There are Two Very Different Accruals Anomalies∗

Andrew DetzelUniversity of Denver

Philipp SchaberlUniversity of Denver

Jack StraussUniversity of Denver

September 14, 2017

Abstract

We document that several well-known asset-pricing implications of accruals differ for in-vestment and non-investment-related components. Exposure to an investment-accrualsfactor explains the cross-section of returns better than the accruals themselves, and thisfactor’s returns are negatively predicted by sentiment. The opposite results hold fornon-investment accruals. Further tests show cash profitability only subsumes long-termnon-investment accruals in the cross-section of returns and economy-wide investmentaccruals negatively predict stock-market returns while other accruals do not. Theseresults challenge existing accruals-anomaly theories and help resolve mixed evidence byshowing that the anomaly is two separate phenomena: a risk-based investment accrualspremium and a mispricing of non-investment accruals.

JEL classification: E44, G12Keywords: Accruals Anomaly, Profitability, Real Investment, Cross-section of Stock Returns.

∗Authors’ emails: Andrew.Detzel@du.edu, Philipp.Schaberl@du.edu, and Jack.Strauss@du.edu, respectively. Forhelpful comments and suggestions, we thank Tony Cookson (Discussant), George Korniotis, and conference partici-pants at the University of Colorado Front Range Finance Seminar.

1. Introduction

Considerable evidence shows that accruals—the non-cash component of earnings—negatively pre-

dict the cross-section of stock returns, and this so-called “accruals anomaly” is unexplained by

modern asset pricing models (e.g., Sloan, 1996; Hou et al., 2015; Fama and French, 2016). Given

the headline nature of earnings, identifying the cause of the accruals anomaly and determining

whether it arises from risk or mispricing is fundamental in understanding whether markets effi-

ciently price accounting information. However, the literature offers conflicting evidence about both

lines of inquiry.

Accruals are less persistent than the cash component of earnings because they negatively predict

future earnings, controlling for current earnings. The seminal study of Sloan (1996) argues that

investors fail to account for this lower persistence and subsequently over-value firms with high

accruals. Consistent with this so-called “earnings fixation” hypothesis, many studies find evidence

of mispricing of accruals, particularly for the least persistent and least reliable components (e.g.,

Xie, 2001; Richardson et al., 2005; Green et al., 2011; Hirshleifer et al., 2012; Momente et al., 2015).

However, other studies find that exposure to a risk factor can explain a large part of the accruals

anomaly and interpret this as evidence of rational pricing (e.g, Khan, 2008; Chichernea et al., 2015;

Guo and Maio, 2016).

In contrast to earnings fixation, Ball et al. (2016) present evidence of a more rational earnings-

related explanation for the accruals anomaly. Using Fama and Macbeth (1973) regressions, they

find that controlling for cash-based operating profitability (COP), certain accruals no longer predict

the cross-section of returns. Alternatively, others argue that accruals predict returns because they

measure real investment and firms should rationally respond to low discount rates with high invest-

ment, all else equal (e.g., Fairfield et al., 2003; Wu et al., 2010). Consistent with this “investment

theory”, Wu et al. (2010) find that exposure to an investment factor explains a large portion of the

average returns on accruals-sorted portfolios.

Overall, prior studies find mixed evidence for both mispricing and investment-versus-profitability

explanations of accruals. One explanation for the mixed evidence is that prior studies do not all

use the same definition of accruals. For example, the seminal study of Sloan (1996) uses “operating

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accruals” (OA), which are defined as working-capital accruals minus depreciation. However, since

OA omits important long-term accruals—such as capitalized intangibles and property, plant, and

equipment (PP&E)—Richardson et al. (2005) propose the use of total accruals, which are mea-

sured by the change in net operating assets (∆NOA). Xie (2001) and Wu et al. (2010) consider

total accruals and/or groups of accruals based on their reliability or level of reporting discretion.

In particular, with the exception of Lewellen and Resutek (2016), prior studies generally do not

decompose accruals into components that directly measure investment and those that measure

non-investment-related adjustments to earnings. To resolve the mixed evidence in prior accruals

studies, we hypothesize that the (total) accruals anomaly is in fact two separate phenomena: a

risk-based investment-accruals premium, and a mispricing of non-investment-related accruals that

is unrelated to risk.

Following Lewellen and Resutek (2016), we decompose total accruals into three components:

working-capital accruals (∆WC), long-term investment accruals (IA), and long-term non-investment

or “nontransaction” accruals (NTA). The IA component includes items such as new PP&E that

represent expenditures in real investment. The ∆WC and NTA include items such as depreciation

that do not represent investment expenditures, hence we refer to ∆WC and NTA collectively as

“non-investment accruals”.

In testing our hypothesis, we examine whether several widely studied asset-pricing implications

differ between investment and non-investment accruals. We begin by investigating whether the

return premium associated with each component of accruals is explained by risk or mispricing.

Our first test in this vein is whether exposure to a risk factor explains returns on accruals-sorted

portfolios better than the accruals themselves. Prior studies that find evidence for “risk-based”

pricing of accruals only propose a risk-factor model and show that it explains a large portion of

the abnormal returns on accruals-sorted portfolios. However, risk-factor betas are highly correlated

with accruals themselves and these studies do not test whether risk factors explain returns better

than the accruals themselves. In one exception, Hirshleifer et al. (2012) perform “characteristics-

versus-covariances” tests following Daniel and Titman (1997) in which they sort stocks on OA and

then on OA-factor betas within OA portfolios. This double sorting produces variation in OA-factor

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risk that is uncorrelated with OA. They find that OA factor betas do not earn a return premium

after controlling for OA, consistent with mispricing.

We reapply the test of Hirshleifer et al. (2012) to investment and non-investment accruals. We

find that exposure to an IA-based risk factor explains the cross-section of returns better than the

IA themselves. In contrast, exposure to a ∆WC- or NTA-based risk factor does not command a

separate premium controlling for the accruals themselves, consistent with mispricing. An implica-

tion of the characteristics-versus-covariances results is that they serve as evidence against earnings

fixation explaining the IA premium because earnings fixation of investors does not naturally gen-

erate return covariance with a common factor. In contrast, our results are consistent with the

IA premium being explained by the investment theory, which is based only on how firms choose

investment given their cost-of-capital, regardless of whether this cost-of-capital is explained by risk

or mispricing (e.g., Lin and Zhang, 2013). A second implication of these results is that the method

from prior studies of showing that a risk factor explains a large portion of returns on accruals-sorted

portfolios does not provide evidence of a risk-based explanation for non-investment accruals.

Kozak et al. (2017) argue that testing whether a premium in returns is best explained by a risk

factor approximately tests whether the premium is consistent with the law of one price. However,

“risk” factors can capture risk that rational investors require compensation for (covariance with

marginal utility), or they can capture common sources of mispricing driven by market-wide investor

sentiment. The latter case is a form of mispricing, but is also consistent with the law of one price.

Hence, we test whether market sentiment predicts returns on the factors we form based on the

different accruals components following Stambaugh and Yuan (2016).

Predictive regressions show that the market sentiment index of Baker and Wurgler (2006), which

is orthogonalized to economic conditions, forecasts returns on the NTA factor, but not on the ∆WC

and IA factors. However, the linear regression specification hides a significant nonlinear relationship

between the accruals components and sentiment. The average (negative) premia associated with

NTA and ∆WC are only significant during times when sentiment is in the lowest quartile. The

concentration of the ∆WC and NTA premia in low-sentiment times challenges extant theories of

the accruals anomaly, which do not predict that investors only overvalue high-accruals firms when

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sentiment is very low.

In contrast, the IA premium is only significant in times of medium and high sentiment, and

is especially large when sentiment is above its 75th percentile. A common misconception is that

the investment theory of accruals is inherently “risk-based” and therefore implicitly rational on

the part of investors.1 The IA premium is risk-based in the sense that it is consistent with factor

pricing. However, the IA factor is driven at least in part by sentiment as opposed to purely rational

investor demand. This finding provides new evidence to the literature that investigates whether

asset-mispricing distorts real investment.2 In the context of the investment theory, the low returns

of high-IA firms in high-sentiment times are consistent with firms responding to sentiment-induced

overvaluation with high levels of real investment.

Next, we extend the results above by investigating whether other well-known asset-pricing

implications of accruals differ for investment- and non-investment components. We estimate Fama-

Macbeth regressions similar to those of Ball et al. (2016) and find that COP does not explain total

accruals in the cross-section of returns. When decomposing total accruals into ∆WC, IA, and NTA,

COP only explains NTA in non-micro-cap stocks. In particular, COP does not explain ∆WC—the

core of OA—which serves as evidence against the profitability theory of accruals, in contrast to Ball

et al. (2016). The Fama and Macbeth (1973) regression framework also provides further evidence

on risk vs mispricing of investment and non-investment-related accruals. Firm risk varies slowly

and therefore patterns in returns attributable to risk should predict returns even with the extra lag.

Thus, we estimate Fama-Macbeth regressions with 1 to 120 months of additional lags relative to

our baseline specification. Consistent with transitory mispricing that gets arbitraged away, ∆WC

and NTA only predict returns for two to eight additional months. In contrast, IA predict monthly

returns at a horizon of more than two and a half years, consistent with risk.

To further understand the differences in asset-pricing implications of investment- and non-

investment accruals, we investigate how each predicts aggregate stock market returns. Hirshleifer

et al. (2009) find that economy-wide (“aggregate”) OA positively predict stock market returns.

1E.g., Momente et al. (2015) refers to the investment theory as “risk-based” seemingly to suggest that it is rational.2See, e.g. Stein (1996), Chirinko and Schaller (2001), Baker et al. (2003), Gilchrist et al. (2005), Massa et al.

(2005), Titman et al. (2004), Polk and Sapienza (2009), Edmans et al. (2012), or Dessaint et al. (2016).

4

However, aggregate IA should negatively predict aggregate returns, because investment should be

high in good economic states of the world when risk premia tend to be low (e.g., Cochrane, 1991;

Zhang, 2005; Cooper and Priestley, 2009). Using similar predictive regressions as Hirshleifer et al.

(2009), we find that aggregate ∆WC does not predict future market returns, nor does aggregate

NTA. It follows from the former result that the predictability of returns by OA shown by Hirshleifer

et al. (2009) is driven by aggregate depreciation and deferred taxes. In contrast, we document that

consistent with theory, aggregate IA negatively predicts stock market returns.

Overall, the results in this paper show several fundamentally different asset-pricing implications

of investment and non-investment accruals that provide new empirical facts to be explained by the

next generation of accruals anomaly theories. Our study extends Lewellen and Resutek (2016) who

are the first to decompose accruals into investment and non-investment components. They focus

on the earnings persistence of each accruals component as well as whether each component predicts

returns. We expand on their analysis by more thoroughly investigating the different asset-pricing

implications of investment and non-investment accruals: whether each component represents risk

and/or mispricing, can be explained by cash profitability, and predicts aggregate market returns.

