The Trend in Firm Profitability and the Cross Section of Stock Returns

The Trend in Firm Profitability and the Cross Section of Stock Returns Ferhat Akbas School of Business University of Kansas 785-864-1851 Lawrence, KS 66045 akbas@ku.edu Chao Jiang School of Business University of Kansas 785-864-7698 Lawrence, KS 66045 chaojiang7@ku.edu Paul D. Koch School of Business University of Kansas Lawrence, KS 66045 785-864-7503 pkoch@ku.edu December 2013 Preliminary. Please do not quote without permission.

The Trend in Firm Profitability and the Cross Section of Stock Returns Abstract This study shows that the recent path of a firm s profitability predicts firm performance and stock returns. Stocks with higher momentum in profitability tend to experience higher profitability and stock returns in the future. The predictive information contained in the recent trend of profitability is incremental beyond that provided by the current level of the firm s profits, and it is not subsumed by other well-documented determinants of returns in the cross-section. Our results are consistent with a risk-based explanation for this trend effect, based on the dividend discount model of Fama and French (2006, 2013), who argue that holding market value fixed, firms with higher expected profits should command higher expected returns. Key Words: market efficiency, anomalies, gross profitability, asset pricing, underreaction. JEL Classification: G12, G14. 1

1. Introduction Emerging literature establishes that a firm s profitability is a significant determinant of future stock returns. For example, Novy-Marx (2012) shows that firms with a high level of gross profitability significantly outperform unprofitable firms. Fama and French (2013) argue that current profitability is a good proxy for expected future profitability, and it thus serves to predict future returns according to the dividend discount model. 1 Another way to interpret these findings is that profitability is a good measure of the productivity of a firm s assets, and investors demand a higher return for firms with higher productivity. Overall, the recent literature provides convincing evidence that selecting firms with a higher level of current profitability is an effective strategy for choosing stocks with more promising growth prospects. This study argues that we must consider the firm s current level of profitability in the context of recent trends in its profitability, in order to have a more complete picture of its prospects for future performance. Current gross profits reflect a firm s current productivity and health in the context of the current competitive environment for its product markets. However, this environment is not static. Over time, firms experience ups and downs in the flow of their performance due to swings in their own competitive position, as well as the overall competitive environment of the product markets in which they participate. Although the level of current profitability is an effective signal of future growth prospects, these prospects for future performance also likely depend on the recent path of the firm s profitability. The following example illustrates our point. Consider two firms with similar levels of current gross profitability. Firm A has a long history of high profitability but, due to recent 1 This model is also illustrated in Fama and French (2006) using earnings rather than profitability. In the dividend discount model, a stock s price equals the present value of its expected dividends, while under clean surplus accounting the change in book equity equals retained earnings. This model suggests that higher valuation implies lower expected returns, while higher expected profitability implies higher expected returns. 2

changes in product market conditions, it is losing its competitive advantage and its profitability has been trending downward. On the other hand, firm B has made recent technological innovations that have given it a competitive advantage in the product market. As a result, firm B has been ramping up its productivity and its profitability is trending upward. If we only compare the current level of profitability for firms A and B, this comparison ignores information about the context in which those profits are generated. If we do not consider the divergent recent trends in profitability for these two firms, then we cannot see that the growth prospects for B are greater than for A. In this light, we conjecture that firms with a higher trend in profitability will outperform those with a lower trend, controlling for the level of profitability. We test this conjecture by analyzing whether the recent trend in a firm s profitability provides incremental predictive information about future stock returns, beyond that contained in the current level of profitability. Following Novy-Marx (2012), we consider gross profitability as the appropriate measure of the firm s profitability, since it represents the cleanest accounting measure of true economic profitability. We estimate the recent trend in profitability each quarter by regressing the firm s current gross profitability on a time trend and a constant, using the past 8 quarters of data. 2 The coefficient of the trend is our measure of recent momentum in the firm s profitability. A larger value for this trend coefficient indicates that the firm has recently experienced a higher trajectory in its profitability growth, likely due to improvements in its competitive position and productivity in the context of the product markets in which it competes. Our results indicate that the recent trend in firm profitability provides positive and significant incremental predictive information about future returns, beyond that included in the level of profitability. A hedge portfolio strategy based on going long stocks with the highest trend in profits each quarter, and shorting stocks with the lowest trend, yields a risk-adjusted 2 We have also measured the trend in profitability using the past twelve quarters, and we find similar results. 3

return of roughly 1% per month. This trend effect represents an incremental predictive yield that is approximately two thirds of the magnitude of that provided by the current level of profitability. The trend effect is larger in magnitude for small stocks, but it also appears in large stocks, indicating that this behavior is not limited to a small stock phenomenon. Throughout this study, the trend effect is robust to controlling for the level of profitability, and it is not subsumed by other well-documented determinants of returns in the cross-section. In particular, our results are robust to controlling for the firm s past price performance, book-tomarket ratio, return volatility, turnover, institutional ownership, the number of analysts, and market liquidity. Our results show that, in addition to the level of profitability, the trend in profitability also contains valuable information about future firm performance and stock returns. As discussed above, one interpretation of our findings is that higher recent momentum in profitability signals higher expected productivity and profitability, beyond that indicated by the current level of profitability. As a result, the trend in profitability is positively related to expected firm performance and thus returns, consistent with the dividend discount model of Fama and French (2006, 2013). According to Fama and French (2013), this higher return could be due to two reasons. First, the trend in gross profits may be associated with some unknown risk factor beyond the market return, firm size, and book-to-market ratio. According to this interpretation of our results, there is no mispricing of current stock prices implied for firms with a higher trend in profitability. The future higher return that we document for these firms is simply a reflection of higher risk. We refer to this explanation as the risk-based explanation. Second, the predictive power of the profitability trend could arise from a slow market correction of short run irrational mispricing that might be related to a firm s trend in profitability. 4

