It follows that for some stocks with very large variance xxx, R2 can be low even while the estimate of Beta is high; in such cases the reaction of the particular stock (or portfolio) to market variations is very sharp, yet market variation explains only a small portion of the stock's large variability. The regression equation for other stocks might have a high R2 but a low BJ estimate; this can occur when variation in the stock's (or portfolio's) risk premium is small in relation to variation in the market risk premium, that is, the ratio of sample variances in Eq, (2.20) is large. Moreover, note that a very low R2 does not invalidate the CAPM framework; rather, it simply indicates that the total risk of a particular company's assets is almost entirely company-specific, unrelated to the market as a whole.
The final typical regression output of particular interest to us here is the r-statistic, Earlier, it was noted that the r-statistic on the estimate of a can be used to test directly the null hypothesis that a = 0 against the alternative hypothesis that a !=O. Failure to reject this null hypothesis might be viewed as evidence in support of the CAPM