Functional Form, Skewness Effect, and the Risk-Return Relationship

In this paper, possible factors affecting the second-pass regression results in capital asset pricing are investigated in detail. First, the true functional form used to test the risk-return relation is determined by using Box and Cox's [2] generalized functional form technique. Secondly, Box and Cox's residual analysis and transformation technique are used to show the importance of the skewness effect in capital asset pricing. Finally, some other factors affecting the results of second-pass regression coefficient in capital asset pricing also are explored. From these analyses, it is found that the functional form, the skewness effect, and the change of market condition are the most important factors in affecting the empirical conclusions in testing the bias of composite performance measures and the risk-return relation.