Psychometricians have also developed methods for working with large matrices of correlations and covariances. Let formula 16 denote the average of the iter-item covariances. An often-seen variant expresses the filter in terms of inverse covariances. This shows that risk premiums are determined by covariances with any SDF. Suppose two classes of observations have means formula 36 and covariances formula 37. Competition, which causes negative covariances, only serves to strengthen these relationships. Factor or components analysis could be applied to correlations or covariances among cases. In practice, the class means and covariances are not known. The results then just give approximations to the means and covariances of the transformed quantities. The matrices below are covariances when there are just three observations across time.