Constructing a Powerful Profitability Factor:

International Evidence

Matthias X. Hanauer and Daniel Huber ∗

First draft: January 31, 2017

This draft: September 25, 2018

Recent findings for the U.S. stock market indicate that cash-based profitability

measures (i.e., profitability measures that exclude accounting accruals) outper-

form measures of profitability that include accruals. We demonstrate that this

result also holds for international markets. In a comparison of different profitabil-

ity definitions, we find that a factor based on cash-based gross profitability (gross

profitability adjusted for accounting accruals) subsumes other popular profitabil-

ity factors based on time-series, factor-spanning, and cross-sectional asset pricing

tests. We therefore propose that a profitability factor based on cash-based gross

profitability should be used in international factor models.

Keywords: Factor models, Profitability, International Markets, Anomalies

JEL Classifications: G11, G12, G15∗Department of Financial Management and Capital Markets, Technische Universitat Munchen (TUM),

Arcisstr. 21, 80333 Munich, Germany.Email: matthias.hanauer@tum.de, daniel.huber@tum.deWe appreciate helpful comments from David Blitz, John Doukas, Jurgen Ernstberger, Ralf Elsaß, RudigerFahlenbrach, Stefano Giglio, Heiko Jacobs, Christoph Kaserer, Laurens Swinkels, Milan Vidojevic, andMichael Weber, as well as conference and seminar participants at the EFMA Doctoral Seminar 2017,the Robeco Research Seminar, the TUM Research Seminar 2017, and the Munich Finance Day 2018.Matthias is also employed by Robeco, an asset management firm that among other strategies offers activefactor investing strategies. The views expressed in this paper are solely those of the authors and do notnecessarily express the views of TUM or Robeco. Earlier versions of this paper were circulated under thetitle “Dissecting Profitability: Evidence from International Stock Markets”. Any remaining errors are ourown.

1

1 Introduction

This paper investigates the relation between average stock returns and various prominent

profitability measures in international stock markets. We document that average returns

increase with profitability in countries outside of the U.S., where recent findings indicate

that cash-based profitability measures (i.e., profitability measures that exclude accounting

accruals) outperform measures of profitability that include accruals. Furthermore, we find

that internationally, a newly introduced profitability factor, based on cash-based gross prof-

itability, has the highest marginal power in a range of time-series, factor-spanning, and

cross-sectional asset pricing tests.

One of the economic motivations for including a profitability factor in an asset pricing

model stems from the rewritten dividend discount model, as stated by Fama and French

(2015):1

Mt

Bt

=∑∞τ=1 E(Yt+τ − dBt+τ )/(1 + r)τ

Bt

. (1)

In the above equation, for a given firm, Mt refers to the total market value at time t, Bt

to the book equity at time t, Yt+τ to the total equity earnings for period t + τ , and r to

the internal rate of return on expected dividends (i.e., approximately the long-term average

expected stock return). The equation states that if current valuation, Mt

Bt, and expected

future investments, dBt+τBt

, are fixed, a higher expected future profitability, Yt+τBt

, implies a

higher expected return, r.

Using current profitability as a proxy for expected future profitability, various researchers

(e.g., Novy-Marx 2013, Ball et al. 2015 and Fama and French 2015) confirm this relationship

empirically for the U.S. stock market, showing that higher stock returns are associated with

higher profitability ratios. This so-called profitability effect is one of the most prominent

asset pricing phenomena documented in the finance literature. However, in contrast to other

1Please note that the q-factor model of Hou, Xue, and Zhang (2015) also contains a profitability factor, butthe economic rationale for the inclusion is different.

2

popular effects—like value, size, and momentum—there is no generally accepted definition

of profitability in the literature.

For instance, Haugen and Baker (1996) show that profitability measured as net income to

book value of equity (hereinafter return on equity or ROE) is positively correlated with future

returns.2 Novy-Marx (2013) shows that gross profitability, defined as gross profits deflated

by the book value of total assets, predicts the cross-section of expected stock returns and

has a higher predictive power than ROE. Ball et al. (2015) confirm these results and point

out that the difference in the marginal predictive power is mainly due to the deflator in the

measures. Furthermore, they develop a new measure—operating profitability—and claim

that it reflects more closely the actual expenses incurred to generate revenue for a given

period. Operating profitability is defined as gross profit less selling, general and administra-

tive expenses (SG&A), excluding research and development (R&D) expenditures, deflated

by the book value of total assets. In a comparison with gross profitability, the authors find

that operating profitability is better suited for predicting the cross-section of expected stock

returns. Another definition of operating profitability by Fama and French (2015) was intro-

duced within the framework of the Fama-French five-factor model: gross profits less SG&A,

less interest expenses, deflated by the book value of equity.

The four measures of profitability introduced so far have something in common: They

include accruals, which are accounting adjustments of operating cash flows used to more pre-

cisely measure periodic firm performance (Ball et al. 2016). Accruals, however, are negatively

correlated with the cross-section of expected returns (Sloan 1996); this phenomenon, which is

also referred to as the accrual anomaly, was confirmed by numerous studies (e.g., Fama and

French 2008, Hirshleifer, Hou, and Teoh 2009, and Polk and Sapienza 2009). Ball et al. (2016)

account for this issue by correcting any accounting accruals adjustments that were made to

operating profitability;3 the result is cash-based operating profitability. They find that this

2Also Hou, Xue, and Zhang (2015) use a factor based on ROE in their q-factor model. However, in order tocalculate this factor, they use more timely information on net income taken from the most recent publicquarterly earnings announcement.

3These adjustments are changes in accounts receivable, inventory, prepaid expenses, deferred revenue, ac-

3

measure dominates operating profitability in the explanation of the cross-section of expected

returns and it even subsumes the accrual anomaly. Furthermore, Fama and French (2018)

also acknowledge that cash-based operating profitability dominates operating profitability

as defined in Fama and French (2015). Consequently, Fama and French (2017) hint at the

possibility that future research might further refine the definition of the profitability factor

in asset pricing models, such as their five-factor model.

Barillas et al. (2017) compare various prominent asset pricing models by their maximum

squared Sharpe ratios and state that “the choice of profitability factor is a key”. More

specifically, they find that models that include a cash-based profitability factor are superior

to models with the more traditional, accruals-based profitability factors. However, all of

the aforementioned results are based on U.S. data only and evidence for a broader set of

profitability measures in international markets is currently rare.4 To investigate if these

findings can be extended to international markets or are a country-specific phenomenon,

we concentrate on international markets outside the U.S.5 The international evidence for

the profitability effect is of particular interest because U.S. studies that investigate periods

prior to the original sample periods (i.e., pre-sample studies) led to conflicting results. For

instance, Linnainmaa and Roberts (2018) find profitability returns that are statistically not

distinguishable from zero between 1926 and 1963, while Wahal (2018) reports a significant

profitability premium over the period from 1940 to 1963, controlling for value.

Drawing on the research findings presented so far, we investigate the following profitability

measures: (i) return on equity (ROE), (ii) gross profitability by Novy-Marx (2013), (iii)

operating profitability by Ball et al. (2015), operating profitability defined in an alternative

way (iv) by Fama and French (2015), and (v) cash-based operating profitability by Ball

counts payable, and accrued expenses.4In this context, Karolyi (2016) speaks of a large U.S. “home bias” in the empirical Finance literature. We

later discuss the papers by Cakici, Chatterjee, and Tang (2017) and Chen et al. (2018) that also compareprofitability measures outside the U.S.

5Examples for findings that do not hold internationally are the momentum echo and the post-publicationdecline in anomalies documented by Novy-Marx (2012) and McLean and Pontiff (2016), respectively, forthe U.S. In contrast, Goyal and Wahal (2015) and Jacobs and Muller (2018) find no robust evidence forthese effects in more than thirty non-U.S. countries.

4

et al. (2016), with two major goals: Evaluating their return predictive power, both (1)

standalone; and (2) in the presence of other factors, including other profitability factors.

We collect monthly equity market data from Datastream and yearly accounting data from

Worldscope from 07/1989 to 06/2016 on firm level for 49 countries and apply common quality

filters that are proposed in the literature. Generally, we include all countries in our analysis

for the periods in which they are classified by MSCI as a developed or an emerging market.

We provide strong evidence that the profitability effect is globally prevalent. Interestingly,

we find that in contrast to the results of Ball et al. (2015), the step from (ii) gross profitability

to (iii) operating profitability (i.e., subtracting SG&A excluding R&D expenditures) results

in a lower forecasting power; whereas, correcting for accounting accruals leads to the same

positive effect as presented by Ball et al. (2016) for the U.S. Thus, in a new approach, we

abstain from the SG&A correction and propose a new profitability measure that adjusts

gross profitability for accounting accruals: (vi) cash-based gross profitability. By performing

a range of factor, portfolio-based, and cross-sectional asset pricing tests, we show that all

profitability definitions besides ROE are robustly priced outside the U.S. Even more striking,

cash-based gross profitability emerges as the strongest of all the profitability measures. We

perform several comparative tests on the profitability measures, which lead to the same

principal result—cash-based gross profitability can subsume the other profitability measures.

Finally, we also provide evidence that comparatively stronger profitability measures are better

suited for the explanation of future earnings growth, which hints at the possibility that future

earnings growth is an important driver of the profitability premium.

Our main goal is to determine the most suitable profitability factor from a global perspec-

tive (excluding the U.S.). However, for robustness reasons, we also perform an analysis on

the basis of regional and country levels. We find that all profitability factors exhibit positive

premiums across regions and that cash-based gross profitability is the dominant profitability

factor for developed and emerging markets as well as for Japan and Asia Pacific excluding

Japan (as part of developed markets). Only for Europe, does cash-based operating profitabil-

5

ity show a slightly better performance than cash-based gross profitability, which is second

in rank. In addition, we find that the cash-based gross profitability factor exhibits positive

average returns and spanning test alphas in the majority of developed and emerging market

countries.

The documented results have important implications for the definition of a powerful em-

pirical asset pricing model. Harvey, Liu, and Zhu (2016) catalog 316 published anomalies as

potential asset pricing factors in the cross-section of stock returns. Researchers have tried

to shrink this list of anomalies using factor models that only include a small number of

characteristic-based factors, e.g., Fama and French (2015) with the five-factor model and

Hou, Xue, and Zhang (2015) with the q-factor model. Both models notably include a prof-

itability factor. Although both papers motivate the inclusion by an economic rationale, the

factor definitions differ from each other, which implies that further empirical tests are re-

quired to contest or to strengthen the underlying rationales. In case of a parsimonious factor

model, however, it is crucial that the implemented factors exhibit high power, that is they (i)

independently display economically substantial and significantly abnormal returns; and (ii)

cannot be subsumed by the remaining factors of the model. Moreover, (iii) small alterations

in the factor definitions (variants) should not lead to abnormal returns relative to the default

factor definitions. Finally, a powerful factor model should also be better suited for reduc-

ing the number of remaining anomalies in the cross-section of stock returns. For instance,

Ball et al. (2016) demonstrate that a model that incorporates a cash-based profitability factor

subsumes the accrual anomaly. Taking these requirements into account, our findings indicate

that a profitability factor based on cash-based gross profitability is more powerful than the

other profitability factors analyzed. We follow that cash-based gross profitability is preferable

for factor models that focus on international markets.

The papers closest to ours are Cakici, Chatterjee, and Tang (2017) and Chen et al. (2018).

