Analyzing Covariation of Returns to Determine Homogeneous Stock Groupings

Abstract

Cohen and Pogue's empirical evaluation of the multi-index and singleindex portfolio selection models showed that the single-index model was superior to the multi-index model in generating efficient sets of portfolios.' The inability of the multi-index model to outperform the singleindex model resulted from the failure of the multi-index model to provide a more accurate representation of the true covariance matrix of security returns. This failure was, in turn, due to the fact that industry indexes used as inputs to the multi-index model were highly collinear. Indexes of stocks are needed that are homogeneous in the sense that they are significantly correlated within their own grouping and, at the same time, generally independent of other groups.2 Use of such noncorrelated indexes in the multi-index model should lead to a more accurately represented covariance matrix and thereby a set of efficient portfolios superior to the single-index model. The purpose of this study is to develop stock groupings that are homogeneous with respect to collinearity characteristics and thus suitable for use as inputs in the multi-index model. Development of such groups, in turn, involves a test for effects additional to market and industry factors that have been shown (by King) to be significant in explaining the covariation of stock returns.; The method that appears to be most promising as representing an additional factor for grouping stocks is