The Value of Growth: Changes in Profitability and Future Stock Returns *

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1 The Value of Growth: Changes in Profitability and Future Stock Returns * Juan Sotes-Paladino, Jiaguo (George) Wang, Yaqiong Yao August 2017 Abstract: The dividend-discount model predicts a positive relation between expected changes in a firm s profitability, or profitability growth, and stock returns. We find this prediction to be borne out in the data. Across U.S. stocks, firms with strong past profitability growth outperform firms with weak past profitability growth. A long-short strategy based on profitability growth yields significant risk-adjusted returns, both in the overall sample and across firm-size levels. The predictive power of profitability growth is economically strong and statistically significant when compared with welldocumented, cross-sectional determinants such as profitability levels, earnings momentum, profit trend, size, book-to-market, or price momentum. JEL classification: G11; G12 Keywords: Profitability; Growth; Return Predictability; Stock Returns * For helpful comments and discussions, we thank Michael Brennan, Igor Goncharov, Bruce Grundy, Allaudeen Hameed, Kewei Hou, Jin-young Jung, Andrew Karolyi, Robert Korajczyk, Spencer Martin, Ron Masulis, Edward Nelling, Ingmar Nolte, Ken Peasnell, Jianfeng Shen, Diamond Wang, Josef Zechner, Lu Zhang, Qi Zeng and seminar participants at Lancaster University and Loughborough University. We also appreciate the comments of participants at the 2016 FIRN Annual Conference, the 2016 International CAFM (Seoul), the 24 th SFM Conference (Kaohsiung), and the 29 th Australasian Finance and Banking Conference (Sydney), and INFINITI Conference in International Finance (Valencia). Senior Lecturer of Finance, Department of Finance, University of Melbourne, VIC 3010, Australia. juan.sotes@unimelb.edu.au; Tel: (+61) Assistant Professor of Finance, Division of Accounting and Finance, Alliance Manchester Business School, Manchester M15 6PB, United Kingdom. george.wang@manchester.ac.uk; Tel: (+44) Assistant Professor of Finance, Department of Accounting and Finance, Lancaster University Management School, Lancaster LA1 4YX, United Kingdom. yaqiong.yao@lancaster.ac.uk; Tel: (+44)

2 1. Introduction The dividend discount model of firm valuation implies a positive relation between future profitability and expected stock returns. Fama and French (2006) characterize future profitability as a combination of current profitability level and future profitability growth. Recent literature has documented a strong predictive relation between the first component, the level of current profitability, and the cross section of stock returns. 1 The second component, profitability growth, has been examined to a much lesser extent. At an intuitive level, the importance of profitability growth for expected stock returns could be illustrated as follows. Consider two firms, A and B, showing equal profitability as of the latest reporting date. Assume that firm A has shown a stable level of profits over time while firm B has reached its current profitability level by growing rapidly over a recent period. If future growth is correlated with current profitability but not with recent growth, the two firms should exhibit similar expected returns according to the dividend discount model. However, if profitability growth is persistent, firm B can be expected to continue growing and its profitability to exceed that of firm A in the future. All else equal, the dividend-discount model predicts higher expected returns to stock B than stock A. In this study, we introduce a new profitability-growth measure and present comprehensive evidence of its empirical relevance as a source of profitability effects. We define profitability growth as the most-recent, year-over-year change in a firm s quarterly profits, scaled by lagged book equity. To better proxy for true economic profitability, we follow the recent strand of the literature that focuses on cleaner earnings measures and examine a firm s changes in operating profitability. 2 Our baseline measure is Fama and French s (2015) operating profits measure, defined as revenue less cost of goods sold, selling, general, and administrative expenses, minus interest expenses. This measure 1 See, e.g., Novy-Marx 2013, Fama and French 2015, Hou, Xue and Zhang 2015, Ball et al., See references in footnote 1. 2

3 removes from accounting earnings items that are harder to relate to a firm s future economic profitability (e.g., tax expense changes). 3 Using a sample of U.S. stocks over the 1975 to 2014 period, we document a strong positive relation between a firm s recent profitability growth and future stock returns. Sorting stocks into deciles according to their most recent operating profitability growth, the value-weighted (VW) returns in the first month after portfolio formation consistently increase with profitability growth across deciles. Firms in the top ( strong ) profitability-growth decile earn a VW return of 1.46% per month, while firms in the bottom ( weak ) profitability-growth decile earn a VW return of 0.70% per month. In other words, a simple long-short strategy, which buys firms with strong profitability growth and short-sells firms with weak profitability growth, can generate a remarkable VW return of 9.0% per annum. The long-short portfolio remains highly profitable over longer holding horizons of up to 18 months. Further, it earns abnormal and positive returns after controlling for exposure to the standard risk models of Fama and French (1993), Carhart (1997), or Fama and French (2015). The three-, four- and five-factor VW alphas on the long-short portfolio are 0.93%, 0.62% and 0.73% per month, respectively. The returns to this portfolio fall with size but remain large and significant even for the top 20% largest firms in our sample. An important result for the potential implementation of profitability-growth strategies is that significant risk-adjusted returns can also be attained with longonly positions. In all cases, the profitability-growth effect manifests strongly also under alternative weighting schemes, such as the return-weighting (RW) method, that give more even weight to the firms in a portfolio. 4 3 Several items lying between profitability and earnings are not related to profitability, yet they convey information about stock returns. Specifically, there are seven Compustat items from income before extraordinary item to gross profits (revenue minus cost of goods sold): Income before extraordinary item=revenue-cost of goods sold-selling, general, and administrative expense-interest-depreciation and amortization-taxes + Nonoperating income + Special items - Minority interest income. For example, Lev and Sougiannis (1996), and Chan, Lakonishok, and Sougiannis (2001) document a positive link between research and development expenditures and future returns, while Hanlon, Laplante, and Shevlin (2005) document a positive association between tax expense changes and future returns. 4 Asparouhova, Bessembinder, and Kalcheva (2013) propose computing weighted mean returns with the priorperiod gross return as a weighting variable to address a potential upward bias, induced by microstructure noise in equal-weighted portfolios. 3