In both of these papers, the authors compare various profitability factors on international

markets; however, they analyze the factor returns only on a standalone basis and do not

6

control for other predictors of realized stock returns. In contrast, we investigate whether the

profitability factors are distinct factors that can expand the efficient frontier constructed by

means of other well-known factors in the literature. Cakici, Chatterjee, and Tang (2017)

document that gross profits are a superior numerator compared to operating income and

earnings before interest and taxes (EBIT), but recommend scaling them by enterprise value

or market value of equity. In line with these results, we also find that a factor based on

cash-based gross profits scaled by enterprise value carries a higher standalone return than

the standard factor variant based on cash-based gross profits scaled by total assets. This

superiority, however, disappears when we control for other factors, like a value factor that

already incorporates a valuation effect, which was induced prior solely by using the enterprise

value as a denominator in the profitability ratio. Chen et al. (2018) find that monthly portfolio

sorts based on quarterly ROE lead to the highest return spreads in most of the countries

of their sample. We do not calculate profitability factors based on quarterly accounting

data as this would substantially reduce our sample and make the factors incomparable.6

Furthermore, Novy-Marx (2015) argues that using quarterly accounting data could induce

a look-ahead bias, because quarterly earnings might include revisions and thus might be

different from the earnings that are actually announced. For the stated reasons, we calculate

all profitability ratios based only on annual accounting information in order to put them on

an equal footing. As a result, we find that a factor based on ROE has only weak predictive

power compared to the factors based on the other profitability ratios. One of the reasons

for this outcome seems to be the mean-reverting character of ROE that we document in an

analysis of future profitability growth. Finally, both of these thematically-related papers are

also different from our analysis in that they do not include a cash-based profitability factor.

Our study also adds to the consistently expanding literature on international evidence for

6Exemplary comparing yearly and quarterly earnings-per-share (EPS) data from Worldscope, we find thatusing quarterly data would imply a total loss of more than 50% of the observations per year, rangingfrom more than 80% at the beginning of the sample to less than 20% at the end of the sample. AlsoWalkshausl and Lobe (2014) state that the reporting of quarterly accounting data has just started and isnot (yet) common practice in many non-U.S. countries of their sample.

7

cross-sectional return predictors that were initially only documented for the U.S. Previous

research in this context includes the studies by Fama and French (1998), Rouwenhorst (1998),

McLean, Pontiff, and Watanabe (2009), and Watanabe et al. (2013), who analyze value,

momentum, share issuance and asset growth, respectively.

The paper is structured as follows: Section 2 describes the data and variables. Section 3

outlines the theoretical framework behind the analysis. Section 4 presents empirical results,

Section 5 contains robustness tests, and Section 6 concludes.

2 Data

We collect monthly equity market data from Datastream and yearly accounting data from

Worldscope from 07/1989 to 06/2016 on firm level for the following 49 countries: Argentina,

Australia, Austria, Belgium, Brazil, Canada, Chile, China,7 Colombia, Czech Republic, Den-

mark, Egypt, Finland, France, Germany, Great Britain, Greece, Hong Kong, Hungary, In-

donesia, India, Ireland, Israel, Italy, Jordan, Japan, Korea, Morocco, Mexico, Malaysia,

Netherlands, Norway, New Zealand, Pakistan, Peru, Philippines, Poland, Portugal, Russia,

Singapore, Spain, South Africa, Sri Lanka, Sweden, Switzerland, Thailand, Turkey, Taiwan,

and Venezuela. As in Jacobs (2016), we include all countries in our analysis for the periods in

which they are classified by MSCI as a developed or an emerging market. Mexico, Sri Lanka,

and Venezuela are later dropped from the sample because they do not fulfill our requirements

to either have the variables needed to construct the profitability measures or to have at least

25 stocks available during any month of the sample period.

The result is a comprehensive, international sample. We do not include the U.S., because

the analysis of profitability for this region is already available, and obviously, including the

U.S. would have a considerable effect on any findings. Table 1 provides an overview of the

sample.

7Chinese “A” shares are excluded from the sample because they were not accessible for international investorsfor a large part of our sample period.

8

[Table 1 about here.]

The sample start date of 07/1990 was chosen specifically, because this is the time when

cross-sectional data becomes more available in Datastream.8 Moreover, other international

studies (e.g., Fama and French 2012 and Fama and French 2017) start in 1990 as well, which

allows for an easier comparison of the results.

As we want to restrict our sample to common stocks, exclusively, and to ensure high data

quality, we conduct the recommended static and dynamic screens proposed by Ince and Porter

(2006), Griffin, Kelly, and Nardari (2010) and Schmidt et al. (2017). More specifically, (i)

we demand that companies are located and securities are listed in the respective domestic

country; (ii) only primary quotations of a security are analyzed; (iii) for firms with more

than one equity security, only the one with the biggest market capitalization and liquidity

is chosen; (iv) securities with quoted currency or with ISIN country codes different from

those of the associated countries are disregarded; (v) following Karolyi, Lee, and Dijk (2012),

Schmidt et al. (2017), and Griffin, Kelly, and Nardari (2010), we also apply name filters in

order to exclude any non-common equity securities like ADRs, investment trusts, REITs,

mutual funds, preferred stocks, and warrants from our sample. Finally, we perform a manual

check of all removed stocks to ensure that none of them was deleted by error. The details of

this comprehensive screening process are provided in Appendix A.1.

Moreover, we consider both active and dead stocks, in order to obviate survivorship

bias. Following Fama and French (1992), Novy-Marx (2013), Ball et al. (2015), and Ball

et al. (2016) among others, all financial firms are dropped.

For the remaining firms, we calculate accruals and cash-based operating profitability ac-

cording to Ball et al. (2016), operating profitability according to Fama and French (2015)

and Ball et al. (2015), and gross profitability according to Novy-Marx (2013). We also calcu-

late cash-based gross profitability, which is defined in a similar way to cash-based operating

profitability; the only difference is that the starting point is gross profitability instead of8The data collection already starts in 07/1989 as we require the returns in the prior twelve months of the

sample start date to calculate momentum.

9

operating profitability.9 Table 2 contains summary statistics of these variables as well as

the following five control variables: the natural logarithm of the book-to-market ratio, with

the book value of equity defined as shareholder’s equity plus balance sheet deferred taxes (if

available), the natural logarithm of the monthly market capitalization lagged by one month,

momentum calculated as the cumulative return from months t − 12 to t − 2, the current

return lagged by one month and the growth rate of total assets. As in McLean, Pontiff, and

Watanabe (2009), we winsorize each of the variables at the top and bottom 1% to eliminate

the effects of outliers. We then calculate the summary statistics as the time series averages

of the measures.

[Table 2 about here.]

For a firm to be part of our empirical analysis, we demand the following variables to be

available: the associated stock return, momentum, sales and costs of goods sold. Moreover,

the following variables must be larger than zero: the one-month lagged market capitalization,

the book-to-market ratio, total assets, and total assets lagged by one year. The remaining

number of firm-months after the application of all these filters is 3,727,579.

We find that the average annual gross profitability is 24%. If we subtract SG&A expenses

(net of R&D expenditures), to calculate operating profitability, this value drops to 11%. If we

additionally account for both interest expenses and R&D expenditures and divide by book

equity, as in the case of the Fama and French (2015) definition, we observe an average value of

22%. If we further perform cash adjustments on operating or on gross profitability, the result

decreases only by 1%, in either case. As before with the non-cash-based measures, there is

a clear effect in the deduction of SG&A expenditures and the addition of R&D expenses.

Accruals are on average -3% of total assets. The values for operating profitability, cash-based

operating profitability, and accruals are close to the values reported in Ball et al. (2016) for

the U.S. (13%, 12%, and -3%, respectively). However, the average gross profitability for the

9The details of the variable constructions are provided in Appendix A.2. To ensure that accounting infor-mation is known before we use it to explain the stock returns, we match accounting information for thefiscal year y − 1 with stock returns from July of year y to June of year y + 1 throughout the paper.

10

U.S. as reported by Ball et al. (2015) is much higher (37%). It seems that SG&A expenses

(net of R&D expenditures and scaled by total assets) have a more dominant role in the U.S.

than in markets outside the U.S.

[Table 3 about here.]

Table 3 displays time series averages of the correlations between the profitability measures

and accruals. The correlation between gross profitability and operating profitability is 0.64

and between gross profitability and operating profitability according to Fama and French is

0.56. Accruals are slightly negatively correlated with operating profitability, as opposed to the

U.S. findings, where the coefficient is positive (cf. Ball et al. 2016). The correlation between

gross profitability and cash-based gross profitability is, however, highly positive, as expected

(0.88). Operating profitability is highly correlated with cash-based operating profitability

(0.78), but not as much with cash-based gross profitability (0.52). The correlation between

cash-based operating profitability and cash-based gross profitability of 0.69 is rather low,

which is similar to the correlation between operating profitability and gross profitability. This

documents once more the notable influences of SG&A and R&D expenses on the profitability

definitions. The table also shows that all profitability measures are negatively correlated with

the book-to-market ratio. This finding indicates that profitable firms exhibit high valuations

and therefore, it is important to control for other factors, such as the value factor, in the

following analyses.

3 Methodology

Based on the results in Ball et al. (2016) and Barillas et al. (2017), we would expect asset

pricing models that incorporate a cash-based operating profitability factor to perform better

than those which do not, or those which rely on another profitability factor that is different

from cash-based operating profitability. In order to test this expectation, we (1) evaluate

different factors by means of descriptive statistics and factor spanning tests and (2) perform

11

asset pricing tests that build on the insights of (1) with regard to the choice of the profitability

measure in the factor creation.

To be more specific, we analyze the following set of factors: the size factor (SMB, small

minus big), the value factor (HML, high minus low), the momentum factor (MOM), the

investment factor (CMA, conservative minus aggressive), several profitability factors (RMW,

robust minus weak) based on the following profitability definitions: ROE, gross profitability

(GP), operating profitability as defined by Ball et al. (2015, OP), operating profitability

as originally defined by Fama and French (2015, OPFF), cash-based operating profitability

(CbOP) and cash-based gross profitability (CbGP), and an accruals factor (ACC).

SMB and HML are constructed as follows: At June of every year, the stocks of every

country are sorted independently into two size groups, Big (B) and Small (S) and three

book-to-market (BM) groups, High (H), Medium (M) and Low (L). At the intersection of

the 2 x 3 size and book-to-market groups, six portfolios are created. SMB is calculated as

the difference between the average monthly portfolio returns of the three small stock and

the three big stock portfolios and HML is calculated as the difference between the average

monthly returns of the two high and the two low BM stock portfolios.

RMW and CMA are constructed analogously to HML, except for the sorting variable

besides size, which is profitability in the case of RMW (measured as ROE, GP, OPFF, OP,

CbOP, or CbGP), and the growth rate of the book value of total assets from year y − 2 to

y − 1, in the case of CMA.

In order to construct MOM, the stocks are sorted every month t by their cumulative past

performance from month t− 12 to month t− 2 into winners (W) and losers (L). In addition,

similar to HML, the stocks are allocated every month t to the two size portfolios, B and S.

Apart from that, the calculation of MOM is analogous to HML.

With regard to the size breakpoints in the 2 x 3 sorts, we follow the common approach of

Fama and French (2012) for international data: the stocks in the top 90% of the aggregate

market capitalization of a country are classified as big and the stocks in the bottom 10% are

12

classified as small. For the other sorting variable besides size, we calculate the breakpoints

as the 30th and 70th percentiles of big stocks per country (cf. Fama and French 2012, 2017).