For example, while we show that the recent trend in a firm s profitability has an important bearing on the future prospects for profitability, investors may fail to properly account for these prospects for performance. As a result, investors may underreact to the information embedded in a higher trend in profitability, so that prices become undervalued. Ultimately, however, the future performance signaled by the recent trend manifests itself, causing prices to continue to move in the same direction as the trend in profitability over time. Of course, it is also possible that investors could overreact to the trend in gross profits due to behavioral biases. Empirically, we find significant positive predictive power for the trend in profitability regarding both future firm performance and stock returns. If rational investors use the trend in profitability as a metric to help form their expectations about the firm s future performance, then we should observe such a link between this trend and future profitability. Our evidence that the trend in profitability significantly predicts both performance and stock returns lends credence to this rationale for investors to rely on this trend to form their expectations about the firm s future performance. Furthermore, we show that the positive return following a high trend in profitability is not followed by a substantive return reversal in subsequent periods. This evidence suggests that the ultimate change in stock prices predicted by the recent trend in profitability tends to be permanent, rather than a temporary manifestation of irrational over-valuation caused by overreaction of investors to recent trends in profitability. On the other hand, we do not find strong evidence that investors are positively surprised by future earnings that can be predicted by the past gross profit trend. In addition, the previous literature argues that mispricing should correlate with overconfidence (e.g., see Cooper, Gutierrez, and Hameed, 2004). Again, we do not 5

find any evidence of such correlation. Therefore, our results are more consistent with the riskbased mechanism, and less consistent with the underreaction or overreaction channels. The remainder of the paper is organized as follows. Section 2 summarizes the literature. Section 3 discusses the data and research methodology. We present portfolio analysis of the association between the trend in profitability and stock returns in section 4. We analyze long run performance in section 5. Fama-MacBeth regression analysis is provided in section 6. We present extensions and robustness tests in section 7. Section 8 empirically analyzes alternative theoretical mechanisms that might help to explain the trend effect. A final section concludes. 2. Literature Review on the Profitability Anomaly Previous literature documents that more profitable firms tend to earn higher future stock returns. Haugen and Baker (1996) argue that more profitable firms have more potential for future growth, and they find positive correlation between profitability and future stock returns. Cohen and Gompers (2002) confirm the above finding and also find that high past profitability, high past stock returns, and institutional ownership predict high future profitability. Fama and French (2006, 2013) use valuation theory to show that, controlling for the firm s book-to-market and expected investment, more profitable firms have higher expected returns. In their dividend discount model, the market value of a firm is the present value of future cash flows, which are expected dividends. Holding everything else constant, higher expected profitability indicates more future cash flows, leading to a higher net present value of the firm. If two firms with different prospects for expected profitability have the same current market value, then the stock with higher profitability must have a higher expected return (or discount rate). If pricing is rational, the higher expected return must indicate higher risk. Fama and French (2006) 6

predict future profitability using past firm information and show that the predicted profitability is positively associated with future stock returns. On the other hand, using equity income scaled by book value as a measure of profitability, Fama and French (2008) conclude that the profitability anomaly is less robust when compared to others, including net stock issues, accruals, and momentum. Novy-Marx (2013, p.2) argues that gross profit represents a better proxy of profitability than equity income, because gross profit is the cleanest accounting measure of true economic profitability, and the further down the income statement one goes, the more polluted profitability measures become. Novy-Marx shows that the gross profit anomaly is both statistically and economically strong. Motivated by Novy-Marx (2013), Fama and French (2013) develop a five-factor asset pricing model, which extends their well-known three factor model by including a profitability factor and an investment factor. They find that the GRS test (see Gibbons, Ross, and Shanken, 1989) rejects the validity of their 5-factor model which is directed at capturing patterns in returns that are due to profitability and investment, in addition to the normal three Fama-French factors. However, their model provides an acceptable of average returns regarding portfolios sorted based on firm size, along with one or two of the other factors, Book-to-Market, Profitability, or Investment. Their analysis motivates further study on the nature and extent of the profitability anomaly. 3. Data and Methodology Our sample includes the common shares (share code 10 and 11) on all NYSE, AMEX, and NASDAQ stocks from CRSP. We exclude financial firms (the four-digit SIC code in the 6000 s) and utility firms (the four-digit SIC code in the 4900 s). We require firms to have a positive book-to-market (BK) ratio. We also restrict the sample to firm-month observations with 7

