What drives the accrual spread evidence from a contemporary decomposition approach

First, stock returns are inversely related to working capital investment that supports growth and accrual estimation error, particularly in firms with higher long-term growth or are expo

What drives the accrual spread?

Evidence from a contemporary decomposition approach

Viet Nga Cao*a, Frankie Chaub and Krishna Paudyalc

Abstract

We examine the main drivers of the accrual spread and the profitability of accrual-based trading strategies by disaggregating total accrual into three components: investment in working capital that supports growth, accrual estimation error, and temporary working capital fluctuation Several findings emerge First, stock returns are inversely related to working capital investment that supports growth and accrual estimation error, particularly in firms with higher long-term growth or are exposed to a higher degree of financial constraints Second, investment in working capital drives the accrual spread through risk, whereas accrual estimation error does so through mispricing The positive relationship between temporary working capital fluctuation and stock returns is also risk-based, implying that timing the input market may amplify firms’ exposure to the cyclicality of the product market Finally, an implementable trading strategy based on a modified version of accrual estimation error can generate superior risk-adjusted returns to investors

JEL Classification: M41, G12, G14

Keywords: accrual decomposition, earnings management, financial constraint, q-theory

a Monash University, 900 Dandenong Road, Caulfield East, VIC 3145, Australia Email:

1 INTRODUCTION

Sloan’s (1996) seminal work shows that long positions in stocks of low accrual firms and short positions in stocks of high accrual firms can generate positive abnormal returns (hereafter the accrual spread)1 More recently, Allen et al (2013) examine Sloan’s functional fixation hypothesis by decomposing total accrual into three components: (a) investment in working

capital that supports growth (MDDGROWTH), (b) accrual estimation error (MDDERROR), and (c) temporary fluctuation in working capital (MDDMATCH) and provide evidence in favor of the

hypothesis Whilst Sloan’s functional fixation hypothesis has been rigorously examined by Allen

et al (2013), detailed examinations of other theories of the accrual spread2 using the components

of total accrual remain Similarly, no study has been devoted to examining the possibility of profitable trading strategies using the three components of accrual To fill these voids, we decompose total accrual into its three components as in Allen et al (2013) and study several theories of the accrual spread and the possibility of profitable trading strategies

Several studies document a positive association between the accrual spread and measures

of firm growth For example, Fairfield et al (2003) argue that the accrual spread arises due to either diminishing marginal returns on physical investment or accounting conservatism Similarly, Zhang (2007) confirms a positive relationship between firms’ employee growth and the accrual spread Building on the works of Fairfield et al (2003) and Zhang (2007), Wu et al (2010) demonstrate that the accrual spread is a manifestation of q-theory where management maintains high working capital (i.e high accrual) in anticipation of low discount rates Q-theory could be particularly useful in explaining the accrual spread contributed by the growth-related

component (MDDGROWTH) of total accrual, as this is the part of accrual which responds to

changes in firms’ investment opportunity sets

1 The functional fixation hypothesis of Sloan (1996) suggests that the positive accrual spread arises because investors fail to distinguish between the persistence levels of cash-based and accrual-based earnings When predicting firms’ future earnings, investors tend to overestimate (underestimate) the persistence of accrual- (cash-) based earnings leading to mispricing of stocks As mispricing is corrected, lower (higher) returns are realized in the stocks of high (low) accrual firms

2 For example, earnings management (Chan et al., 2006; Kothari et al., 2006), analyst upward bias or agency problem (Bradshaw et al., 2001; Teoh and Wong, 2002), investors’ failure to recognize the variation in accrual reliability (Richardson et al., 2005), and firm growth (Fairfield et al., 2003; Zhang, 2007; Wu et al., 2010)

Allen et al (2013) suggest that the second accrual component, i.e MDDERROR, reflects either earnings management or management’s poor forecasts Kothari et al (2006) and Chan et

al (2006) suggest that the accrual spread is attributable to earnings management when realized

growth fails to meet investors’ expectations Hence, we argue that MDDERROR may contribute

to the accrual spread through earnings management In addition, Lakonishok et al (1994) suggest that investors are prone to error-in-expectation bias when firm growth is high If management also suffers from the same bias, they may over-estimate future growth opportunities and over-invest, which may result in the accrual spread (Wei and Xie, 2008) Hence

MDDERROR may also contribute to the mispricing of the accrual spread due to over-investment

The sources of the final accrual component relating to working capital fluctuation

(MDDMATCH) and its impact on the accrual spread are less understood Allen et al (2013) suggest that MDDMATCH reflects management’s taking advantage of temporary mispricing in

the input market Building on Allen et al.’s (2013) insights, we conjecture that the relationship

between MDDMATCH and stock returns can be explained by risk More specifically, firms that

time the input market may face an amplified exposure to the cyclicality of the product market The additional input that the firm accumulates may support future sales when the product market condition improves By contrast, if the future product market condition deteriorates, the additional input from previously timing the input market may become a burden as it ties up the firm’s financial resources when final products become slow-moving

