Econometric Properties of Alternative Security Return Methods

Abstract

In recent years, security price research has experienced a proliferation of research designs. As a result, there is a lack of interstudy comparability, which is aggravated by the absence of a formal analysis of the properties of the alternative designs under various conditions. The purpose here is to examine one important aspect of research design-the choice of the security return measure-in a simple, but well-defined setting of limited parameter uncertainty. The analysis leads to the following results. (1) With respect to raw versus returns, it explicitly offers three potential rationales for residual returns. As such, the analysis provides a formal statement of the reasons for residual analyses to supplement the intuitive, but less precise statements in the early literature. (2) With respect to return versus difference in returns methods, the analysis indicates the conditions under which: (a) the approach dominates the difference in returns approach as judged by the statistical criteria examined, (b) the converse holds, and (c) the two methods possess the same econometric properties. (3) The relative properties described in (2) are derived for a general model of nonzero covariation among and for two important special cases, the zero-beta model and the industry effects model.

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