Moreover, we aim to investigate if international asset pricing models can be improved

substantially by adding a profitability factor if it was not already included, or by the choice

of the profitability measure underlying the factor. We analyze the following asset pricing

models: the Capital Asset Pricing Model (CAPM), the Fama-French three-factor model

(FF3FM), the Fama-French-Carhart four-factor model (FFC4FM), the Fama-French five-

factor model (FF5FM), a modified Fama-French five-factor model based on CbGP instead

of OPFF (FF5FMCbGP), and the modified model plus momentum (FF5FMCbGP+MOM).

4 Empirical Results

4.1 Factor Analysis

Table 4 provides an overview of the average monthly returns, the monthly standard deviations

and the t-values of the aforementioned factors. The returns of the traditional four factors are

in line with earlier international evidence as, e.g., in Fama and French (2012). The average

returns for the market and size premiums are 31 bp and -3 bp, respectively, however, both are

not significantly different from zero (t-values of 1.12 and -0.28). In contrast, the value and

momentum premiums are both economically and statistically significant with average returns

of 46 bp (t-value of 3.70) and 70 bp (t-value of 3.74), respectively. The average returns of 26 bp

and 14 bp for the investment and accruals factors, respectively, are smaller but still more than

two standard errors away from zero. Among the profitability factors, the premiums range

from 13 bp for RMWROE to 36 bp for RMWCbGP. These premiums are also highly significant,

with t-values ranging from 3.09 for RMWOPFF to 4.67 for RMWCbGP. Only the premium that

is based on ROE (t-value of 1.86) is below the traditional threshold of two standard errors.

We can also confirm the results of Novy-Marx (2013) and Ball et al. (2016) that top-line

profitability measures, such as gross profitability and operating profitability, are superior

13

to bottom-line net income and that correcting for accounting accruals (the step from gross

profitability or operating profitability to their cash-based variants) leads to higher average

returns. In contrast to the findings in Ball et al. (2015), the step from (cash-based) gross

profitability to (cash-based) operating profitability leads to lower premiums in international

markets. Overall, all profitability factors besides RMWROE exhibit strong statistical and

economical significance and RMWCbGP shows the highest premium individually.

[Table 4 about here.]

To understand which of the factors are more important than others, or which of them are

possibly redundant, we perform factor spanning tests as follows: The asset pricing model to

be tested in a single test is used to explain a factor, which by definition is not part of the

explanatory variables of the model. If the model generates sizable and statistically significant

alphas, the omitted factor contains important information, which is not covered by the model

under observation.

For the first set of spanning regressions (Panel A) we use the FFC4FM complemented

by the investment factor CMA in order to explain RMW, based on ROE, GP, OPFF, OP,

CbOP, CbGP and, ACC. For the second set of regressions (Panel B), we add RMWCbGP to

the model and then rerun the tests. In the final set of regressions (Panel C), RMWCbGP

is the dependent variable, and we add separately RMWOPFF , RMWOP, and RMWCbOP as

independent variable instead. The results are presented in Table 5.

[Table 5 about here.]

Panel A shows that each of the six profitability factors and the accruals factors exhibit

significant alphas when regressed on the remaining factors. The accruals factor has an al-

pha of 11 bp (t-value of 2.15) and the profitability factor alphas range from 0.20 bp for

RMWROE and RMWOPFF (t-values of 3.08 and 3.32, respectively) to 46 bp for RMWGP and

RMWCbGP (t-values of 7.23 and 7.60, respectively). These results confirm our hypothesis,

that profitability is a separate factor in the cross-section of realized stock returns and con-

14

tains valuable information, which is not already included in the FFC4FM complemented by

CMA. When we augment the explanatory factors with RMWCbGP in Panel B, the augmented

model captures the average returns of all other profitability factors and the accruals factor.

The remaining alphas range from 0 bp to 6 bp and are all insignificant (maximum t-value

of 1.16). Our third set of regressions, presented in Panel C, shows that the converse is not

true. When RMWCbGP is the dependent variable and RMWOPFF or RMWOP or RMWCbOP is

added to the independent variables, the alpha stays significant and ranges between 19 bp and

39 bp, with t-values greater than 4.23.10 This confirms the previous results, that RMWCbGP

is superior to the other profitability measures.

To evaluate the consistency of the profitability premium over time, Figure 1 plots the

cumulative sum of factor returns and spanning alphas over time. The plot uses the full

sample estimates of the spanning betas to estimate the monthly alphas.

[Figure 1 about here.]

Figure 1 shows that the returns for the cash-based gross profitability factor are quite

consistent over time with high returns from 1990 to 2000 and from 2008 to 2016. Between

2000 and 2008, the performance is rather flat until 2005 and the years between 2005 and

2008 are the only period with a prolonged negative performance. This period, however, also

exhibits a strong positive performance for the value factor (not shown in the graph). As

the value and profitability factors are typically negatively correlated, we also analyze the

cumulative performance of the spanning alpha. When controlling for the other factors, the

cumulative performance becomes even stronger and more stable with only a short period of

negative to flat returns between 2005 and 2008.

In order to measure the economic significance of our findings, we follow Ball et al. (2016)

and calculate the ex-post maximum Sharpe ratios associated with various factor combinations

from the viewpoint of an investor who is trading these factors. In this analysis, the lower

10In unreported tests, we find that the RMWCbGP alpha also remains positive and significant when RMWROEor RMWGP is added to the independent variables.

15

bound for the weights is zero and the sum of the weights has to add up to 1. Table 6 displays

the factor weights of the factor portfolios and the corresponding maximum Sharpe ratios.

[Table 6 about here.]

The (annualized) Sharpe ratio on the international market portfolio (CAPM) is 0.22 and

it increases to 0.83 when we extend the factor set with the classical size and value factors

(FF3FM). Further adding the momentum factor (FFC4FM) or the two new factors of the

Fama and French (2015) five-factor model (FF5FM) leads in both cases to a Sharpe ratio

of 1.28. When the factors are jointly added instead (FF5FM + MOM), the Sharpe ratio

amounts to 1.48. An investor who holds the securities underlying the previously mentioned

factors could only marginally profit by adding an accruals factor (FF5FM + MOM + ACC)

as the Sharpe ratio increases only to 1.53 in this case. However, replacing the profitability

factor of the Fama and French (2015) five-factor model by an alternative profitability factor

would be clearly beneficial. The highest Sharpe ratio with a value of 2.07 can be achieved by

adding a cash-based gross profitability factor (FF5FMCbGP + MOM + ACC). The investment

opportunity set that consists of all possible factors (ALL) on the other hand, only obtains

a marginally higher Sharpe ratio of 2.09 and the associated tangency portfolio places the

highest weight on the cash-based gross profitability factor (34%).

The results above indicate again that a cash-based gross profitability factor (RMWCbGP)

is superior to alternative profitability factor definitions. Next, we investigate if this result

also holds in the context of finer portfolio sorts.

We form quintile portfolios and the associated 5-1 (high-minus-low) portfolios based on

every sorting profitability variable at June of every year, from 07/1990 to 06/2016, and

calculate value-weighted monthly excess returns from July of year t until June of year t+1,

respectively. As in the factor analysis, the breakpoints are estimated based on big stocks.

Panel A in Table 7 presents the average value-weighted excess returns of these portfolios.

The 5-1 portfolios will be analyzed in greater detail, so we also state the respective t-values in

this case. In Panel B, we investigate if the 5-1 portfolio excess returns can be explained by the

16

CAPM, the FF3FM, the FFC4FM, the FF5FM, a modified FF5FM based on CbGP instead

of OPFF (FF5FMCbGP), and the modified model plus momentum (FF5FMCbGP+MOM).

[Table 7 about here.]

The excess returns on the 5-1 (high-minus-low) quintile portfolios created based on ROE,

gross profitability (GP), operating profitability (OP), cash-based operating profitability (CbOP),

and cash-based gross profitability (CbGP) are between 29 bp (OP) and 40 bp (CbGP), and

the associated t-values range from 2.47 (OP) to 3.46 (CbGP). Only the 5-1 portfolio based

on operating profitability by Fama and French (OPFF) has a low return of 4 bp, with an

associated t-value of 0.40—it seems that deducting interest rate expenses generally has also

a considerable effect on the profitability definition. The return on the 5-1 accruals (Accr)

portfolio is -0.10 bp with a t-value of -1.06.

The regressions in Panel B show that neither the CAPM, nor the FF3FM, nor the FFC4FM,

nor the FF5FM can capture the average 5-1 portfolio return for most of the profitability

measures. The only notable exception is the 5-1 Accr portfolio return, which can be explained

by each of the models, but especially well by the FF5FM (alpha = -0.01, t-value -0.09). The

biggest improvement in the models appears if we look at the FF5FMCbGP. All the alphas,

except for the one based on ROE (which is 22 bp), are below or equal to an absolute value

of 10 bp, and not significant. If we further add momentum to the model, the alphas are

almost unchanged. We conclude, that in particular the substitution of OPFF by CbGP can

be recommended to improve on the FF5FM definition on international markets.

4.2 Fama-MacBeth (1973) Regressions

In this subsection, we investigate the suitability of the six profitability measures to predict

future returns in cross-sectional regressions. Every month, from 07/1990 until 06/2016,

we perform Fama and MacBeth (1973) regressions of monthly stock returns on one of the

six profitability measures (models 1 to 6), on accruals (model 7) and on cash-based gross

17

profitability in combination with each of the other profitability definitions and accruals,

respectively (models 8 to 13). Moreover, every model includes the five control variables

introduced in Section 2 and country dummies to control for potential country effects. The

results are shown in Table 8.11

[Table 8 about here.]

We find that the most prominent profitability definitions in the literature, namely gross

profitability, operating profitability (according to Fama and French 2015 as well as Ball et

al. 2015), and cash-based operating profitability, exhibit positive average regression slopes

that are significantly different from zero. Our newly introduced measure, cash-based gross

profitability, however, has the highest statistical significance in either the individual tests

(models 1 to 6), or when testing against other profitability ratios (Panel B). Model 7 confirms

the existence of the accrual anomaly in our sample and Panel B shows that this anomaly

becomes less prevalent if we add cash-based gross profitability as explanatory variables to

the model.

We can confirm the result by Novy-Marx (2013) internationally: that gross profitability

is a superior profitability measure to ROE. Moreover, similar to Ball et al. (2016), there

is a clear positive effect in the adjustment for accounting accruals; in other words, cash-

based operating profitability according to Ball et al. (2016) is superior to its non-cash-based

predecessor. We can also confirm Fama and French (2018) in their assertion that cash-based

operating profitability beats their original version of operating profitability. Furthermore, we

infer, in particularly from models 5, 6 and 12, that cash-based gross profitability is superior

to cash-based operating profitability.

4.3 Current profitability and future profitability

The profitability variables analyzed in this study refer to the most recent reporting period at

a time. However, Yt+τBt

in equation (1) stands for the (expected) future profitability of a given11The coefficients for the country dummies are not reported for the purpose of conciseness.

18

firm. It follows that if a profitability variable is priced in the cross-section of stock returns,

it should be also an indicator of future profitability.

In order to test this assertion, we follow Novy-Marx (2013) and Kyosev et al. (2018), and

perform monthly Fama-MacBeth regressions to predict three-year growth in ROE. Table 9

reports the results. The analysis is performed from 07/1990 to 06/2016 for a global sample

of developed market and emerging market countries (as in Section 4.2). As ROE growth

exhibits some persistence by construction, the t-values are calculated using Newey and West

standard errors with 35 lags.

[Table 9 about here.]

