Overcoming the Lack of Identification in Bowman’s Paradox Tests: Heteroskedastic Behavior of Returns

Abstract

To date, the validity of the empirical tests that employ the mean‐variance approach for testing the risk‐return relationship in the research stream named Bowman’s paradox is inherently unverifiable, and the results cannot be generalized. However, this problem can be solved by developing an econometric model with two fundamental characteristics: first, the use of a time‐series model for each firm, avoiding the traditional cross‐sectional analysis; and, second, the estimation of a model with a single variable (firm’s rate of return), whose expectation and variance are mathematically related according to behavioral theories, forming a heteroskedastic model similar to GARCH (generalized autoregressive conditional heteroskedasticity). The application of this methodology for Bowman’s paradox is new, and its main advantage is that it solves the previous criticism of the lack of identification. With this model, we achieve results that agree with behavioral theories and show that these theories can also be carried out with market measures.