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Nonspherical disturbances and the implications for research on capital market anomalies
Abstract
This study investigates the implications of the potential bias inherent in some studies on anomalies. This potential bias is largely due to specification of the residual error structure. As an example, this study re-examines the size-January effect in an attempt to document empirically the suspected bias. Prior empirical research on this effect has relied almost exclusively on the market model (OLS) approach in establishing expected returns and computing estimates for abnormal returns. While considerable research exists on the possible violations of the model's underlying assumptions under various research designs, little or no attention has been given (empirically) to the implications of such violations in certain stock-market-return based anomalies. Test procedures using the market model assume that abnormal returns are generated from a single homogeneous population and that the cross-sectional residuals are uncorrelated. Significant departures from homogeneity of variance and/or the presence of contemporaneous correlations can lead to unwarranted errors of inference in studies that ignore these issues. Consequently, what has supposedly been shown as anomalies may not qualify as such or at least the significance may be much less than has been claimed in prior empirical tests. In this study, we present an alternative test procedure, based on generalized least squares (GLS), that accommodates non-spherical disturbances. Fewer restrictions on the error structure mean that more information is used in the estimation process. As such, incorporating non-spherical disturbances should lead to more powerful tests. The empirical results indicate that average cross-correlations for size-sorted portfolios are of sufficient magnitude to warrant consideration in the analysis of January abnormal returns. The observed pattern of correlations is approximately U-shaped across size, indicating that ignoring cross-sectional dependence can indeed lead to serious errors of inference regarding the significance of mean excess returns for size-sorted portfolios. This bias is serious not only for small-firm portfolios but large-firm portfolios as well. The bias is minimal and virtually non-existent for intermediate portfolios. Overall, the OLS approach shows significance in the mean abnormal returns while the GLS-based approach indicates that those returns are mostly not significant. In general, these errors are a direct result of understating the variance of the mean excess return when (positive) dependencies are ignored. The methodology in the present study could be applied with equal validity in similar settings where firms are grouped on some partitioning variable(s) and/or the assumption of spherical disturbances is not tenable.
Subject Area
Finance|Business administration|Statistics
Recommended Citation
Chikaonda, Mathias Aurelious, "Nonspherical disturbances and the implications for research on capital market anomalies" (1990). Doctoral Dissertations Available from Proquest. AAI9022672.
https://scholarworks.umass.edu/dissertations/AAI9022672