize-Explain-Predict (SEP) for generating explainable stock predictions using self-reflective large language models (LLMs). The SEP framework enables an LLM to autonomously learn how to generate explainable stock predictions by combining a self-reflective agent with Proximal Policy Optimization (PPO). The framework consists of three components: a Summarize module that generates summaries of factual information from unstructured text inputs, an Explain module that generates explanations for stock predictions through an iterative self-reflective process, and a Predict module that generates predictions based on the summaries and explanations. The SEP framework is evaluated on a dataset of stock price movements and their associated text inputs. The results show that the SEP model outperforms traditional deep-learning and LLM methods in terms of prediction accuracy and the quality of explanations. The model is also tested on a portfolio construction task, where it generates explainable weights for a stock portfolio. The results demonstrate that the SEP framework is effective in generating explainable stock predictions and can be generalized to other finance-related tasks. The main contributions of this paper are: (1) investigating the limitations of teaching LLMs to weigh information in multiple texts for stock prediction in an explainable manner without expert-annotated explanation samples, and (2) proposing a solution that utilizes a self-reflective agent and PPO techniques to allow an LLM to teach itself how to make explainable stock predictions in a fully autonomous manner. The results show that the SEP framework is effective in generating explainable stock predictions and can be generalized to other finance-related tasks.This paper presents a framework called Summarize-Explain-Predict (SEP) for generating explainable stock predictions using self-reflective large language models (LLMs). The SEP framework enables an LLM to autonomously learn how to generate explainable stock predictions by combining a self-reflective agent with Proximal Policy Optimization (PPO). The framework consists of three components: a Summarize module that generates summaries of factual information from unstructured text inputs, an Explain module that generates explanations for stock predictions through an iterative self-reflective process, and a Predict module that generates predictions based on the summaries and explanations. The SEP framework is evaluated on a dataset of stock price movements and their associated text inputs. The results show that the SEP model outperforms traditional deep-learning and LLM methods in terms of prediction accuracy and the quality of explanations. The model is also tested on a portfolio construction task, where it generates explainable weights for a stock portfolio. The results demonstrate that the SEP framework is effective in generating explainable stock predictions and can be generalized to other finance-related tasks. The main contributions of this paper are: (1) investigating the limitations of teaching LLMs to weigh information in multiple texts for stock prediction in an explainable manner without expert-annotated explanation samples, and (2) proposing a solution that utilizes a self-reflective agent and PPO techniques to allow an LLM to teach itself how to make explainable stock predictions in a fully autonomous manner. The results show that the SEP framework is effective in generating explainable stock predictions and can be generalized to other finance-related tasks.