The first column in Table 9 depicts that high positive ROE implies negative future ROE

growth, or in other words, there is a mean reversion in ROE. This possibly explains why a

profitability factor based on ROE has shown the weakest results in our previous analyses.

By controlling for this effect, we observe that the other profitability variables have a positive

relation and accruals have a negative relation with future profitability. Gross profitability

and cash-based gross profitability carry the highest t-values, which might indicate why the

factors based on these measures have shown particularly strong results. These results are

in line with the recent findings of Bouchaud et al. (2018) that indicate that sticky earnings

expectations drive the profitability anomaly.

The important role of the ROE factor in the Hou, Xue, and Zhang (2015) q-factor model

might appear inconsistent with these findings at first sight. However, as Novy-Marx (2015)

points out, the ROE factor in the q-factor model is based on the most recently announced

quarterly earnings; as a consequence, it profits from the post-earnings-announcement drift. In

contrast, our ROE factor is based on the most recently announced annual earnings, because

of the limited data availability on international markets. Therefore, it cannot be directly

compared to the ROE factor in the model of Hou, Xue, and Zhang (2015), which has the

advantage of utilizing more timely and more frequently updated information.

19

5 Robustness

5.1 The Role of the Denominator

In the previous section, we have focused on the numerator and have scaled the respective

measures of profit by the current book value of total assets (equity) for measures before

(after) interest expenses. Zhang (2017) argues that with scaling by current total assets and

not by one-year-lagged assets, the profitability effect is contaminated by a hidden investment

effect. Although we demonstrated in Section 4 that the profitability effect is also present after

controlling for the investment effect in factor and portfolio sorts as well as in cross-sectional

regressions, we also show the results for scaling cash-based gross profits by one-year lagged

assets in this section.

Novy-Marx (2013) scales gross profits by the book value of total assets and not a market-

based measure to avoid causing conflict in the productivity measure with a valuation measure

(book-to-market). Also in equation (1) profits are scaled by a book measure and company

valuation is reflected by the book-to-market ratio. Nevertheless, Cakici, Chatterjee, and Tang

(2017) find that for average portfolio returns that do not control for other factors such as

book-to-market, the relation of firm profitability and stock returns is more pronounced when

profits are scaled by enterprise value or market value of equity. Therefore, we also present the

results for scaling cash-based gross profits by enterprise value.12 We scale cash-based gross

profits by enterprise value, not market value of equity, because cash-based gross profits are

measured before interest expenses and are independent of leverage; therefore, they represent

an asset level measure of earnings.

Table 10 shows results for profitability factors based on cash-based gross profits scaled by

current total assets as in the previous analyses (RMWCbGP), but also scaled by one-year-

lagged assets (RMWCbGP/LagA) and by enterprise value (RMWCbGP/EV). Panel A reports

the summary statistics. Echoing the results from Table 4, the average monthly return for

12Enterprise value is defined as market capitalization plus preferred stock plus minority interest, plus long-and short-term debt, less cash and short-term investments.

20

RMWCbGP is 36bp (t-value of 4.67). When cash-based gross profits are scaled by one-year-

lagged total assets, the average premium for RMWCbGP/LagA decreases to 26 bp (t-value of

3.14) but remains highly significant. Therefore, we can confirm that a profitability measure

can benefit from the investment effect by measuring the denominator timely and we can also

rule out that the profitability effect is just an investment effect in disguise. When cash-based

gross profits are scaled by enterprise value, the RMWCbGP/EV premium increases to 63 bp

(t-value of 7.57). This confirms the standalone factor results of Cakici, Chatterjee, and Tang

(2017). However, standalone factor returns do not provide evidence on the predictive power

of factors in the presence of other factors that also predict stock returns. Therefore, we also

implement factor spanning tests and Sharpe ratio analyses.

[Table 10 about here.]

Panel B reports the results for factor spanning regressions. The first regression shows that

the RMWCbGP/LagA returns are completely spanned by the FF5FMCbGP complemented by a

momentum factor and an accruals factor. The negative loading of CMA on RMWCbGP/LagA

demonstrates that scaling by lagged assets instead of current assets implies a negative invest-

ment effect. In contrast, RMWCbGP/EV cannot be spanned by these factors and a significant

spanning alpha of 10 bp (t-value of 2.36) remains. This raises the question of whether

RMWCbGP/EV also dominates RMWCbGP. We find that this is not the case: By switching the

positions of RMWCbGP and RMWCbGP/EV in the third regression, an even bigger spanning

alpha of 17 bp (t-value of 3.57) remains. These findings imply that both RMWCbGP and

RMWCbGP/EV contain important information that is not covered by the other profitability

factors as well as other model factors.

Panel C finally answers the question of which profitability factor variant adds the most

value in a parsimonious factor model that only includes one profitability factor. Echoing

the results of Table 6, the investment opportunity set that comprises the factors of the

FF5FMCbGP, complemented by a momentum factor and an accruals factor achieves an (an-

nualized) Sharpe ratio of 2.07. When we replace RMWCbGP by RMWCbGP/LagA and by

21

RMWCbGP/EV, the maximum ex post Sharpe ratios decrease to 2.01 and 1.91, respectively.

Therefore, we conclude that a profitability factor based on cash-based gross profits scaled by

current total assets exhibits the highest predictive power in the presence of other factors.

5.2 Regional Analysis

In this section, we analyze how the results from our global analysis (excluding the U.S.) for

the different profitability factors can be attributed to different regions, namely developed

markets (DM), emerging markets (EM), Europe, Asia Pacific ex Japan, and Japan. We are

particularly interested in which of these regions CbGP dominates CbOP. Thus, in Table

11 we repeat our analysis from section 4.1 on a regional basis. Panel A shows the average

monthly returns for the profitability factors based on ROE, GP, OPFF, OP, CbOP, and CbGP.

CbGP yields significant profitability premiums for all regions and dominates all the other

profitability factors in the following regions: DM, EM, Asia Pacific (excluding Japan), and

Japan. The results for Asia Pacific and Japan are remarkable in that the profitability factor

of the Fama and French (2015) five-factor model does not exhibit a significant premium (cf.

Fama and French 2017). In Europe, however, CbOP has the highest average return and

CbGP ranks only second.

[Table 11 about here.]

Panel B presents the results from factor spanning regressions. The dependent variables

are the profitability factors listed above, with the exception of RMWCbGP. The indepen-

dent variables are the factors of the FF5FMCbGP complemented by momentum, as in the

previous analysis for the global sample in Table 5, panel B. The independent factors (includ-

ing RMWCbGP) nearly completely span the returns of the different profitability factors that

are tested in each of the regions. The spanning alphas range from -2 bp to 11 bp (with a

maximum absolute t-value of 1.77). The only exceptions are emerging markets and Europe,

where OPFF and CbOP exhibit significant alphas of 18 bp (t-value of 1.98) and 11 bp (t-value

22

of 2.35), respectively. Based on these results, we conclude that our global findings can be

attributed to the majority of regions.

5.3 Cash-based Gross Profitability Factors per Country

So far, we analyzed global (excluding the U.S.) and regional profitability factors, but we

have not broken down our analysis on a country level. By doing this we intend to determine

whether our results are mainly driven by a handful of countries with many big firms (based

on market capitalization) or whether the profitability effect can be verified in the majority of

the countries of our sample. As shown in Section 4.1, cash-based gross profitability dominates

the other profitability measures internationally based on a portfolio analysis. For compari-

son, we now create country-specific RMWCbGP factors and analyze the associated monthly

average returns and associated t-values. Moreover, we also perform factor spanning tests,

by regressing the country-specific RMWCbGP factors on the following (also country-specific)

factors: RMRF, SMB, HML, CMA, and MOM. We report the alphas and the associated

t-values; the results are displayed in Table 12.13

[Table 12 about here.]

The average RMWCbGP returns are positive in 36 out of 42 countries and range from -64

bp for Hungary to 131 bp for Argentina. The associated t-values are larger or equal to 2.0

in the following countries: Argentina, Denmark, France, Germany, Hong Kong, Indonesia,

Japan, Korea, Poland, Portugal, Singapore, Switzerland, Thailand and Taiwan. In general,

the spanning test alphas are even higher. They are positive in 39 out of 42 countries and

range from -23 bp for Belgium to 134 bp for Indonesia. In addition to the countries stated

previously, the following countries also carry t-values of the spanning alphas larger or equal

to 2.0: Australia, Brazil, Canada, Great Britain, India, Malaysia, Philippines, and South

Africa. This implies that in 22 out of 42 countries, the cash-based gross profitability factor

13To be included in the country-specific analysis, we require at least ten years of available factor return data.Therefore, Colombia, Czech Republic, Jordan, and Morocco drop out of the sample in this analysis.

23

contains statistically significant information that is not already covered by the other factors.

For the remaining 20 countries, the alpha is positive in 17 cases; however, in most cases it

is not statistically significantly different from zero, although some of the alphas are sizable

(e.g., Greece, Israel, and Peru have alphas of more than 50 bp). Shorter factor return time-

series and/or less diversified factor portfolios due to a lower number of stocks per portfolio

could lead to power issues in case of smaller countries. Figure 2 provides an overview of the

spanning test alphas per country. It appears that the cash-based profitability factor exhibits

positive average returns and spanning test alphas in a majority of the investigated countries.

Thus, we conclude that the profitability effect presents a broad and global phenomenon.

[Figure 2 about here.]

6 Conclusion

In this study, we analyze the most prominent profitability measures in the literature, namely

(i) return on equity (ROE), (ii) gross profitability by Novy-Marx (2013), (iii) operating

profitability by Ball et al. (2015) and defined in an alternative way (iv) by Fama and French

(2015), (v) cash-based operating profitability by Ball et al. (2016) and (vi) cash-based gross

profitability, for a total of 46 countries, from 07/1990 to 06/2016. We intentionally exclude

the U.S. as it has already been analyzed thoroughly in the past.

To compare the profitability measures, we perform time-series, factor-spanning, and cross-

sectional asset pricing tests. We calculate the six profitability factors following the standard

procedures of Fama and French (1993, 2012, 2015). Based on the average factor returns and

the associated t-statistics, cash-based gross profitability exhibits the best performance. We

verify this assertion by performing a series of factor spanning and mean-variance spanning

tests.

Moreover, we form quintile portfolios and the associated 5-1 (high-minus-low) portfolios

for all six profitability measures as well as accruals. We then test if the 5-1 portfolio re-

24

turns can be explained by either of the following models: the CAPM, the Fama-French

three-factor model, the Fama-French-Carhart four-factor model, the Fama-French five-factor

model, a modified Fama-French five-factor model based on cash-based gross profitability (in-

stead of operating profitability) and the modified model plus momentum. Based on alphas

and t-statistics, we find that the modified Fama-French five-factor model (with and without

momentum) explains the 5-1 portfolio returns particularly well. Thus, in an international

context, we recommend the substitution of operating profitability according to Fama and

French (2015) by cash-based gross profitability, to improve on the Fama and French five-

factor model definition.

We also conduct Fama and MacBeth (1973) cross-sectional regressions of monthly stock

returns on (i) individual profitability measures plus a set of control variables; and (ii) the

individually best profitability measure from (i) jointly with each of the other profitability

measures plus control variables. We find that cash-based gross profitability has the highest

marginal power to explain future stock returns in the individual as well as in the simultaneous

tests. With regards to accruals, we find similar results to the U.S. in that accruals negatively

predict future returns individually; however, in the presence of any cash-based profitability

measure, its predictive power substantially decreases.