Using similar intuition as our characteristics vs covariances tests, Momente et al. (2015) also argue

that mispricing theories of accruals are idiosyncratic in nature, while risk-based theories involve

commonality. Consistent with mispricing, they find that it is idiosyncratic variation in accruals

that predicts returns. These results are consistent with our mispricing evidence for non-investment

accruals, but they do not differentiate between investment and non-investment components.

Our study is also related to recent literature that finds that many anomalies, including the OA

anomaly—but not the total accruals anomaly—are insignificant out of the sample period in which

they were originally discovered. Green et al. (2011) find that the OA anomaly was no longer reliably

profitable following the discovery of Sloan (1996). Similarly, Linnainmaa and Roberts (2016) find

that the operating accruals anomaly does not exist prior to the beginning of the Sloan sample.3 Our

sentiment results provide a new explanation for both the Green et al. (2011) and Linnainmaa and

Roberts (2016) findings: both studies’ sample periods exclude the times of abysmally low sentiment

3Mclean and Pontiff (2016) do not focus on the accruals anomaly, but generally find that anomaly returns generallydiminish post-discovery.

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of the 1960s and 1970s. Our evidence suggests that if low sentiment recurs for longer periods in

the future, the OA anomaly could be profitable again.

The remainder of the paper proceeds as follows. Section 2 explains relevant theory and prior

findings. Section 3 describes the data we use in the paper, section 4 presents our risk-versus-

mispricing results, and Section 5 presents extensions. Section 6 concludes.

2. Theory and prior findings

Earnings consist of cash flow and accruals. Total accruals can in turn be decomposed into invest-

ment and non-investment components that represent transitory adjustments to earnings. Hence,

accruals anomaly theories generally involve the relationship between returns and profitability or

real investment.

Irrational theory: The seminal study of Sloan (1996) documents that firms with high OA

(∆WC minus depreciation and deferred taxes) have abnormally low subsequent returns. Sloan

argues that investors over-rely (“fixate”) on earnings in estimating expected future profitability.

Investors subsequently overvalue stocks of firms whose high accruals lead to high earnings that are

not indicative of commensurately higher expected future earnings. Consistent with the mispricing

of accruals, Hirshleifer et al. (2012) find that the operating accruals characteristic predicts returns

better than exposure to an OA-based risk factor. Similarly, many other studies show evidence

consistent with mispricing of OA and total accruals (e.g., Xie, 2001; Richardson et al., 2005; Green

et al., 2011; Momente et al., 2015).

Rational theory: Prior studies document that profitability (investment) positively (negatively)

predicts returns in the cross-section (e.g., Novy-Marx, 2013, Fama and French, 2015, Hou et al.,

2015, and Ball et al., 2016). These findings can be rationalized with the following 2-period q-

theory model similar to that of Hou et al. (2015). Each firm i chooses time-0 investment (Ii0) to

maximize firm value, that is the present value of current and expected future dividends (Di0, and

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Di1, respectively):

maxIi0

Ai0Πi0 − Ii0 −a

2

(Ii0Ai0

)2

Ai0︸ ︷︷ ︸Di0

+E0 (A1iΠi1)

1 + ri1︸ ︷︷ ︸+

Di11+ri1

(1)

s.t. Ai1 = Ii0 + (1− δ)Ai0 (2)

The Ait (Πit) denote assets (profitability) at time t. Firm i takes as given the depreciation rate δ

and the discount rate ri1. Having a > 0 implies convex adjustment costs. The Πit are assumed to

be constant with respect to Ait, but the model would produce similar predictions with diminishing

marginal returns (∂Πit∂Ait

< 0) and a = 0 (e.g., Wu et al., 2010).

The first-order condition for the problem given by Eq. (1) yields the following relationship

between the expected return (E0(ri1)) and each of expected future profitability (E(Πi1)) and con-

temporaneous investment (Ii0/Ai0) via:

E0(ri1) =E0 (Πi1)

1 + a(Ii0/Ai0)− 1. (3)

In the “profitability theory” of accruals, once profitability is properly measured, accruals no longer

predict returns, consistent with Eq. (3) via the numerator. Empirical work typically uses a measure

of recent accounting profitability as a proxy for expected future profitability (E0(Πi1)). Ball et al.

(2016) argue that cash-based operating profitability (COP) is the best measure of profitability for

predicting returns because it does not contain transitory accruals. Consistent with the profitability

theory, they find that controlling for COP, OA no longer predict returns.

In contrast, Wu et al. (2010) argue that accruals represent a form of investment, and therefore

a relationship like Eq. (3) can explain the accruals anomaly via the denominator. We refer to this

explanation as the “investment theory” of accruals. Consistent with this theory, Wu et al. (2010)

find that an asset pricing model that includes an investment factor explains much of the returns

on strategies portfolios formed on OA, total accruals, and discretionary accruals.4

Whether IA are mispriced has important economic implications that can be understood in the

4Fama and French (2006), Novy-Marx (2013), and Fama and French (2015) also show that comparative staticsfrom the basic dividend-discount model of stock prices also generate joint predictability of returns by profitabilityand investment, similar to Eq. (3).

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context of the investment theory. The discount rate E0(ri1) in the model given by Eq. (1) can be

irrational regardless of whether firm i optimally responds to it. Indeed, a large body of evidence

shows that firms respond to over/under-valuation in choosing the level of real investment.5 If high

IA correspond to firms’ rationally responding to irrational discount rates, capital is not efficiently

allocated.

3. Data

Following Sloan (1996) and most of the prior studies in accruals, we define operating accruals (OA)

as follows [Compustat mnemonics in brackets]:

OA ≡ ∆noncash current assets [(ACTt − CHEt)− (ACTt−1 − CHEt−1)] (4)

−∆current liabilities [LCTt − LCTt−1]

+ ∆short-term debt [DLCt −DLCt−1]

+ ∆taxes payable [TXPt − TXPt−1]

− depreciation and amortization expense [DP ].

Richardson et al. (2005) argue that OA omit important accruals and deferrals related to non-current

operating assets and liabilities as well as non-cash financial assets and liabilities. They argue via

balance sheet identities that a more comprehensive measure of total accruals is given by the change

in net operating assets (∆NOA), where:

NOA = total assets [AT ]− cash [CH]− total liabilities [LT ] + debt [DLC +DLTT ]. (5)

Following Lewellen and Resutek (2016), we decompose total accruals (∆NOA) into accruals that

represent investment expenditures (IA) and nontransaction accruals (NTA) that represent non-

investment adjustments to earnings. Conceptually, NOA is the sum of net working capital (WC )

5See, e.g. Stein (1996), Chirinko and Schaller (2001), Baker et al. (2003), Panageas (2003), Chirinko and Schaller(2004), Gilchrist et al. (2005), Massa et al. (2005), Titman et al. (2004), Polk and Sapienza (2009), Panageas (2011),Edmans et al. (2012), or Dessaint et al. (2016)

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and long-term net operating assets (LTNOA). Hence, ∆NOA can be decomposed as follows:

∆NOA = ∆WC + ∆LTNOA, (6)

where

WC = current assets [ACT ]− cash [CHE] (7)

− current liabilities [LCT ] + short term debt [DLC].

Ideally, one would be able to further decompose ∆WC and ∆LTNOA into a component that

captures a firm’s new investment and a component that reflects ‘nontransaction’ accruals, which

are the result of changes in the book values of assets and liabilities already in place, rather than

new investment expenditures. The goal is to come up with a metric that captures all accruals that

are distinct from investments in ∆WC and ∆LTNOA. Following Lewellen and Resutek (2016),

we define nontransaction accruals (NTA) by using information about NTA from the Statement of

Cash Flows and the earlier flow-of-funds statement as follows:

NTA ≡− (depreciation and amortization [DP ] (8)

+ deferred taxes [TXDC]

+ loss (gain) on sale of property, plant, and equipment and investments [SPPIV ]

+ funds from operations-other [FOPO]

+ extraordinary items and discontinued operations [XIDOC]).

Lewellen and Resutek (2016) argue that NTA mainly reflects investment in LTNOA rather than

net working capital. Under this assumption, we decompose ∆LTNOA into investment accruals

(IA) and nontransaction accruals (NTA) as follows:

∆LTNOA = IA+NTA. (9)

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Substituting Eq. (9) into Eq. (6) yields

∆NOA = ∆WC + IA+NTA. (10)

The decomposition shown in Eq. (10) allows us to isolate accruals that are linked primarily to

new investment in long-term operating assets (IA), rather than accounting policy. In principle,

∆WC can include items such as changes in inventory that can be interpreted as real investment

along with items such as changes in accounts payable that can not. However, the sensitivity of

short-term investment such as new inventory to cost of capital is confounded by other short-term

frictions such as storage costs, seasonal variation in demand, risk of obsolescence, and short-term

cash management concerns. Thus, following Lewellen and Resutek (2016), we rely on IA as our

measure of investment accruals.

Following Ball et al. (2016), we calculate operating profitability (OP) and cash-based operating

profitability (COP) as follows:

OP ≡ Revenue [REV T ] (11)

− Cost of goods sold [COGS]

− Sales, general, and administrative expenses [XSGA]

+ Research and development expenses [XRD].

COP ≡ OP (12)

−∆Accounts receivable [RECTt −RECTt−1]

−∆Inventory [INV Tt − INV Tt−1]

−∆Prepaid expenses [XPPt −XPPt−1]

+ ∆Deferred revenue [(DRCt +DRLTt)− (DRCt−1 +DRLTt−1)]

+ ∆Trade accounts payable [APt −APt−1]

+ ∆Accrued expenses [XACCt −XACCt−1].

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For our empirical analysis, we obtain accounting data from the Compustat annual file and stock

return data from CRSP. We exclude financial firms (those with a 1-digit SIC code of 6). Further,

we eliminate firm-year observations with insufficient accounting data in Compustat to compute the

main financial statement variables for our empirical tests. We replace missing values with zero for

variables necessary to calculate ∆NOA, OA, WC, and COP. These data requirements yield a final

sample with a total of 115,163 firm-years, covering fiscal years 1971 to 2015.6 We also obtain the

sentiment index of Baker and Wurgler (2006), which is updated through 2015:9, from the website

of Jeffrey Wurgler.7 Wurgler provides two versions of the index: one that is orthogonalized to

economic conditions, and one that is not. We choose the former to isolate the effect of sentiment.

Panel A of Table 1 reports descriptive statistics for the accruals variables, COP, and change in

assets (∆A). OA, COP , and ∆AT are scaled by lagged total assets to maintain comparability to

Ball et al. (2016), while ∆NOA, IA, and NTA are scaled by average total assets for the year to

maintain comparability with Lewellen and Resutek (2016).8 In our sample, average OA are -2.3%

of assets and COP is 11%. Ball et al. (2016) report -2.9% and 11.7%, respectively. On average,

IA are 11% of assets and NTA are -7.3%. Lewellen and Resutek (2016) report 11% and -8%,

respectively.