stock prices above one dollar. 3 The sample period extends from July 1980 through December 2011. Our sample begins in July 1980 due to the availability of data on institutional ownership. Following Novy-Marx (2013), we calculate quarterly gross profit (GPQ) as quarterly sales (item SALEQ) minus quarterly cost of goods sold (item COGSQ) scaled by assets (item ATQ). We estimate the trend of GPQ (TRENDGPQ) for firm i in quarter q, by estimating the following trend regression each quarter: ( ). (1) In other words, we run a rolling window regression of GPQ on a deterministic time trend variable covering the previous eight quarters. The trend of GPQ (TRENDGPQ) for firm i in quarter q is the coefficient,, from the above regression model. We also compute a moving standard deviation of GPQ over the previous eight quarters covering quarter q-7 to quarter q (MOVSTDGPQ). Our remaining control variables include the natural log of the book-to-market ratio (LOGBK), the volatility of past stock returns (STDRET), share turnover (TURNOVER), the Amihud (2002) illiquidity measure (MEANAMI), the natural log of the firm s market capitalization (LOGMKTVALUE), institutional ownership (IO), the number of analysts (NUMEST), and cumulative stock returns over the past 6 months (RET6M) and the past 3 years (RET36M). Please see Appendix I for details regarding the description and construction of all variables used in this paper. For each month (t), we match the stock price information from CRSP with annual accounting data that are 7 to 18 months old, along with the most recent publicly available quarterly accounting data determined by the public earnings announcement month (item RDQ) in Compustat. To be conservative and to ensure that our results are robust, we skip one month 3 We have also restricted the sample to all stocks priced above five dollars, with similar results. 8

between the portfolio formation month and the holding month when we measure future returns. For example, for our portfolio approach, we form portfolios based on information in month t. Then, starting from the beginning of month t+2, we hold the portfolio for one month. Similarly, for the Fama-MacBeth regression analysis, in each moth (t), we run the following regression: (2) Tables 1 and 2 present the time series averages of the cross-sectional summary statistics and correlations, respectively. In our sample, the monthly average raw stock return is about 1.3%. Firms operate with a mean gross profit margin of 10%. The average trend in gross profits is approximately zero indicating that gross profits tend to be flat over the previous eight quarters. On the other hand, there is significant variation in this trend across firms, ranging from a growth rate of -2.2% to +2.4% per quarter. The mean firm size is $1.6 Billion, while the median size is $200 Million. Institutional investors own 41% of the average company, and there are roughly five analysts following the typical firm. According to Table 2, the average correlation between the current level and the recent trend in gross profitsl (GPQ and TRENDGPQ) is 0.21. This evidence indicates that the recent trend in gross profits provides substantive new information beyond that present in the current level of gross profit. Similar to Novy-Marx (2013), we also show that the level of gross profits is negatively correlated with the book-to-market ratio (the correlation of -0.26 from Table 2 is comparable to the value of -0.18 from Novy-Marx, 2013). In contrast, the correlation between the trend in gross profits and the book-to-market ratio is smaller in magnitude, although it is also 9

negative. As expected, the level of gross profits is highly autocorrelated. The correlation between GPQ t and GPQ t-1 (LAG1GPQ) is 0.91. This autocorrelation reflects substantial persistence in gross profits over time. Finally, the moving standard deviation of GPQ (MOVSTDGPQ) is positively correlated with the current level of GPQ (0.25). 4. Portfolio Approach For each month (t), we sort the stocks into deciles based on the most recent publicly available information on the quarterly level or trend in gross profits. Once again, we skip one month between the portfolio formation period and the holding period. Starting from the beginning of month t+2, we hold the portfolio for one month to obtain our measure of the future returns one month later (LEADRET2). We report the portfolio returns in Table 3. We first replicate the findings in the previous literature on the gross profit anomaly, and present the results in the first two rows of Table 3. Consistent with previous research, we find that the most profitable firms outperform the least profitable firms. The most profitable firms (Decile 10) outperform the least profitable firms (Decile 1) by an equally-weighted monthly raw return of 1.35%. We next perform the same analysis for the trend in gross profits, and report the results in the last two rows of Table 3. The long-short hedge portfolio that is based on going long firms with the highest trend (Decile 10) and short firms with the lowest trend (Decile 1) earn an equally-weighted monthly raw return of 0.99%. The Fama-French three factor model alpha for monthly returns on this long-short hedge portfolio based on the trend is 1.02%. The value-weighted results are also economically and statistically significant. Overall, the magnitude of the trend effect is comparable with the impact of the level of gross profits documented in previous research. 10

Next, we distinguish between the gross profit trend anomaly and the gross profit level anomaly by forming portfolios using on a two-way sorting scheme based on both the level and the trend in profitability. Specifically, we first sort the stocks into terciles by the level of gross profits. Then, within each tercile, we independently sort the stocks into quintiles by the trend in gross profits. Panel A of Table 4 shows both the raw average returns and Fama-French three factor model alphas for the resulting two-way sorted portfolios. Note that the level of gross profits increases as we move from left to right horizontally, and the trend in gross profits increases as we go from the top to the bottom. The results show that neither anomaly is subsumed by the other. We find that future returns increase significantly with the trend in profits within all terciles based on the level of profits. We also perform two-way sorting analysis based on the trend in gross profits, along with other attributes of the firm. Specifically, we replace the level of gross profits in the sorting scheme from Panel A of Table 4 by either firm size (MKTVALUE) or book-to-market (BK), in Panels B and C, respectively. Panel B indicates that the gross profit trend anomaly remains both economically and statistically significant within all three terciles by firm size. For small stocks, the long-short hedge portfolio based on the trend in profits earns an equally-weighted monthly raw return of 1.01% per month. For large stocks, this number is smaller, but still significant, at 0.35% per month. The Fama-French three factor alphas for the monthly returns on these hedge portfolios based on small, medium, and large stocks reveal the same pattern. Therefore, the trend effect appears in both small stocks and large stocks, indicating that this behavior is not limited to a small stock phenomenon. Finally, in Panel C we provide the analogous evidence regarding the trend anomaly while controlling for the book-to-market ratio (BK). Once again, the trend effect appears in all three book-to-market subgroups. Overall, the two-way sorting analysis shows that 11

