Anomalies and the Expected Market Return
異常現象和預期市場回報

A. Data-Generating Process
A. 資料產生過程

Equation (4) provides a general representation for the mispricing component in each leg, as any stationary autoregressive moving-average (ARMA) process can be expressed via the infinite-order moving-average (MA) process. The equation expresses the current-period level of mispricing as a function of current and past mispricing shocks. The MA process can be interpreted as an impulse-response function: $$ is the response (ceteris paribus) of $$ for $$ to a period $$ unit mispricing shock. For example, consider a unit overpricing shock and suppose that $$, $$, and $$ for $$. The pricing error is $$ at the end of the period immediately after the shock, so that $$, that is, 10% of the overpricing shock is corrected during the first period after the shock. The pricing error is $$ at the end of the second period after the shock, which means that an additional 45% ($$) of the overpricing shock is corrected. Finally, the remaining 45% of the overpricing shock is corrected during the third period after the shock ($$).

B. Mispricing Correction Persistence

In sum, two opposing effects determine $$: (i) the extent to which the overpricing associated with a new shock is corrected in the next period and (ii) the extent to which the overpricing associated with old overpricing shocks is corrected in the current and next periods. These two effects are evident in the expression in brackets in equation (9), which accounts for all of the consecutive pairs of return responses to new and old overpricing shocks. The first term, $$, is the product of the period $$ and period $$ return responses to a new unit overpricing shock, which captures the potential reversal due to the immediate correction of the overpricing induced by the new shock. The second term, $$, reflects the potential momentum due to the persistent correction of the overpricing induced by old shocks. For example, $$ is the product of the period $$ and period $$ overpricing corrections corresponding to a period $$ unit overpricing shock, $$ is the product of the period $$ and period $$ overpricing corrections corresponding to a period $$ unit overpricing shock, and so forth.9

The previous example ($$, $$, and $$ for $$) numerically illustrates the intuition. A unit overpricing shock increases both the price and return by one unit at the time of the shock. Since $$, the price falls in the period after the shock, corresponding to a return of $$, so that the magnitude of the reversal effect is 0.10. The size of the momentum effect associated with old unit overpricing shocks is given by the second term is brackets, which equals $$. In this case, the magnitude of the momentum effect outweighs that of the reversal effect, so that $$ in equation (9).11

C. Noise Reduction

D. Extensions

For expositional ease, we assume that the long and short legs cover the market in equation (3). When the long and short legs are the last and first decile portfolios, respectively—as in our empirical application—the same intuition applies. We address this issue empirically in Section V.B, where we show that the predictive ability of long-short anomaly returns extends across multiple market segments. Thus, our intuition behind market return predictability based on long-short anomaly returns extends beyond serial dependence in the long and short legs (especially the latter) and includes the relevance of long-short anomaly returns for signaling mispricing correction more generally across the market.12

A. Forecast Construction

Suppose that we want to forecast the market excess return ($$) and that we have multiple potential predictors; in our context, the predictors are 100 long-short anomaly portfolio returns. We are interested in generating $$, a forecast of the month $$ market excess return based on information available through month $$. All of our market excess return forecasts are out of sample, as we only use data available through month $$ to forecast $$.

The prevailing mean forecast, which implicitly assumes that the market excess return is unpredictable (apart from its mean value), is the most popular benchmark in the literature. The prevailing mean forecast is simply the average of the market excess return observations available at the time of forecast formation. Because the predictable component in the monthly market excess return is inherently small (i.e., return data are quite noisy), the prevailing mean forecast is difficult to beat in practice (e.g., Goyal and Welch (2008)). With this in mind, successful out-of-sample strategies effectively shrink the market excess return forecast toward the prevailing mean benchmark to reduce the likelihood of overreacting to the noise in return data.