Panel B reports the Pearson (Spearman) in the top (bottom) triangle. The reported statistics

are calculated as the time-series averages of the annual cross-sectional correlations. The following

discussion is based on the Pearson correlation coefficients, but the Spearman coefficients are similar.

Consistent with Ball et al. (2016), we find a significantly negative correlation between OA and COP

(-0.288). Consistent with Lewellen and Resutek (2016), we report a negative correlation (-0.361)

between IA and NTA. Interestingly, COP is positively correlated with IA (0.154) and negatively

correlated with NTA (-0.093). This result suggests that firms with higher cash-based profitability

invest more in long-term assets.

6Firms with fiscal years of 1971 (2015) are only included if their year end is late (early) enough to be matchedwith our returns (1972:5-2015:12).

7http://people.stern.nyu.edu/jwurgler/8Inferences in this paper are robust to using lagged assets for all variables OR average assets for all variables.

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4. Risk and return properties of accruals

To test whether each component of accruals is mispriced, it is necessary to make assumptions about

what empirical properties rational prices should exhibit. Perhaps the most commonly examined

property of rational prices is that expected excess returns should be explained by betas with respect

to common risk factors (e.g., Fama and French, 1993; Cochrane, 2005; and Cochrane, 2011). Based

on this intuition, a voluminous literature seeks to empirically “explain” anomalies by identifying

a risk-factor model—such as the Fama and French (1993) three-factor model—and showing that

it eliminates most of the alphas on portfolios formed on some anomaly characteristic—such as

size or book-to-market ratio. Prior papers that provide a “risk-based explanation” for accruals

all fall in this category (e.g., Khan, 2008; Wu et al., 2010; Chichernea et al., 2015; Guo and

Maio, 2016). However, Daniel and Titman, 1997 argue that this approach does not test risk versus

mispricing because the loadings on risk factors are highly correlated with the anomaly characteristics

themselves. Rather, to test risk (“covariances”) versus characteristics, it is necessary to identify

variation in risk that is uncorrelated with the characteristics. Hirshleifer et al. (2012) apply the

methodology of Daniel and Titman (1997) to OA and find that variation in OA better explains the

cross-section of returns than variation in risk associated with an OA-based risk factor, consistent

with mispricing.9

We apply the methodology of Daniel and Titman (1997) and Hirshleifer et al. (2012) to

investment- and non-investment-related accruals as opposed to just OA. Specifically, for each com-

ponent of accruals (Acc ∈ {∆WC, IA, NTA}), we test the null hypothesis that expected returns

rit are explained by the following model:

rit − rft = αi + β′ift + hA,iHMLAcc,t + εt, (13)

with αi = 0, against the characteristics-based alternative:

rit − rft = a+ b′xi,t−1 + c′Accit + εt. (14)

9This methodology is also used by Davis et al. (2000).

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The HMLAcc denotes an accruals-based risk factor, ft denotes control factors that are excess

returns (e.g. MKT , SMB, and HML), and the xi,t are control characteristics (e.g. size and

book-to-market).

In this section, after we construct accruals factors, we identify variation in HMLAcc factor

loadings (hA) that is independent of the accruals characteristics and test whether this variation

in loadings is associated with spreads in average returns (as predicted by the risk model given by

Eq. (13)). In contrast, the characteristics alternative (Eq. (14)) predicts that the hA will have no

incremental predictive power after controlling for variation in accruals.

4.1. Accruals factors

We construct our accruals factors similarly to the HML of Fama and French (1993), but follow

Lewellen and Resutek (2016) in assigning accounting data to returns. Each month we sort all

stocks on NYSE, AMEX, and NASDAQ with size and accruals data into two size groups (S or

B) based on whether their market capitalization is below or above the NYSE median breakpoint,

respectively. For each measure of accruals, we also sort stocks independently each month into three

accrual portfolios (Low (L) to High (H)) based on the 30th and 70th breakpoints for NYSE stocks,

respectively. We form six value-weighted size/accruals portfolios (S/L, S/M, S/H, B/L, B/M, and

B/H) as the intersections of the two size groups and the three accruals groups. HMLAcc is the

difference between the equal-weighted average of the returns on the two high-accrual portfolios

(S/H and B/H) minus the equal-weighted average of the returns on the two low-accrual portfolios

(S/L and B/L). Thus, HMLAcc = (rS/H + rB/H)/2 − (rS/L + rB/L)/2. Each stock is assigned to

an accruals portfolio based on its accruals measured at the end of the most recent fiscal year that

is at least four months prior.

Table 2 presents summary statistics of the base-asset returns (Panel A) used to make the

accruals factors HMLAcc, as well as factor summary statistics (Panel B) and correlations (Panel

C). Panel A reveals that for each measure of accruals, returns are generally lowest in the high

accruals portfolios, and this difference is greater (24 to 48 vs 9 to 20 basis points per month) in

small-cap stocks than large-cap stocks. Panel C presents average factor returns and t-statistics for

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the Fama-French factors as well as the accruals factors. Panel B shows that the IA and ∆WC

factors have significant average returns with t-statistics greater than 3. In contrast, HMLNTA

has only a marginally average significant return of -0.17% per month (t = −1.93). Coupled with

the significance of NTA in the cross-section of non-micro-cap stock returns found by Lewellen and

Resutek (2016), NTA is evidently more significant in the cross-section of mid-cap stock returns

than large-cap stock returns.

Panel C shows pairwise correlations between each of the Fama-French and accruals factors. All

of the factors are less than perfectly correlated with the strongest correlation (-0.55) between the

NTA and IA factors. In particular, the relatively low correlations between factors indicate that the

different accruals represent economically distinct anomalies.

Examining average factor returns does not fully describe the incremental ability of factors to

explain asset prices relative to benchmark factors. For example, two factors could have average

excess returns of 0, but if one factor has a significant beta, then the 0 average return still represents

an anomaly. Table 3 presents abnormal returns of the accruals factors with respect to the Fama-

French 3-factor (columns 1 to 3) and 5-factor (columns 4-6) models. All three accruals factors earn

3-factor alphas that are significant at the 5% level. Columns (4) and (6) show that controlling for

the 5 factors only increases the size and significance of the ∆WC and NTA factors. In contrast,

column (5) shows that exposure to the Fama-French profitability and investment factors explains

the abnormal returns on the IA factor. Overall, the evidence in Tables 2 and 3 show that each

accruals factor earns a significant premium and that the IA premium appears economically distinct

from the ∆WC and NTA.

4.2. Comovement and accruals measures

Testing the “risk” model (Eq. (13)) relative to the characteristics model (Eq. (14)) is uninformative

if the risk model does not perform reasonably well at pricing portfolios sorted by size and accruals.

Hence, Table 4 presents estimates of the four-factor regression:

rit − rft = ai + biMKTt + siSMBt + hiHMLt + hA,iHMLAcc,t + εt, (15)

14

for the post-formation returns on nine portfolios formed in June each year as the intersections of

independent sorts of stocks into three size groups and three accruals groups following Daniel and

Titman (1997), Davis et al. (2000), and Hirshleifer et al. (2012). Panels A, B, and C, respectively,

use ∆WC, IA, and NTA.

Overall, Table 4 shows that the four-factor model (Eq. (15)) does a reasonably good job ex-

plaining the returns on the size/accruals portfolios. Sorting on size and each measure of accruals,

the loadings (hA) on the accruals factors increase monotonically and significantly with accruals

within each size group. Moreover, while the four-factor model does not eliminate all alphas of

the size/accruals portfolios, the relationship between each measure of accruals and alpha is not

monotonic for most size groups. Hence the four-factor model, like any model, is not perfect, but

Table 4 does not indicate that the characteristics model is any better.

4.3. Tests of characteristics versus covariances

To isolate variation inHMLAcc risk that is unrelated to accruals, we triple-sort stocks into portfolios

based on size, accruals, and hA. Specifically, for each measure of accruals, and each of the associated

nine size/accrual portfolios from Table 4, we further divide the portfolio into three value-weighted

subportfolios (L to H) based on the pre-formation hA estimated over the previous 60 months (24

months minimum) using regression Eq. (15). The cutoffs for hA are again set at the 33rd and

67th percentiles. The resulting three subportfolios within each of the size/accrual portfolios thus

consist of stocks of similar size and accrual characteristics but different levels of hA, and therefore

should exhibit sufficiently low correlation between their hA and accruals. We use these portfolios

(denoted size/accruals/hA) to test whether hA can predict returns after controlling for variation in

the accrual characteristic.

Under the risk-factor model of Eq. (13), average returns should decrease with hA within each

size/accruals group, but the difference in returns between high- and low-loading-stock returns

should have an intercept of 0 in the regression given by Eq. (15). Conversely, under the charac-

teristics alternative, within each size/accruals group, there should not be a large spread in returns

across hA sub-portfolios. Moreover, stocks with high (low) hA should earn positive (negative) inter-

15

cepts to offset the returns implied by the positive (negative) hA times the accruals factor that has

a negative average return. To formally test Eq. (13) vs Eq. (14), we form a portfolio HhA − LhA

that is the long (short) in an equal-weighted average of the 9 portfolios with high (low) hA:

HhA − LhA = (1/9)

B∑i=S

H∑j=L

ri/j/H − (1/9)

B∑i=S

H∑j=L

ri/j/L. (16)

Under the risk-factor model of Eq. (13), HhA−LhA should have an intercept of 0 in the four-factor

model given by Eq. (15). For each measure of accruals, E(HMLAcc) < 0 and by construction,

the HMLAcc loading (hA,HhA−LhA) of HhA − LhA is positive. Under the characteristics model,

E(rHhA−LhA) = 0 so it must be the case that the intercept (aHhA−LhA

) from the four-factor

regression is positive (and approximately equal to −hA,HhA−LhA∗ E(rHhA−LhA

)).

For each of the three types of accruals, Table 5 presents size and accruals characteristics,

average excess returns, and estimations of the four-factor model Eq. (15) for the 27 size/accruals/hA

portfolios as well as HhA−LhA for each of the three accruals measures. Panels A, B, and C present

results for ∆WC, IA, and NTA, respectively.

Panel A shows results for ∆WC that differ slightly from those Hirshleifer et al. (2012) show for

OA (which differ from ∆WC by depreciation and deferred taxes). While they find a statistically

significant four-factor α on HhOA−LhOA, we find an insignificant (t=1.42) α on Hh∆WC−Lh∆WC .

So, using α we can not reject that ∆WC is mispriced relative to the four-factor model. However, the

average return of Hh∆WC −Lh∆WC is positive, which is the opposite sign that would be generated

under the risk model (because the average return on HML∆WC is negative). Moreover, since

the spread in post-ranking h∆WC is insignificant (t = 0.97), the prior covariance with HML∆WC

does not represent a persistent risk exposure. Overall, Panel A provides evidence that the ∆WC

premium is better explained by the ∆WC themselves than by risk.

