CAPM and Empirical Embedding: When is 'near enough', good enough?

Abstract

Empirical testing for the existence of a CAPM relationship among a group of securities has been hampered by the lack of structure under the alternative hypothesis. This paper examines what happens when the chosen or available group is embedded within a larger group ( the global set). A risk premium process defined with respect to the more embracing group allows securities to be priced, and those pricing relationships are embodied in the chosen set. If one then fits a CAPM with respect to a market index constructed from the chosen set, the resulting betas will be biased even up to a factor of proportionality. By demonstrating the follD of the bias, however, we can show how to correct it and demonstrate conditions under which the more limited market index can suffice for such purposes as cost of capital studies. A simple test for spanning emerges, which can be reinterpreted as providing an alternative hypothesis for the CAPM itself The resulting empirical methodology is a straightforward two step modification ofOLS, from which tests of structural stability over time can also be derived. The methods are applied to monthly data on a set ofNew Zealand stocks.