the predictive power of the trend in gross profits is not subsumed by the level of gross profits, firm size, or book-to-market ratio. 5. Fama-MacBeth Regression Approach The one- or two-way sorting schemes behind the portfolio approach are only capable of capturing limited dimensions of the firm that could affect future stock returns. It is possible that the trend in gross profits is associated with several other previously documented factors that also predict future stock returns. If this is the case, the results from the portfolio approach provided above may just be replicating previous findings. We attempt to rule out this possibility by performing further tests using Fama-MacBeth regressions to control for other well-known factors related to future stock returns, including the level of gross profits, book-to-market, past stock return volatility, turnover, illiquidity, firm size, institutional ownership, the number of analysts, medium term past stock returns, long term past stock returns, and the volatility of gross profits over the previous 8 quarters. The results are presented in Table 5 for the analysis of future returns over several time frames. The dependent variables analyzed include the monthly return in the leading month t+2 (LEADRET2), three-month cumulative returns from month t+2 through t+4 (LEADRET2_4), and the six-month cumulative returns from month t+8 through t+13 (LEADRET8_13). These results are provided in the left, the middle, and the right panels of Table 5, respectively. The coefficient of the trend in gross profits (TRENDGPQ) is significant in all specifications, although the coefficients become smaller in magnitude when we control for the level of gross profits. In terms of economic significance, for the second regression on LEADRET2 (column 2 of Table 5), a one standard deviation increase in the trend of gross profit leads to a 0.22% 12

increase in the future one-month return in period t+2. 4 Similarly, for the third regression on LEADRET2 (column 3 of Table 5), a one standard deviation change in the trend leads to 0.15% increase in monthly returns. 5 The results for the other control variables are generally consistent with previous findings. The gross profit level (GPQ) is significant in all specifications, and across all different holding periods analyzed in Table 5. Stocks with high book-to-market ratios tend to earn higher future stock returns. Higher volatility of past stock returns predicts lower future stock returns. Similar to Amihud (2002), we find that stock returns increase in illiquidity. Consistent with the welldocumented size and momentum anomalies, small stocks and winners in the past 6 months experience higher future stock returns. Overall, the Fama-MacBeth regression results are consistent with those from the portfolio approach in section 4, indicating that firms with a higher trend in gross profits outperform those with lower trend. 6. Long Term Performance In this section, we analyze the long run profitability of the trading strategy based on the trend in gross profits. The positive returns on the long-short hedge portfolio documented above could be due to investor overreaction, underreaction, or risk. This analysis will help to inform us about whether this behaviori results from investor underreaction or overreaction. For example, if we find no long run reversal of the long-short hedge portfolio returns, such an outcome would be less consistent with the investor overreaction mechanism. We first analyze the long term performance of the hedge portfolio based on the level of gross profits, after which we provide similar analysis for the hedge portfolio based on the trend in gross profits. In this analysis, we first sort the stocks in month t=0 into deciles, based on the 4 This result is obtained by multiplying one standard deviation in the trend by the coefficient: 0.648%*0.347=0.22%. 5 This result is obtained by multiplying one standard deviation in the trend by the coefficient: 0.648%*0.235=0.15%. 13

available information regarding the level or trend in gross profits. Then, we analyze the returns of the resulting hedge portfolios starting from three years prior to portfolio formation (in month t=-36) and continuing through five years after portfolio formation (in month t=60). The resulting performance of the portfolios based on a high versus a low level of gross profits are plotted in Figures 1.1 and 1.2, and show that the least (most) profitable firms as of month t=0 had experienced decreasing (increasing) abnormal returns during the three years before the portfolio was formed. Over the following five years, Figure 1.2 reveals that the most profitable firms as of month t=0 continue to earn positive abnormal returns over the long term. In contrast, consistent with Fama French (2013), Figure 1.1 does not indicate that the least profitable firms underperform. When we combine the results from Figures 1.1 and 1.2, Figure 1.3 indicates that the resulting the long-short hedge portfolio based on the level of profits generates high abnormal returns that persist over the long term. There is no evidence of a reversal during this five-year period. Similarly, Figures 2.1-2.3 plot the analogous results for the portfolios based on the trend in gross profits. Firms in the group with the lowest trend in gross profits (Decile 1) as of month t=0 experienced high abnormal returns in the beginning of the portfolio formation period (during months -24 through -16). This evidence is consistent with the view that those firms that experienced the steepest downward trend in profitability had been the most profitable firms up to three years before. In contrast, firms that experienced the steepest upward trend in profitability (Decile 10) as of month t=0 experienced large negative abnormal returns in the beginning of the portfolio formation period. Then, during the years just prior to portfolio formation, as their gross profits trended up, these firms had strong positive stock returns. In the subsequent period, after portfolio formation in month t=0, Figure 2.1 shows that the firms with the lowest trend continue 14