B. Forecast Evaluation—Statistical Accuracy

C. Forecast Evaluation—Economic Value

A. Forecast Accuracy

Figure 1 depicts monthly market excess return forecasts based on the 100 long-short anomaly portfolio returns and strategies described in Section II.A. The conventional OLS forecast is highly volatile. In fact, the conventional OLS forecast is more than 6% (72% annualized) in magnitude for a number of months; such extreme forecasts point to severe overfitting. The other forecasts are substantially less volatile than the conventional OLS forecast. In other words, as intended, the ENet, simple combination, C-ENet, predictor average, principal component, and PLS strategies shrink the forecasts toward the prevailing mean (while still incorporating information from the 100 long-short anomaly portfolio returns). The simple combination forecast exerts a particularly strong shrinkage effect (as discussed in Section II.A). Excluding the conventional OLS forecast, the PLS forecast demonstrates the most volatility, with the volatilities for the ENet, C-ENet, predictor average, and principal component forecasts falling between those for the simple combination and PLS forecasts. We note that the market excess return forecasts in Figure 1 are typically more volatile around business-cycle recessions, which indicates that the long-short anomaly portfolio returns themselves are more volatile around recessions.

Table II reports $$ statistics for monthly market excess return forecasts based on the 100 long-short anomaly portfolio returns. The conventional OLS forecast produces a negative $$ statistic that is extremely large in magnitude, confirming that the forecast is plagued by overfitting.19 In sharp contrast, the other forecasts all generate positive $$ statistics, so that they are more accurate than the prevailing mean benchmark over the 1985:01 to 2017:12 out-of-sample period. Using the Campbell and Thompson (2008) threshold of 0.5%, the monthly $$ statistics for all six of the forecasts designed to guard against overfitting are economically significant; indeed, the $$ statistics for the ENet, C-ENet, predictor average, and PLS forecasts are quite sizable (2.03%, 2.81%, 1.89%, and 2.06%, respectively), making them among the highest in the literature to date. Furthermore, according to the Clark and West (2007) statistics, all six of the forecasts designed to guard against overfitting provide statistically significant improvements in MSFE vis-à-vis the prevailing mean benchmark.

Overall, we find that the information in the group of 100 long-short anomaly portfolio returns is quite useful for predicting the monthly market excess return, provided that we employ forecasting strategies that guard against overfitting. The fact that the ENet, simple combination, C-ENet, predictor average, principal component, and PLS forecasts all generate statistically and economically significant improvements in out-of-sample accuracy indicates that our results are robust and not overly reliant on a particular method for circumventing overfitting.

Table II also reports results for monthly market excess return forecasts based on long- and short-leg anomaly portfolio excess returns. A clear pattern emerges: The short-leg excess returns provide some evidence of statistically and economically significant predictive ability, while there is no statistically or economically significant evidence of predictive ability for the long-leg excess returns. As discussed in Section I.B, this pattern is consistent with asymmetric limits of arbitrage and stronger MCP for overpricing vis-à-vis underpricing.

Comparing the results in Table II for the long-short and short-leg excess returns, the former perform better than the latter for forecasting the monthly market excess return. As explained in Section I.C (and supported by the average volatilities reported in Table I), the long-short return can provide a sharper predictive signal when the long and short legs contain a sizable common component that is unrelated to the future market excess return, as the long-short return filters the common component to produce a less-diluted signal.

B. Economic Value

As described in Section II, we also measure the marginal economic benefit of the predictive ability of long-short anomaly portfolio returns for a mean-variance investor with a relative risk aversion coefficient of three who allocates between the market portfolio and risk-free Treasury bills. Figure 2 plots log cumulative excess returns for portfolios using market excess return forecasts based on the 100 long-short anomaly returns. The figure also depicts the log cumulative excess return for the portfolio based on the prevailing mean benchmark forecast, as well as that for the market portfolio. Figure 2 reveals that portfolios that incorporate the information in the 100 long-short anomaly returns generally exhibit superior performance compared to both the portfolio based on the prevailing mean benchmark forecast and the market portfolio.

