The effect of extreme points (outliers or influential points) on systematic risk estimates is not fully captured through least squares estimation. This problem is particularly severe when many such points exist, because their presence can be masked and hence go undetected by the usual least squares procedure. Rousseeuw's reweighted least median squares (RWLMS) approach is used to detect the presence of outliers and influential and masked points in a sample of 1,350 NYSE/AMEX firms. When zero weights are assigned to such observations, the resulting RWLMS estimates of beta are on average 10 - 15 percent smaller than in least squares estimation.