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This paper provides some theoretical foundations for using moving average (MA) rules in the stock market. In particular, the paper analyzes the conditional probability of price increments and examines how this probability varies over time. We prove under certain assumptions that the probability of being in an uptrend is greater than the probability of being in a downtrend. This demonstration partially justifies the common use of MA rules in the stock market. Finally, we propose an ex-post empirical analysis to evaluate and compare the performance of some MA rules and other portfolio strategies in the US stock market. In this context, we also suggest a methodology that incorporates these trading rules as alarm rules to predict potential market failures. Our ex-post results confirm the advantages of using these trading rules to predict market trends and crises. [ABSTRACT FROM AUTHOR]