Panel B shows that within the size/IA portfolios, sorting on hIA generates little spread in size

and IA. It does, however, generate a significant spread in post-formation hIA loadings, consistent

with these loadings representing a persistent risk exposure. Moreover, we can reject at the 5%

level the characteristics model, which predicts that E(HhIA − LhIA) = 0 in favor of the one-sided

16

covariances alternative, which predicts that E(HhIA − LhIA) < 0 with a t-statistic of tE(r) =

−1.67.10 We can not, however, reject the risk model in favor of the characteristics model as

HhIA − LhIA does not earn a significant four-factor α, because its average return is accounted for

by a significant hIA (t = 8.70). Thus, the risk model (Eq. (13)) explains the investment accruals

premium better than the characteristics model.

The evidence in Panel C is generally consistent with the characteristics model and mispricing

of NTA. Size and NTA do not vary with pre-formation hNTA, however the pre-formation hNTA

are persistent, leading to a significant spread in post-ranking hNTA and a significant hNTA for

HhNTA − LhNTA. This spread in loadings does not explain the average returns on the HhNTA −

LhNTA leading to a significant (t = 3.77) four-factor α and therefore a rejection of the covariances

model in favor of the characteristics alternative.

Overall, the results from Table 5 show the IA premium is best explained by exposure to a risk

factor while the non-investment accruals premia are better explained by the accruals themselves.

4.4. Caveats and interpretation

The characteristics versus covariances tests presented above come with at least two caveats that

impact the interpretation of their results: one economic, and the other statistical in nature. The

economic caveat is that although exposure to a risk factor explains returns in rational asset pricing

models, factor pricing and mispricing are not mutually exclusive. Kozak et al. (2017) argue that

sentiment can generate covariance with a common factor (that is unrelated to rational marginal

utility) when trading against the sentiment demand exposes arbitrageurs to factor risk.11 Stam-

baugh and Yuan (2016) provide empirical evidence consistent with the Kozak et al. (2017) argument

by showing sentiment predicts returns on factors thought to represent mispricing.

Following Stambaugh and Yuan (2016), we test whether market sentiment predicts returns

10As noted by Davis et al. (2000), a one-sided test is appropriate because the covariances alternative predicts thatE(HhIA − LhIA) will be the same sign as the IA premium, which is negative.

11In spite of this possibility, it is still commonly assumed that mispricing generally does not generate covariancewith a common factor. For example, Cochrane (2011) writes: “Behavioral ideas [...] are good at generating anomalousprices and mean returns in individual assets or small groups. They do not [...] naturally generate covariance. Forexample, extrapolation generates the slight autocorrelation in returns that lies behind momentum. But why shouldall the momentum stocks then rise and fall together the next month, just as if they are exposed to a pervasive,systematic risk?”

17

on the three accruals factors from above (HMLWC , HMLIA, HMLNTA), as well as a similarly

constructed HMLOA that facilitates comparison with prior studies on the OA anomaly. Panel A

of Table 6 presents the results of predictive regressions of the form:

HMLAcc,t = a+ b · St−1 + ut, (17)

where HMLAcc,t is the monthly return on one of the accruals factors, and St−1 is the Baker and

Wurgler sentiment index that is orthogonalized to macroeconomic conditions at the end of the

previous month. Only HMLNTA and HMLOA have a significant b, and their slopes indicate that

a one-standard deviation increase in sentiment increases their expected returns 2.21% and 2.32%

per annum, respectively.

Panel B shows, however, that the simple predictive regression hides a significant nonlinear

relationship between returns on the accruals factors and sentiment. The panel presents average

returns (% per annum) for the accruals factors during times of low, medium, and high (lagged)

sentiment. Sentiment is defined to be low, medium, or high, respectively, if it is less than its

historical 25th percentile, between its 25th and 75th percentiles, or above its 75th percentile.

HMLWC , HMLNTA, and HMLOA only earn statistically significant average returns in times of

low market sentiment, however the difference between high-sentiment and low-sentiment average

returns is insignificant for HMLWC . Moreover, the average returns for HMLNTA are economically

trivial (-11 to 5 basis points per year) when sentiment is medium or high. In contrast, HMLIA

has significant average returns only when sentiment is medium or high.

Overall, the combined evidence in Panels A and B shows that sentiment affects the average

returns of all three of the accruals factors from Table 5, although the effect is strongest on HMLIA

and HMLNTA. Given the evidence of Table 5 that risk explains the IA premium, the sentiment

results for IA are noteworthy. While factor covariance explains the IA return premium, the under-

lying IA factor is at least partially driven by sentiment as opposed to rational risk (covariance with

rational marginal utility), consistent with the Kozak et al. (2017) argument. This in turn has the

important implication that irrational—though risky to arbitrage—variation in equity cost-of-capital

is associated with variation in real investment measured by IA.

18

Figure 1 depicts a time series of the Baker and Wurgler (2006) sentiment measure. Coupled

with the evidence from Table 6, this Figure presents an explanation for why Green et al. (2011) and

others find that strategies based on OA are unprofitable after the year 2000: sentiment is mostly

medium and high during the post-2000 sample period. Conversely, this predominantly medium

and high sentiment explains why Lewellen and Resutek (2016) find strategies based on investment

accruals are still profitable in this period. When sentiment is low again—as it was in the 1960s and

1970s—our results predict that the OA strategy would be profitable again.

The statistical caveat of characteristics vs covariances tests is that measured covariances contain

estimation error, while characteristics are directly observed (e.g., Lin and Zhang, 2013). This has

a tendency to bias these tests in favor of characteristics. For IA, the bias does not impact inference

because the tests in Table 5 provide evidence in favor of the risk-factor model for IA in spite of

the bias. In contrast, the evidence against the risk-factor model of ∆WC and NTA in Table 5

could be partially explained by estimation error. However, a careful examination of the evidence

mitigates these concerns. First, the significant post-ranking spread in hNTA across high- and low-

hNTA portfolios is associated with a significantly positive α earned by the HhNTA − LhNTA. If

estimation error were driving the results, it should attenuate the relationship between estimated

covariances and average returns, not reverse the sign of the risk premium. Second, for ∆WC,

the post-ranking h∆WC of Hh∆WC − Lh∆WC is statistically insignificant and economically small

(0.08). The h∆WC we estimate are the HMLWC betas investors face, so this result implies very

little persistent risk investors have to bear by trading based on ∆WC. Hirshleifer et al. (2012) raise

a related point: “If estimation noise is so severe that the estimated loadings do not explain the

accrual anomaly, this raises the question of how investors can identify true factor loadings and place

high premia on them.” Thus, considering economic significance, the results from Table 5 generally

serve as evidence against a risk-based explanation for ∆WC and NTA.

19

5. Extensions

5.1. Cash-based operating profitability

Ball et al. (2016) argue that cash-based operating profitability (COP) better captures the economic

concept of profitability in asset pricing models such as Eq. (3) than other commonly used measures.

Consistent with the profitability theory of accruals, Ball et al. (2016) find that controlling for COP,

OA no longer predict the cross-section of returns. However, they do not distinguish between

investment and non-investment components of accruals, which in theory, should jointly predict

returns (e.g. Eq. (3)). To test this hypothesis, we investigate whether COP subsumes ∆WC, IA,

and NTA in explaining returns.

Table 7 presents Fama and Macbeth (1973) regressions of monthly stock returns on cash-based

operating profitability (COP), OA, total accruals (∆NOA), ∆WC, IA, and NTA. Following Ball

et al. (2016), we include the following control variables: the natural logarithm of the book-to-market

ratio, the natural logarithm of the market value of equity, and past returns for the prior month and

for the prior 12-month period, excluding month t− 1. We estimate the regressions monthly using

data from May 1972 through December 2015. Our sample is therefore 10 years shorter than that

of Ball et al. (2016) due to availability of IA. Following Lewellen and Resutek (2016), we match

returns in a given month with annual accounting data from the most recent fiscal year that ended

at least four months prior.12

Panel A presents results for non-microcap stocks (firms with market value of at least the NYSE

20%-ile), and Panel B presents results for microcaps. Consistent with Sloan (1996) and the prior

accruals anomaly literature, column (1) of Panel A shows that OA is negatively priced in the cross-

section of non-microcap returns without controlling for COP. Like Ball et al. (2016) though, we

see in column (2) that controlling for COP renders OA insignificant in non-microcaps. In contrast,

Columns (3) and (4) show that the more comprehensive ∆NOA are negatively priced, but are

unexplained by COP. Thus, cash profitability does not explain the total accruals anomaly.

Perhaps surprisingly, Columns (5) and (6) show that ∆WC —the core of OA— are negatively

12Thus, our accounting data is more timely than that of Ball et al. (2016), who use a six-month lag. However,untabulated results show inferences remain unchanged using either lag specification.

20

priced but not subsumed by COP. Thus, the Ball et al. (2016) result depends on including depreci-

ation and deferred taxes in OA, whereas we include these items in NTA. Consistent with Ball et al.

(2016), columns (7) and (8) show that COP renders NTA insignificant. Columns (7) and (8) also

show that COP does not subsume IA in the cross-section of non-microcap stock returns.

Panel B shows slightly different results in micro-cap stocks than for non-micro-cap stocks.

Similar to Panel A, OA are still subsumed by COP in micro-caps. However, unlike Panel A, ∆WC

are subsumed by COP instead of NTA. Regardless of the discrepancy between micro-caps and non-

micro-caps, the main takeaway is the same for both Panels. While COP subsumes OA, COP does

not subsume all non-investment accruals, nor does it subsume investment accruals in predicting

the cross-section of returns. This is evidence against the rational profitability theory of accruals.

The Fama-Macbeth framework provides additional evidence of risk versus mispricing. Ball

et al. (2016) argue that risk should be more persistent than mispricing and investigate whether

longer lags of OA and COP continue to predict returns in Fama-Macbeth regressions. Based on

the same motivation, Figure 2 presents Fama-Macbeth regression slopes and their corresponding

95% confidence intervals from regressions of monthly stock returns on control variables and lagged

values of the three accruals measures (∆WC, IA, and NTA). The control variables, which we do not

lag, are the same as those in Table 7 and the lags of the accruals increase in one-month increments

up to ten years. The regressions use data for non-microcaps each month from May 1982 through

December 2015 so that the same data are used for all lags. A lag of 0 in Figure 2 indicates that

no additional lags are used relative to the Fama-Macbeth regressions in Table 7; there is still a

4-month-minimum lag for accounting data relative to the returns they predict.

Figure 2 demonstrates NTA and ∆WC have the least persistent predictive power for returns.

Lagging NTA by more than 2 additional months in Table 7 renders NTA insignificant. ∆WC

remains significant for up to 8 extra months relative to Table 7. In contrast, IA is a more persistent

predictor of returns and remains significant for up to 28 additional months. Overall, the evidence

from Figure 2 is consistent with the IA premium arising from risk, whereas ∆WC and NTA premia

appear to be consistent with mispricing that is arbitraged after several months.