4 In comparing profitability growth with other well-documented determinants of profitability premia in cross-sectional regressions, we find that profitability growth remains a strong predictor of stock returns. First, the level of profitability does not subsume the information contained in profitability growth. When we compare profitability growth with book-to-market, firm size, return reversal or price momentum, 5 the coefficients on profitability growth are highly statistically significant across All-but-microcaps (stocks above the 20th NYSE market capitalization percentile) and Microcaps. When the level of profitability is included in the regressions, the economic and statistical significance of profitability growth remains robust across firm size groups. Second, the predictive information of profitability growth remains strong when we further control for profit-trend effects (Akbas, Jiang, and Koch, 2017). Profitability growth is highly statistically significant, with t- values at least twice as large as those for the profit trend, among All-but-microcaps as well as Microcaps. Our profitability-growth measure is conceptually related to, but different from, earnings surprises, whose relation to stock returns has been well documented by the post-earningsannouncement drift (PEAD) literature (Ball and Brown, 1968; Bernard and Thomas, 1989, 1990; Chan, Jegadeesh, and Lakonishok, 1996; Novy-Marx, 2015a, b). First, we follow the recent profitability literature in focusing on operating profits instead of earnings to approximate a firm s true economic profitability. Second, consistent with our goal of testing the underlying economic relation between expected returns and profitability growth embedded in the valuation formula, we construct our measure using accounting data at the firm level, instead of at the per-share level (Aharoni, Grundy, and Zeng, 2013). 6 Third, we do not standardize the changes in profitability by a statistical measure the standard deviation of past changes in earnings to scale the information 5 See, for example, Banz, 1981; Rosenberg, Reid, and Lanstein, 1985; Fama and French, 1992, 1993, 1996; Jegadeesh, 1990; Jegadeesh and Titman, Aharoni, Grundy, and Zeng (2013) point out that the valuation formula of the dividend-discount model does not necessarily hold in a per-share analysis. Hence, tests of this formula that use per-share proxies such as profitability growth for expected profitability can be misspecified. 4

5 content of profitability growth. Thus, our measure is easier to integrate within the valuation equation framework and does not conflate the effect of earnings risk and surprises on future stock returns. We find that these differences between profitability growth and earnings surprises translate into dissimilar variable dynamics and return patterns across investment horizons in the data. More importantly, we provide comprehensive evidence of the incremental explanatory power of profitability growth beyond earnings surprises in the cross-section of stock returns. Specifically, using Fama and MacBeth (1973) regressions, we compare our profitability-growth measure with a battery of earnings surprise measures that have been used to proxy for the PEAD in the literature. The measures differ by conceptual similarity to profitability growth. Notably, none of them subsumes profitability growth as a cross-sectional predictor. Moreover, the significance of profitability growth remains strong after simultaneous controls for profitability in levels, among All-but-microcaps as well as Microcaps. Our tests suggest that profitability growth could represent a cleaner measure of innovations to true economic profitability than earnings innovations once both are scaled by a similar variable lagged book equity. Our results are robust to a number of additional controls and alternative specifications. First, the significance of profitability growth in multivariate regressions is robust to correction for potential biases arising from microstructure noise (Asparouhova, Bessembinder, and Kalcheva, 2010). Second, the profitability-growth effect becomes stronger after controlling for the January size effect (Rozeff and Kinney, 1976; Keim, 1983; Reinganum, 1983). Third, our results are robust to the use of alternative definitions of profitability and scaling variables, as proposed by the prior literature, in the construction of profitability growth. Fourth, the incremental effect of profitability growth over other cross-sectional determinants does not depend on the parametric assumptions underlying the regression framework. Specifically, two-way portfolio sorts that condition on profitability growth attain significant raw and risk-adjusted returns across VW and RW portfolios that are already sorted 5