Figure 2 also shows annualized average utility gains when the investor uses a competing forecast of the market excess return in lieu of the prevailing mean benchmark. For the conventional OLS forecast based on the 100 long-short anomaly returns (not shown in the figure), there is a large loss of −4.97%, which further manifests the overfitting problem for the conventional approach. In contrast, the forecasts designed to guard against overfitting all generate substantial utility gains. The smallest annualized gain obtains for the simple combination forecast (2.59%), which is still economically sizable.20 The annualized gain reaches as high as 6.38% for the PLS forecast, and it is above 600 basis points for the ENet and C-ENet forecasts (6.26% and 6.06%, respectively).

Although largely ignored by the market return predictability literature, it is important to assess the statistical significance of the average utility gains. To do so, we use the moving-block bootstrap procedure recommended by McCracken and Valente (2018) to compute critical values for testing $$: $$ against $$: $$ in equation (34). The utility gains for the portfolios based on the ENet, predictor average, and principal component (simple combination, C-ENet, and PLS) forecasts are significant at the 5% (1%) level. Overall, the utility gains provide further evidence that long-short anomaly portfolio returns contain valuable information for predicting the market excess return.21

For the portfolios based on the ENet, C-ENet, predictor average, principal component, and PLS forecasts, the information in the long-short anomaly returns appears especially valuable for improving performance during the latter half of the Great Recession. It is worth noting that most of the 100 anomalies were published before that time, suggesting that the utility gains accruing to the information in the group of anomalies are not limited to the anomalies' prepublication periods.22

C. Additional Results

Because the long- and short-leg anomaly returns are components of the market return, the lagged market return itself potentially contains relevant information for forecasting the monthly market return. For the 1970:01 to 2017:12 sample period, the autocorrelation for the market excess return is 0.08 (significant at the 10% level). However, the lagged market excess return does not evince significant out-of-sample predictive ability for the 1985:01 to 2017:12 out-of-sample period. As explained in Section I.C, this is not surprising, since the market return is a noisier predictor than the long-short anomaly portfolio return.

Long-short anomaly portfolio returns also show stronger predictive power for the monthly market excess return than popular predictors from the literature for the 1985:01 to 2017:12 out-of-sample period. Table IA.VI in the Internet Appendix reports $$ statistics for univariate predictive regression forecasts based on 16 popular predictors, including a variety of economic variables (e.g., valuation ratios, interest rates, interest rate spreads, and inflation) from Goyal and Welch (2008) and technical indicators from Neely et al. (2014).23 Among the 16 predictors, three produce a positive $$ statistic: the 10-year Treasury bond yield (0.54%, significant at the 10% level) and two of the technical indicators, MA(1,12) and MOM(6) (0.45% and 0.19%, respectively). When we aggregate the information in the 16 predictors using the methods in Section II.A, only the simple combination forecast outperforms the prevailing mean benchmark ($$).24 Hence, these predictors appear less useful than long-short anomaly returns for predicting the market excess return.

To directly compare the information in the popular predictors to that in the long-short anomaly returns, Table IA.VIII in the Internet Appendix reports Harvey, Leybourne, and Newbold (1998) forecast encompassing test results for monthly market excess return forecasts based on the two sets of predictors. Forecasts based on the popular predictors do not encompass those based on the long-short anomaly returns, and thus the anomaly returns contain information useful for forecasting the monthly market excess return beyond that contained in the popular predictors. The information content of long-short anomaly returns therefore appears quite different from that of popular predictors from the literature.25 Moreover, as shown in Table II and Figure 2, the differential information in long-short anomaly returns delivers statistically and economically significant out-of-sample gains.