Before embarking on the tests of alternative theories of accrual spread, we verify Allen et

al.’s (2013) finding that MDDGROWTH and MDDERROR (MDDMATCH) are negatively

(positively) related to raw returns and therefore contribute to (mitigate) the accrual spread Hereafter, we primarily concentrate on testing the validity of the various other hypotheses of the accrual spread by examining the roles of the three components of accrual We also shed new

light on the risk versus mispricing nature of these accrual components Finally, we develop an

implementable trading strategy based on the mispricing of a specific component of accrual

The study makes several contributions to the literature While Wu et al (2010) suggest that the accrual spread is partially explained by q-theory, we provide the first evidence that

MDDGROWTH, i.e the accrual component reflecting the working capital investment that

supports growth, is responsible for this accrual explanation The observed steeper slope of stock

returns on MDDGROWTH amongst more financially constrained firms suggests that the relationship between MDDGROWTH and stock returns is likely to be a manifestation of q-theory

with investment friction as stipulated by Li and Zhang (2010) We also find a more pronounced

relationship between MDDGROWTH and stock returns amongst firms with higher growth, suggesting that MDDGROWTH contributes to the accrual spread through firm growth (Fairfield

et al., 2003; Zhang, 2007; Wu et al., 2010) Using the asset pricing framework of Avramov and

Chordia (2006), we show that the relationship between MDDGROWTH and stock returns is

driven by risk as it can be explained by several factor models.3

Second, we contribute to the mispricing strand of the accrual anomaly literature by

examining the potential mispricing of MDDERROR, an accrual component that reflects accrual estimation error MDDERROR remains significantly negatively related to risk-adjusted stock

returns, suggesting that it contributes to the accrual spread through mispricing The results

further show that the inverse relationship between MDDERROR and stock returns becomes

increasingly prominent for firms with higher long-term growth or which are exposed to a higher degree of financial constraints This is possible because high firm growth may expose investors

to error-in-expectation (Lakonishok et al., 1994) and induce management to manage earnings (Kothari et al., 2006; Chan et al., 2006) Financial constraints may also trigger upwards earnings management (Jha, 2013) while curbing over-investment (Wei and Xie, 2008) Hence, our results

suggest that earnings management is likely to be the source of mispricing of MDDERROR which

leads to the accrual spread

Third, this study provides new evidence on the relationship between fluctuation in

working capital (MDDMATCH) and stock returns We find that the positive relationship between MDDMATCH and stock returns increases with firm growth and the degree of financial constraints Further, the positive relationship between MDDMATCH and stock returns, which

partially mitigates the accrual spread, can be explained by the asset pricing factor models

Therefore, the results support our view that the relationship between MDDMATCH and stock

returns is driven by risk, as timing the input market may amplify firms’ exposure to the product market condition Not only do we extend the understanding of the contribution of this accrual

3Hence, our investigation differs from Allen et al (2013) who associate both MDDGROWTH and MDDERROR

with the accrual spread through their lack of persistence relative to cash-based earnings.

component to the accrual spread, but also identify a potential source of systematic risk arising from working capital management

Finally, our analysis is also of value to investors wishing to take advantage of mispricing

Based on our findings of the mispricing of accrual estimation error (MDDERROR), we modify

the portfolio sorting dimension to include only the information that is available to investors at the time of portfolio formation and develop a long-short trading strategy The profitability of this new trading strategy, which has not been examined earlier, is about 60% higher than the conventional accrual-based trading strategies The profitability of our strategy can be improved further (up to 1.38% per month in raw returns and 1.33% in risk-adjusted returns) when it is implemented amongst high growth or financially constrained firms

2 HYPOTHESES DEVELOPMENT

Although the accrual spread is known to be a worldwide phenomenon4, what actually drives it remains debatable Several possible explanations have been put forward in the extant literature For example, Sloan (1996), in his functional fixation hypothesis, suggests that investors fail to recognize the difference in the persistence of the accrual and cash components of earnings leading to the mis-valuation of firms Zhang (2007), however, fails to find evidence to support the functional fixation hypothesis Using a novel accrual decomposition approach, Allen

et al (2013) document that the growth-related accrual component and accrual estimation error are both less persistent than the cash-based component of earnings They conclude that the accrual spread is driven by the mispricing of these two components due to investors’ functional fixation, as Sloan (1996) suggests

The accrual decomposition approach of Allen et al (2013) is different from the previous approaches (such as Jones, 1991; Defond and Park, 2001; Xie, 2001) in the way ‘abnormal’ accrual is measured While the other approaches consider the accrual component not related to growth as ‘abnormal’, Allen et al (2013) suggest that part of it reflects temporary fluctuation in working capital associated with realized future benefits They find that the accrual spread is