6 on profitability levels, standardized unexpected earnings, profit trend, book-to-market, or price momentum. Our study contributes to two strands of the literature. First, it contributes to the literature on the valuation theory and the cross-sectional determinants of stock returns. We follow closely the approach in Fama and French (2006), who adopt the valuation equation in the dividend-discount model to examine the impact of firm characteristics on stock returns in a unified framework. Following this model, Fama and French (2008) measure profitability as earnings scaled by the book value of equity but fail to find a significant relation between profitability and stock returns. Aharoni, Grundy, and Zeng (2013) find that profits-to-equity do not significantly enhance the performance of a portfolio that controls for other well-known signals, such as size or book-to-market. We decompose future profitability in the valuation equation into current level- and future-growth components, and document a strong persistence in growth that has been relatively overlooked by prior studies. Using past profitability growth as a proxy for future growth, we support the role of the growth component of profitability in empirically reconciling future profits-to-equity to stock returns within the valuation framework. Second, our paper contributes a new dimension to the recent literature on profitability and stock returns. Novy-Marx (2013) and Ball et al. (2015) argue that deflating profits by the book value of assets recovers the predictive power of profitability on stock returns. Akbas, Jiang, and Koch (2017) find that the deterministic trend in firms gross profits scaled by the book value of assets is closely related to stock returns. We use the insight in this literature that profit measures provide a less polluted proxy for a firm s true economic profitability in constructing our profitability-growth measure. However, our measure is fundamentally different from the measures of prior studies. Unlike Novy-Marx (2013) and Ball et al. (2015), our focus is not the level but the growth component of profitability. Unlike Akbas, Jiang, and Koch (2017), we do not decompose profits into a 6

7 predictable trend or unpredictable components, but rather examine the change in profitability that is readily available, without applying statistical filters to accounting variables. In both cases, we provide evidence of incremental informational content of profitability growth to predict the cross section of stock returns. The paper proceeds as follows. In Section 2, we describe the data and variable construction, and examine the persistence of profitability growth in the regression analysis. In Section 3, we test the presence and economic significance of a profitability-growth effect in the cross section of stock returns using portfolio analyses. In Section 4, we examine the incremental explanatory power of profitability growth over other cross-sectional determinants using regression analyses. In Section 5, we assess the robustness of strategies to controls for seasonal effects, alternative profitability definitions, and the parametric assumptions in the regression analyses. In Section 6 we discuss the limitations of our analysis. Section 7 concludes. 2. Profitability Growth and Returns Fama and French (2006) use the dividend-discount model to relate firm profitability and investment, in addition to book-to-market and firm size, to average stock returns. According to this model, a firm s stock price is the present value of expected dividends. Clean-surplus accounting along with the dividend-discount model then imply: M E( Y db ) / (1 r), (1) t t t 1 where M is the market value of the firm s equity, Y is the firm s profits, dbt 1 Bt 1 Bt is the t t change in the book value of equity, and r is the discount rate of return on expected dividends. Dividing by time-t book equity gives the Miller and Modigliani (1961) valuation equation: µ M t B t = ( åe(y t+t - db t+t ) / (1+ r) t ) B t, (2) t =1 7

8 holding all else equal, future stock returns should be positively related to future profits relative to book equity and to current book-to-market, and negatively related to growth in book equity due to reinvestments in profits (i.e., asset growth). Following Fama and French s (2006, pp. 495) characterization of future profitability as a mix of the current profitability level and future profitability growth, we can rewrite Eq. (2) as follows: M t B t = µ å t =1 E(Y t+t -Y t+t -1 +Y t+t -1 - db t+t ) / (1+ r) t B t = µ å t =1 E(dY t+t +Y t+t -1 - db t+t ) / (1+ r) t B t, (3) where dyt 1 Yt 1 Yt is the one-period change in profits. According to Eq. (3), holding all else equal, future stock returns should be positively related to the ratios of the current profitability level and future profitability growth to current book equity. Fama and French (2006) document a strong persistence in profits-to-equity. However, Fama and French (2008) and Aharoni, Grundy, and Zeng (2013) find that profits-to-equity do not significantly enhance the performance of a portfolio that controls for other well-known signals such as size or book-to-market. Subsequent literature has been more successful in using profits-related proxies for future profitability to predict future returns (Novy-Marx, 2013; Ball et al., 2015; Akbas, Jiang and Koch, 2017). Unlike the profit ratio implied by the valuation Eq. (3), these proxies deflate profits by the book value of assets instead of by book equity. Ball et al. (2015) find that the predictive power of profits-to-assets comes from the multiplicative interaction of its two components, namely profit deflated by the market value of equity and the ratio of market value of equity to total assets. In what follows, we examine the role of the growth component of profitability scaled by book equity in Eq. (3) in empirically reconciling future profits-to-equity to stock returns. 8

