Simultaneous Test for the Equivalence of Alphas and Betas in the Capital Asset Pricing Regression Models
by
Hubert J Chen
Zhejiang Ujiversity, China and National Cheng Kung University, Taiwan
Coauthors: Jevons Chi-Wen Lee and Lei-Wei You,Zhejiang Ujiversity, China and National Cheng Kung University, Taiwan

A studentized range test is proposed to test the hypothesis of equivalence of alpha intercepts and beta slopes for the linear regressions derived from capital asset pricing models against an alternative hypothesis of inequivalence. By “equivalence” we mean that the parameters (intercepts or slopes) are falling into a practically small but negligible zone judged by a practitioner in his area of study. Both the maximum level of the proposed test in terms of the probability of rejecting a true null hypothesis and the minimum power in terms of the probability of accepting a correct alternative are obtainable at their corresponding least favorable mean configurations. Therefore, the power and hence the level are completely independent of the unknown alphas, betas and the variance. For a given null, a specified alternative, a required level and a guaranteed power, the critical value and the sample size for an experiment can be simultaneously determined. Statistical tables and computer programs to calculate the critical values, the powers and the needed sample sizes are provided for practitioners. A real example in mutual funds is demonstrated.

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Date received: February 21, 2007