to experience negative returns. However, in the long-run, their abnormal returns gradually turn positive. As a result of this behavior, in the short-run, investors are better off by holding the long-short hedge portfolio, while in the long-run, shorting firms with the lowest gross profit trend make the investors somewhat worse off. On the other hand, Figure 2.2 reveals that firms with the highest trend continue to experience positive abnormal returns after portfolio formation in month t=0, which persist in the long run. Similar to the results based on the level of gross profits, it is surprising that firms in decile 10 based on the trend in profits have both economically and statistically significant abnormal returns for up to five years after the portfolio is formed. 6 As a result, Figure 2.3 indicates that the long-short hedge portfolio based on the trend in profits earns positive abnormal returns for up to two years following portfolio formation, and there is no evidence of a substantive reversal in the long run. We also perform Fama-MacBeth regression analysis regarding the long term stock returns of hedge portfolios based on the trend in profits, and we report the results in Table 6. This analysis indicates that the gross profit trend continues to have strong predictive power for the second year following portfolio formation (covering months t=13 through t=24). The coefficient of the trend then becomes insignificant in the third year following portfolio formation (over months t=25 through t=36). Subsequently, in the fourth and fifth year following portfolio formation, although the coefficient of the trend in gross profits becomes negative, this coefficient is never significantly negative. We conclude that, in the long term, the level of gross profits, the book-to-market ratio, firm size, and the number of analysts continue to predict future stock returns. In sum, the results in this section are not consistent with our results being due to investor overreaction, since we do not observe any significant indication of a stock return reversal in the 6 It would be interesting to test why the abnormal returns are not arbitraged away in the long run. One possible explanation is that investors face risk of gross profit mean reversion in the long-run. It is also possible that investors get used (underreact) to the persistently high profits over the long term. 15

long run. In contrast, this evidence is more consistent with the interpretation that investors tend to underreact to the positive information embedded in a larger upward trend in profits. They are also consistent with the interpretation that a high trend in profits is associated with higher unknown risk. We provide more analysis and discussion on this issue in section 8. 7. Additional Predictive Information in the Curvature of the Trend in Profitability We extend our analysis on the gross profit trend to investigate whether any curvature in this trend contains additional information about future performance and stock returns.. Specifically, we examine the information content contained in the convexity or concavity of the recent path of gross profits. Compared to the trend itself, the convexity of this trend may contain different information about the firm s prospects for performance. For example, consider two firms - A and B. Both firms have the same average trend growth in profits over the previous 8 quarters, but firm A s profits have increased at an accelerating rate, while firm B s profits have increased at a decelerating rate. Therefore, firm A s profit curve over this period is concave upward, while B s is concave downward. It is possible that these two patterns contain divergent information about the firms future growth potential, and investors might interpret these two patterns differently. Consider another extreme example. Suppose that firms C and D have the same average trend slope of zero, indicating flat growth in profits over the previous 8 quarters. However, suppose that firm C s profit path first goes up then down (an inverted U ), while firm D s profit path first goes down then up (a regular U ). Clearly, the recent evolution of the profits for these two firms are markedly different, with divergent implications for investors about future firm performance. 16

We investigate these issues by performing tests that are similar to those for the trend in gross profits. We now calculate the convexity of the recent trend path in gross profits (PSQTRENDGPQ) as the coefficient, γ, from the following quadratic trend regression model: ( ) ( ), (3) where this regression is estimated each quarter, looking back at the path in gross profits over the previous 8 quarters. We then relate the level, the trend, and the convexity of this trend in gross profits to future stock returns. We report the results of this analysis in Table 7. Column one indicates that the convexity of the trend in gross profits (PSQTRENDGPQ) is positively related to future stock returns. In terms of economic significance, a one standard deviation increase in gross profit convexity is associated with a 0.25% increase in future monthly returns. 7 From month 2 to month 7, the six month cumulative holding period returns continue to increase with the convexity of the trend in gross profits. However, starting from month 8 to month 13, we find a reversal in this effect, as indicated by the negative coefficient on the convexity term. Recall that, in Tables 5 and 6, there is no such evidence of a reversal in the effect of the trend in gross profits by itself. Together, this evidence indicates that the gross profit convexity provides substantive new information beyond that present in the current level of gross profit and the recent trend in gross profits. As a matter of fact, when both the gross profit level and trend are added to the regression model, the magnitude of the coefficient on gross profit convexity (in column 2) remains stable (compared to column 1). We observe similar results for longer holding period returns in columns 4 and 6. This evidence further suggests that the convexity of the trend in gross profits contains unique incremental information about future performance beyond that provided by the level or trend in gross profits. 7 One standard deviation of PSQTRENDGPQ mutiplies the coefficient as follows: 0.209%*0.183=0.25%. 17

8. Risk or Mispricing? In this section, we try to identify potential causes of the gross profit trend anomaly. There are two possible explanations risk or mispricing due to investor underreaction 8. According to the valuation model by Fama and French (2006, 2013), higher expected profitability indicates more future cash flows and consequently higher current market value. If two firms with different expected profitability have the same current market value, the stock with higher profitability must have higher expected return or discount rate. If pricing is rational, the higher expected return must indicate higher risk. Therefore, one explanation is that the gross profit trend is associated with some unobserved risk factors beyond those related to market return, size, and book-to-market. On the other hand, if the pricing is irrational, the positive return from the longshort hedge portfolio (long the stocks with the highest trend and short those with the lowest trend) could arise from mispricing. For example, it is possible that current gross profit trend contains valuable information about future firm underlying condition, which affects stock prices. If investors are conservative (Edwards, 1968), they might be slow in updating their beliefs in the face of new evidence, leading to mispricing today and stock price adjustment in the future as such information becomes more evident. We first analyze whether firms with high gross profit trend continue to have higher gross profit levels in the future. Each quarter, we sort stocks according to their gross profit trend in the past eight quarters into quintiles (Quintile 1=the lowest trend, Quintile 5= the highest trend). Then, we examine the average gross profit levels of the five portfolios in the next 12 quarters. Figure 3 presents the results. From Figure 3.1 (Figure 3.2), for firms that experienced the lowest (highest) trend, their gross profit levels decreased (increased) monotonically from quarter -7 to 8 As discussed above, investor overreaction is also possible; however, our empirical results in the previous sections have already ruled out this possibility. 18