9 2.1. Data and profitability growth measure Our sample includes all common stocks (share codes 10 or 11) traded on the New York Stock Exchange (NYSE), the American Stock Exchange (Amex), and NASDAQ comprised in the Center for Research in Security Prices (CRSP) monthly files. We obtain accounting data from Compustat. We exclude financial firms (i.e., firms with one-digit standard industrial classification codes of six), closed-end funds, real estate investment trusts, American depository receipts, foreign stocks, and stocks with non-positive book equity from our sample. Our main variable of concern, profitability growth, is measured as the change in profits over the book value of equity. Novy-Marx (2013) argues for gross profits (revenue minus costs of goods sold) as a clean profitability measure. Fama and French (2015) use operating profits instead of gross profits to construct their five-factor model in which operating profits are defined as revenue less cost of goods sold and selling, general, and administrative expenses, minus interest expenses. Ball et al. (2015) propose an operating profits measure defined as revenue less cost of goods sold and selling, general, and administrative expenses, but not expenditures on research and developments. The authors argue that this alternative measure can better match current expenses with current revenues. 7 We use the operating profits definition of Fama and French (2015) to construct our baseline profitability-growth measure. Our choice is meant to facilitate a comparison with those of Fama and French (2006) and Aharoni, Grundy, and Zeng (2013) who examine the explanatory power of profits deflated by book equity in the context of the Miller-Modigliani valuation equation, as we do. Specifically, our baseline operating profitability growth (PG) measure at month t is defined as: PG ( OP OP ) BE, (4) i, q i, q i, q 4 i, q 4 7 According to their argument, research and development (R&D) expenses should be subtracted because Compustat defines selling, general, and administrative expenses as the sum of firms actual selling, general, and administrative expenses as well as their R&D expenses. Since R&D expenses reduce current profits while generating future revenues, eliminating their influence should lead to a cleaner measure of a firm s profit. 9

10 where OPi,q is the most recent quarter operating profits (Compustat items REVTQ COGSQ XSGAQ XINTQ), OPi,q 4 is the operating profits lagged four quarters, and BEi,q 4 is the book equity lagged four quarters. For robustness, we also construct alternative profitability-growth measures based on Novy-Marx s (2013) gross profit (Compustat items REVTQ COGSQ) and Ball et al. s (2015) operating profit (Compustat items REVTQ COGSQ XSGAQ+XRDQ) measures. Following Aharoni, Grundy, and Zeng (2013), we construct all our accounting measures using data at the firm level, instead of at the per-share level. As these authors point out, the valuation formula of the dividend-discount model does not necessarily hold in a per-share analysis. Hence, tests of this formula that use proxies such as profitability growth for expected profitability at the per-share level can be misspecified. 8 To avoid results driven by tiny stocks, in all of our regression analyses we split firms into Allbut-microcaps and Microcaps. We define Microcaps as stocks with a market value of equity below the 20th percentile of the NYSE market capitalization distribution (Fama and French, 2008; Ball et al. 2015). Our sample covers the period from January 1975 to December 2014, in which the start date is determined by the availability of Compustat quarterly files Persistence in profitability growth The valuation equation (3) implies a relation between expected returns and future values of profitability growth. Observed values of profitability growth could explain expected returns if they helped predict future growth i.e., growth is persistent. To assess the persistence in profitability growth, in Table 1 we report Fama and MacBeth (1973) regressions of firm profitability growth on 8 For instance, at the per-share level, Fama and French (2006) find limited empirical support for the positive predicted relation between expected profitability and returns, and fail to provide support for a negative predicted relation between investment and returns, of the dividend-discount model. By contrast, Aharoni, Grundy, and Zeng (2013) show that once the corresponding accounting variables are measured at the firm level, both empirical predictions are validated in the data. 10

11 its own lagged values, up to eight quarters, using our baseline definition of operating profitability. We present results for All-but-microcaps in Panel A and for Microcaps in Panel B. Profitability growth is highly persistent among both All-but-microcaps and Microcaps. A firm s profitability growth is strongly related to its past growth in the most recent quarter, as a 1% increase in growth leads to an expected increase in growth of around 0.5% in the next quarter for both Allbut-microcaps and Microcaps. Current profitability growth can impact future profitability growth even after several quarters. Up to three quarters ahead, the impact decreases gradually relative to the one-quarter effect but remains positive and statistically significant, with similar magnitude across firm size groups. The impact of profitability growth on its future values turns negative after four quarters, although the negative slope is partly explained by the construction of our profitability-growth measure. 9 Notably, the relation between current and future profitability growth turns positive and significant after five to seven quarters. The relation becomes significantly negative again only after eight quarters. [Insert Table 1 here] In non-tabulated exercises, we repeat our test using the definitions of profitability of Ball et al. (2015) and of Novy-Marx (2013) with similar results. The results support the use of past profitability growth as a cross-sectional signal of future profitability growth. Given the predicted relation Eq. (3) between future growth and expected returns, one can wonder whether conditioning on this signal creates economically significant dispersion in average returns. We examine this question using portfolio sorts in the next section, and control for other well-known, cross-sectional predictors within a multivariate regression framework afterwards. 9 By Eq. (4), current profitability enters positively in the definition of current-quarter profitability growth, but negatively in the definition of the profitability growth four quarters ahead. 11