21

5.2. Return forecasting

To further examine the different asset-pricing implications of investment and non-investment accru-

als, we investigate the predictive relationship between economy-wide accruals and aggregate stock

market returns. Hirshleifer et al. (2009) find that aggregate OA is a significant positive predictor

of aggregate stock-market returns, which does not follow from any of the theories of accruals cited

above. In particular, investment, and therefore IA should be lower in good economic states when

risk premia are relatively low, which would result in IA negatively predicting stock market returns

(e.g., Cochrane, 1991; Zhang, 2005; Cooper and Priestley, 2009). Following Hirshleifer et al. (2009),

Table 8 presents univariate predictive regressions of one-year ahead aggregate log stock returns on

aggregate OA, ∆WC, IA, and NTA.

Column 1 in Panel A confirms the Hirshleifer et al. (2009) finding that aggregate OA positively

predicts stock market returns over the following year from 1971-2015. However, columns 2 and

4 show that ∆WC and NTA do not predict returns. Thus, the Hirshleifer et al. (2009) result

of positive return predictability depends on including depreciation and deferred taxes in OA. In

contrast, column 3 shows that IA significantly and negatively predict returns, consistent with

theory. Panel B presents similar forecasts as Panel A, but with log excess returns. Comparing the

two Panels shows that for both OA and IA, most of the return predictability comes from predicting

the risk premium component of expected stock-market returns.

6. Conclusion

The evidence in this paper shows that the asset-pricing implications of investment and non-

investment components are fundamentally different. These findings challenge existing theories

of the accruals anomaly and demonstrate that there are not one, but two, accruals anomalies to

explain: a risk-based investment accruals premium and a short-lived mispricing of non-investment

accruals.

Characteristics versus covariances tests show that an investment accruals factor better explains

the cross-section of returns than the investment accruals themselves. This result is evidence against

22

earnings fixation and profitability-related mispricing explanations of the investment accruals pre-

mium, which do not predict a factor structure of returns. In contrast, the opposite pattern holds

for non-investment accruals, consistent with mispricing in the form of a violation of the law of one

price. These results are corroborated by evidence that investment accruals predict the cross-section

of returns for more than two years—consistent with persistent risk—while non-investment accruals

only predict returns for 1 to 8 months—consistent with short-lived mispricing.

While the investment accruals premium is explained by a risk factor and is therefore not an

arbitrage opportunity, the underlying factor is at least partially driven by sentiment as opposed to

entirely rational demand. The negative investment accruals premium is most significant in times

of high sentiment, which is consistent with firms responding to sentiment-induced overvaluation

with high levels of real investment. In contrast, the negative non-investment accruals premium is

significant only when sentiment is in its bottom quartile. This finding challenges existing mispricing

explanations of accruals that do not predict that overvaluation of high-accruals firms should be

concentrated in low-sentiment periods.

We also find that investment and working-capital accruals are not subsumed by cash-based op-

erating profitability in the cross-section of returns, refuting the theory that accruals are only priced

because they proxy for properly measured profitability. Finally, in contrast to the anomalous result

that aggregate operating accruals positively predict stock-market returns, we find that aggregate

investment accruals negatively predict stock-market returns.

23

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-2-10

123

Fama-MacBeth

regression slope

1970 1975 1980 1985 1990 1995 2000 2005 2010 2015Horizon (years)Low sentiment Medium sentiment High sentimentFigure 1: Baker and Wurgler (2006) sentiment index orthogonalized to economicconditions.

This figure presents a plot of the Baker and Wurgler (2006) sentiment index that is orthogonalized to eco-nomic conditions. Sentiment is considered low, medium, or high based on the 25th and 75th percentiles of itsdistribution.

27

-2-1

01

Fam

a-M

acBe

th re

gres

sion

slo

pe

0 2 4 6 8 10Horizon (years)

-2-1

01

2Fa

ma-

Mac

Beth

regr

essi

on s

lope

0 2 4 6 8 10Horizon (years)

Panel (A): Working-capital accruals Panel (B): Investment accruals

-4-2

02

4Fa

ma-

Mac

Beth

regr

essi

on s

lope

0 2 4 6 8 10Horizon (years)

Panel (C) Non-transaction accruals

Figure 2: Fama and MacBeth (1973) regressions of stock returns on lagged operatingprofitability, cash-based operating profitability, and accruals.

Panels A, B, and C of this figure present average Fama and MacBeth (1973) regression slopes (multipliedby 100) and their corresponding 95% confidence intervals from regressions of monthly stock returns on controlvariables and lagged values of the three accruals measures (working-capital, investment, and non-investment).The control variables in the regressions are: prior one-month return, prior one-year excluding prior-month return,log-book-to-market, and log-size. The lags increase in one-month increments up to ten years. The control variables(but not the three accruals variables) are updated over time. The regressions are estimated for each month fromMay 1982 through December 2015 using data for all-but-microcaps, which are stocks with a market value of equityabove the 20th percentile of the NYSE market capitalization distribution. The same data are used for all lags.

28

Table 1: Descriptive statistics of accounting variables Panel A presents time-series averages of cross-sectional means, standard deviations, and percentiles. Panel B presents time-series averages of cross-sectional correlations. Pearson (Spearman) correlation coefficients are reported in the top (bottom) triangle. For detailed variable definitions please see the Data section in the text. The accounting variables in our sample, which has 115,163 firm-year observations, cover fiscal years 1971-2015.

Panel A: Distributions

Variable Mean SD 1st 25th 50th 75th 99th

Total accruals (𝛥NOA) 0.049 0.361 -0.632 -0.040 0.040 0.137 0.770 Working-capital accruals (𝛥WC) 0.014 0.162 -0.434 -0.035 0.013 0.065 0.446 Investment accruals (IA) 0.108 0.316 -0.319 0.030 0.074 0.152 0.796 Non-transaction accruals (NTA) -0.073 0.137 -0.470 -0.086 -0.053 -0.031 0.110 Operating accruals (OA) -0.023 0.517 -0.385 -0.084 -0.034 0.019 0.404 Cash-based operating profitability (COP) 0.108 0.441 -0.629 0.042 0.130 0.213 0.593 Change in total assets (𝛥AT) 0.173 1.494 -0.524 -0.038 0.066 0.202 2.163 Panel B: Correlations 𝛥NOA OA COP 𝛥WC IA NA 𝛥AT Total accruals (𝛥NOA) 0.459 0.017 0.655 0.620 0.170 0.769 Operating accruals (OA) 0.479 -0.288 0.679 -0.059 0.231 0.292 Cash-based operating profitability (COP) 0.055 -0.281 -0.101 0.053 0.058 0.018 Working-capital accruals (𝛥WC) 0.659 0.701 -0.101 0.002 0.079 0.409 Investment accruals (IA) 0.567 -0.049 0.154 0.034 -0.361 0.588 Non-investment accruals (NTA) 0.105 0.306 -0.093 0.087 -0.398 0.074 Change in total assets (𝛥AT) 0.783 0.330 0.184 0.444 0.517 0.087

Table 2: Descriptive statistics of accruals factor returns Each month, we sort all NYSE, AMEX, and NASDAQ stocks into two size groups (S or B) based on whether their market capitalization is above or below the NYSE median breakpoint, respectively. For each of the three types of accruals (𝛥WC, IA, and NTA), we also sort stocks independently into three accrual portfolios (L to M to H) based on the 30th and 70th percentiles for NYSE firms. Six value-weighted portfolios (S/L, S/M, S/H, B/L, B/M, and B/H) are formed as the intersections of the size and accrual groups. For each type of accruals (𝐴𝐶𝐶), we construct a high-minus-low accruals factor, 𝐻𝑀𝐿'(( =(S/L + B/L)/2 − (S/H + B/H)/2. The portfolios formed monthly are based on accruals measured at the end of the most recent fiscal year end that is at least four months prior. Panel A presents means and t-statistics for (S/L, S/M, S/H, B/L, B/M, and B/H). Panel B presents mean returns on the Fama-French factors (MKT, SMB, and HML) as well as the three accruals factors (𝐻𝑀𝐿*( , 𝐻𝑀𝐿+',and 𝐻𝑀𝐿,-'). Panel C reports the correlation matrix of the factors in Panel B. *, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively. The sample period is 1972:5-2015:12 (N=524).

Panel A: Base assets used to make high-minus-low accruals factors S/L S/M S/H B/L B/M B/H 𝛥𝑊𝐶 Mean 1.26*** 1.26*** 0.96*** 1.08*** 1.04*** 0.88*** t (4.22) (4.74) (3.12) (4.72) (5.24) (3.43) IA Mean 1.33*** 1.27*** 0.85*** 0.95*** 1.11*** 0.86*** t (4.69) (4.57) (2.73) (4.23) (5.42) (3.50) NTA Mean 1.23*** 1.20*** 0.99*** 0.93*** 1.13*** 0.84*** t (3.98) (4.36) (3.41) (3.91) (5.38) (3.65) Panel B: Factor mean returns (4-month minimum lag) MKT SMB HML 𝐻𝑀𝐿*( 𝐻𝑀𝐿+' 𝐻𝑀𝐿,-' Mean 0.52*** 0.19 0.36*** -0.25*** -0.29*** -0.17* t (2.59) (1.41) (2.73) (-3.26) (-3.42) (-1.93) Panel C: Factor Correlations MKT SMB HML 𝐻𝑀𝐿*( 𝐻𝑀𝐿+' 𝐻𝑀𝐿,-' MKT 1.00 0.24 -0.32 0.23 0.25 -0.08 SMB 0.24 1.00 -0.11 0.06 0.02 0.00 HML -0.32 -0.11 1.00 -0.38 -0.40 0.10 𝐻𝑀𝐿*( 0.23 0.06 -0.38 1.00 0.19 0.26 𝐻𝑀𝐿+' 0.25 0.02 -0.40 0.19 1.00 -0.55 𝐻𝑀𝐿,-' -0.08 0.00 0.10 0.26 -0.55 1.00

Table 3: Fama-French 3- and 5-factor-model estimations of accruals factors The first three columns present estimates of time-series regressions of the form: 𝐻𝑀𝐿'((,0 = 𝑎 +𝑏𝑀𝐾𝑇0 + 𝑠𝑆𝑀𝐵0 + ℎ𝐻𝑀𝐿0 + 𝜖0, for each of the three accruals factors (𝐻𝑀𝐿*( , 𝐻𝑀𝐿+', and 𝐻𝑀𝐿,-'). The last three columns present estimates of regressions of the form: 𝐻𝑀𝐿'((,0 = 𝑎 + 𝑏𝑀𝐾𝑇0 + 𝑠𝑆𝑀𝐵0 + ℎ𝐻𝑀𝐿0 + 𝑐𝐶𝑀𝐴0 + 𝑟𝑅𝑀𝑊0 + 𝜖0, for each of the three accruals factors. 𝑡-statistics are below point estimates in parentheses. *, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively. The sample period is 1972:5-2015:12 (N=524).