Several robustness checks are performed. First, we analyze the role of the denominator

and scale cash-based gross profits (i.e., the numerator) by total assets, by one-year lagged

assets, and by enterprise value. We find that a factor based on cash-based gross profits scaled

by enterprise value (by one-year lagged assets) has a higher (a lower) standalone return than

the factor variant based on cash-based gross profits scaled by current total assets. However,

when controlling for other factors, we find that the standard cash-based profitability factor

(based on current assets) adds the most value to the investment opportunity set. Second, we

perform a regional factor analysis in order to see if our results are mainly driven by certain

regions or are more evenly distributed among regions. The following regions are analyzed:

Developed markets, emerging markets, Europe, Asia Pacific (excluding Japan), and Japan.

25

We find that a profitability factor based on cash-based gross profitability dominates the other

profitability factors in all regions except Europe, where, similar to the U.S., a factor based on

cash-based operating profitability shows a slightly better performance than the factor based

on cash-based gross profitability (which ranks second in Europe). Regional factor spanning

tests confirm this finding. Thus, we conclude that our global (excluding the U.S.) findings

can be attributed to the majority of regions. Finally, we perform a country-based analysis to

determine if our results are only driven by a subsample of rather big and influential countries

or are more evenly distributed between countries. We expect a higher influence the larger the

size, because usually this implies more data coverage, higher data quality and generally, more

listed stocks, which, in turn leads to larger weights in a value-weighted return analysis. More

specifically, we (i) calculate country-specific robust-minus-weak factors based on cash-based

gross profitability and (ii) perform factor spanning tests by regressing these factors on the

following (also country-specific) factors: RMRF, SMB, HML, CMA and MOM. Next, in case

of (i), we analyze the mean factor returns and in case of (ii), the respective alphas. Based

on this analysis, we document that cash-based gross profitability is a priced factor in the

majority of developed and emerging markets countries, controlling for other common factors,

such as market, size, value, investment and momentum.

The findings of this paper have important implications for the specification of a powerful

empirical asset pricing model. Parsimonious factor models that only include a small num-

ber of characteristic-based factors and are able to shrink the list of asset pricing anomalies

significantly should only include factors with a high power. These factors should (i) exhibit

substantial and significant returns, (ii) not be subsumed by the other model factors, and (iii)

not be susceptible to small alterations in the factor definitions (variants). We show that a

profitability factor based on cash-based gross profitability should be used in factor models for

international markets because it robustly outperforms the other profitability factors analyzed

in the study.

26

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32

Table 2: Summary statistics for profitability measures and control variablesThe table presents time-series averages of the cross-sectional means, standard deviations and1%-, 25%-, 50%-, 75%- and 99%-quantiles of the following variables: (1) Gross profitability(GP) according to Novy-Marx (2013), defined as revenues minus costs of goods sold, dividedby the book value of total assets, (2) Operating profitability (OPFF) according to Fama andFrench (2015), defined as gross profit minus selling, general, and administrative expenses,interest expenses and costs of goods sold, divided by the book value of equity, (3) Operatingprofitability (OP) according to Ball et al. (2016), defined as gross profit minus selling, general,and administrative expenses (excluding R&D expenditures) and costs of goods sold, dividedby the book value of total assets, (4) Cash-based operating profitability (CbOP) accordingto Ball et al. (2016), defined as OP minus the change in accounts receivable, the changein inventory, and the change in prepaid expenses, plus the change in deferred revenues, thechange in accounts payable, and the change in accrued expenses, deflated by the book valueof assets, (5) Cash-based gross profitability (CbGP), defined the same way as CbOP, butstarting with GP instead of OP, (6) Accruals (Accr), defined as the change in current assetsminus the change in cash, the change in current liabilities, the change in current debt, thechange in income taxes payable, and depreciation, divided by the book value of total assets,(7) the natural logarithm of book-to-market (log(B/M)), (8) the natural logarithm of the 1-month lagged market value (log(MV)), (9) the 1-month lagged return (r1,1), (10) momentum(r12,2) and (11) the growth in total assets (dA/A) from t−1 to t. The analysis is performedfrom 07/1990 to 06/2016.

GP OPFF OP CbOP CbGP Accr log(B/M) log(MV) r1,1 r12,2 dA/Amean 0.24 0.22 0.11 0.10 0.23 -0.03 -0.37 11.59 0.01 0.10 0.17sd 0.21 0.44 0.14 0.16 0.22 0.10 0.95 1.93 0.13 0.52 0.521st -0.18 -1.51 -0.39 -0.47 -0.29 -0.38 -3.57 7.30 -0.32 -0.73 -0.4625th 0.11 0.06 0.04 0.02 0.09 -0.07 -0.90 10.27 -0.06 -0.21 -0.0250th 0.20 0.18 0.10 0.09 0.20 -0.03 -0.31 11.49 -0.00 0.01 0.0575th 0.33 0.34 0.17 0.17 0.33 0.01 0.23 12.80 0.06 0.29 0.1899th 1.05 2.12 0.60 0.66 1.08 0.28 1.92 16.57 0.51 2.43 3.71

33

Table 3: Correlation coefficientsThe table reports the time-series averages of the cross-sectional spearman correlation coeffi-cients between the following variables: (1) Gross profitability (GP) according to Novy-Marx(2013), (2) Operating profitability (OP) according to Ball et al. (2016), (3) Cash-based oper-ating profitability (CbOP) according to Ball et al. (2016), (4) Cash-based gross profitability(CbGP), (5) Operating profitability (OPFF) according to Fama and French (2015), and (6)Accruals (Accr). For details with regard to variable construction, see Table 2. The sampleis described in Table 1. The analysis is performed from 07/1990 to 06/2016.

GP OP CbOP CbGP OPFF Accr log(B/M) log(MV) r1,1 r12,2 dA/AGP 1.00 0.64 0.52 0.88 0.56 -0.07 -0.19 0.14 0.07 0.10 0.03OP 1.00 0.78 0.52 0.88 -0.08 -0.20 0.21 0.07 0.17 0.17CbOP 1.00 0.69 0.66 -0.45 -0.11 0.16 0.07 0.14 -0.10CbGP 1.00 0.44 -0.33 -0.14 0.11 0.08 0.08 -0.16OPFF 1.00 -0.07 -0.23 0.23 0.07 0.16 0.17Accr 1.00 -0.01 0.01 -0.02 -0.03 0.27log(B/M) 1.00 -0.32 0.07 -0.12 -0.19log(MV) 1.00 0.08 0.22 0.14r1,1 1.00 0.07 -0.03r12,2 1.00 0.06dA/A 1.00

34

Table 4: Factor summary statisticsThe table reports the average monthly returns, the monthly standard deviations and thet-values of the following factors: robust minus weak (RMW), based on (1) ROE, (2) GP,(3) OPFF, (4) OP, (5) CbOP and (6) CbGP, accruals (ACC), small minus big (SMB), highminus low (HML), conservative minus aggressive (CMA), momentum (MOM) and the marketreturn minus the risk-free rate (RMRF), from 07/1990 to 06/2016. The factors are createdat June of every year (except for MOM, which is created at every month t) based on 2x3sorts of size and the second sorting variable of the respective factor. The holding period is 12months (except for MOM, where it is 1 month). SMB is calculated as the difference betweenthe average monthly value-weighted portfolio returns of the three small stock and the threebig stock portfolios. The other factors are calculated as the difference between the averagemonthly value-weighted returns of the two highly and the two lowly ranked portfolios withregard to the respective sorting variable.

mean return standard deviation t-valueRMRF 0.31 4.89 1.12SMB -0.03 1.97 -0.28HML 0.46 2.20 3.70MOM 0.70 3.33 3.74CMA 0.26 1.52 3.02ACC 0.14 0.97 2.53RMWROE 0.13 1.25 1.86RMWGP 0.33 1.43 4.11RMWOPFF 0.19 1.11 3.09RMWOP 0.27 1.41 3.44RMWCbOP 0.30 1.26 4.14RMWCbGP 0.36 1.35 4.67

35

Table 5: Factor spanning testsThe table presents the results from factor spanning regressions. The dependent variablesare the monthly factor returns of robust minus weak (RMW), based on (1) ROE, (2) GP,(3) OPFF, (4) OP, (5) CbOP, (6) CbGP and (7) ACC. The independent variables are theexcess return of the market (RMRF), small minus big (SMB), high minus low (HML), conser-vative minus aggressive (CMA), momentum (MOM), RMWCbGP, RMWOPFF , RMWOP andRMWCbOP. The analysis is performed from 07/1990 to 06/2016.

Intercept RMRF SMB HML CMA MOM RMWCbGP RMWOPFF RMWOP RMWCbOP

Panel A: Spanning tests w/o other profitability factorsRMWROE 0.20 −0.09 −0.10 −0.05 −0.26 0.08

(3.08) (−7.02) (−3.17) (−1.64) (−5.51) (4.17)RMWGP 0.46 −0.13 −0.17 −0.23 −0.14 0.08

(7.23) (−10.17) (−5.47) (−6.95) (−2.99) (3.98)RMWOPFF 0.20 −0.06 −0.14 −0.03 −0.11 0.08

(3.32) (−5.03) (−4.98) (−0.90) (−2.40) (4.44)RMWOP 0.35 −0.11 −0.27 −0.15 −0.21 0.10

(5.81) (−8.37) (−9.20) (−4.64) (−4.65) (5.47)RMWCbOP 0.35 −0.10 −0.24 −0.15 −0.07 0.08

(6.26) (−8.84) (−8.80) (−5.08) (−1.60) (4.73)RMWCbGP 0.46 −0.13 −0.15 −0.24 −0.04 0.08

(7.60) (−10.23) (−5.21) (−7.59) (−0.86) (4.17)ACC 0.11 −0.02 −0.14 −0.10 0.23 0.02

(2.15) (−1.36) (−5.37) (−3.65) (5.77) (1.07)Panel B: Spanning tests with RMWCbGP

RMWROE 0.06 −0.05 −0.05 0.02 −0.25 0.06 0.31(0.83) (−3.65) (−1.66) (0.54) (−5.48) (3.00) (5.30)

RMWGP 0.00 −0.01 −0.02 0.01 −0.10 0.00 1.00(0.02) (−1.25) (−1.60) (0.75) (−6.92) (0.06) (52.76)

RMWOPFF 0.04 −0.02 −0.09 0.05 −0.09 0.05 0.33(0.72) (−1.42) (−3.27) (1.63) (−2.23) (3.12) (6.30)

RMWOP 0.04 −0.02 −0.17 0.01 −0.18 0.05 0.67(0.89) (−1.76) (−7.35) (0.55) (−5.47) (3.51) (15.75)

RMWCbOP 0.05 −0.02 −0.14 0.01 −0.04 0.03 0.66(1.16) (−1.96) (−6.91) (0.36) (−1.41) (2.45) (17.40)

ACC 0.02 0.01 −0.11 −0.05 0.24 0.00 0.21(0.29) (1.00) (−4.05) (−1.71) (6.14) (0.06) (4.38)

Panel C: Spanning tests to explain RMWCbGP

RMWCbGP 0.39 −0.11 −0.10 −0.23 −0.00 0.05 0.35(6.75) (−8.70) (−3.59) (−7.72) (−0.05) (2.74) (6.30)

RMWCbGP 0.22 −0.06 0.03 −0.14 0.10 0.01 0.67(4.73) (−5.62) (1.13) (−5.83) (2.93) (0.64) (15.75)

RMWCbGP 0.19 −0.05 0.03 −0.13 0.01 0.02 0.76(4.23) (−5.03) (1.26) (−5.42) (0.39) (1.13) (17.40)

36

Tab

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09

37

Table 7: Quintile Portfolio AnalysisThis table reports the results from a quintile portfolio analysis based on different profitabilitymeasures. Panel A shows the average monthly value-weighted excess returns of the quintileportfolios as well as the 5-1 portfolios and the associated t-values in brackets, based on(1) ROE, (2) GP, (3) OPFF, (4) OP, (5) CbOP, (6) CbGP and (7) Accr, respectively. InPanel B, we test if the 5-1 portfolio excess returns can be explained by the following assetpricing models: (1) the CAPM, (2) the Fama-French three-factor model (FF3FM), (3) theFama-French-Carhart four-factor model (FFC4FM), (4) the Fama-French five-factor model(FF5FM), (5) a modified Fama-French five-factor model based on CbGP (FF5FMCbGP) and(6) the modified model plus momentum (FF5FMCbGP+MOM). The panel reports the alphasand the associated t-values in brackets. The analysis is performed from 07/1990 to 06/2016.