quarter 0, which is expected because we sorted the stocks based on past gross profit trend. Firms in quintile 1 used to be more profitable firms. In contrast, firms in quintile 5 used to beless profitable firms. Starting from quarter zero, gross profit levels of firms in both Quintile 1 and Quintile 5 show the pattern of mean reversion. However, firms in Quintile 5 continue to have higher gross profit levels than those in Quintile 1. To see this more clear, Figure 3.3 plots the difference between gross profit levels of firms in Quintile 5 and Quintile 1. The difference is always positive up to 12 quarters in the future. Therefore, these results imply that past gross profit trend is positively related to future firm profitability. We also perform more formal tests using Fama-MacBeth regression, and the results are reported in Table 8. The past gross profit trend is positively related to future gross profit levels. Such positive relation lasts for several quarters in the future. Although investors might gradually adjust their beliefs on future firm profitability, it is possible that investors are unable to fully adjust to the correct level before the earnings announcement. In other words, if investors underreact to the information in the past trend in profits, they might be surprised by the unexpected positive earnings. To test this, we relate the past gross profit trend to future earnings surprise. We measure earnings surprise by cumulative abnormal return (CAR) around the earnings announcement day. Specifically, we use CAR3 starting from day -1 to day 1, where day 0 is the earnings announcement day. We use the same independent variables as our main tests above, and report the results in Table 9. We only find suggestive or weak evidence that the investors are positively surprised by next quarter s earnings that can be predicted by past trend in gross profits. We also plot the long-term earnings surprise for portfolios in the highest gross profit trend group (Quintile 5), those in the lowest gross profit 19

trend group (Quintile 1), and their differences in Figure 4. The results are similar to those in the regression analysis. 9 Cooper, Gutierrez, and Hameed (2004) argue that mispricing is related with the level of overconfidence in the past, and they use past market returns as a proxy for overconfidence. To further distinguish the risk and mispricing mechanism, in unreported analysis, we regress the long-short hedge portfolio (long the stocks with the highest trend and short those with the lowest trend) returns on the cumulative market returns in the past 36 months or 12 months. We find no evidence that the long-short hedge portfolio profitability is related to previous market returns or overconfidence. We also relate the long-short hedge portfolios to investor sentiment. Specifically, we create a dummy variable which takes value of one if the Baker and Wurgler (2005) investor sentiment index in month t-1 is above the medium over the sample period and zero otherwise. Then, we regress this dummy variable on the hedge portfolio returns in month t. The sentiment index dummy is not statistically significant. We get similar results when we use the sentiment index value instead of the dummy variable. Overall, our empirical evidence is more consistent with the risk-based explanation, while less consistent with the investor underreaction channel. 9. Conclusions This study documents that the past trend in a firm s gross profits is significantly associated with future firm performance and stock returns. A hedge portfolio strategy that is based on going long stocks with the highest upward trend in profits and short stocks with the 9 It is interesting that the gross profitability convexity is a strong predictor of future positive earnings surprise. Intuitively, future profitability of firms that have profitability increasing at an accelerating rate is harder to predict. In addition, behavioral biases are more likely to exist in the case of convex gross profits. For example, convex profitability in the past might suggest strong growth potential in the future. However, due to the general belief of mean reverting profitability, investors might put less weight on the potential information contained in the convex profitability path. It is also possible that investors are more likely to overreact in this case. Taking evidence from Table 7 together, it seems that for the gross profit convexity, investors first underreact (positively surprised) to the past convexity. When they observe the above-expectation earnings in the next quarter, they start to overreact as suggested by the reversal from month 8 to month 13. 20

lowest downward trend yields a risk-adjusted return of about 1% per month. This predictive power is incremental to that contained in the level of gross profits itself. We find that a higher trend in gross profits predicts higher stock returns for up to two years. In addition, there is no evidence of a substantive reversal in stock returns over longer horizons. Finally, our results are robust when we account for many previously documented factors that have been shown to affect returns, including the firm s past medium and long term price performance, book-to-market ratio, return volatility, turnover, institutional ownership, the number of analysts, and market liquidity. Our evidence is consistent with a risk-based explanation for the relation between the trend in profits and future stock returns. According to the dividend discount model of Fama and French (2006), stock prices represent discounted values of future expected cash flows (dividends or excess earnings). They argue that, if the market values of two firms are identical, then higher expected profitability for one firm means higher expected cash flows for that firm. For prices to be equal, this expectation of higher cash flows requires higher returns (or higher discount rates) for the firm with greater expected profitability. Thus, higher returns or discount rates presumably can arise from higher risk associated with greater expected profitability, when the current stock price is rational. Alternatively, such higher returns could arise from mispricing due to irrational investor overreaction or underreaction to the information contained in the trend in firm profits. We investigate these issues by examining whether the trend in gross profits predicts firm performance, as an explanation for the link we find between this trend and future stock returns. We find that the trend in gross profits significantly predicts future firm profitability. This finding is consistent with the dividend discount model by Fama French (2006), suggesting that our empirical results are more consistent with the risk-based explanation and less consistent with possible investor underreaction or overreaction. 21