4 For evidence on the accrual spread in international markets, see LaFond (2005) and Pincus et al (2007) In the U.S market, Fama and French (2008) report that the accrual spread is among the most robust phenomena

driven by the growth-related component (MDDGROWTH) and accrual estimation error (MDDERROR) By contrast, the component reflecting temporary working capital fluctuation (MDDMATCH) moderates it MDDGROWTH and MDDMATCH reflect ‘good accrual’ associated with realized future benefits, whereas MDDERROR reflects accrual estimation not

eventually materialized

This paper utilizes the more refined accrual decomposition approach of Allen et al (2013) to examine several other theories of the accrual spread Wu et al (2010) suggest that q-theory and an investment-based risk factor partially explain the accrual spread By contrast, Hirshleifer et al (2012) examine whether the return predictability of total accrual reflects firm risk or characteristics and find support for the latter Their results lend support to a mispricing explanation irrespective of the mechanisms A more refined accrual decomposition approach will extend our understanding of (a) how different mechanisms may give rise to the accrual spread and (b) through which mechanisms each accrual component contributes to that spread

2.1 Firm growth and the accrual spread

A growing strand of the literature views the accrual spread as a function of firm growth Accrual reflects, at least in part, firm growth as it represents firms’ investment in working capital Fairfield et al (2003) and Zhang (2007), among others, document that the accrual spread

is driven by the growth information contained in the accrual Fairfield et al (2003) also attribute the accrual spread to either diminishing marginal returns on investment or accounting conservatism

Building on the works of Fairfield et al (2003) and Zhang (2007), Wu et al (2010) argue that q-theory can explain a large part of the total accrual spread This theory maintains that management rationally adjusts firms’ investment in working capital as the discount rate changes When discount rates (expected returns) are lower, more investment projects become profitable and firms invest more in both fixed- and working-capital Hence, to the extent that total accrual reflects firms’ investment in working capital, higher accrual would be associated with lower expected stock returns, and vice versa In line with this prediction, Wu et al (2010) document that the returns on the accrual-based trading strategies can be partially explained by Fama and French’s (1996) three-factor model augmented with an investment-based factor (i.e returns to the portfolio long in low-investment stocks and short in high-investment stocks)

Firms’ investments serve two purposes, (a) to maintain the current production capacity, and (b) to support changes in operation scale (either contraction or expansion) An example of investment for the first purpose is to replace fully depreciated assets, which tends to be routine

On the other hand, investment to support growth tends to be more sensitive to expected changes

in discount rates as they affect firms’ investment opportunity sets High growth firms, having a higher proportion of their investment to support growth, are likely to be more sensitive to discount rate changes Since q-theory attributes the accrual spread to the negative relationship between working capital investment and discount rates, the accrual spread is expected to be more

pronounced among high growth firms As MDDGROWTH consists of “accrual related to growth

in the working capital base required to support changes in the firm’s scale of operations” (Allen

et al., 2013, p.118), we argue that the q-theory explanation for the accrual spread operates

through MDDGROWTH Specifically, q-theory explains the negative relationship between MDDGROWTH and stock returns, and this relationship becomes more prominent with firm growth The negative relationship between MDDGROWTH and stock returns is manifest in a positive MDDGROWTH spread5 and we conjecture that:

H 1a : The MDDGROWTH spread is positive, and its magnitude increases with firm growth

The relationship between the total accrual spread and firm growth might also be driven

by accrual estimation error (MDDERROR) Allen et al (2013) argue that MDDERROR reflects

either management’s poor forecasts or earnings management Kothari et al (2006) suggest that the accrual spread is attributable to earnings management in order to prolong stock overvaluation due to positive investor sentiment They further argue that earnings management is more likely

to take place when realized growth fails to meet investor expectation Chan et al (2006) suggest that earnings management tends to happen when a firm’s realized growth is slower than the historical level and management wishes to delay reporting the slow growth Lakonishok et al (1994) suggest that investors investing on high growth firms are prone to error-in-expectation bias whereby they expect a higher level of growth than the firm can deliver as a result of their

5 The MDDGROWTH spread is defined as the hedge return to the portfolio long in low MDDGROWTH stocks and short in high MDDGROWTH stocks

extrapolation of past growth into the future Hence, we conjecture that MDDERROR contributes

to the relationship between firm growth and the accrual spread through earnings management

Further, high growth firms are more likely to witness management’s poor forecasting if the management is also subject to error-in-expectation bias Wei and Xie (2008) suggest that when management overestimates future growth, they over-invest and face a subsequent negative stock market reaction Working capital may be accumulated in response to management’s over-estimation of future growth that is not eventually realized Hence, management’s estimation

error, captured by MDDERROR, contributes to the relationship between firm growth and the

accrual spread Overall, both earnings management and management’s over-estimation of future

growth imply a positive relationship between firm growth and the MDDERROR spread:6

H 1b : The MDDERROR spread is positive and its magnitude increases with firm growth

Finally, we examine the way in which temporary fluctuation in working capital

(MDDMATCH) may contribute to the accrual spread Allen et al (2013) describe MDDMATCH

as reflecting management’s taking advantage of temporary mispricing in the input market For example, facing a temporarily low price in the input market, management may stock inventories

to a higher level than normal Consistent with the expectation that the inventory level will

eventually converge to the normal level, Allen et al (2013) report that MDDMATCH exhibits the

strongest reversal pattern out of all the accrual components.7

We argue that firms timing the input market face an amplified exposure to the cyclicality

of the product market These firms face the risk that the accumulated input will not materialize into future benefits when the future product market condition deteriorates Investors may

therefore request the additional premium to hold the stocks of firms with high MDDMATCH, causing a positive association between MDDMATCH and future returns.8 This positive

relationship would translate into a negative MDDMATCH spread, defined as the return to the portfolio long in low MDDMATCH firms and short in high MDDMATCH firms Further, when

firms have high long-term growth potential, management is more likely to take advantage of the