The out-of-sample predictive ability of long-short anomaly portfolio returns at longer horizons is also of interest. Table IA.X in the Internet Appendix reports $$ statistics for market excess return forecasts based on the 100 anomalies for horizons of two, three, six, and 12 months.26 Predictability tends to fall as the horizon increases, and we find no significant evidence of predictability at the 12-month horizon. The results are consistent with our economic explanation, as we expect the mispricing related to anomalies to correct reasonably quickly, so that long-short anomaly returns are primarily short-horizon predictors.

As an external validity test, we examine the out-of-sample predictive ability of long-short anomaly portfolio returns for industry excess returns.27 Specifically, we consider five industry portfolios (spanning the market) from Kenneth French's Data Library: Consumer, Manufacturing, Hi-Tech, Health, and Other.28 Table IA.XI in the Internet Appendix reports $$ statistics for the five industry excess returns. The conventional OLS forecast continues to perform poorly, as the $$ statistics are negative and large in magnitude for all of the industries. As with the market excess return, the forecasting strategies designed to guard against overfitting perform substantially better, producing positive $$ statistics for three to five of the industries. For these strategies, 21 of the 30 $$ statistics are significant at conventional levels. Out-of-sample return predictability is especially strong for Consumer, Manufacturing, and Other, and a number of the $$ statistics are above 3% for these industries.29 The results for the industry excess returns provide further evidence that long-short anomaly portfolio returns are genuine predictors of the market excess return.

As a final assessment of out-of-sample return predictability in this section, we explore the effects of the selection of the long-short portfolio returns used to forecast the market excess return.30 We begin with a set of more than 18,000 long-short portfolio returns from Yan and Zheng (2017), which are constructed by sorting on individual firm characteristics from Compustat.31 From the complete set of long-short portfolio returns, we form two subsets with insignificant and significant alphas.32 Based on the evidence in Yan and Zheng (2017), long-short portfolio returns with highly significant alphas are likely to be meaningful anomalies and not the result of data mining. We randomly draw two groups of 100 long-short portfolio returns from the respective subsets. For each group, we generate out-of-sample market excess return forecasts beginning in 1985:01 using the predictor average and compute the $$ statistics. Repeating this process 1,000 times generates empirical distributions for the $$ statistics for market excess return forecasts based on randomly selected groups of 100 insignificant and significant long-short portfolio returns.

Figure 3 presents histograms for the $$ statistics for the two subsets of long-short portfolio returns. The $$ statistics corresponding to the significant long-short portfolio returns are clustered to the right of those for the insignificant long-short portfolio returns. The difference between the two distributions' means (1.91) is significant at the 1% level. The histograms in Figure 3 indicate that groups of significant long-short portfolio returns generally improve out-of-sample market excess return forecasts. Overall, groups of long-short portfolio returns that are significantly more likely to constitute anomalies appear more informative for predicting the market excess return, providing further evidence for the importance of anomalies.

A. Slope Coefficients

We first examine recursive estimates of the slope coefficients in the predictive regressions underlying the predictor average, principal component, and PLS forecasts. These predictive regressions provide a convenient means for capturing the information in all 100 of the long-short anomaly portfolio returns in a single slope coefficient.

Panels (a) to (c) of Figure 4 depict recursive estimates of the standardized slope coefficients in equation (35) and their 90% confidence intervals when the explanatory variable is $$, $$, and $$, respectively.33 The recursive estimates are always negative, consistent with stronger MCP for overpricing vis-à-vis underpricing. As expected, the 90% confidence intervals tend to narrow as the estimation sample lengthens. For the predictor average (principal component) regression, the recursive estimates become significant starting in the mid-to-late 1990s (early 2000s) and remain significant thereafter; for the PLS regression, the recursive estimates are always significant. The recursive estimates are quite stable in all three panels of Figure 4 from the early to late 2000s. They then become larger in magnitude around the Global Financial Crisis and concomitant Great Recession and remain relatively stable thereafter, suggesting that asymmetric limits of arbitrage have not substantially diminished in importance since the early 2000s.34

B. Market Segments

According to the intuition in Section I, an important part of the predictive ability of long-short anomaly portfolio returns stems from their lead-lag covariances with segments of the market return. To obtain insight into this mechanism, we examine the cross-autocovariances between long-short anomaly portfolio returns and decile excess returns. This allows us to investigate the relevance of the information contained in long-short anomaly returns for different segments of the market related to the anomalies.

