This paper provides an explanation of investing in stock market anomalies in an expected utility paradigm. Classical selection rules fail to provide a preference for high expected return portfolios. The paper utilizes the almost dominance rules to examine the practice of investing in size, book-to-market, momentum, short-term and long-term reversal anomalies. The results indicate that popular investment choices such as value and small stocks do not dominate growth and big stocks. However, the short-term reversal and momentum strategies create efficient investment alternatives. Bilateral comparisons of stock market anomalies provide evidence for the superior performance of size, short-term reversal, and momentum for 1-month to 12-month horizon and book-to-market and long-term reversal for longer term horizons of 3 to 5 years. The relative strength of small, value, momentum-winner, short-term and long-term losers becomes more prevalent when the time-varying conditional distributions are examined.