6 The MDDERROR spread is defined as the hedge return to the portfolio long in low MDDERROR stocks and short

in high MDDERROR stocks

7 Allen et al (2013) argue that the strong reversal pattern of MDDMATCH questions the practice of associating

accrual reversal with earnings management in the literature

8 We formalize our conjecture on risk versus mispricing of the accrual components in section 2.3

input market in anticipation that the additionally accumulated input will help support future sales (or reduce production costs) Hence, we expect a positive relationship between firm growth and

the magnitude of the MDDMATCH spread and expect that:

H 1c : The MDDMATCH spread is negative and its magnitude increases with firm growth

2.2 Financial constraints and the accrual spread

The extent to which firms are financially constrained is likely to affect the accrual spread for several reasons Wu et al (2010) suggest that management adjusts working capital in response to changes in discount rates (expected returns) When discount rates are lower, more potential projects become investable and firms increase their working capital level accordingly Hence, a higher working capital level (which corresponds to higher total accrual) is associated with lower expected future returns In a two period setting, Li and Zhang (2010) analytically show that the negative slope of stock returns on corporate investment is steeper (i.e more negative) when firms are subject to higher investment adjustment costs They report supporting evidence for their conjecture on the slopes of returns on several investment-related variables when investment adjustment costs are measured by financial constraints Applying this interpretation of q-theory to the context of the accrual spread, we expect the negative slope of stock returns on accrual to be more negative when firms face higher financial constraints

Hypothesis H 1a attributes the q-theory explanation to MDDGROWTH Hence, we also conjecture that the negative relationship between MDDGROWTH and stock returns is more pronounced in

more financially constrained firms:

H 2a : The magnitude of the MDDGROWTH spread increases with the degree of financial constraints

Financial constraints may also affect the accrual spread through MDDERROR DeAngelo

et al (1994) show that firms facing financial difficulties manage earnings downwards to utilize the contractual re-negotiation opportunities However, Rosner (2003) reports that firms that

eventually go bankrupt (ex post), but do not appear in distress ex ante, manipulate their earnings

upwards Firms which are close to covenant violations are also more likely to manage earnings upwards (Jha, 2013) In addition, financial constraints may also indirectly motivate management

to manage earnings upwards through the adverse impact of financial constraints on firm growth (Chan et al., 2006; Kothari et al., 2006) These scenarios may give rise to a positive association

between financial constraints and the MDDERROR spread On the other hand, financial

constraints may curb the degree of over-investment (Wei and Xie, 2008) and hence should

reduce the MDDERROR spread Taken together, although financial constraints are likely to affect the accrual spread due to MDDERROR, the sign of the relationship between financial constraints and the MDDERROR spread remains an empirical question:

H 2b : The magnitude of the MDDERROR spread is significantly related to the degree of financial constraints

Finally, we examine how financial constraints affect the relationship between temporary

working capital fluctuation (MDDMATCH) and stock returns As argued above, firms involved

in timing the input market face an amplified exposure to the cyclicality of the product market,

which may attract a premium in holding their stocks (hypothesis H 1b) We argue that when firms face financial constraints, timing the input market may incur more inherent risk as the limited financial resources would be stretched even further to fund the temporary accumulation of inputs.9 Hence, financial constraints may amplify the exposure of those firms involved in timing the input market to future product market condition Accordingly, these firms may attract an even higher risk premium when also facing financial constraints:

H 2c : The magnitude of the MDDMATCH spread increases with the degree of financial constraints

2.3 Risk versus mispricing of the accrual spread

Our investigation also addresses the much debated question of whether the accrual spread arises because of the compensation for risk or mispricing Hirshleifer et al (2012) report that the accrual spread is due to the mispricing of total accrual By contrast, Wu et al (2010) argue that part of the anomaly is a manifestation of q-theory, and the accrual spread can be partially explained by the Fama and French three-factor model augmented with an investment-based

factor We argued in sections 2.1 and 2.2 that MDDGROWTH is likely to be associated with the q-theory explanation for the accrual spread, as Wu et al (2010) advocate MDDERROR is

potentially mispriced as a result of earnings management or management’s error in estimating

9 Livdan et al (2009) also suggest that financial constraints expose firms to aggregate shocks as they limit firms’ ability to smooth the dividend stream

accrual The relationship between MDDMATCH and stock returns could be associated with risk,

since firms involved in input market timing may be exposed to shocks in the product market If the product market condition deteriorates and demand declines, firms engaged in timing the input market may have their funds tied up in working capital and suffer more than those not engaging

in such activities By contrast, input market timing may allow firms with spare working capital capacity to take advantage of the improved product market condition Hence, timing the input market potentially increases firms’ exposure to the cyclicality of the business environment,

hence higher systematic risk Our final hypothesis tests the risk versus mispricing nature of the

accrual spread, contributed to by its three components as follows:

H 3 : The accrual spread reflects the net impact of (a) systematic risk associated with MDDGROWTH and MDDMATCH, and (b) the mispricing of MDDERROR

3 VARIABLES AND DATA

3.1 Measurement of Variables

This section describes the variables used in this study Further details on the construction

of these variables are given in the Appendix

3.1.1 Total accrual and its components

In the literature, accrual has been measured in various ways including total accrual and normal/abnormal accrual, using the items reported in the balance sheet and/or the cash flow statement This paper measures total accrual using the information contained in the balance sheet.10 Following Sloan (1996), we estimate total accrual (ACCBS) as in equation (1):

the average total assets Following Allen et al (2013), we decompose total accrual into three components as in equation (2):

The component of total accrual relating to working capital growth is 𝑀𝐷𝐷𝐺𝑅𝑂𝑊𝑇𝐻𝑡 =

∝̂ +∝0 ̂ 𝑆𝐺𝑅1 𝑡+∝̂ 𝐸𝑀𝑃𝐺𝑅2 𝑡 The error term (ε) in equation (2) captures the estimation error of

total accrual (MDDERROR) The component of total accrual relating to temporary fluctuations in

working capital is 𝑀𝐷𝐷𝑀𝐴𝑇𝐶𝐻𝑡=∝̂ 𝐶𝐹3 𝑡−1+∝̂ 𝐶𝐹4 𝑡+∝̂ 𝐶𝐹5 𝑡+1

3.1.2 Long-term growth

We use the M/B (market-to-book value) decomposition method proposed by

Rhodes-Kropf, Robinson and Viswanathan (2005) (hereafter RKRV, 2005) to measure long-term growth

As M/B contains information both about firms’ long-term growth and mispricing, we use the

long-term growth component from its decomposition to avoid contaminating growth with

mispricing Following RKRV (2005), M/B is decomposed as in equation (3):

where, 𝑚, 𝑏 and 𝑣 are the natural logarithm of market value, book value, and fundamental value

of the stock, respectively For firm 𝑖 in industry 𝑗 at time 𝑡, the fundamental value (𝑣) can be expressed as a function of firm-specific accounting information 𝜃𝑖,𝑡, a vector of industry average contemporaneous accounting variables 𝛼𝑗,𝑡, and a vector of long-run industry average accounting variables 𝛼𝑗 The natural logarithm of M/B for firm 𝑖 in industry 𝑗 at time 𝑡 can therefore be

decomposed as in equation (4):

(𝑚𝑖,𝑡− 𝑏𝑖,𝑡) = [𝑚𝑖,𝑡− 𝑣(𝜃𝑖,𝑡, 𝛼𝑗,𝑡)] + [𝑣(𝜃𝑖,𝑡, 𝛼𝑗,𝑡) − 𝑣(𝜃𝑖,𝑡, 𝛼𝑗)] + [𝑣(𝜃𝑖,𝑡, 𝛼𝑗) − 𝑏𝑖,𝑡] (4)

The third term [𝜈(𝜃𝑖,𝑡, 𝛼𝑗) − 𝑏𝑖,𝑡] is the difference between the firm’s intrinsic value implied by long-run industry average multiples and its book value (i.e the long-run growth component of

M/B)

The RKRV’s approach, as outlined in their equation 15 (p 577), is employed to empirically estimate the values of (𝜃𝑖,𝑡, 𝛼𝑗) Equation (5), (i.e equation 15 in RKRV) is estimated for each year in the sample separately for the 12 industry groups categorized by Fama and French (1996).11

(2005), our proxy for long-term growth (LTG) is obtained by subtracting the book value from

this “fitted” value, which reflects the deviation of the book value from the long-term intrinsic value

3.1.3 Financial Constraints

The literature offers various measures of firms’ financial constraints such as the KZ and

WW indexes by Kaplan and Zingales (1997) and Whited and Wu (2006), respectively More recently, using the qualitative information from financial filings to identify financially distressed firms, Hadlock and Pierce (2010) cast doubt on the ability of KZ and WW in predicting distress and suggest a firm’s total asset and age as alternative measures Hence, we use total assets and firm age as the proxy measures for financial constraints Firms with small (large) total assets are classified as financially constrained (unconstrained) Firm age is determined as the number of years firms have been reporting financial data in Compustat Young (old) firms are classified as financially constrained (unconstrained)

11 Available from http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html#Research

3.2 Data and Summary Statistics

The sample comprises all stocks listed on the three major US stock exchanges: NYSE, AMEX and NASDAQ, and are included in the merged CRSP and Compustat database Financial (SIC code 6000 - 6999) and utilities (SIC code 4900 - 4999) stocks are excluded.12 We also exclude observations with month-end stock prices falling below $5 so that our results are not driven by small and illiquid stocks or bid-ask bounce Only firms with ordinary common equity (security types 10 and 11 in CRSP) are included Further, we exclude firm-year observations with a negative book value of equity Finally, we exclude observations with insufficient

information to calculate total accrual (ACCBS) The sample with ACCBS covers 450 months

from July 1973 to December 2010 with 8,785 firms and 840,915 firm-month observations When

requiring sufficient data for the decomposition of total accrual (hereafter MDD sample), the

sample shrinks to 7,431 firms and 752,666 firm-month observations covering the same time period We use the risk-free rate, the Fama and French factors, and the Carhart momentum factor from CRSP, which were originally sourced from Kenneth French’s website