𝐻𝑀𝐿*( 𝐻𝑀𝐿+' 𝐻𝑀𝐿,-' 𝐻𝑀𝐿*( 𝐻𝑀𝐿+' 𝐻𝑀𝐿,-' a -0.20*** -0.23*** -0.18** -0.21*** -0.09 -0.27***

(-2.81) (-2.97) (-2.02) (-3.24) (-1.19) (-3.10) b 0.05*** 0.06*** -0.03 0.03** 0.02 -0.01

(2.91) (3.50) (-1.22) (2.09) (1.08) (-0.72) s -0.01 -0.03 0.02 0.08*** -0.05** 0.10***

(-0.32) (-1.29) (0.54) (3.43) (-2.04) (3.43) h -0.20*** -0.23*** 0.06* -0.07** -0.05 0.07*

(-8.10) (-8.64) (1.91) (-2.32) (-1.44) (1.82) c -0.35*** -0.41*** -0.08

(-7.50) (-7.46) (-1.28) r 0.26*** -0.15*** 0.32***

(8.30) (-4.15) (7.65) N 524 524 524 524 524 524 Adj-𝑅2 0.15 0.18 0.01 0.35 0.26 0.12

Table 4: Factor regressions for portfolios formed from independent sorts on size and accruals For each measure of accruals, at the end of June of each year t, all stocks on the NYSE, AMEX, and NASDAQ are assigned independently into three size groups (S to M to B) and three accrual groups (L to M to H) based on the 33rd and 67th percentile breakpoints for NYSE firms. Size is measured at the end of June of year t and accruals are measured at the end of fiscal year 𝑡 − 1. The intersections of the two sorts produce 9 size-accruals (S/Acc) portfolios (S/L, S/M, S/H, M/L, M/M, M/H, B/L, B/M, and B/H), which are value weighted. For each portfolio, columns 2 and 3 present average returns (𝐸(𝑟)) and 𝑡-statistics tE r . Columns 3 through 13 present estimates and t-statistics from the four-factor model: 𝑟B0-𝑟C0 = 𝑎 + 𝑏𝑀𝐾𝑇0 + 𝑠𝑆𝑀𝐵0 + ℎ𝐻𝑀𝐿0 + ℎ'𝐻𝑀𝐿'DD,0 + 𝜖0, where 𝐻𝑀𝐿'DD,0 denotes one of the accruals factors defined in Table 2. Panels A, B, and C report estimates for portfolios based on working-capital, investment, and non-transaction accruals, respectively. The sample is 1972:7-2015:12 (𝑁=522).

Panel A: Working Capital Accruals S/Acc 𝐸(𝑟) 𝑡F G 𝑎 𝑏 𝑠 ℎ ℎ*( 𝑡(𝑎) 𝑡(𝑏) 𝑡(𝑠) 𝑡(ℎ) 𝑡 ℎ*( 𝑅2 S/L 0.78 2.61 -0.07 1.04 1.20 -0.08 -0.41 -0.98 61.00 49.53 -2.89 -9.26 0.94 S/M 0.86 3.24 0.05 0.99 0.99 0.22 -0.07 0.72 66.95 47.42 9.30 -1.72 0.95 S/H 0.59 1.99 -0.18 1.04 1.18 -0.02 -0.02 -2.65 67.22 54.01 -0.99 -0.59 0.95 M/L 0.73 2.68 -0.05 1.10 0.79 -0.03 -0.24 -0.70 68.38 35.01 -1.10 -5.82 0.94 M/M 0.73 2.95 0.00 1.01 0.71 0.24 0.12 0.05 61.71 30.94 9.42 2.75 0.92 M/H 0.58 2.07 -0.06 1.08 0.83 -0.09 0.21 -0.90 73.58 40.07 -3.97 5.60 0.95 B/L 0.62 2.74 0.04 1.02 0.03 -0.27 -0.56 0.46 53.46 1.06 -8.97 -11.22 0.88 B/M 0.61 3.10 0.11 0.95 -0.07 0.03 -0.03 1.63 61.93 -3.17 1.38 -0.87 0.90 B/H 0.53 2.06 0.23 1.04 0.01 -0.33 0.50 2.50 49.61 0.43 -9.83 9.12 0.88 Panel B: Investment Accruals S/Acc 𝐸(𝑟) 𝑡F G 𝑎 𝑏 𝑠 ℎ ℎ+' 𝑡(𝑎) 𝑡(𝑏) 𝑡(𝑠) 𝑡(ℎ) 𝑡(ℎ+') 𝑅2 S/L 0.83 2.91 0.03 1.01 1.15 0.08 -0.08 0.38 63.14 50.98 3.24 -2.20 0.95 S/M 0.91 3.19 0.15 1.01 1.11 0.05 0.02 2.31 67.31 52.40 1.97 0.47 0.95 S/H 0.48 1.58 -0.23 1.03 1.19 0.04 0.28 -3.05 60.23 49.35 1.53 6.79 0.94 M/L 0.77 2.95 -0.01 1.05 0.79 0.05 -0.18 -0.13 68.52 36.43 2.14 -5.02 0.94 M/M 0.81 3.15 0.11 1.01 0.79 0.04 -0.01 1.61 66.22 36.82 1.86 -0.33 0.94 M/H 0.50 1.76 -0.14 1.10 0.79 0.00 0.31 -1.99 67.14 34.02 0.00 7.84 0.94 B/L 0.65 2.99 0.02 1.04 -0.04 -0.10 -0.42 0.31 61.85 -1.53 -3.83 -10.55 0.90 B/M 0.63 2.97 0.15 0.97 0.00 -0.11 -0.03 2.07 57.30 -0.15 -4.07 -0.69 0.89 B/H 0.51 2.13 0.26 0.99 0.02 -0.09 0.81 3.97 64.18 0.78 -3.63 21.90 0.93 Panel C: Non-transaction Accruals S/Acc 𝐸(𝑟) 𝑡F G 𝑎 𝑏 𝑠 ℎ ℎ,' 𝑡(𝑎) 𝑡(𝑏) 𝑡(𝑠) 𝑡(ℎ) 𝑡(ℎ,') 𝑅2 S/L 0.81 2.63 -0.07 1.04 1.22 0.01 -0.53 -0.93 63.18 51.87 0.48 -15.09 0.95 S/M 0.80 2.91 0.02 0.98 1.10 0.10 -0.09 0.34 73.27 57.59 5.20 -3.09 0.96 S/H 0.57 2.01 -0.20 1.01 1.13 0.06 0.01 -2.92 65.73 51.44 2.46 0.19 0.95 M/L 0.71 2.55 -0.05 1.07 0.82 -0.05 -0.36 -0.76 65.73 35.24 -1.97 -10.31 0.94 M/M 0.69 2.74 0.01 1.04 0.72 0.09 0.17 0.14 68.02 33.01 3.81 5.23 0.94 M/H 0.61 2.24 -0.10 1.09 0.82 0.02 0.19 -1.55 75.83 39.90 1.13 6.16 0.95 B/L 0.55 2.35 -0.07 1.00 0.02 -0.14 -0.83 -1.04 68.10 0.75 -6.22 -26.56 0.93 B/M 0.69 3.27 0.23 0.96 -0.03 -0.09 -0.01 2.76 50.04 -1.21 -3.26 -0.28 0.86 B/H 0.50 2.15 0.07 1.06 -0.01 -0.19 0.36 1.05 67.64 -0.37 -7.89 10.72 0.92

Table 5: Four-factor regressions for portfolios formed on size, accruals, and 𝐻𝑀𝐿'DD,0 loading At the end of June of each year t, we divide all 9 size/accruals portfolios from Table 4 into three sub-portfolios (L to H) based on the 33rd and 67th percentiles of preformation-𝐻𝑀𝐿'DD loading (ℎ') estimated from the following regression:

𝑟B0 − 𝑟C0 = 𝑎 + 𝑏𝑀𝐾𝑇0 + 𝑠𝑆𝑀𝐵0 + ℎ𝐻𝑀𝐿0 + ℎ'𝐻𝑀𝐿'DD,0 + 𝜖0, (1) for each stock 𝑖 over the previous 60 months (24 months minimum). We value weight the resulting 27 portfolios and denote them by 𝑆/𝐴𝑐𝑐/ℎ', where S, Acc and ℎ' are the size-, accruals-, and ℎ'-portfolio assignments, respectively. For each measure of accruals, we also form a high-minus-low-ℎ' portfolio as follows:

𝐻ℎ' − 𝐿ℎ' = 19 𝑟B/I/J

H

j=L

N

B=O− 1

9 𝑟B/I/P

H

j=L

N

B=O.

For each portfolio, we report average size and accruals, average excess returns (E(r)) and estimates of the four-factor model given by Eq. (1). The sample is 1977:7-2015:12 (𝑁=462).