To incorporate information from the entire group of 100 anomalies and construct market segments without overlapping stocks, we proceed as follows.35 For a given month, we sort stocks according to each anomaly characteristic (considered in turn). For each stock, we then take the average of its ranks across the anomalies; we take the average of the ranks to account for the fact that some stocks have missing observations for some characteristics in a given month. We then sort stocks into value-weighted decile portfolios according to their average ranks, with the first (tenth) decile constituting the most overvalued (undervalued) stocks. The long-short portfolio again goes long (short) the tenth (first) decile portfolio.

Panel (a) of Figure 5 plots estimates of $$ for the decile excess returns, indexed by $$. The cross-autocovariances are all negative. The first decile excess return ($$) displays the largest covariance in magnitude with $$, so that MCP appears most relevant in the short leg. Nevertheless, the covariances of many of the other decile excess returns with the lagged long-short anomaly return are often significant at conventional levels, so that the mispricing detected in the long-short anomaly return has important implications for the market more broadly. The magnitudes of the cross-autocovariances tend to decrease from the first to the tenth deciles, and the cross-autocovariance for the tenth decile excess return ($$) is the smallest in magnitude (and statistically insignificant). Lagged long-short anomaly returns thus appear more relevant for segments of the market that contain stocks that are relatively more overpriced on average according to the anomalies, consistent with asymmetric limits of arbitrage.36

To further explore the relevance of overpricing correction persistence, we examine return predictability for portfolios of stocks that are most overvalued according to the predictor average.38 The predictor average (i.e., the cross-sectional average of the long-short anomaly portfolio returns) for a given month is effectively a portfolio of all of the individual available stocks for the month (although some stocks may receive zero weights). Each month, we back out the portfolio weights corresponding to the predictor average and sort stocks according to the predictor average weights. We then form a portfolio (NEG10-PA) that consists of the 10% of stocks with the largest negative weights (in magnitude) in the predictor average portfolio; the weights for the stocks in the NEG10-PA portfolio are proportional to the absolute values of their weights in the predictor average portfolio. Based on a univariate predictive regression, we then use the excess return on the NEG10-PA portfolio to predict the excess return on a portfolio of the same stocks with the same weights in the next month. For the 1985:01 to 2017:12 out-of-sample period, the $$ statistic for the predictive regression forecast is 1.87%, which is significant at the 5% level. We then repeat the same analysis using the same 10% of stocks each month, but instead use portfolio weights proportional to market capitalization. The $$ statistic in this case is nearly a third smaller (0.65%) and insignificant at conventional levels. In sum, we find stronger out-of-sample return predictability for a portfolio of overvalued stocks (as detected by the predictor average) when we weight the stocks according to their relative importance in the predictor average portfolio rather than simply by their market capitalization. This result indicates that the information in the long-short anomaly portfolio returns is linked to overpricing correction persistence.

C. Subgroups

In this section, we generate out-of-sample forecasts based on subgroups of anomalies formed according to proxies for asymmetric limits of arbitrage.39 We form subgroups based on three proxies: bid-ask spread (BA), idiosyncratic volatility (IDIO), and market capitalization (SIZE).40 For a given month and anomaly characteristic, we first sort stocks into deciles as described in Section III and compute the average values for a given proxy for the stocks in the long and short legs. We then compute the long-leg average value for the proxy minus the short-leg average value for the proxy for each month. Finally, we compute the time-series average of the differences for 1970:01 to 1984:12. We denote the time-series averages for the differences for the bid-ask spread, idiosyncratic volatility, and size proxies by DTSA-BA, DTSA-IDIO, and DTSA-SIZE, respectively.

