Investment Strategies to Exploit the Small Firm and January Anomalies

Abstract

In recent years a number of empirical studies have established that equity returns on small-capitalization firms are abnormally high in January. Debate continues as to whether this small-f idJanuary anomaly represents a real market inefficiency, or is simply an apparent contradiction resulting from inadequate allowance for differential transaction costs or incorrect pricing of risk. The present paper addresses this concern indirectly by asking whether there exists an explicit investment strategy which would successfully exploit the anomaly over the historical time period.We demonstrate that a simple equity-switch strategy, specifically to hold a broad-based market portfolio for eleven months of the year and a small-firm portfolio in January, would have generated a compound annual return of 15.8 percent over the period 1926-85. This compares to buy-and-hold returns of 12.6 and 9.8 percent for the market and small-firm funds, respectively. Furthermore, we show, using only weak assumptions about risk preferences and the nature of the returns distributions, that this active approach largely stochastically dominated the two alternative policies over this long historical time period.Therefore, within the limits of the (rather weak) empirical assumptions, our results strongly suggest that the January-based small-firm anomaly does represent a market inefficiency, which is independent of the model of risk pricing. Two reasonable objections also are addressed. First, although differential transaction costs are not considered, given the existence of no-load mutual funds and index options, it is very unlikely that such an extension would alter the qualitative nature of the conclusions. Second, a more serious concern is how to incorporate, within the exploitation strategy, a procedure for recognizing the very real possibility (indeed the expectation) that any such market inefficiency eventually will be arbritraged away. We suggest that the strategy must strike a balance between the relative probabilities and relative costs of two types of error: missing an exploitable investment inefficiency versus choosing an investment policy based upon false expectations of excess returns.To have any operational meaning such a procedure must specify a clear null hypothesis for comparison. For example, in a CAPM world, the cost of following a false equity-switch strategy arises because any portfolio other than the market portfolio contains non-systematic risk, which is not priced (and therefore not rewarded) by the market. As an initial step in this direction, we specified a null (joint) hypothesis of market efficiency and the CAPM. Using the historical data set, we calculate that for annual holding periods, the gain (if the discretionary strategy is right) is an excess return of about 5.2 percent a year, while the cost (if the CAPM is right) is a return deficiency of less than half a percent each year.