Panel A: Working capital accruals S/Acc/ℎ' Size Acc E(r) 𝑡F G 𝑎 𝑏 𝑠 ℎ ℎ' 𝑡(𝑎) 𝑡(𝑏) 𝑡(𝑠) 𝑡(ℎ') 𝑡(ℎ') 𝑅2 S/L/L 0.17 -0.09 0.78 2.48 -0.17 1.05 1.16 -0.02 -0.37 -1.61 38.90 25.40 -0.38 -5.42 0.89 S/L/M 0.19 -0.07 0.91 3.38 0.06 0.94 1.01 0.18 -0.15 0.61 39.94 22.02 3.93 -2.35 0.90 S/L/H 0.18 -0.08 1.01 3.22 0.04 1.03 1.23 0.09 -0.29 0.39 33.42 19.70 1.56 -3.80 0.89 M/L/L 0.19 0.01 0.66 2.27 -0.20 1.10 0.68 0.01 -0.18 -1.49 30.18 10.57 0.10 -2.15 0.83 M/L/M 0.21 0.01 0.84 3.17 0.04 1.01 0.70 0.16 0.02 0.38 34.24 14.26 2.88 0.19 0.84 M/L/H 0.20 0.01 0.90 2.97 0.02 1.09 0.84 -0.03 -0.19 0.16 36.82 17.66 -0.60 -2.19 0.85 B/L/L 0.19 0.12 0.62 2.40 -0.08 1.04 -0.08 -0.11 -0.55 -0.49 25.84 -1.24 -1.72 -5.14 0.68 B/L/M 0.20 0.10 0.62 2.49 0.01 1.01 -0.02 -0.24 -0.23 0.13 31.01 -0.51 -3.75 -2.53 0.77 B/L/H 0.19 0.12 0.99 3.37 0.32 1.05 0.20 -0.39 -0.39 1.86 22.35 2.29 -4.85 -2.90 0.69 S/M/L 0.87 -0.06 0.98 3.52 0.14 0.96 1.01 0.16 -0.03 1.37 40.70 24.74 3.75 -0.43 0.88 S/M/M 0.92 -0.06 0.96 3.89 0.14 0.93 0.77 0.45 0.12 1.52 30.06 12.33 7.59 1.63 0.86 S/M/H 0.89 -0.06 0.97 3.46 0.08 1.01 0.93 0.28 -0.05 0.69 31.34 16.65 5.96 -0.60 0.86 M/M/L 0.89 0.01 0.74 2.89 -0.03 0.98 0.56 0.24 0.06 -0.27 25.79 9.85 3.48 0.80 0.79 M/M/M 0.92 0.01 1.00 4.01 0.24 0.97 0.60 0.33 0.22 2.16 30.87 15.79 6.28 3.20 0.84 M/M/H 0.91 0.01 0.88 3.31 0.08 1.01 0.66 0.33 0.22 0.68 32.01 14.84 4.88 2.30 0.82 B/M/L 0.88 0.11 0.67 3.05 0.07 0.93 -0.15 0.09 -0.19 0.57 32.16 -3.43 1.65 -2.10 0.71 B/M/M 0.90 0.09 0.74 3.53 0.19 0.88 -0.02 0.06 0.01 1.75 29.69 -0.43 1.03 0.16 0.74 B/M/H 0.87 0.10 0.65 2.58 0.05 1.00 0.05 -0.05 0.11 0.38 22.53 0.66 -0.79 1.15 0.74 S/H/L 54.02 -0.04 0.61 2.01 -0.25 1.02 1.11 -0.03 -0.05 -2.57 40.54 26.33 -0.73 -0.76 0.91 S/H/M 43.06 -0.04 0.96 3.56 0.18 0.92 0.99 0.11 0.10 2.09 44.44 28.66 2.76 1.66 0.90 S/H/H 21.13 -0.06 0.73 2.41 -0.13 1.02 1.13 0.01 0.03 -1.33 40.59 25.30 0.25 0.39 0.91 M/H/L 53.57 0.01 0.73 2.52 0.00 1.04 0.75 -0.02 0.34 -0.03 31.01 12.35 -0.29 4.67 0.87 M/H/M 49.83 0.01 0.86 3.24 0.14 1.00 0.63 0.27 0.50 1.26 32.92 11.08 4.10 6.22 0.85 M/H/H 20.72 0.01 0.61 2.04 -0.18 1.10 0.81 0.00 0.27 -1.62 39.34 17.71 -0.06 2.86 0.88 B/H/L 38.86 0.08 0.51 1.83 -0.02 1.08 -0.10 -0.15 0.43 -0.11 24.70 -1.43 -2.22 4.22 0.74 B/H/M 27.97 0.08 0.70 2.65 0.22 1.04 -0.10 -0.08 0.60 1.66 30.77 -1.58 -0.93 5.17 0.77 B/H/H 34.84 0.09 0.94 3.00 0.47 1.07 0.09 -0.51 0.43 2.68 22.92 1.18 -5.84 2.95 0.74 Hℎ'-Lℎ' 0.15 1.57 0.14 0.02 0.11 -0.05 0.08 1.42 0.71 2.13 -0.95 0.97 0.04

Table 5: Continued

Panel B: Investment accruals S/Acc/ℎ' Size Acc E(r) 𝑡F G 𝑎 𝑏 𝑠 ℎ ℎ' 𝑡(𝑎) 𝑡(𝑏) 𝑡(𝑠) 𝑡(ℎ') 𝑡(ℎ') 𝑅2 S/L/L 0.18 -0.01 1.00 3.37 0.12 0.97 1.17 -0.01 -0.19 1.13 39.31 33.34 -0.33 -3.28 0.89 S/L/M 0.19 0.00 0.86 3.17 -0.07 0.98 1.02 0.23 -0.22 -0.88 49.18 35.76 7.55 -4.74 0.91 S/L/H 0.16 -0.01 0.76 2.56 -0.11 1.03 1.03 0.11 0.00 -1.10 41.44 29.08 2.80 -0.01 0.89 M/L/L 0.20 0.08 0.89 3.24 0.02 1.03 0.72 -0.01 -0.30 0.20 36.46 17.84 -0.31 -4.53 0.83 M/L/M 0.20 0.08 0.82 3.27 -0.04 0.99 0.63 0.17 -0.25 -0.34 39.07 17.43 4.39 -4.27 0.84 M/L/H 0.19 0.08 0.63 2.14 -0.26 1.12 0.80 0.18 0.00 -2.16 38.31 19.36 4.02 0.02 0.84 B/L/L 0.20 0.26 0.78 3.30 0.06 0.98 -0.19 -0.06 -0.56 0.45 29.10 -3.97 -1.23 -7.16 0.67 B/L/M 0.20 0.24 0.78 3.45 0.04 0.97 0.03 -0.05 -0.51 0.35 33.55 0.68 -1.18 -7.67 0.74 B/L/H 0.19 0.26 0.56 1.89 -0.11 1.14 0.00 -0.14 -0.02 -0.66 27.47 0.04 -2.14 -0.17 0.68 S/M/L 0.87 0.00 1.08 3.58 0.14 1.05 1.06 0.08 -0.16 1.38 42.02 29.71 2.01 -2.68 0.89 S/M/M 0.88 0.00 1.05 4.00 0.21 0.93 0.89 0.19 -0.13 1.95 36.34 24.34 4.72 -2.25 0.85 S/M/H 0.87 0.00 0.91 3.09 0.06 1.03 1.01 0.15 0.09 0.57 39.44 27.33 3.77 1.44 0.88 M/M/L 0.89 0.08 0.98 3.74 0.17 0.98 0.68 0.03 -0.19 1.51 35.39 17.41 0.70 -2.97 0.82 M/M/M 0.92 0.08 1.01 4.01 0.19 1.00 0.63 0.17 -0.15 1.76 39.31 17.32 4.40 -2.52 0.84 M/M/H 0.90 0.08 0.80 2.87 0.01 1.05 0.70 0.14 0.14 0.13 39.62 18.43 3.36 2.25 0.85 B/M/L 0.87 0.24 0.69 3.02 0.03 0.97 -0.13 0.04 -0.30 0.19 30.45 -2.83 0.72 -4.01 0.69 B/M/M 0.93 0.23 0.79 3.55 0.25 0.94 -0.13 -0.19 -0.13 2.33 37.19 -3.47 -4.75 -2.18 0.79 B/M/H 0.89 0.25 0.75 2.72 0.25 1.00 0.14 -0.08 0.42 1.63 27.18 2.68 -1.43 4.96 0.71 S/H/L 38.43 0.01 0.76 2.47 -0.06 0.95 1.26 0.04 0.09 -0.61 37.85 35.18 1.09 1.58 0.89 S/H/M 28.99 0.01 0.95 3.39 0.14 0.93 1.06 0.10 0.03 1.45 39.33 31.38 2.77 0.48 0.89 S/H/H 25.77 -0.01 0.47 1.47 -0.37 1.08 1.00 0.28 0.36 -2.65 32.80 21.23 5.42 4.70 0.82 M/H/L 45.52 0.08 0.63 2.25 -0.12 1.00 0.77 -0.03 0.06 -1.11 38.17 20.43 -0.76 1.06 0.86 M/H/M 44.54 0.08 0.76 2.91 -0.02 1.02 0.62 0.14 0.04 -0.19 42.10 18.06 3.77 0.80 0.86 M/H/H 33.39 0.08 0.57 1.78 -0.12 1.11 0.79 0.18 0.68 -0.87 33.55 16.81 3.57 8.85 0.83 B/H/L 30.79 0.22 0.82 3.42 0.29 0.94 0.05 -0.16 0.10 2.45 33.40 1.36 -3.55 1.50 0.78 B/H/M 38.11 0.22 0.68 2.68 0.19 0.99 0.05 -0.08 0.41 1.73 36.98 1.36 -1.90 6.64 0.82 B/H/H 54.05 0.22 0.53 1.67 0.32 1.02 -0.04 -0.08 1.30 1.97 26.66 -0.78 -1.28 14.78 0.76 Hℎ'-Lℎ' -0.18 -1.67 -0.11 0.08 0.01 0.09 0.49 -1.08 3.22 0.15 2.47 8.70 0.19

