Early researchers of the random walk theory were startled by how accurately it described the behavior of security prices. They were aware, however, that the model was not perfect. Slight serial correlations did appear in the data they studied. For the purposes of the day, these inconsistencies were not significant, In practical work, they were largely ignored.

Recent research suggests that those slight correlations persist and accumulate over longer horizons. Over three to five years, financial markets lose much of their randomness. This finding of non-randomness has important implications for investing.

Simple beta/variance based models define risk as a function of asset class stocks, bonds, derivatives, etc. and the correlations between these. In performing risk analyses, investors make fine distinctions between investment classes Treasuries versus agencies, or 1.2 beta stocks versus 0.8 beta stocks. Despite the fine gradations, however, most risk measures remain one-dimensional. In a world of random walks, this is theoretically appropriate. Absent a random walk, the equation becomes more involved. Risk becomes a two-dimensional quantity, with holding period almost as important a consideration as asset class.