12 3. Portfolios Tests We first examine the presence and economic significance of a profitability-growth effect in the cross section of stock returns using portfolio sorts. At each month t, we sort stocks into deciles based on the NYSE breakpoints, according to their most recent publicly available operating profitability growth. To ensure that the corresponding information is publicly available at the time of portfolio formation, we use quarterly accounting data that have been announced prior to the date of portfolio formation. In particular, we require the quarterly earnings announcement dates (Compustat item RDQ) to take place before the portfolio formation date, namely, the beginning of month t+1. For example, if the profit-related variables for the fourth fiscal quarter of 2012 are publicly announced on March 10 (or 20) of 2013, we use these variables to form portfolios at the beginning of April Furthermore, we require the quarterly earnings announcement date (RDQ) to be within three months preceding portfolio formation to avoid stale accounting data. We then examine the performance of the profitability-growth decile portfolios from month t+1 onwards. 10 The top decile consists of the stocks with the strongest operating profitability growth, while the bottom decile consists of those with the weakest growth. The tables in this section report portfolio characteristics and average returns on a value weighted (VW) basis. For comparability with the rest of the literature, we also discuss results under alternative weighting (e.g., return weighting, as introduced below) schemes Summary characteristics Table 2 reports summary statistics for the ten-decile portfolios. A large cross-sectional dispersion in profitability growth exists. The profitability of the top decile portfolio grows at an average annual rate of 17.1%, while the bottom decile grows at an average annual rate of 16.0%. Consistent with our results of Section 2.2, there is strong persistence in profitability growth both before and after 10 The timing of our portfolio construction methodology follows the standard in the literature; e.g., Hou, Xue, and Zhang (2015, p. 660) and Akbas, Jiang, and Koch (2017, p. 15). 12

13 portfolio formation. Strong- (weak-) profitability-growth firms experience the strongest (weakest) profitability growth in the quarters before and after the formation quarter. For example, over the quarter following the formation period, the strong-growth firms grow at an average annual rate of 7.7%, while the weak-growth firms grow at an average annual rate of -5.9%. A similar dispersion is observed for the quarter preceding the formation period. Moreover, the pattern is remarkably monotonic across deciles in both cases. [Insert Table 2 here] In general, firms with weak (decile 1) and strong (decile 10) profitability growth are relatively smaller than their middle-profitability growth counterparts. Moreover, weak profitability-growth firms show the smallest market capitalization. Strong-growth firms tend to exhibit the lowest bookto-market ratios, while weak-growth firms place around the middle of the distribution in book-tomarket across profitability-growth deciles. Table 2 also indicates a strong positive association between profitability growth and both operating profits-to-equity and profits-to-asset ratio. 11 From a stock performance standpoint, profitability growth exhibits a positive relation with price momentum as proxied by prior 6- or 12- month returns. To the extent that profitability growth captures innovations to profits, and such innovations were correlated to earnings surprises, this relation might be attributable to the relation between earnings momentum and price momentum documented by Chordia and Shivakumar s (2006) and Novy-Marx s (2015). To disentangle the effect of profitability growth from the effects of each of these correlated characteristics on portfolio returns, we apply two types of additional tests. First, in subsection 3.3 we adjust the return on profitability growth-sorted portfolios for their exposure to the size, book-tomarket, momentum, investment, and profitability factors within standard risk models. Second, in 11 This is consistent with the observation in Novy-Marx (2013) that profitable firms also tend to grow faster. 13

14 Sections 4 and 5.3, we control for these characteristics using, respectively, multivariate Fama and MacBeth (1973) regressions, or double-sorted portfolio tests Raw returns Table 3 reports returns to the ten profitability growth-sorted portfolios, along with the return on the zero-cost investment portfolio that buys the strong-profitability-growth decile and shorts the weak-profitability-growth decile. Panels A and B present the average monthly returns over different holding periods for, respectively, value weighting (VW) and return weighting (RW). Specifically, after assigning firms to one of the ten deciles based on profitability growth at the beginning of month t + 1, we calculate the VW and RW monthly returns for the following month t + k after portfolio formation (Mk), for k=1,3,6,9,12,18 and 24. Consistent with profitability growth being a strong predictor of returns, in the first month after portfolio formation, the VW returns (M1) to the profitability-growth portfolios increase with profitability growth. With the exception of decile 7, the relation between profitability growth and average returns is monotonic. Weak profitability-growth firms earn VW portfolio returns of 0.70% per month and strong profitability-growth firms earn average returns of 1.46% per month, resulting in a monthly spread of 0.75% (t-statistic of 4.37). This spread amounts to a remarkable VW return of 9.0% per year on the long-short, profitability-growth portfolio. 12 [Insert Table 3 here] Notably, the profitability-growth effect remains large and highly statistically significant for up to 18 months after portfolio formation. In all cases, strong-growth and weak-growth firms yield, respectively, the highest and lowest VW returns in the cross section of profitability growth. As a result, the return spread between strong- and weak-growth portfolios remains economically large at 12 We show in Section 5.2 that the one-month return spread between strong- and weak-profitability growth portfolio remains large and significant when we use alternative definitions of profitability such as those of Ball et al. (2015) and Novy-Marx (2013). 14