Table 1 (Panel A) reports summary statistics of the key variables Total accrual and its

components show a small degree of skewness Firms’ long-term growth (LTG) extracted from M/B is not skewed The other variables, including financial constraints (i.e TA and AGE) and M/B, show a high degree of skewness, indicated by the considerable differences between their

means and medians The mean (median) total accrual approximates -2% (-3%) of average total assets These figures are comparable to the evidence in the literature.13

Panel B of Table 1 shows the time series average of the Spearman’s annual sectional correlations among firm level variables Not surprisingly, total accrual and its three components are positively correlated, with the correlation ranging from 0.25 to 0.71 The correlations amongst the three accrual components are modest, suggesting that they proxy for

cross-distinct economic concepts As expected, M/B is positively correlated with LTG (0.59) M/B and ACCBS have a very low correlation (0.12), possibly driven by the long-term growth component

of M/B.14,15 Surprisingly, MDDGROWTH (i.e the accrual component reflecting working capital growth) is virtually uncorrelated with LTG (i.e firms’ long-term growth derived from M/B) By contrast, MDDERROR (i.e the accrual estimation error component of total accrual) has a reasonably high correlation (0.24) with LTG This is potentially because higher long-term growth

makes it harder to estimate accrual, hence the higher accrual estimation error The correlation

between the financially constrained proxies (i.e TA and AGE) is reasonably high (0.45), suggesting that incumbent firms are often big firms Their negative correlations with LTG

suggest that being small and young, high growth firms tend to face financial constraints

[Insert Table 1 about here]

significant (t=5.28) The magnitude of the accrual spread is comparable with the literature (e.g

Wei and Xie (2008) report an accrual spread of 0.56% per month)

Panel B of Table 2 reports the returns to the hedge portfolios of stocks sorted by the three components of total accrual obtained from its decomposition described in section 3.1.1 As Allen

et al (2013) point out, it uses cash flow information available in year t+1 and hence the hedge

returns are not achievable by investors Therefore, we limit our investigation using

MDDGROWTH, MDDERROR and MDDMATCH to verifying the theoretical motivations of the

accrual spread We discuss the implications to investors, including investable strategies, in section 4.4

14 Desai et al (2004) suggest that the accrual anomaly and the value anomaly are the same We find a positive

correlation of 0.12 between ACCBS and M/B which is too low for the two anomalies to be the same

15 The correlation between LTG and ACCBS is 0.13, approximating that between M/B and ACCBS

Statistically significant and positive monthly hedge returns are observed on the portfolios

sorted by MDDGROWTH (0.31%) and MDDERROR (1.12%) By contrast, the hedge return is negative (-0.51%) when stocks are sorted by MDDMATCH The results suggest that the accrual spread is attributable to both MDDGROWTH and MDDERROR, with the latter exhibiting a dominant impact By contrast, MDDMATCH generates a negative spread The results support our conjectures on the sign of these spreads in hypotheses H 1a to H 1c These findings are also consistent with the results from Allen et al.’s (2013) cross-sectional regressions that

MDDGROWTH and MDDERROR are negatively related to future raw returns whereas MDDMATCH is positively related Allen et al (2013) further document that MDDGROWTH and MDDERROR are less persistent than cash-based earnings and conclude that these components

give rise to the accrual anomaly, consistent with Sloan’s (1996) functional fixation hypothesis

We explore other theories on the accrual spread in the following sections

[Insert Table 2 about here]

4.1 Firms’ Long-Term Growth and the Accrual Spread

This section investigates the association between firms’ long-term growth and the spreads constructed from portfolios sorted by total accrual or its components While the accrual anomaly literature documents a positive relationship between firm growth and the accrual spread (Fairfield et al., 2003; Zhang, 2007), there is much less consensus on the reason behind this

relationship Table 3 reports the results of portfolio sorts in testing hypotheses H 1a , H 1b and H 1c

on different channels through which the positive relationship between firm growth and the accrual spread may arise

[Insert Table 3 about here]

Columns (1) to (3) of Table 3 report the association between the accrual spread and LTG

Calculated as [𝜈(𝜃𝑖,𝑡, 𝛼𝑗) − 𝑏𝑖,𝑡] (see equation 4), LTG reflects the difference between a firm’s

fundamental value implied by long-term industry average multiples and its book value.16 An independent double sorting approach is employed Firms with sufficient data to estimate both

LTG and ACCBS are independently sorted into terciles (30-40-30) by LTG and into quintiles by

