Market Line Deviations and Market Anomalies with Reference to Small and Large Firms

Previous anomaly research may have misinterpreted corrected, for the market index, mean returns on small firms. Assuming mean-variance preferences, it is shown theoretically that corrected mean returns (i.e., market line deviations) are not indicative of the relative desirability of increasing the proportional investment in small firms. The correct improvement criterion is derived and estimated. Tests indicate that the value-weighted market index is not significantly improved with greater weight on small firms, in the average month. When seasonality is considered, the observed performance improvements due to small or large firms are significant in some months, but the required portfolio position is unclear. If a case exists for a small firm anomaly in January, it probably exists in other months and it also exists for large firms. It is doubtful whether such an anomalous stock market exists.