We form the subgroups BA-NEG, IDIO-NEG, and SIZE-NEG (BA-POS, IDIO-POS, and SIZE-POS), which are the subgroups of anomalies for which DTSA-BA, DTSA-IDIO, and DTSA-SIZE, respectively, are negative (positive). In line with our out-of-sample focus, we exclude data from the forecast evaluation period when determining the subgroups.41 Stocks with larger bid-ask spreads, greater idiosyncratic volatility, and smaller market capitalization are typically viewed as having stronger limits of arbitrage. We therefore expect greater market return predictability based on BA-NEG, IDIO-NEG, and SIZE-POS compared to BA-POS, IDIO-POS, and SIZE-NEG, respectively, as the former three subgroups represent anomalies with asymmetrically strong limits of arbitrage in their short legs vis-à-vis their long legs. To combine the information in the different proxies, we also form a subgroup that is the union of the anomalies in BA-NEG, IDIO-NEG, and SIZE-POS, as well as a subgroup that comprises the complement of the union. We expect the union subgroup to have stronger predictive ability relative to its complement.

Table III reports $$ statistics for the different subgroups using the strategies designed to guard against overfitting.42 Although the bid-ask spread, idiosyncratic volatility, and size are quite noisy proxies for limits of arbitrage, the results generally support the relevance of asymmetric limits of arbitrage and stronger MCP for overpricing vis-à-vis underpricing. For example, Panel A reports results for the two subgroups formed using the bid-ask spread. The $$ statistics for the BA-NEG subgroup are all positive and sizable in magnitude, well above the Campbell and Thompson (2008) threshold for economic significance. The $$ statistics for the ENet, C-ENet, and PLS forecasts are particularly large (3.57%, 3.65%, and 2.94%, respectively). All six of the forecasts based on the BA-NEG subgroup are significant at conventional levels according to the Clark and West (2007) statistics. For each forecasting strategy, the $$ statistic for the BA-POS subgroup is always lower than the corresponding statistic for the BA-NEG subgroup. Two of the $$ statistics for the BA-POS subgroup are negative, and only two are above the 0.5% threshold. The results in Panel A align with the intuition in Section I, with relatively stronger limits of arbitrage in the short leg producing greater market return predictability. The results for the subgroups based on idiosyncratic volatility and size in Panels B and C, respectively, deliver similar messages as those for the subgroups based on the bid-ask spread in Panel A. Panel D of Table III reports $$ statistics for the union of the BA-NEG, IDIO-NEG, and SIZE-POS subgroups. All of the $$ statistics for the union subgroup are statistically and economically significant. For the complement subgroup, five of the $$ statistics are negative, and the positive statistic is neither statistically nor economically significant. Continuing the pattern in Panels A to C, the $$ statistics for the subgroup that we expect to have stronger predictive ability (union) are always larger than the corresponding statistics for the subgroup that we expect to have weaker predictive ability (complement).

We also form subgroups via a double sort to identify subgroups of anomalies with both high limits of arbitrage overall and high asymmetric limits of arbitrage with respect to their short legs. To do so, for BA, we first identify anomalies with relatively low and high average values for the proxy for the stocks in their long and short legs (BA-LOW and BA-HIGH, respectively). For each of the BA-LOW and BA-HIGH subgroups, we then form NEG and POS subgroups as described above, resulting in four subgroups based on BA (BA-LOW-NEG, BA-LOW-POS, BA-HIGH-NEG, and BA-HIGH-POS). For compactness, we take the union of the BA-LOW-NEG, BA-LOW-POS, and BA-HIGH-POS subgroups to form the BA-REST group. We then compare the results between the BA-HIGH-NEG and BA-REST subgroups. In a similar manner, we form IDIO-HIGH-NEG and IDIO-REST (SIZE-LOW-POS and SIZE-REST) subgroups based on IDIO (SIZE). We expect the BA-HIGH-NEG, IDIO-HIGH-NEG, and SIZE-LOW-POS subgroups to exhibit stronger predictive ability compared to the BA-REST, IDIO-REST, and SIZE-REST subgroups, as the former three subgroups are the anomalies with both high limits of arbitrage overall and high asymmetric limits of arbitrage with respect to their short legs. As shown in Table IA.XIV in the Internet Appendix, this is indeed what we find.

