We construct a zero net-worth uninformed " naive investor" who uses a random portfolio allocation strategy. We then compare the returns of the momentum strategist to the return distribution of naive investors. For this purpose we reward momentum profits relative to the return percentiles of the naive investors with scores that are symmetric around the median. The score function thus constructed is invariant and robust to risk factor models. We find that the average scores of the momentum strategies are close to zero (the score of the median) and statistically insignificant over the sample period between 1926 and 2005, various sub-sample periods including the periods examined in Jegadeesh and Titman (1993, 2001). The findings are robust with respect to sampling or period-specific effects, tightened score intervals, and the imposition of maximum-weight restrictions on the naive strategies to mitigate market friction considerations.