This paper investigates whether large language models (LLMs) can generate reliable stock market predictions. We evaluate four state-of-the-art models - ChatGPT, Gemini, DeepSeek, and Perplexity - across three prompting strategies: a naive query, a structured approach, and chain-of-thought reasoning. Our results show that LLM-generated recommendations are hindered by recurring reasoning failures, including financial misconceptions, carryover errors, and reliance on outdated or hallucinated inform