16 In untabulated results, we find that LTG increases almost monotonically across the ACCBS quintiles

ACCBS measured at the end of the previous fiscal year (t-1) The equally weighted portfolios are held from July of year t to June of year t+1 Reading down column (3), the monthly accrual spread (L-H) increases monotonically from 0.05% in the low LTG tercile to 0.58% in the high LTG tercile The difference of 0.53% in the accrual spread residing in the low versus high LTG

tercile is both economically and statistically significant The results support a positive relationship between the accrual spread and firms’ long-term growth Our results are consistent with the earlier studies which associate the accrual spread with some forms of growth (e.g inventories in Thomas and Zhang, 2002; employee growth in Zhang, 2007; and growth in operating assets in Fairfield et al., 2003) We add to this literature by using a more refined growth proxy that captures firms’ overall long-term growth potential and avoids the

contamination of stock mispricing potentially inherent in M/B

Table 3 also dwells on how firm growth is related to the spreads constructed from each component of total accrual Columns (4) to (6) report the equally weighted returns to the

portfolios of stocks independently sorted by LTG (terciles) and MDDGROWTH (quintiles) The

monthly hedge return (L-H, reading down column 6) to the portfolio short on low

MDDGROWTH and long on high MDDGROWTH (0.43%) is statistically significant only in the high LTG tercile The MDDGROWTH spread stays positive but insignificant in the middle LTG tercile, and becomes negative and insignificant in the low LTG tercile The difference (0.66%) in the MDDGROWTH spread between the extreme LTG terciles is significant As the MDDGROWTH spread increases with firm growth, hypothesis H 1a is supported The results suggest that the working capital investment in total accrual becomes more responsive to discount rates (proxied by future returns) when firms have higher long-term growth, lending support to the q-theory explanation of the accrual spread

In columns (7) to (9), stocks are independently sorted by LTG (terciles) and MDDERROR

(quintiles) Reading down column (9), the monthly hedge returns (L-H) to the long-short

MDDERROR sorted portfolios vary from 0.52% in the bottom LTG tercile to 1.04% in the top LTG tercile The difference of 0.52% is statistically significant, supporting hypothesis H 1b that

the MDDERROR spread increases with firm growth The results may be consistent with

management’s attempt to manage earnings to meet the unrealistically high investor expectation

of growth due to error-in-expectation bias (Lakonishok et al., 1994) If management is also

subject to this bias, they may genuinely overestimate growth and consequently over-accumulate

of accrual, hence the positive accrual spread (Wei and Xie, 2008)

Finally, columns (10) to (12) of Table 3 report the hedge returns (L-H) to the long-short

MDDMATCH portfolios in LTG terciles Reading down column (12), the MDDMATCH spread across all the three LTG terciles is negative, similarly to the MDDMATCH spread in the overall sample reported in Table 2 While the monthly MDDMATCH spread is negligible (-0.18%) in the bottom LTG tercile, it is approximately 0.40% and is statistically significant in the top two LTG terciles However, the difference in the MDDMATCH spread between the extreme LTG terciles

is not statistically significant Hence, the portfolio sort results do not support hypothesis H 1c that

the magnitude of the MDDMATCH spread increases with firm growth

To control for other factors that may affect stock returns and hence may contaminate their relations with total accrual and its components, Table 4 reports the results of the following cross-sectional Fama-MacBeth regression:

(𝑅𝑗,𝑡− 𝑅𝐹𝑡) = 𝑎0+ 𝑎1𝐴𝐶𝐶𝑗,𝑡−1+ ∑ 𝑏𝑖

8 𝑖=1

𝐶𝑜𝑛𝑡𝑟𝑜𝑙𝑠𝑖,𝑗,𝑡−1+ 𝑒𝑗𝑡 (6)

where R,t is the return on stock 𝑗 and R Ftis the risk free rate at month 𝑡 𝐴𝐶𝐶𝑗,𝑡−1 is either

ACCBS or its components (i.e MDDGROWTH, MDDERROR or MDDMATCH) measured at the end of the previous fiscal year for the regression of excess returns from July (month t) to the following June (month t+11) Following Lam and Wei (2011), we add the control variables

previously documented to predict stock returns in the cross-section 𝐶𝑜𝑛𝑡𝑟𝑜𝑙𝑠𝑖,𝑗,𝑡−1 includes (i)

the natural logarithm of M/B measured at the same time as total accrual, (ii) the natural logarithm

of market capitalization measured at the end of month t-1, (iii) past cumulative returns of months

2 to 3, 4 to 6, and 7 to 12, (iv) the natural logarithm of the NYSE/AMEX and NASDAQ

turnovers at the end of month t-1, and (v) the NASDAQ dummy To be consistent with the portfolio sort results in Table 3, the coefficient a 1 attached to ACCBS has to be negative (i.e evidence of the positive accrual spread) In addition, the coefficient a 1 being larger in magnitude

as LTG increases, would imply a positive relationship between the accrual spread and LTG Similar behaviors of MDDGROWTH and MDDERROR would reconcile with the results from Table 3 and further support hypotheses H 1a and H 1b

[Insert Table 4 about here]