References Amihud, Y., 2002. Illiquidity and stock returns: Cross-section and time-series effects, Journal of Financial Markets 5, 31-56. Baker, M. and Wurgler, J.,2006. Investor Sentiment and the Cross-Section of Stock Returns. The Journal of Finance, 61: 1645 1680. Barberis, Nicholas, Andrei Shleifer, Robert Vishny, 1998. A model of investor sentiment, Journal of Financial Economics, Volume 49, Issue 3, 1 September 1998, Pages 307-343. Cohen, Randolph B., Paul A. Gompers, Tuomo Vuolteenaho, 2002. Who underreacts to cash-flow news? evidence from trading between individuals and institutions, Journal of Financial Economics, Volume 66, Issues 2 3, November December 2002, Pages 409-462. Cooper, M. J., Gutierrez, R. C. and Hameed, A., 2004. Market States and Momentum. The Journal of Finance, 59: 1345 1365. Edwards, W., 1968. Conservatism in human information processing. In: Kleinmutz, B. (Ed.), Formal Representation of Human Judgement. John Wiley and Sons, New York, pp. 17-52. Fama, E. F., and J. D. MacBeth, 1973. Risk, return, and equilibrium: empirical tests. Journal of Political Economy 81, 607 636. Fama, E. F., and K. R. French, 1993. Common risk factors in the returns on stocks and bonds. Journal of Financial Economics 33, 3 56. Fama, E. F., and K. R. French, 2006. Profitability, investment and average returns. Journal of Financial Economics 82, 491 518. Fama, E. F., and K. R. French, 2008. Dissecting anomalies. Journal of Finance 63, 1653 1678. Fama, Eugene F. and French, Kenneth R., 2013. A Five-Factor Asset Pricing Model. Fama-Miller Working Paper. Freeman, Robert N., James A. Ohlson, and Stephen H. Penman, 1982, Book rate-of-return and prediction of earnings changes: An empirical investigation, Journal of Accounting Research 20, 639 653. Gibbons, Michael R., Stephen A. Ross, and Jay Shanken, 1989. A test of the efficiency of a given portfolio. Econometrica 57, 1121-1152. Haugen, Robert A., Nardin L. Baker, 1996. Commonality in the determinants of expected stock returns, Journal of Financial Economics, Volume 41, Issue 3, July 1996, Pages 401-439 Mueller, D.C., 1977. The persistence of profits above the norm, Economica, 44 (1977), pp. 369 380. Novy-Marx, Robert, 2013. The other side of value: The gross profitability premium, Journal of Financial Economics, 108, issue 1, p. 1-28. 22

PÁstor, Ľ. and Pietro, V. (2003), Stock Valuation and Learning about Profitability. The Journal of Finance, 58: 1749 1790. Sloan, Richard G., 1996. Do stock prices fully reflect information in accruals and cash flows about future earnings?. The Accounting Review, Vol 71, No 3, Spring 1996. Stigler, G.J.1963. Capital and Rates of Return in Manufacturing Industries. Princeton, N.J.: Princeton University Press. 23

Table 1. Summary Statistics The sample includes common shares (CRSP share code 10 and 11) on NYSE, AMEX, and NASDAQ (CRSP exchange code 1, 2, 3) from CRSP and Compustat (both annual files and quarterly files). We exclude financial firms (the four-digit SIC code in the 6000 s) and utility firms (the four-digit SIC code in the 4900 s). We require firms to have positive book-to-market (BK) ratio. Further, the sample is restricted to firm-month observations with stock prices above one dollar and observations with non-missing values for all of the variables in this table. Each month t, we match the stock price information from CRSP with annual accounting data that are 7 to 18 months old and the most recent publicly available quarterly accounting data determined by public earnings announcement month (item RDQ) in Compustat. LEADRET2 is the leading two month (t+2) monthly stock return. Quarterly gross profit (GPQ) is quarterly sales (item SALEQ) minus quarterly costs of goods sold (item COGSQ) scaled by assets (item ATQ). To get the trend of GPQ (TRENDGPQ) for firm i in quarter q, we run the following Ordinary Least Square (OLS) regression: ( ). In other words, we run a rolling window regression of GPQ on a time variable. The trend of GPQ (TRENDGPQ) of firm i in quarter q is the coefficient from the above regression. Similarly, the convexity of gross profits (PSQTRENDGPQ) is the coefficient γ from OLS regression: ( ) ( ). MOVSTDGPQ is the moving standard deviation of GPQ in the past 8 quarters from quarter q-7 to quarter q. Market value (MKTVALUE) is the number of shares (SHROUT) times price per share (abs (PRC)). BK is the book-to-market ratio. STDRET is the volatility of daily stock returns over the previous month. Turnover (TURNOVER) is trading volume (VOL) divided by the number of shares (SHROUT). MEANAMI is the Amihud (2002) illiquidity measure. The institutional ownership (IO) data are lagged by one quarter. NUMEST denotes number of analysts information in month t. RET6M (RET36M) is the cumulative stock return in the past 6 (36) months. To get the descriptive statistics, we first obtain the corresponding statistics for each month. Then, we get the means of each statistics while controlling for heteroskedasticity and autocorrelation in error terms by a Newey-West standard error. All variables except LEADRET2 are winsorized at 1% and 99% level. The sample period is July 1980 to December 2011. VARNAME MEAN MIN MEDIAN MAX STDDEV LEADRET2 0.013-0.643 0.003 1.443 0.14 GPQ 0.1-0.093 0.092 0.328 0.072 TRENDGPQ 10 2-0.014-2.163-0.015 2.397 0.648 PSQTRENDGPQ 10 2-0.006-0.851-0.001 0.707 0.209 MOVSTDGPQ 0.022 0.002 0.015 0.125 0.021 MKTVALUE (billion) 1.589 0.005 0.201 37.317 4.964 BK 0.777 0.053 0.584 4.243 0.704 STDRET 0.032 0.007 0.027 0.104 0.018 TURNOVER 0.783 0.019 0.531 4.551 0.818 MEANAMI 10 5 0.406 0 0.016 9.295 1.305 IO 0.41 0.002 0.407 0.978 0.256 NUMEST 5.57 0 2.69 30.511 6.985 RET6M 0.088-0.54 0.041 1.446 0.341 RET36M 0.573-0.818 0.259 6.573 1.24 Main sample size: 851,182 firm-month observations. 24