15 the different holding horizons. This pattern is consistent with the positive autocorrelation at several lags that we document in Section 2.2. For example, the long-short, profitability-growth portfolio returned a VW average 0.60% (t-value of 3.92), 0.37% (t-value of 2.64) and 0.31% (t-value of 2.42) per month over 6-month, 12-month and 18-month holding periods. 13 Using alternative weighting schemes for the stocks in each portfolio also leads to economically large and statistically significant excess returns. In particular, Panel B of Table 3 shows a strong profitability-growth effect under the return-weighting (RW) method proposed by Asparouhova, Bessembinder, and Kalcheva (2013) to correct an upward bias in equal-weighted (EW) portfolios. These authors suggest that the cross-sectional mean returns to EW portfolios are upward biased by the cross-sectional average of the individual security biases. If profitability growth were positively correlated with the magnitude of this bias, the EW returns to the strong-minus-weak portfolio could be upward biased as well. If this were the case, the profitability-growth effect could turn insignificant once the bias is corrected using RW mean returns, in which the weighting variable is the prior-period gross return. The results in Panel B indicate otherwise. Across investment horizons, portfolio returns typically increase monotonically with profitability growth. For instance, the 1-month, 12-month and 18-month RW average monthly spreads amount to 1.72% (t-value of 12.84), 0.40% (t-value of 3.65), and 0.24% (t-value of 2.47). Similar results (unreported) are obtained when we calculate initial-equal weighted (IEW) portfolios, as alternatively suggested by Asparouhova, Bessembinder, and Kalcheva (2013) to correct for microstructure noise Factor-adjusted returns The returns to a profitability-growth strategy remain significant after adjusting for their exposure to systematic risk and of similar magnitude to raw returns. In Table 4, we tabulate the one-month- 13 We show in Section 5.2 that using an alternative scaling variable (lagged book assets) for our profitability growth measure does not change conclusions, as portfolio sorts on profitability growth still generate significant spreads across both short and long (up to 18 months) investment horizons. 15

16 ahead three-factor (Fama and French, 1993), four-factor (Carhart, 1997) and five-factor (Fama and French, 2015) alphas of the ten profitability growth-sorted portfolios over our sample period. 14 Panels A and B present, respectively, the factor-adjusted returns and factor loadings for VW or RW portfolios. [Insert Table 4 here] The three-factor VW alphas typically increase with profitability growth. The values for the strong-growth and weak-growth decile portfolios are, respectively, 0.38% (t-value of 3.38) and % (t-value of -4.33) per month. The three-factor VW alphas on the extreme deciles are the highest and lowest in the cross section, and lead to a corresponding alpha on the long-short, profitability-growth portfolio of 0.93% (t-value of 5.55). The portfolio has a negative exposure to both the size (SMB) and value (HML) factors. The pattern is very similar when we examine the four- and five-factor VW alphas in the cross section of profitability growth. Again, the strong-profitability-growth portfolios earn the highest VW alphas whereas the weak-profitability-growth portfolios earn the lowest VW alphas across both factor models. The strong-minus-weak profitability-growth portfolio earns a four-factor VW alpha of 0.62% (t-value of 3.90) and a five-factor VW alpha of 0.73% (t-value of 4.18) per month. Abnormal returns are large despite the positive association between profitability growth and either operating profitability or price momentum that we report in Table 2. Indeed, the strong-minus-weak profitability-growth portfolios load positively on the momentum and profitability factors. Still, alphas are statistically significant in all cases, indicating that the high returns to profitability-growth strategies cannot be fully explained by their exposure to momentum and profitability factors. We note that risk-adjusted returns are not only economically large but their associated t-values generally exceed the cut-off of three in Harvey, Liu, and Zhu (2016). We further note that the strong-minus- 14 The three factor of Fama and French (1993), the four factors of Carhart (1997), the five factors of Fama and French (2015) are obtained from Kenneth French s webpage. 16

17 weak profitability-growth strategy is a growth strategy it loads negatively on the value (HML) factor and thus provides a good hedge, similar to the profitability (Novy-Marx, 2013) strategy, for value strategies. Table 4 further shows that significant risk-adjusted returns can be attained with long-only positions that condition on profitability growth. The strong profitability-growth portfolio (decile 10) consistently earns large and significant VW alphas across all three-factor models. For example, the monthly five-factor VW alpha for a long position in the strong-profitability growth portfolio is 0.48% (t-value of 4.04). The strong performance of long-only and VW positions is particularly important for the potential implementation of profitability-growth-based strategies, given that smaller stocks are more costly to short sell and trade. Panel B of Table 4 shows that the profitability-growth effect on alphas holds remarkably strong when the stocks in the portfolios are return weighted instead of value weighted. 15 First, RW alphas are perfectly monotonic increasing in profitability growth across factor models. Second, RW alphas on the strong-minus-weak portfolio are highly economically and statistically significant in all cases. Finally, the RW alphas on the long-only portfolio of top profitability-growth stocks are also large and significant Analysis by firm size Our results in the previous two sections indicate a strong relation between profitability growth and returns. They also suggest that the relation is not driven by the influence of a large number of relatively small firms, as the returns to profitability growth-sorted portfolios are significant on a VW basis. A few relatively large firms do not drive our results either, as the returns are even larger on a RW basis, which gives more even weight to the firms in each portfolio. In this section, we take a closer look at the prevalence of profitability-growth effects across different size groups. 15 Results are qualitatively identical if, as alternatively suggested by these authors, we apply initial-equal weighting instead of return weighting, to the stocks in each decile. 17

