After Markowitz [14, p. 100] and Sharpe [19, 20] suggested estimating the beta systematic risk coefficient for market assets, finance professors, stock brokers, investment managers, and others began expending large quantities of resources each year on estimating betas. Unfortunately however, it appears that the ordinary least-squares (OLS) regressions used in nearly every instance may be inappropriate. This paper suggests that many stocks' beta coefficients move randomly through time rather than remain stable as the OLS model presumes.