ROE GP OPFF OP CbOP CbGP AccrPanel A: Monthly excess returns

1 (low) 0.04 0.09 0.22 0.12 0.11 0.10 0.372 0.36 0.24 0.37 0.33 0.31 0.22 0.353 0.47 0.41 0.31 0.37 0.34 0.35 0.284 0.40 0.38 0.48 0.36 0.35 0.37 0.345 (high) 0.37 0.47 0.26 0.41 0.43 0.50 0.275-1 0.33 0.38 0.04 0.29 0.32 0.40 −0.10

(2.77) (3.36) (0.40) (2.47) (2.82) (3.46) (−1.06)Panel B: Alphas and t-values from asset pricing tests

CAPM 0.37 0.41 0.06 0.31 0.35 0.43 −0.11(3.31) (3.71) (0.57) (2.73) (3.22) (3.94) (−1.22)

FF3FM 0.24 0.62 0.13 0.45 0.47 0.64 −0.14(2.33) (6.76) (1.34) (4.78) (5.26) (7.04) (−1.54)

FFC4FM 0.18 0.53 0.05 0.40 0.43 0.56 −0.13(1.72) (5.69) (0.54) (4.11) (4.59) (6.01) (−1.41)

FF5FM 0.13 0.49 −0.22 0.21 0.26 0.54 −0.01(1.34) (5.48) (−3.44) (2.67) (3.17) (5.90) (−0.09)

FF5FMCbGP 0.22 0.00 −0.03 0.10 0.08 0.01 0.04(1.94) (−0.06) (−0.28) (1.06) (0.90) (0.09) (0.43)

FF5FMCbGP+MOM 0.19 −0.01 −0.06 0.10 0.08 0.00 0.02(1.63) (−0.17) (−0.57) (1.00) (0.93) (0.05) (0.27)

38

Tab

le8:

Aco

mpa

riso

nof

profi

tabi

lity

mea

sure

san

dac

crua

lsin

Fam

a-M

acB

eth

regr

essi

ons

The

tabl

ere

port

sav

erag

eFa

ma-

Mac

Beth

prem

ium

s(m

ultip

lied

by10

0)an

dth

eirt

-val

ues

from

mon

thly

cros

s-se

ctio

nalr

egre

s-sio

nsto

pred

ict

stoc

kre

turn

s(m

odel

1to

13).

The

regr

essio

nsar

epe

rform

edfro

m07

/199

0to

06/2

016

for

agl

obal

sam

ple

ofD

Man

dEM

coun

trie

s,as

defin

edin

the

lege

ndof

Tabl

e1,

cont

rolli

ngfo

rpot

entia

lcou

ntry

effec

tsw

ithco

untr

ydu

mm

ies.

The

inde

pend

entv

aria

bles

aret

he1-

mon

th-la

gged

stoc

kre

turn

(r1,

1),m

omen

tum

(r12,2

),th

enat

ural

loga

rithm

ofth

eboo

k-to

-mar

ket

ratio

(log(

B/M

)),t

hena

tura

llog

arith

mof

the

lagg

edm

arke

tva

lue

(log(

MV

)),t

hegr

owth

rate

ofto

tala

sset

s(d

A/A

),re

turn

oneq

uity

(RO

E),g

ross

profi

tabi

lity

(GP)

,ope

ratin

gpr

ofita

bilit

yac

cord

ing

toFa

ma

and

Fren

ch(O

P FF),

oper

atin

gpr

ofita

bilit

y(O

P),c

ash-

base

dop

erat

ing

profi

tabi

lity

(CbO

P),c

ash-

base

dgr

ossp

rofit

abili

ty(C

bGP)

and

accr

uals

(Acc

r).F

urth

erde

tails

onth

eva

riabl

eco

nstr

uctio

nar

egi

ven

inTa

ble

2.T

hela

stro

wco

ntai

nsth

eav

erag

ead

just

edR

2 .

Pane

lA:I

ndiv

idua

lfor

ecas

ting

pote

ntia

lofp

rofit

abili

tym

easu

res

Pane

lB:M

argi

nale

ffect

sfor

cash

-bas

edgr

ossp

rof-

itabi

lity

and

the

othe

rpr

ofita

bilit

ym

easu

res

Mod

1M

od2

Mod

3M

od4

Mod

5M

od6

Mod

7M

od8

Mod

9M

od10

Mod

11M

od12

Mod

13r 1,1

−4.

69−

4.74

−4.

70−

4.72

−4.

71−

4.74

−4.

68−

4.76

−4.

75−

4.75

−4.

76−

4.75

−4.

74(−

10.9

0)(−

11.0

2)(−

10.9

2)(−

10.9

4)(−

10.9

2)(−

11.0

1)(−

10.8

4)(−

11.1

0)(−

11.0

4)(−

11.1

0)(−

11.0

8)(−

11.0

6)(−

11.0

4)r 1

2,2

0.33

0.30

0.32

0.32

0.32

0.30

0.33

0.29

0.30

0.30

0.30

0.30

0.30

(1.7

0)(1.5

8)(1.6

9)(1.6

6)(1.6

6)(1.5

8)(1.7

3)(1.5

5)(1.5

8)(1.5

7)(1.5

6)(1.5

8)(1.5

8)lo

g(B/

M)

0.27

0.33

0.28

0.29

0.29

0.33

0.29

0.32

0.33

0.32

0.33

0.33

0.33

(6.8

8)(8.3

0)(6.8

9)(7.1

7)(7.3

0)(8.3

2)(7.3

4)(8.2

7)(8.3

1)(7.8

7)(8.1

3)(8.3

2)(8.2

4)lo

g(M

V)

−0.

18−

0.17

−0.

18−

0.18

−0.

18−

0.17

−0.

17−

0.17

−0.

17−

0.18

−0.

17−

0.17

−0.

17(−

6.79

)(−

6.27

)(−

6.78

)(−

6.95

)(−

6.82

)(−

6.21

)(−

6.24

)(−

6.52

)(−

6.24

)(−

6.54

)(−

6.55

)(−

6.37

)(−

6.23

)dA

/A−

0.48

−0.

45−

0.49

−0.

47−

0.40

−0.

38−

0.41

−0.

37−

0.39

−0.

39−

0.38

−0.

37−

0.35

(−8.

63)

(−8.

55)

(−9.

08)

(−8.

95)

(−7.

72)

(−7.

12)

(−7.

70)

(−6.

67)

(−7.

20)

(−7.

19)

(−7.

10)

(−7.

05)

(−6.

65)

ROE

0.12

0.01

(1.3

4)(0.0

6)G

P1.

100.

34(7.9

6)(1.6

4)O

P FF

0.33

0.16

(5.9

5)(3.1

2)O

P1.

130.

37(5.8

0)(2.0

8)C

bOP

1.09

0.22

(7.5

3)(1.5

2)C

bGP

1.05

1.04

0.78

0.94

0.93

0.95

0.97

(9.0

6)(9.5

2)(5.0

4)(8.3

8)(8.9

9)(7.5

1)(7.7

6)A

ccr

−1.

18−

0.52

(−7.

82)

(−3.

06)

R2

12.8

6%12.8

8%12.8

4%12.8

6%12.8

5%12.8

7%12.8

1%12.9

2%12.8

8%12.8

9%12.8

9%12.8

7%12.8

7%

39

Tab

le9:

Pro

fitab

ility

mea

sure

san

dR

OE

grow

thT

heta

ble

repo

rts

aver

age

Fam

a-M

acBe

thpr

emiu

ms

(mul

tiplie

dby

100)

and

thei

rt-

valu

esfro

mm

onth

lycr

oss-

sect

iona

lre-

gres

sions

topr

edic

tth

ree-

year

grow

thin

profi

tabi

lity,

mea

sure

dasy t

=IBt+

3−IBt

BEt

,with

IB

asin

com

ebe

fore

expe

nditu

res

and

BE

asbo

okeq

uity

.T

here

gres

sions

are

perfo

rmed

from

07/1

990

to06

/201

6fo

ra

glob

alsa

mpl

eof

DM

and

EMco

untr

ies,

asde

fined

inth

ele

gend

ofTa

ble

1,co

ntro

lling

for

pote

ntia

lcou

ntry

effec

tsw

ithco

untr

ydu

mm

ies.

The

inde

pend

ent

varia

bles

are

mom

entu

m(r

12,2

),th

ena

tura

llog

arith

mof

the

book

-to-

mar

ket

ratio

(log(

B/M

)),t

hena

tura

llog

arith

mof

the

lagg

edm

arke

tva

lue

(log(

MV

)),t

hegr

owth

rate

ofto

tala

sset

s(dA

/A),

retu

rnon

equi

ty(R

OE)

,gro

sspr

ofita

bilit

y(G

P),o

pera

ting

profi

tabi

l-ity

acco

rdin

gto

Fam

aan

dFr

ench

(OP F

F),

oper

atin

gpr

ofita

bilit

y(O

P),c

ash-

base

dop

erat

ing

profi

tabi

lity

(CbO

P),c

ash-

base

dgr

oss

profi

tabi

lity

(CbG

P)an

dac

crua

ls(A

ccr)

.Fu

rthe

rde

tails

onth

eva

riabl

eco

nstr

uctio

nar

egi

ven

inTa

ble

2.T

hela

stro

wco

ntai

nsth

eav

erag

ead

just

edR

2 .T

het-

valu

esar

eca

lcul

ated

usin

gN

ewey

and

Wes

tst

anda

rder

rors

with

35la

gs.

Mod

1M

od2

Mod

3M

od4

Mod

5M

od6

Mod

7r 1

2,2

0.09

0.09

0.09

0.09

0.09

0.09

0.09

(4.4

8)(4.1

5)(4.3

0)(4.4

6)(4.4

5)(4.1

7)(4.4

7)lo

g(B/

M)

−0.

010.

010.

000.

000.

000.

00−

0.01

(−0.

69)

(0.3

1)(0.2

5)(0.1

2)(−

0.23

)(0.1

6)(−

0.72

)lo

g(M

V)

0.02

0.02

0.02

0.02

0.02

0.02

0.02

(4.6

6)(4.9

6)(4.9

8)(4.9

1)(4.8

0)(4.9

0)(4.6

5)dA

/A−

0.06

−0.

05−

0.05

−0.

05−

0.03

−0.

03−

0.05

(−5.

33)

(−4.

54)

(−5.

14)

(−4.

70)

(−2.

47)

(−2.

99)

(−4.

44)

ROE

−0.

65−

0.68

−0.