D. Market Frictions

As Gârleanu and Pedersen (2013, 2016) and Dong, Kang, and Peress (2020) argue, frictions such as limited risk-bearing capacity and transaction costs induce arbitrageurs to slowly respond to mispricing, resulting in MCP. If our predictability finding is driven by arbitrageurs slowly correcting mispricing in the presence of asymmetric limits of arbitrage and stronger MCP for overpricing vis-à-vis underpricing, then long-short anomaly portfolio returns should contain more relevant information for predicting the market excess return during times of high frictions. We investigate this issue by testing for an increase in the $$ statistic during periods of high frictions using equation (29).

We consider a variety of proxies for market frictions from the literature. We begin with the level of and innovations to aggregate liquidity from Pástor and Stambaugh (2003). We also consider idiosyncratic volatility, which is widely believed to be a major implementation cost of short arbitrage (e.g., Pontiff (2006)). We measure aggregate idiosyncratic risk for a given month by first calculating the idiosyncratic volatility of individual stocks following Ang et al. (2006) and then computing the value-weighted average of the idiosyncratic volatilities for the individual stocks. Furthermore, we use trading noise (Hu, Pan, and Wang (2013)), which tracks the shortage in arbitrage capital via noise in Treasury security prices, and short fees (Asness et al. (2018)), which measure the cost of shorting stocks. For the latter, we again aggregate to the market level by computing the value-weighted average of short fees for individual stocks.43

In addition to the above variables, we consider risk, uncertainty, and risk aversion indices as proxies for the frictions affecting the risk-bearing capacity of arbitrageurs. Along with the VIX, we use macroeconomic, financial, and real uncertainty indices from Jurado, Ludvigson, and Ng (2015), who construct the indices by estimating stochastic volatility series for the residuals from fitted dynamic diffusion-index models based on macroeconomic and financial variables. Finally, we consider the jointly estimated economic uncertainty and risk aversion indices from Bekaert, Engstrom, and Xu (2021). For all of the proxies, we separate high- and low-friction regimes using the sample median.

Table IV reports differences in $$ statistics (in percentage points) between high- and low-friction regimes for market excess return forecasts based on the 100 long-short anomaly portfolio returns. In support of the relevance of asymmetric limits of arbitrage and stronger MCP for overpricing relative to underpricing, the $$ statistics are almost always higher during high-friction periods, and the vast majority of the increases are significant according to the augmented Clark and West (2007) test. Furthermore, the magnitudes of the increases in the $$ statistics are economically sizable, exceeding 10 percentage points for some of the forecasts for frictions proxied by liquidity innovations, trading noise, and short fees.

E. Arbitrage Trading

Next, we examine whether long-short anomaly portfolio returns predict arbitrageurs' trading in the broad market and the tone of market-wide news. If the overpricing correction signaled by long-short anomaly returns during month $$ is only partial and continues to spread throughout the market in the subsequent month, then we expect an increase in long-short anomaly returns in month $$ to lead to a reduction in arbitrageurs' net positions (i.e., long minus short positions) in the broad market in month $$, which is likely to be driven primarily by an increase in their short positions; we also expect more negative market-wide news tone in month $$.

