Insignificant Betas and the Efficacy of the Sharpe Diagonal Model for Portfolio Selection

When both practitioners and theorists apply Sharpe's diagonal model [15] to simplify the portfolio selection problem, they assume that the entire covariation structure of each stock (i.e., with all other stocks) is captured in that stock's covariance with the market (or β). Furthermore, it is well known that the selection algorithm itself has a marked tendency to select stocks with the lowest βs, ceteris paribus. When a stock's β is statistically indistinguishable from zero, it is an empirical issue whether the market model is (a) less appropriate for that particular stock relative to those with statistically significant βs; or is (b) a viable model in that the covariance of this stock's rate‐of‐return with all other stocks' rates‐of‐return vanishes. The objective of this paper is to distinguish empirically between (a) and (b), and to propose a heuristic which will improve the ex‐post performance of the diagonal model. The possible benefits of this heuristic are also demonstrated in a rigorous statistical framework.