18 In Table 5 we apply dependent double sorts by sorting first on size and then on profitability growth, using NYSE breakpoints in both cases. 16 We denote the bottom- and top-size quintiles by Small and Large, respectively, and group the middle three-size quintiles under the Mid category. Panel A shows raw returns, whereas Panel B reports the risk-adjusted return spreads between strong- and weak-growth stocks after controlling for their exposure to the Fama and French s (1993, 2015) three and five factors, and by Carhart s (1997) four factors. In both panels, we present results for the VW (second thru fourth columns) and RW (fifth thru seventh columns) portfolios. [Insert Table 5 here] In Panel A, firms with strong profitability growth earn the highest returns, while firms with weak profitability growth earn the lowest returns, across size categories. Moreover, returns increase monotonically with profitability growth among the Small- and Mid-size firms. These patterns are true for both VW and RW portfolios strategies, suggesting that the profitability-growth effect is not limited to either the smallest or the largest firms in each portfolio. The raw VW spreads on the strong-minus-weak profitability-growth portfolio for the Small, Mid, and Large stocks are 1.77% (tvalue of 12.88), 0.56% (t-value of 4.23), and 0.36% (t-value of 2.14) per month. The corresponding raw RW spreads rise to 2.14% (t-value of 17.06), 0.77% (t-value of 6.28), and 0.44% (t-value of 2.89) per month. Panel B shows that returns to the strong-minus-weak profitability-growth portfolios for different firm sizes remain significant after controlling for risk. 17 The alphas with respect to the three-, four-, and five-factor models are comparable in magnitude to the raw returns in Panel A. For instance, the Fama and French (1993) five-factor VW alphas on the profitability-growth portfolio for the Small, 16 We use dependent instead of independent sorts to examine whether the profitability-growth effect remains robust after controlling for size. Regardless, we repeat our analysis using independent sorts (unreported) with qualitative similar results. 17 Novy-Marx (2015) finds that a strategy based on year-over-year change in earning per share also earns significant three- and four-factor VW alphas consistently across size quintiles. 18

19 Mid, and Large stocks are 1.51% (t-value of 10.04), 0.49% (t-value of 3.75), and 0.43% (t-value of 2.33) per month. The corresponding VW four-factor alphas are slightly smaller but remain positive, with values of 1.48% (t-statistic of 10.17), 0.38% (t-statistic of 3.10), and 0.21% (t-statistic of 1.41) per month, respectively. Once again, under a return weighting scheme alphas are highly economically and statistically significant across size groups and factor risk models. 18 For instance, the four-factor RW alphas on the profitability-growth portfolio for the Small, Mid, and Large stocks are 1.86% (t-value of 12.75), 0.55% (t-value of 4.92), and 0.28% (t-value of 2.25) per month Comparing Profitability Growth to Other Cross-sectional Predictors The portfolio tests of Section 3 establish a strong relation between profitability growth and the cross section of future returns. In this section, we run Fama and MacBeth (1973) regressions to examine whether the returns on profitability-growth strategies are absorbed by variations in other well-documented determinants of the cross section of stock returns. In particular, we seek to assess to what extent profitability growth reflects profitability (Novy-Marx, 2013), post-earningsannouncement drift (e.g., Ball and Brown, 1968), or profit trend (Akbas, Jiang, and Koch, 2017) anomalies. In all cases, we control for a base set of cross-sectional determinants that include the log of book-to-market ratio, the log of size, prior one-month returns and prior-year returns (Banz, 1981; Rosenberg, Reid, and Lanstein, 1985; Fama and French, 1992, 1993, 1996; Jegadeesh, 1990; Jegadeesh and Titman, 1993). 20 To reduce the impact of extreme values, we trim the independent 18 In an unreported analysis, we repeat the tests in Sections 3.2 and 3.3 by splitting the sample of all firms into Allbut-microcaps and Microcaps. The profitability-growth effect remains strong and significant in all cases. 19 The sizable alphas on the portfolio-growth strategy among large firms is particularly remarkable considering the vast average size of the firms in this group, as indicated in Panel D. 20 We follow the construction of book-to-market in Fama-French (1992), who measure book equity at the fiscal year end of the previous calendar year and define market equity as the market capitalization in December of the previous year. Market capitalization is the price times share outstanding from CRSP, in million dollars. Book equity is shareholder equity, plus deferred taxes, minus preferred stock where available. Stockholders equity is as given in Compustat data item (SEQ) if available, or common/ordinary equity plus the carrying value of preferred stock (CEQ+PSTX) if available, or total assets minus the sum of total liabilities and minority interest (AT (LT+MIB)). Deferred taxes are deferred taxes and investment tax credits (TXDITC) if available. Preferred stock is redemption value (PSTKR) if available, or liquidating value (PSTKRL) if available, or carrying value (PSTK). The profitability 19