Table 5: Continued Panel C: Non-transaction accruals S/Acc/ℎ' Size Acc E(r) 𝑡F G 𝑎 𝑏 𝑠 ℎ ℎ' 𝑡(𝑎) 𝑡(𝑏) 𝑡(𝑠) 𝑡(ℎ) 𝑡(ℎ') 𝑅2 S/L/L 0.18 -0.14 0.79 2.34 -0.23 1.09 1.08 0.16 -0.78 -1.72 26.83 12.72 2.27 -9.51 0.85 S/L/M 0.18 -0.12 1.13 3.96 0.26 0.95 1.08 0.14 -0.25 2.81 34.88 30.09 3.94 -4.15 0.91 S/L/H 0.19 -0.13 1.09 3.51 0.22 0.97 1.24 0.03 -0.10 2.11 34.73 21.79 0.62 -1.72 0.90 M/L/L 0.19 -0.05 0.62 1.85 -0.33 1.12 0.79 -0.02 -0.92 -2.33 30.40 12.42 -0.23 -9.80 0.82 M/L/M 0.21 -0.05 0.88 3.31 0.09 1.00 0.75 0.10 0.08 0.91 38.63 20.02 2.08 1.30 0.86 M/L/H 0.20 -0.05 1.00 3.61 0.21 1.02 0.80 0.06 0.16 1.89 36.75 18.38 1.24 2.92 0.86 B/L/L 0.17 -0.01 0.54 1.72 -0.22 1.02 -0.01 -0.17 -1.61 -1.54 23.96 -0.13 -2.58 -21.76 0.81 B/L/M 0.19 -0.01 0.65 2.51 -0.02 1.06 -0.01 -0.10 -0.35 -0.20 32.42 -0.16 -2.07 -5.26 0.82 B/L/H 0.20 -0.01 0.79 3.45 0.21 0.96 0.00 0.04 0.15 1.71 28.58 0.04 0.65 2.47 0.74 S/M/L 0.88 -0.13 0.82 2.83 -0.06 1.00 0.97 0.13 -0.27 -0.54 32.62 14.66 2.45 -4.19 0.88 S/M/M 0.92 -0.11 0.96 3.56 0.12 0.92 1.04 0.23 0.03 1.36 32.84 27.43 6.49 0.58 0.90 S/M/H 0.87 -0.11 0.95 3.40 0.12 0.97 1.03 0.16 0.17 1.31 42.04 26.21 3.82 3.14 0.90 M/M/L 0.90 -0.05 0.65 2.27 -0.20 1.10 0.66 0.09 -0.10 -1.66 34.00 12.13 1.52 -1.51 0.84 M/M/M 0.91 -0.05 0.97 3.99 0.24 0.98 0.55 0.25 0.37 2.20 33.65 11.26 4.61 7.05 0.83 M/M/H 0.89 -0.05 0.96 3.73 0.25 0.98 0.63 0.11 0.38 2.13 28.75 8.34 1.69 5.52 0.81 B/M/L 0.91 -0.01 0.62 2.54 0.05 0.93 -0.08 -0.16 -0.45 0.35 26.70 -1.71 -2.73 -6.72 0.75 B/M/M 0.91 -0.02 0.81 3.52 0.27 0.94 -0.10 -0.01 0.15 2.15 28.23 -1.79 -0.12 1.96 0.70 B/M/H 0.85 -0.02 0.74 3.00 0.18 1.00 -0.02 -0.01 0.44 1.29 25.88 -0.33 -0.17 4.65 0.70 S/H/L 38.62 -0.10 0.65 2.17 -0.21 1.02 1.03 0.00 -0.14 -1.98 34.52 23.76 0.08 -2.70 0.89 S/H/M 24.38 -0.10 0.76 2.86 -0.04 0.91 1.00 0.14 0.06 -0.43 34.76 21.13 3.57 1.22 0.90 S/H/H 17.85 -0.10 0.73 2.63 -0.11 0.99 0.99 0.23 0.24 -1.16 36.95 19.07 5.03 4.15 0.88 M/H/L 75.67 -0.05 0.58 1.98 -0.29 1.13 0.71 0.08 -0.10 -2.59 33.51 14.28 1.52 -1.63 0.86 M/H/M 47.21 -0.05 0.63 2.50 -0.12 1.02 0.56 0.15 0.29 -1.11 39.19 9.93 2.99 5.25 0.85 M/H/H 27.68 -0.05 0.81 2.95 0.01 1.05 0.79 0.13 0.42 0.15 43.74 20.47 3.45 8.62 0.88 B/H/L 28.33 -0.01 0.61 1.97 -0.09 1.14 0.17 -0.32 -0.30 -0.56 25.98 2.75 -4.59 -3.07 0.75 B/H/M 26.06 -0.02 0.61 2.67 0.10 0.98 -0.16 -0.07 0.42 0.93 31.23 -3.08 -1.35 7.35 0.79 B/H/H 39.21 -0.02 0.84 3.49 0.32 1.02 -0.08 -0.06 0.68 2.81 32.83 -1.83 -1.21 9.89 0.79 Hℎ'-Lℎ' 0.23 1.92 0.33 -0.07 0.00 0.10 0.80 3.77 -2.68 0.14 2.56 17.45 0.47

Table 6: Investor sentiment and accruals factors Panel A reports estimates of the regression:

𝐻𝑀𝐿'((,0 = 𝑎 + 𝑏𝑆0−1 + 𝑢0, 2 where 𝐻𝑀𝐿'((,0 is the return in month 𝑡 on one of the accruals factors (𝐻𝑀𝐿*( , 𝐻𝑀𝐿+', 𝐻𝑀𝐿,-', or 𝐻𝑀𝐿S') and 𝑆0−1 is the previous month’s level of the investor-sentiment index of Baker and Wurgler (2006) that is orthogonalized to economic conditions. Returns are expressed as % per annum and sentiment is standardized so that the 𝑏 coefficient represents the impact of a one-standard deviation increase in 𝑆0−1 on 𝐻𝑀𝐿'DD,0. Panel B presents averages of 𝐻𝑀𝐿'((,0 when lagged sentiment is high, medium, or low, as defined by the 25th and 75th percentiles of the sentiment index. 𝑝(High − Low) denotes the p-value for the test of the null hypothesis that average returns for 𝐻𝑀𝐿'((,0 are the same in High and Low sentiment months. 𝑡-statistics are in parentheses. *, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively. The sample period is 1972:5-2015:10 (𝑁=522).

Panel A: Predictive regression 𝐻𝑀𝐿*( 𝐻𝑀𝐿+' 𝐻𝑀𝐿,-' 𝐻𝑀𝐿S' b 0.62 -1.54 2.21** 2.32** t(b) (0.67) (-1.51) (2.11) (2.18)

Panel B: Factor premia in low to high sentiment 𝐻𝑀𝐿*( 𝐻𝑀𝐿+' 𝐻𝑀𝐿,-' 𝐻𝑀𝐿S' High sentiment -2.39 -6.34*** -0.11 -1.79

(-1.30) (-3.13) (-0.05) (-0.85) Medium -2.08 -3.22** 0.05 -1.82

(-1.59) (-2.24) (0.03) (-1.21) Low sentiment -5.62*** -1.07 -8.09*** -9.29*** (-3.05) (-0.53) (-3.90) (-4.39) 𝑝(High − Low) 0.22 0.07 0.01 0.01

Table 7: Cash-based operating profitability and accruals in Fama and MacBeth (1973) regressions This table presents average regression slopes (multiplied by 100) and their t-statistics from monthly cross-sectional regressions of returns on each accruals measure we consider, cash-based operating profitability, and control variables. Control variables include: the natural logarithm of the book-to-market ratio (log(BE/ME)) and prior-month market capitalization (log(ME)), the prior-month return (𝑟1,1), and the prior 12-month excluding prior-month return (𝑟12,2). Accounting variables come from the most recent fiscal year end that is at least four-months prior. Panels A presents results for all-but-microcaps (stocks whose market capitalization is below the 20th NYSE percentile). Panel B presents results for microcaps which are defined to be stocks with market values of equity below the 20th percentile of the NYSE market capitalization distribution. Variables in each regression are trimmed at the 1st and 99th percentiles based on all explanatory variables so the sample is constant across columns. t-statistics are below estimates in parentheses. *, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively. The sample is 1972:5-2015:12 (N=522). Panel A: All-but-microcaps (1) (2) (3) (4) (5) (6) (7) (8) Operating accruals -0.81*** -0.38

(-4.09) (-1.63) Cash-based operating profitability

0.84***

0.93***

0.93***

0.95***

(5.24)

(7.12)

(6.87)

(6.69)

Total Accruals

-0.74*** -0.64***

(-6.18) (-5.39)

Working Capital Accruals

-0.67*** -0.49*** -0.69*** -0.51***

(-3.75) (-2.64) (-3.84) (-2.80)

Investment accruals

-0.70*** -0.67***

(-4.98) (-4.77)

Non-transaction accruals

-0.87** -0.46

(-2.37) (-1.19)

log(BE/ME) 0.10*** 0.15*** 0.09*** 0.14*** 0.11*** 0.16*** 0.09*** 0.14***

(3.23) (4.55) (2.80) (4.38) (3.40) (4.88) (2.78) (4.34) log(ME) -0.03 -0.04* -0.03 -0.04* -0.03 -0.03* -0.03 -0.04*

(-1.49) (-1.76) (-1.33) (-1.72) (-1.30) (-1.67) (-1.39) (-1.78) 𝑟1,1 -1.48*** -1.47*** -1.49*** -1.46*** -1.46*** -1.44*** -1.52*** -1.50***

(-6.00) (-6.00) (-6.05) (-5.99) (-5.92) (-5.88) (-6.23) (-6.20) 𝑟12,2 0.39*** 0.41*** 0.37*** 0.39*** 0.40*** 0.42*** 0.37*** 0.39***

(4.16) (4.45) (3.97) (4.23) (4.22) (4.46) (4.02) (4.29) Adj-𝑅2 0.055 0.060 0.055 0.059 0.054 0.058 0.062 0.066

Table 7: Continued Panel B: Microcaps (1) (2) (3) (4) (5) (6) (7) (8) Operating accruals -0.87*** -0.29

(-5.41) (-1.39) Cash-based operating profitability

1.14***

1.15***

1.18***

1.23***

(7.02)

(8.57)

(8.27)

(8.71)

Total Accruals

-0.85*** -0.74***

(-8.25) (-6.95)

Working Capital Accruals

-0.58*** -0.26 -0.55*** -0.23

(-3.79) (-1.53) (-3.67) (-1.37)

Investment accruals

-1.10*** -1.16***

(-8.15) (-8.63)

Non-transaction accruals

-1.60*** -1.41***

(-4.49) (-3.96)

log(BE/ME) 0.17*** 0.18*** 0.16*** 0.16*** 0.17*** 0.18*** 0.16*** 0.16***

(5.11) (5.33) (4.79) (5.00) (5.21) (5.39) (4.85) (4.98) log(ME) -0.13*** -0.16*** -0.11*** -0.15*** -0.13*** -0.16*** -0.11*** -0.15***

(-3.83) (-5.07) (-3.43) (-4.58) (-3.86) (-5.06) (-3.38) (-4.59) 𝑟1,1 -2.60*** -2.64*** -2.62*** -2.66*** -2.58*** -2.62*** -2.64*** -2.69***

(-10.31) (-10.51) (-10.38) (-10.57) (-10.25) (-10.45) (-10.49) (-10.69) 𝑟12,2 0.49*** 0.47*** 0.47*** 0.44*** 0.50*** 0.47*** 0.46*** 0.43***

(5.42) (5.21) (5.16) (4.95) (5.51) (5.29) (5.20) (4.92) Adj-𝑅2 0.033 0.036 0.033 0.035 0.032 0.035 0.036 0.039

Table 8: Predictive regressions of one-year-ahead aggregate returns on aggregate accruals Each column reports estimates of time series regressions of the form: 𝑟0+1 = 𝛼 + 𝛽𝐴𝐶𝐶0 + 𝜖0+1, where ACC denotes aggregate operating, working-capital, investment, or non-transaction accruals, respectively. The four accruals measures are measured at the end of year t and are standardized to have zero mean and unit variance. In Panel A, 𝑟0+1 denotes the compounded monthly total log return on the CRSP value-weighted index over May of year 𝑡 + 1 through April of year 𝑡 + 2. In Panel B, 𝑟0+1 denotes the compounded monthly log return on the CRSP value-weighted index over May of year 𝑡 + 1 through April of year 𝑡 + 2 minus the one-month log Treasury bill rate. t-statistics are below estimates in parentheses. *, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively. The accounting data covers fiscal years 1971-2014 and return data covers 1972-2015 (𝑁=44).

Panel A: Total Log Returns

(1) (2) (3) (4)

Operating accruals 0.06**

(2.43)

Working-capital accruals

-0.01

(-0.52)

Investment accruals

-0.05**

(-2.03)

Non-transaction accruals

0.00

(0.16)

Adj-𝑅2 0.10 -0.02 0.07 -0.02 Panel B: Excess Log Returns

(1) (2) (3) (4)

Operating accruals 0.05*

(1.99)

Working-capital accruals

-0.02

(-0.98)

Investment accruals

-0.05**

(-2.08)

Non-transaction accruals

0.01

(0.28)

Adj-𝑅2 0.10 -0.02 0.07 -0.02