Our paper explores how a host of capital market anomalies have evolved in recent years, as stocks have become more liquid and more actively traded, and hedge funds that exploit these anomalies have become more popular. We empirically explore how the Fama and MacBeth (FM) (1973) cross-sectional coefficient estimates and the decile-based hedge portfolio returns, have changed over time. We find that most of the hedge portfolio returns and regression coefficients for the anomalies attenuate towards zero over time.
We conduct additional analysis to identify the reason behind the attenuation of the anomaly profits. Specifically, we try different identification schemes, including (i) the decrease in the tick size due to decimalization, (ii) the impact of hedge fund assets under management (AUM), (iii) the impact of the aggregate short interest, and (iv) aggregate share turnover. All of above variables are proxies for arbitrage activity.
We find that the characteristic premiums (i.e., FM coefficients) of almost all anomalies have attenuated from before to after decimalization. The average returns as well as the Sharpe ratio from a comprehensive anomaly-based trading strategy have more than halved after the shift to decimal pricing. Further, the returns to several anomalies are negatively related to hedge funds' AUM, short interest, and aggregate trading activity, indicating a link between arbitrage proxies and attenuation in anomalies.
The included firm characteristics to capture equity market anomalies are
The base sample includes common stocks listed on the NYSE/AMEX (NYAM) from 1976 to 2011. A second Nasdaq sample begins in 1983, because trading volume on Nasdaq, required for computation of turnover and the illiquidity measure, is not available prior to this date.
We analyze the economic and statistical significance of anomalies in two ways.
The first way constructs extreme decile portfolios that are long the high characteristic values and short the low characteristic values. Table 1 provides the coefficients of the exponential time trend for the hedge portfolio returns (all coefficients are multiplied by 10). The coefficient estimate on time, , for the NYAM portfolio returns formed by sorting on the past one month return (reversal strategy) is 0.0124. An attenuation obtains when the trend is in the opposite direction of the baseline effect in Table 1. Because the return from buying (selling) stocks with low (high) values of the past month's return is –0.5% (from Table 1) per month, a positive trend coefficient is consistent with a decline in profits to a reversal strategy over time. The coefficient on cumulative returns over the past two to twelve months (momentum strategy) is –0.0142. Because the return to the momentum strategy is positive, a negative coefficient signifies a decline in profits over time. Similarly, the negative trend coefficient suggests a decline in profits to supplying liquidity. The signs of the NYAM trend coefficient estimates suggest an attenuation in anomaly-based trading profits for ten of twelve anomalies.
There is a significant decline (10% level cutoff) in the profitability of eight of twelve of the anomalies for NYAM stocks. In the case of Nasdaq stocks, ten of twelve anomalies attenuate, with four (value, momentum, profitability, and PEAD) demonstrating significant attenuation. In Table 1, we also show the number of significant accentuations (at the 10% level, i.e., the number of trend coefficients with a -value exceeding 0.9). There is a strong asymmetry in significant attenuations and accentuations. While eight anomalies have significantly attenuated for NYAM stocks (four for Nasdaq stocks), only one anomaly has accentuated for NYAM stocks, and no anomaly has significantly accentuated for Nasdaq stocks. The overall picture is quite consistent with attenuation in anomaly profits over time.
In the last row of Panel A of Table 1, we also present the result of fitting the exponential trend to the portfolio return obtained by equally weighting the twelve individual anomaly-based hedge portfolios (henceforth termed the “EW hedge portfolio”). The returns on this portfolio show a significant attenuation for both NYAM and Nasdaq stocks.
The second way show that these results also obtain in Fama-Macbeth specifications. In eleven of twelve cases, the characteristic premiums attenuate for NYAM stocks. Six of the twelve NYAM characteristic premiums (those for size, monthly reversals, momentum, accruals, and profitability IVOL, and PEAD) exhibit a significant declining trend (five of these six cases attenuate with -values of 0.05 or less). The half-lives for reversals, accruals, and SUE, are 5.4, 9.3, 10.2, and 6.7 years, respectively. Size, R1, R212, IVOL, and SUE had predicted coefficients in 2010 that were just about zero.
Our paper studies several equity market anomalies over more than three decades. It finds that the regime of increased liquidity, trading activity, and hedge funds' assets under management have resulted in a decrease in the economic and statistical significance of these anomalies.
In order to establish a link between increased arbitrage activity and the decline in the profitability of the anomaly based trading strategies we examine (i) the impact of the decline in the tick size due to decimalization and (ii) the impact of hedge fund assets under management, short interest, and trading activity on the anomaly based predictability. The decrease in the tick size is associated with improvements in liquidity and a decline in trading costs. We find that the characteristic premiums have declined towards zero for several anomalies in the post-decimal period, and the profits to a comprehensive anomaly-based portfolio have declined by about half in the post-decimal period. Moreover, the impact of many anomalies such as size, reversals, momentum, and PEAD, as well as the return to a composite portfolio have declined with an increase in hedge fund assets, short interest, and aggregate share turnover, suggesting that arbitrage activity has indeed led to a decline in the profitability of the anomaly based trading strategies.
These results are relevant because they indicate that it may be challenging to attain consistent profits from well-documented anomalies in the future. Note, however, that while anomaly profits, based on a comprehensive hedge portfolio, decline significantly in the recent high-liquidity era, they remain statistically significant. Looking to the future, these profits may not disappear completely because of limits to arbitrage or imperfect competition amongst arbitrageurs that preserves some rents.
Our analysis suggests that it might be fruitful to explore the effect of mechanisms and policies that remove trading frictions and improve liquidity in markets. The results suggest that cross-sectional return predictability would diminish to a greater extent in countries that have experienced greater enhancements in trading technologies and larger increases in trading activity and liquidity. This hypothesis awaits rigorous testing in an international context.
Attenuation | ||
b | p-value | |
SIZE | 0.082 | 0.045^{**} |
BM | –0.047 | 0.076^{**} |
R1 | 0.124 | 0.001^{**} |
R212 | –0.142 | 0.012^{**} |
TURN | 0.046 | 0.103 |
ILLIQ | –0.058 | 0.074^{**} |
ACC | 0.028 | 0.082^{**} |
AG | 0.027 | 0.123 |
ISSUE | 0.036 | 0.046^{**} |
IVOL | –0.026 | 0.687 |
PROFIT | 0.058 | 0.961^{**} |
SUE | –0.048 | 0.006^{**} |
Number of attenuations | 10 of 12 | |
(significant attenuations) | (8 of 12) | |
(significant accentuations) | (1 of 12) | |
EW hedge portfolio return | –0.045 | 0.001^{**} |