The Power of Beaver's U against a Variance Increase in Market Model Residuals
To detect variance effects, researchers have primarily relied on the square of the standardized market model residual, i.e., Beaver's U.1 A similar statistic, the absolute value of the standardized residual, has also been used for this purpose. We call this statistic May's U.2 The rationale for using either Beaver's U or May's U is that, in a portfolio, a variance increase will be reflected in unusually large negative and positive residuals. These will tend to cancel out in a test based on ordinary residuals, but squared residuals or their absolute values will yield a cumulative effect. If the residuals are normally distributed (as assumed by the linear model), then Beaver's U is the best statistic, being most likely to detect a variance effect. Weekly and daily residuals are not normally distributed. They are leptokurtic (heavy-tailed) and skewed. Marais [1984] notes that the normal approximation to Beaver's U is unreliable for significantly leptokurtic residuals and attempts to correct this unreliability through bootstrapping. Marais does not, however, consider the impact of leptokurtosis on the optimality of Beaver's U. We show that Beaver's U is no longer optimal for leptokurtic residuals and that it is dominated by May's U.