74−

0.73

−0.

69−

0.67

−0.

64(−

14.2

8)(−

15.6

7)(−

21.6

9)(−

19.7

1)(−

17.0

1)(−

15.1

4)(−

13.9

3)G

P0.

24(9.9

6)O

P FF

0.19

(6.3

7)O

P0.

52(8.2

4)C

bOP

0.37

(8.2

1)C

bGP

0.22

(9.7

3)A

ccr

−0.

22(−

8.23

)R

226.2

4%26.9

3%27.6

2%27.4

7%27.2

0%26.9

1%26.3

9%

40

Tab

le10

:T

hero

leof

the

deno

min

ator

The

tabl

esh

ows

resu

ltsfo

rpr

ofita

bilit

yfa

ctor

sba

sed

onca

sh-b

ased

gros

spr

ofits

scal

edby

diffe

rent

deno

min

ator

s.R

MW

CbG

Pus

escu

rren

tto

tala

sset

sas

deno

min

ator

,RM

WC

bGP

/Lag

Aus

eson

e-ye

arla

gged

tota

lass

ets,

and

RM

WC

bGP

/EV

uses

ente

rpris

eva

lue.

Pane

lAre

port

sth

eav

erag

em

onth

lyre

turn

s,th

em

onth

lyst

anda

rdde

viat

ions

,and

the

t-va

lues

ofth

eth

ree

fact

ors.

Pane

lBsh

owss

pann

ing

test

s.Pa

nelC

pres

ents

the

max

imum

ex-p

osta

nnua

lized

Shar

pera

tiost

hatc

anbe

achi

eved

byad

ding

the

diffe

rent

varia

ntso

fthe

cash

-bas

edpr

ofita

bilit

yfa

ctor

toth

eot

herf

acto

rsan

dth

ein

divi

dual

fact

orwe

ight

s.T

here

mai

ning

fact

ors

are

desc

ribed

inTa

ble

4.T

hean

alys

isis

perfo

rmed

from

07/1

990

until

06/2

016.

Pane

lA:F

acto

rsu

mm

ary

stat

istic

sfo

rdi

ffere

ntde

nom

inat

ors

mea

nst

.dev

.t-

valu

eR

MW

CbG

P0.

361.

354.

67R

MW

CbG

P/L

agA

0.26

1.45

3.14

RM

WC

bGP

/EV

0.63

1.47

7.57

Pane

lB:S

pann

ing

test

sA

lpha

t-va

lR

MR

FSM

BH

ML

WM

LC

MA

AC

CR

MW

CbG

PR

MW

CbG

P/E

V

RM

WC

bGP

/Lag

A0.

000.

22-0

.01

-0.0

1-0

.04

-0.0

0-0

.23

0.07

0.92

RM

WC

bGP

/EV

0.10

2.36

0.02

0.09

0.61

0.03

0.10

-0.0

40.

56R

MW

CbG

P0.

173.

57-0

.09

-0.1

3-0

.58

0.02

-0.1

40.

190.

75Pa

nelC

:Max

imum

expo

stSh

arpe

ratio

sR

MR

FSM

BH

ML

WM

LC

MA

AC

CR

MW

CbG

PR

MW

CbG

P/L

agA

RM

WC

bGP

/EV

SRFF

5FM

CbG

P+

MO

M+

AC

C0.

100.

080.

220.

050.

070.

020.

462.

07FF

5FM

CbG

P/L

agA

+M

OM

+A

CC

0.09

0.07

0.22

0.05

0.15

0.00

0.41

2.01

FF5F

MC

bGP

/EV

+M

OM

+A

CC

0.11

0.03

0.00

0.11

0.00

0.19

0.57

1.91

41

Table 11: Factor summary statistics - Regional AnalysisThe table shows results for the different regions. Panel A reports the average monthly returnsand the t-values of the profitability factors (RMW, robust minus weak) based on (1) ROE,(2) GP, (3) OPFF, (4) OP, (5) CbOP and (6) CbGP. Panel B presents the results from factorspanning regressions. The dependent variables are the factors listed above with the exceptionof RMWCbGP. The independent variables are the market, size, value, investment, momentumfactors plus the profitability factor based on CbGP. The factors are constructed as in Table 4.The regions besides emerging markets are defined as in Fama and French (2012) or Famaand French (2015). The analysis is performed from 07/1990 to 06/2016.

DevelopedMarkets

EmergingMarkets Europe Asia Pacific

ex Japan Japan

Panel A: Monthly average returns

RMWROE 0.13 0.19 0.18 0.09 -0.01(1.69) (1.54) (2.06) (0.57) (-0.05)

RMWGP 0.33 0.38 0.29 0.24 0.26(3.94) (2.8) (3.83) (1.31) (2.02)

RMWOPFF 0.19 0.32 0.19 0.24 0.03(2.82) (2.71) (2.58) (1.42) (0.3)

RMWOP 0.29 0.24 0.28 0.22 0.2(3.52) (1.85) (3.68) (1.25) (1.35)

RMWCbOP 0.31 0.27 0.34 0.32 0.12(4.11) (2.35) (4.59) (2.29) (1.04)

RMWCbGP 0.35 0.41 0.31 0.35 0.26(4.44) (3.39) (4.27) (2.35) (2.2)

Panel B: Spanning alphas

RMWROE 0.05 0.04 0.02 0.14 0.03(0.65) (0.49) (0.26) (1.13) (0.41)

RMWGP 0 0.09 0.04 0.04 0(-0.13) (1.48) (1.41) (0.44) (-0.03)

RMWOPFF 0.04 0.18 -0.02 0.11 -0.05(0.58) (1.98) (-0.27) (1.17) (-0.6)

RMWOP 0.06 0.04 0.08 0.11 0.05(1.17) (0.45) (1.58) (1.17) (0.56)

RMWCbOP 0.07 -0.08 0.11 0.1 -0.06(1.44) (-1.13) (2.35) (1.77) (-0.77)

42

Table 12: Country-specific RMW-factors based on cash-based gross profitabilityThe table reports the average monthly returns of country-specific RMW-factors based onCbGP (column 2) and associated spanning test alphas, employing the following (country-specific) factors: the excess market return and the size, value, investment, and momentumfactors (column 4), and the associated t-values one column to the right, respectively (column3 and 5). The analysis is performed from 07/1990 to 06/2016.

Country averagereturn t-value spanning

alpha t-value

Argentina 1.31 2.50 1.20 2.05Australia 0.27 1.64 0.44 3.22Austria 0.16 0.74 0.23 1.03Belgium -0.29 -1.40 -0.23 -1.14Brazil 0.81 1.92 1.04 2.56Canada 0.46 1.95 0.74 4.28Chile 0.03 0.17 0.22 1.17China 0.39 1.11 0.54 1.57Denmark 0.85 3.35 1.02 4.24Egypt 0.12 0.18 0.38 0.68Finland 0.24 0.74 0.32 1.18France 0.38 2.93 0.49 4.19Germany 0.61 4.44 0.64 4.50Great Britain 0.22 1.69 0.40 4.08Greece 0.47 1.69 0.51 1.95Hong Kong 0.54 2.47 0.82 4.69Hungary -0.64 -1.40 0.24 0.48India 0.44 1.52 0.71 2.90Indonesia 1.03 3.02 1.34 4.00Ireland -0.04 -0.08 -0.06 -0.12Israel 0.57 1.50 0.57 1.65Italy 0.19 0.99 0.27 1.52Japan 0.26 2.20 0.40 3.85Korea 0.73 2.57 0.98 3.81Malaysia 0.49 1.96 0.73 4.05Netherlands 0.20 0.92 0.33 1.60New Zealand -0.06 -0.22 0.20 0.79Norway 0.42 1.62 0.45 1.80Pakistan 0.13 0.27 0.50 1.23Peru 0.28 0.49 0.79 1.07Philippines 0.33 0.82 0.85 2.30Poland 0.64 2.00 0.73 2.82Portugal 0.63 2.18 0.72 2.61Russia -0.23 -0.54 -0.08 -0.20Singapore 0.56 2.60 0.73 4.21South Africa 0.45 1.87 0.63 2.85Spain 0.19 0.96 0.29 1.57Sweden 0.19 0.94 0.28 1.61Switzerland 0.47 2.59 0.55 3.23Taiwan 0.50 2.28 0.51 3.29Thailand 0.60 2.10 0.89 3.68Turkey -0.07 -0.20 0.48 1.36

43

Figure 1: Cumulative Performance of the Cash-based Gross Profitability FactorThe figure plots the cumulated performance of the monthly time-series of CbGP and thespanning alpha of CbGP. The sample period starts in 7/1990 and ends in 06/2016.

0

50

100

150

1990 2000 2010

Year

Cum

. Per

form

ance

variable RMWCbGP αRMWCbGP

44

Figure 2: Spanning test alphas for country-specific cash-based gross-profitabilityfactorsThe figure shows country-level alphas obtained from regressing the profitability factorsbased on cash-based gross-profitability on the excess market return (RMRF), small minusbig (SMB), high minus low (HML), conservative minus aggressive (CMA) and momentum(MOM). The analysis is performed from 07/1990 to 06/2016.

0.0

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45

A Appendix

A.1 Sample definition

Constituent lists

Datastream comprises three types of constituent lists: (1) research lists, (2) Worldscope lists

and (3) dead lists. By using dead lists, we ensure to obviate any survivorship bias. For

every country we use the intersection of all available lists and eliminate any duplicates. As a

result, we have one remaining list for every country, which can subsequently be used in the

static filter process. Table A.1 and Table A.2 provide an overview of the constituent lists for

developed markets and emerging markets, respectively, used in our study.

Static screens

We restrict our sample to common stocks exclusively by performing several static screens, as

displayed in Table A.3. Screen (1) to (7) are standard filter rules that are straightforward

to apply. Screen (8) is performed as follows: Ince and Porter (2006), Campbell, Cowan, and

Salotti (2010), Griffin, Kelly, and Nardari (2010), and Karolyi, Lee, and Dijk (2012), among

others, have provided generic filter rules for the exclusion of non-common equity securities

in Datastream. The authors provide certain keywords, which are searched for in the name

of the Datastream securities. We follow these studies and delete a stock only, if a keyword

within the name of the stock fulfills the following conditions: (1) There is a whitespace (or

tab) directly before the keyword; (2) There is a whitespace or a dot after the keyword, or

the name of the stock ends with the keyword. We use the following three Datastream items

as name, respectively: “NAME”, “ENAME”, and “ECNAME”. This process prevents that

stocks are deleted by accident, which otherwise could happen, if a keyword was part of a

regular, larger word that actually was to be accepted. Finally, we also perform a quality

review of all deleted stocks in order to make sure that all the deletions have been justified.

Table A.4 provides an overview of the keywords used in our study. Furthermore, Griffin,

46

Kelly, and Nardari (2010) have introduced country-specific keywords that we also apply in

our study. In general, this process is very similar to the generic filter rules presented above,

but now we have to filter for a certain country before we can apply the associated keyword

tests. Table A.5 provides an overview of the country-specific keywords used in our study.

Dynamic screens

Moreover, we perform several dynamic screens in order to ensure high data quality and to

limit data errors, which have become standard in the literature on the analysis of international

stock markets. Table A.6 provides an overview.

A.2 Variable definitions

In this section, we first state the variable definitions used within this study and then give a

tabular overview of all the required Datastream items.