RET36M RET6M NUMEST IO MEANAMI LOGTURNOVER STDRET LOGBK LOGMKTVALUE MOVSTDGPQ PSQTRENDGPQ LAG1TRENDGPQ TRENDGPQ LAG1GPQ GPQ LEADRET2 Table 2. Spearman Correlations of Key Variables This table presents the spearman correlations. The sample includes common shares (CRSP share code 10 and 11) on NYSE, AMEX, and NASDAQ (CRSP exchange code 1, 2, 3) from CRSP and Compustat (both annual files and quarterly files). We exclude financial firms (the four-digit SIC code in the 6000 s) and utility firms (the four-digit SIC code in the 4900 s). We require firms to have positive book-to-market (BK) ratio. Further, the sample is restricted to firm-month observations with stock prices above one dollar and observations with non-missing values for all of the variables in this table. Each month t, we match the stock price information from CRSP with annual accounting data that are 7 to 18 months old and the most recent publicly available quarterly accounting data determined by public earnings announcement month (item RDQ) in Compustat. LEADRET2 is the leading two month (t+2) monthly stock return. Quarterly gross profit (GPQ) is quarterly sales (item SALEQ) minus quarterly costs of goods sold (item COGSQ) scaled by assets (item ATQ). To get the trend of GPQ (TRENDGPQ) for firm i in quarter q, we run the following Ordinary Least Square (OLS) regression: ( ). In other words, we run a rolling window regression of GPQ on a time variable. The trend of GPQ (TRENDGPQ) of firm i in quarter q is the coefficient from the above regression. Similarly, the convexity of gross profits (PSQTRENDGPQ) is the coefficient γ from OLS regression: ( ) ( ). MOVSTDGPQ is the moving standard deviation of GPQ in the past 8 quarters from quarter q-7 to quarter q. Market value (MKTVALUE) is the number of shares (SHROUT) times price per share (abs (PRC)). BK is the book-to-market ratio. STDRET is the volatility of daily stock returns in the past 30 days. Turnover (TURNOVER) is trading volume (VOL) divided by the number of shares (SHROUT). MEANAMI is the Amihud (2002) illiquidity measure. The institutional ownership (IO) data are lagged by one quarter. NUMEST denotes number of analysts information in month t. RET6M (RET36M) is the cumulative stock return in the past 6 (36) months. LOG denotes the natural log. All variables except LEADRET2 are winsorized at 1% and 99% level. The sample period is July 1980 to December 2011. VARNAME LEADRET2 1 GPQ 0.03 1 LAG1GPQ 0.03 0.91 1 TRENDGPQ 0.02 0.21 0.17 1 LAG1TRENDGPQ 0.01 0.13 0.22 0.75 1 PSQTRENDGPQ 0.02 0.08-0.05-0.04-0.35 1 MOVSTDGPQ -0.03 0.25 0.25-0.04-0.04-0.02 1 MKTVALUE 0.04-0.01-0.01-0.01 0 0-0.32 1 BK 0-0.26-0.26-0.09-0.11 0.03-0.14-0.37 1 STDRET -0.06-0.04-0.04 0.01 0 0 0.3-0.46 0.05 1 TURNOVER 0-0.01-0.01 0.01 0.02-0.01 0 0.47-0.27 0.1 1 MEANAMI -0.03 0.01 0 0-0.01 0.01 0.26-0.93 0.37 0.44-0.65 1 IO 0.04 0.01 0.01-0.04-0.03-0.01-0.28 0.7-0.11-0.36 0.44-0.68 1 NUMEST 0.03 0.01 0.01-0.05-0.04-0.01-0.23 0.79-0.27-0.31 0.49-0.78 0.66 1 RET6M 0.03 0.13 0.11 0.18 0.11 0.14-0.04 0.16-0.27-0.14 0.08-0.16 0.03 0.03 1 RET36M 0.03 0.19 0.2 0.06 0.10-0.05-0.06 0.33-0.49-0.24 0.17-0.33 0.17 0.17 0.36 1 * Bold numbers indicate significance at 5% level. 25