20 variables at the 0.5% and 99.5% levels. 21 To be included in the cross-sectional regression analysis in a given month, we require that a firm has (1) return data in CRSP for the month, t + 1, the previous month, t, and the consecutive 11-month returns from month t 11 to t 1; (2) sufficient data available on the Compustat annual and quarterly files to calculate the book-to-market ratio and profitability growth Profitability growth and levels We observed in Table 2 that strong-profitability growth firms typically exhibit high profitability levels. Several authors show that profitability is positively related to cross-sectional returns after controlling for size and book-to-market ratios (Novy-Marx, 2013; Ball et al., 2015; Fama and French, 2015; Akbas, Jiang, and Koch, 2017). To ensure that our profitability-growth strategy does not simply mirror profitability-level strategies, we first compare the explanatory power of profitability growth (PG) with profitability levels (P/BE). Following this literature, we compute profitability level using Compustat annual items. We report average slopes and t-values from Fama and MacBeth (1973) cross-sectional regressions in Table 6. To limit the influence of microcaps on the regression estimates, we report the results for All-but-microcaps in Panel A and for Microcaps in Panel B. [Insert Table 6 here] Profitability growth (PG) has incremental explanatory power over book-to-market, size, return reversal, and momentum. Consistent with valuation Eq. (3) and the one-way sorts of Table 3, firms with stronger profitability growth exhibit higher future returns. In models (1) and (5), the average slopes on PG are positive and highly statistically significant, with t-values of 6.17 for All-butmicrocaps and for Microcaps. In line with prior literature (Banz, 1981; Fama and French, in level for year t is measured as operating profits (REVT COGS XSGA XINT) scaled by book equity with fiscal year ending in (any month of) calendar year t 1. Market equity is lagged six months to avoid taking unintentional positions in momentum (Novy-Marx, 2013). 21 Using 1% and 99% as the cut-offs produces similar results but significantly reduces the number of observations, especially for the regressions with many independent variables. 20

21 1992, 1996; Jegadeesh, 1990; Rosenberg, Reid, and Lanstein, 1985), the coefficient on book-tomarket ratio is significantly positive, while the coefficients on market capitalization and prior onemonth returns are negative. Prior-year returns, which proxy for price momentum effects, turn insignificant once profitability growth is controlled for. This suggests that profitability growth may absorb part of the momentum effect. 22 The level of profitability does not subsume the information contained in profitability growth. Consistent with previous literature, higher current profitability levels (P/BE) predict higher future stock returns after controlling for book-to-market, size, return reversal and momentum in models (2) and (6). 23 The coefficient of P/BE is positive and significant, with t-values of 4.50 for All-butmicrocaps and 4.02 for Microcaps. When both PG and P/BE are included in specifications (3) and (7), the economic and statistical significance of PG remains high, with t-values of 6.71 for All-butmicrocaps and for Microcaps. By contrast, among All-but-microcaps the t-values associated with P/BE drop relative to specifications (2) and (6). Since P/BE remains significant in (3) and (7), we conclude that both profitability growth and levels have independent explanatory power on the cross section of stock returns. The significance of profitability growth in multivariate regressions is robust to correction for microstructure noise. Asparouhova, Bessembinder, and Kalcheva (2010) show that, when running ordinary least squares (OLS) regressions with rates of return as the dependent variable, noisy prices can lead to biased estimates of the intercept and slopes. The bias can artificially inflate the t-value for a regressor that is positively correlated with price noise. They suggest correcting this bias by replacing OLS by weighted least squares (WLS) in cross-sectional regressions, with the prior-period 22 In other words, firms with positive profitability growth tend to become momentum winners while firms with negative profitability growth tend to become momentum losers. In related studies, Novy-Marx (2015a, b) finds that earnings innovations are a driver of price momentum effects. In the same vein, Hou, Xue, and Zhang (2015) suggest that shocks to profitability in levels are positively correlated to stock returns. 23 We note that, before the addition of the profitability-growth variable in models (3) and (7), the momentum effect is not absorbed by the profitability in levels. 21

22 gross return as the weighting variable. We follow this approach in models (4) and (8). Most of the results remain unaltered. In particular, the average slopes on PG and P/BE remain positive and highly statistically significant for both All-but-microcaps and Microcaps Profitability growth, PEAD, and fundamental momentum Our profitability-growth measure reflects the most recent changes in firm profitability. Under a seasonal random-walk model for firm profits, these changes might reflect the surprise component of the firm s most recent profits or profit innovations. A large literature documents that innovations in earnings (e.g., Ball and Brown, 1968; Foster, Olsen, and Shevlin, 1984; Bernard and Thomas, 1989; Chan, Jegadeesh, and Lakonishok, 1996; Novy-Marx, 2015a, b), or earnings surprises, are positively related to future returns. This phenomenon is known as the post-earnings-announcement drift (PEAD), or fundamental momentum anomaly. In particular, Novy-Marx (2015a) shows that a factor based on the year-over-year changes in earnings, scaled by lagged book equity, can price momentum portfolios. Given the positive relation between profitability growth and price momentum that we report in Table 2, these findings raise the question of whether profitability growth purely mirrors the PEAD effect. To answer this question, we first note that the dynamics of profitability growth, as well as the predicted return pattern at different horizons, differ from those documented by the PEAD literature. Indeed, Bernard and Thomas (1990) document a strong positive autocorrelation in earnings surprises at lags 1 to 3, but a reversion in the sign of the autocorrelation coefficients at lags 4 to 8. Unlike this literature, the regression coefficients of profitability growth on its lags 5 to 7 that we report in Section 2.2 are positive and statistically significant. Moreover, Bernard and Thomas (1989) show 24 We obtained similar supporting results (unreported) when estimating WLS regressions with initial-equal weight instead of prior-period gross returns. Furthermore, the incremental effect of profitability growth over profitability levels does not depend on the parametric assumptions underlying the regression framework of this section. Indeed, we show in Section 5.3 that two-way portfolio sorts that condition on profitability growth attain significant raw and risk-adjusted returns across profitability level-sorted portfolios. 22