Return on equity (ROE):

ROE = Income before expendituresBook equity

with:

Book equity = Common equity + Deferred taxes

Gross profits (GP), according to Novy-Marx (2013):

GP = Sales − COGSTotal assets

47

Operating profitability according to Ball et al. (2015):

OP = Sales − COGS − Reported SG&ATotal assets

with:

Reported SG&A = SG&A− R&D expenditures

Operating profitability according to Fama and French (2015):

OPFF = Sales − COGS − SG&A− Interest expensesBook equity

Cash-based Operating profitability according to Ball et al. (2016):

CbOP = OP + Cash-based adjustmentsTotal assets

with:

Cash-based adjustments = −∆Accounts receivable −∆Inventory −∆Prepaid expenses

+ ∆Deferred revenue + ∆Trade accounts payable + ∆Accrued expenses

Cash-based gross profitability:

CbGP = GP + Cash-based adjustmentsTotal assets

48

Accruals according to Ball et al. (2016):

Accr = ∆Current assets −∆Cash −∆Current liabilitiesTotal assets

+ ∆Debt in current liabilities + ∆Income tax payable −∆DepreciationTotal assets

The accounting variables used so far and their Datastream equivalents are depicted in

Table A.7.

49

Table A.1: Constituent lists: Developed marketsThe table contains the Research lists, Worldscope lists and Dead lists of developed marketscountries in our sample.

Country Lists Country Lists

Australia DEADAU Japan DEADJPFAUS FJASDAQWSCOPEAU FOSAKA

Austria ALLAS FTOKYODEADOE FUKUOKAFOST JAPALLWSCOPEOE JAPOTC

Belgium DEADBG WSCOPEJPFBEL Netherlands ALLFLWSCOPEBG DEADNL

Canada DEADCN1 FHOLDEADCN2 WSCOPENLDEADCN3 New Zealand DEADNZDEADCN4 FNWZDEADCN5 WSCOPENZDEADCN6 Norway DEADNWFTORO FNORFVANC WSCOPENWLTTOCOMP Portugal DEADPTWSCOPECN FPOM

Denmark DEADDK FPORFDEN FPSMWSCOPEDK WSCOPEPT

Finland DEADFN Singapore DEADSGFFIN FSINWSCOPEFN FSINQ

France ALLFF WSCOPESGDEADFR Spain DEADESFFDOM FBILFFOTC FBRCLFFRA FSPDOMWSCOPEFR FSPN

Germany DEADBD1 FSPNQDEADBD2 FVALDEADBD3 WSCOPEESDEADBD4 Sweden DEADSDDEADBD5 FSWDDEADBD6 WSCOPESDFGERDOM Switzerland DEADSWFGERIBIS FSWAFGKURS FSWSWSCOPEBD WSCOPESW

Greece DEADGR Great Britain DEADUKFGREE FBRITFGRMM LSETSCOSFGRPM LSETSMMFNEXA LUKPLUSMWSCOPEGR WSCOPEJE

Hong Kong DEADHK WSCOPEUKFHKQWSCOPEHK

Ireland DEADIRFIRLWSCOPEIR

Italy DEADITFITAWSCOPEIT

50

Table A.2: Constituent lists: Emerging marketsThe table contains the Research lists, Worldscope lists and Dead lists of emerging marketscountries in our sample.

Argentina FPARGA Morocco DEADMORWSCOPEAR FMORDEADAR WSCOPEMC

Brazil DEADBRA Pakistan DEADPAFBRA FPAKWSCOPEBR WSCOPEPK

Chile DEADCHI Peru DEADPEFCHILE FPERUFCHILE10 WSCOPEPEWSCOPECL Philippines DEADPH

China DEADCH FPHIFCHINA FPHILAWSCOPECH FPHIMN

Columbia DEADCO FPHIQFCOL WSCOPEPHWSCOPECB Poland DEADPO

Czech Republic DEADCZ FPOLFCZECH WSCOPEPOWSCOPECZ Russia DEADRU

Egypt DEADEGY FRUSFEGYPT WSCOPERSWSCOPEEY South Africa DEADSAF

Hungary DEADHU FSAFFHUN WSCOPESAWSCOPEHN Sri Lanka DEADSL

India DEADIND FSRILAFBSE WSCOPECYFINDIA Korea DEADKOFNSE FKORWSCOPEIN WSCOPEKO

Indonesia DEADIDN Taiwan DEADTWFINODB FTAIQFINOMB WSCOPETAFINOQ Thailand DEADTHWSCOPEID FTHAQ

Israel WSCOPEIS WSCOPETHFISRAEL Turkey DEADTKDEADIS FTURK

Jordan FJORD WSCOPETKWSCOPEJO Slovakia DEADSLODEADJO FSLOVAK

Malaysia DEADMY FSLOVALLFMAL WSCOPESXFMALQ Venezuela DEADVEWSCOPEMY WSCOPEVE

Mexico DEADME FVENZFMEXMEX101WSCOPEMX

51

Table A.3: Static ScreensThe table displays the static screens applied in our study, mainly following Ince and Porter(2006), Schmidt et al. (2017) and Griffin, Kelly, and Nardari (2010). Column 3 lists theDatastream items involved (on the left of the equality sign) and the values which we setthem to in the filter process (on the right of the equality sign). Column 4 indicates thesource of the screens.

Nr. Description Datastream item(s)involved

Source

(1) For firms with more than onesecurity, only the one with thebiggest market capitalization andliquidity is used.

MAJOR = Y Schmidt et al. (2017)

(2) The type of security must be eq-uity.

TYPE = EQ Ince and Porter(2006)

(3) Only the primary quotations of asecurity are analyzed.

ISINID = P Fong, Holden, andTrzcinka (2017)

(4) Firms are located in the respec-tive domestic country.

GEOGN = countryshortcut

Ince and Porter(2006)

(5) Securities are listed in the respec-tive domestic country.

GEOLN = countryshortcut

Griffin, Kelly, andNardari (2010)

(6) Securities with quoted currencydifferent from the one of the as-sociated country are disregarded.a

PCUR = currencyshortcut of the coun-try

Griffin, Kelly, andNardari (2010)

(7) Securities with ISIN country codedifferent from the one of the asso-ciated country are disregarded.b

GGISN = countryshortcut

Annaert, Ceuster,and Verstegen (2013)

(8) Securities whose name fields indi-cate non-common stock affiliationare disregarded.

NAME, ENAME,ECNAME

Ince and Porter(2006), Campbell,Cowan, and Salotti(2010), Griffin, Kelly,and Nardari (2010)and Karolyi, Lee, andDijk (2012)

a In this filter rule also the respective pre-euro currencies are accepted for countries withinthe euro zone. Moreover, in Russia “USD” is also accepted as currency, besides “RUB”.

b In Hong Kong, ISIN country codes equal to “BM” or “KY” and in the Czech RepublicISIN country codes equal to “CS” are also accepted.

52

Table A.4: Generic Keyword DeletionsThe table reports the generic keywords, which are searched for in the names of all stocks ofall countries. If a harmful keyword is detected as part of the name of a stock, the respectivestock is removed from the sample.

Non-common equity Keywords

Duplicates 1000DUPL, DULP, DUP, DUPE, DUPL, DUPLI,DUPLICATE, XSQ, XETa

Depository Receipts ADR, GDRPreferred Stock PF, ’PF’, PFD, PREF, PREFERRED, PRFWarrants WARR, WARRANT, WARRANTS, WARRT, WT, WTS,

WTS2Debt %, DB, DCB, DEB, DEBENTURE, DEBENTURES, DEBTUnit Trusts .IT, .ITb, INV, INV TST, INVESTMENT TRUST,

RLST IT, TRUST, TRUST UNIT, TRUST UNITS, TST,TST UNIT, TST UNITS, UNIT, UNIT TRUST, UNITS,UNT, UNT TST, UT

ETFs AMUNDI, ETF, INAV, ISHARES, JUNGE, LYXOR, X-TRExpired securities EXPD, EXPIRED, EXPIRY, EXPYMiscellaneous (mainly taken fromInce and Porter, 2006)

ADS, BOND, CAP.SHS, CONV, CV, CVT, DEFER,DEP, DEPY, ELKS, FD, FUND, GW.FD, HI.YIELD,HIGH INCOME, IDX, INC.&GROWTH, INC.&GW,INDEX, LP, MIPS, MITS, MITT, MPS, NIKKEI, NOTE,OPCVM, ORTF, PARTNER, PERQS, PFC, PFCL, PINES,PRTF, PTNS, PTSHP, QUIBS, QUIDS, RATE, RCPTS,REAL EST, RECEIPTS, REIT, RESPT, RETUR, RIGHTS,RST, RTN.INC, RTS, SBVTG, SCORE, SPDR, STRYPES,TOPRS, UTS, VCT, VTG.SAS, XXXXX, YIELD, YLD

53

Table A.5: Country-specific Keyword DeletionsThe table reports the country-specific keywords, which are searched for in the names of allstocks of the respective countries. If a harmful keyword is detected as part of the name of astock, the respective stock is removed from the sample.

Country Keywords

Australia PART PAID, RTS DEF, DEF SETT, CDIAustria PC, PARTICIPATION CERTIFICATE, GENUSSSCHEINE,

GENUSSCHEINEBelgium VVPR, CONVERSION, STRIPBrazil PN, PNA, PNB, PNC, PND, PNE, PNF, PNG, RCSA,

RCTBCanada EXCHANGEABLE, SPLIT, SPLITSHARE, VTG\\.,

SBVTG\\., VOTING, SUB VTG, SERIESDenmark \\)CSE\\)Finland USEFrance ADP, CI, SICAV, \\)SICAV\\), SICAV-Germany GENUSSCHEINEGreat Britain PAID, CONVERSION TO, NON VOTING,

CONVERSION ’A’Greece PRIndia FB DEAD, FOREIGN BOARDIsrael P1, 1, 5Italy RNC, RP, PRIVILEGIESKorea 1PMexico CPO, ’L’, ’C’Malaysia ’A’Netherlands CERTIFICATE, CERTIFICATES, CERTIFICATES\\),

CERT, CERTS, STK\\.New Zealand RTS, RIGHTSPeru INVERSION, INVN, INVPhilippines PDRSouth Africa N’, OPTS\\., CPF\\., CUMULATIVE PREFERENCESweden CONVERTED INTO, USE, CONVERTED-,

CONVERTED - SEESwitzerland CONVERTED INTO, CONVERSION, CONVERSION SEE

54

Table A.6: Dynamic ScreensThe table displays the dynamic screens applied in our study, following Ince and Porter (2006)and Schmidt et al. (2017). Column 3 lists the Datastream items required and column 4 statesthe sources of the screens.

Nr. Description Datastream item(s)involved

Source

(1) We delete the zero returns atthe end of the return time-series,which exist, because in case ofa delisting Datastream displaysstale prices from the date ofdelisting until the end of the re-spective time-series. We alsodelete the associated market cap-italizations.

TRI, MV Ince and Porter (2006)

(2) We delete the associated returnsand market capitalizations in caseof abnormal prices (unadjustedprices > 1000000).

TRI, MV, UP The screen originallystems from Schmidt etal. (2017), but con-trary to this study,we employ the unad-justed price instead ofthe price index for thedetermination of ab-normal prices

(3) We delete returns and the asso-ciated market capitalizations incase of return spikes (returns >990%).

TRI, MV Schmidt et al. (2017)

(4) We delete returns and the asso-ciated market capitalizations incase of strong return reversals, de-fined as follows: Rt−1 or Rt >=3.0 and (1 + Rt−1)(1 + Rt)− 1 <0.5.

TRI, MV Ince and Porter (2006)

55

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56