We first examine changes in arbitrageurs' aggregate net position in the broad market, where we follow Chen, Da, and Huang (2019) in constructing the net arbitrage trading measure. Specifically, we compute aggregate value-weighted long positions for hedge funds across all stocks in the market, where hedge funds' long positions in individual stocks are based on quarterly reported holdings in the 13F database. Agarwal et al. (2013) identify hedge funds by combining the information in the 13F database and five hedge fund databases. The 13F holdings data cover the largest number of institutional investors, as all institutional investment managers that have discretion over $100 million or more in Section 13(f) securities need to report their quarter-end holdings in these securities. A 13F-filing institution is classified as a hedge fund if its major business is sponsoring and/or managing hedge funds according to information from various sources (such as institution websites, SEC filings, industry publications, and news articles). Our final sample consists of 1,710 unique hedge funds.44 We construct the value-weighted short-selling positions across all stocks in the market by aggregating short interest in individual stocks. A stock's short interest in a month is the total number of uncovered shares sold short for transactions settled on or before the 15th of the month (from Compustat) divided by the total number of shares outstanding (from CRSP). We use short interest from the last month of each quarter to match the quarterly data frequency for hedge-fund holdings. The sample period covers 1980:1 to 2017:4.

Since hedge funds' aggregate long positions and short interest display trends, we compute deviations in the long positions of hedge funds and short interest from trailing four-quarter MAs. Chen, Da, and Huang (2019) show that the difference between the long and short arbitrage trading measures (i.e., net arbitrage trading) effectively aggregates the actions of arbitrageurs.

Table V reports standardized slope coefficient estimates for predictive regressions that relate quarterly arbitrage trading measures to lagged long-short anomaly portfolio returns, where we use long-short anomaly returns from the last month in the quarter. As in Section V.A, to capture the aggregate information across the 100 anomalies in a single slope coefficient, we estimate predictive regressions with $$, $$, and $$ serving as the predictor (considered in turn). The estimates for the net market position regressions in the second column are all significant (at the 5% or 1% level). The estimates are all negative, which implies that an increase in long-short anomaly returns leads arbitrageurs to decrease their net positions in the market. The coefficient estimates are also economically sizable: A one-standard-deviation increase in the predictor corresponds to a 4.81% to 5.81% reduction in the net arbitrage market position (in terms of value-weighted shares outstanding).

The third and fourth columns of Table V report results for arbitrageurs' long and short positions, respectively. The coefficient estimates are all negative (positive) for the long (short) trading measure, indicating that arbitrageurs reduce (increase) their long (short) positions in the market in response to an increase in long-short anomaly returns. The estimates are all significant at the 5% level for the regressions for the short market position, while they are all insignificant for the regressions for the long market position. Comparing the results in the third and fourth columns, the coefficient estimates are larger in magnitude for the short side than for the long side, consistent with stronger MCP for overpricing. Decomposing the net change in the second column, approximately one-third comes from declines in long positions and two-thirds from increases in short positions.

Finally, the last column of Table V reports predictive regression results for monthly U.S. financial market news tone. The news tone measure, from Calomiris and Mamaysky (2019), is based on English-language news articles from Thomson Reuters. Monthly news tone is an aggregation of differences in word tone among news articles on the topic of U.S. financial markets. We detrend news tone by computing deviations from a trailing 12-month MA. To incorporate information from the 100 anomalies into a single slope coefficient, we again estimate predictive regressions with $$, $$, and $$ serving as the predictor (considered in turn). We standardize both the dependent variable and the predictor before estimating the predictive regressions. The sample period is 1996:01 to 2017:12.45

To the extent that asymmetric limits of arbitrage generate relatively strong overpricing correction persistence, we expect an increase in long-short anomaly returns to lead to more negative market-wide news tone in the next month; in other words, public news is more likely to confirm that shares were broadly overvalued. The results in the last column of Table V support this conjecture. The coefficient estimates are all significantly negative (at the 1% level), and the economic magnitudes are sizable: A one-standard-deviation increase in the predictor results in a 0.32- to 0.36-standard-deviation drop in market news tone. Overall, the results in Table V are consistent with the view that long-short anomaly portfolio returns predict market returns because arbitrageurs slowly correct market-wide overpricing.