Column (1) of Table 4 reports coefficient a 1 attached to ACCBS in each LTG tercile ACCBS is always negatively related to future returns, consistent with the positive ACCBS spread documented in Table 2 The ACCBS coefficient is negative (-0.77) but insignificant in the low LTG tercile It becomes increasingly more negative and statistically significant as LTG increases

In the high LTG tercile, the negative coefficient of ACCBS (-2.23) is highly significant The difference between the ACCBS coefficient residing in the high versus low LTG tercile is

significant The results are consistent with the findings in Table 3 that the magnitude of the

ACCBS spread increases with LTG

Columns (2) to (4) of Table 4 report the coefficient a 1 attached to MDDGROWTH, MDDERROR and MDDMATCH respectively The MDDGROWTH coefficient is positive and insignificant in the low LTG tercile, and becomes negative in the medium and high LTG terciles The difference in the MDDGROWTH coefficient between the extreme LTG terciles is negative,

but not significant The results do not statistically support the positive relationship between the

MDDGROWTH spread and LTG (hypothesis H 1a) documented in Table 3 Reading down column

(3) in Table 4, the MDDERROR coefficient remains negative and significant, with its magnitude increasing with LTG The difference (-1.69) in the MDDERROR coefficients between low and high LTG terciles is significant, consistent with a positive relationship between the MDDERROR spread and firm growth (hypothesis H 1b ) Finally, the MDDMATCH coefficient is positive in all the LTG terciles, consistent with a negative return (L-H) to the hedge MDDMATCH portfolio documented in Table 2 The MDDMATCH coefficient (0.62) is statistically insignificant in the low LTG tercile, but increases monotonically and becomes significant as LTG increases (1.79 and 2.52 in medium and high LTG terciles, respectively) The difference in the MDDMATCH coefficient between the extreme LTG terciles is also significant The results are consistent with the MDDMATCH spread increasing in magnitude with firm growth, lending support to hypothesis H 1c

Taken together, the results of our portfolio sorts and cross-sectional regressions

demonstrate that hypotheses H 1a , H 1b and H 1c are generally supported Firm growth’s positive

relationship with the MDDGROWTH spread (H 1a) lends support to Wu et al.’s (2010) q-theory

Its positive relationship with the MDDERROR spread (H 1b) is consistent with either earnings management (Chan et al., 2006; Kothari et al., 2006) or over-investment (Wei and Xie, 2008) due to error-in-expectation bias (Lakonishok et al., 1994) When investors are subject to this

bias, their over-estimation of firm growth may induce management to manage earnings upwards Alternatively, management itself being exposed to the error-in-expectation bias, may over-invest

in working capital The positive relationship between firm growth and the magnitude of the

MDDMATCH spread (H 1c) lends support to our conjecture that when firms experience high growth, management is more likely to time the input market, consequently increasing the firm’s exposure to the cyclicality of the product market

4.2 Financial Constraints and the Accrual Spread

As discussed in section 2.2, several theories suggest a positive association between

financial constraints and the accrual spread Under q-theory, the MDDGROWTH spread increases with financial constraints (H 2a) The direction of the relationship (negative or positive)

between the MDDERROR spread and financial constraints is unclear and depends on how firms manage earnings when faced with financial difficulties (H 2b) Financial constraints may also curb

over-investment and reduces the MDDERROR spread Finally, the MDDMATCH spread is expected to increase in magnitude with financial constraints (H 2c) as the riskiness of timing the input market is heightened when firms have to further stretch their limited financial resources

Table 5 reports the returns to the equally weighted portfolios of stocks independently

sorted by financial constraints (30-40-30 terciles) and either ACCBS or its components (quintiles) In Panel A, financial constraints are proxied by total assets (TA) Columns (1) to (3)

of Panel A report the returns to the portfolios double sorted by TA and ACCBS Reading down column (3) of Panel A, the monthly ACCBS hedge return declines monotonically from the constrained (1.13%) to the unconstrained (0.28%) tercile The difference (0.85%) in the ACCBS spread between the extreme TA terciles is statistically significant

[Insert Table 5 about here]

Reading down column (6) of Panel A (Table 5), the monthly MDDGROWTH spread is

0.69% and statistically significant in the constrained tercile, yet economically negligible and statistically insignificant in the medium and unconstrained terciles The difference of 0.67% in

the MDDGROWTH spread between the extreme constrained terciles is statistically significant The results support hypothesis H 2a that the MDDGROWTH spread is positively related to the degree of firms’ financial constraint In column (9) of Panel A, the monthly MDDERROR spread

also monotonically decreases from the constrained tercile (1.74%) to the unconstrained tercile

(0.81%) Their difference is also statistically significant The results support hypothesis H 2b that

financial constraints systematically affect the MDDERROR spread The positive relationship between financial constraints and the MDDERROR spread lends support to the earnings

management explanation of the accrual spread (Chan et al., 2006; Kothari et al., 2006) as financially constrained firms may manage earnings upward to avoid covenant violations (Jha, 2013) Wei and Xie’s (2008) view on over-investment is not supported, as financial constraints may curb over-investment leading to lower accrual spread Column (12) of Panel A (Table 5)

shows that the hedge return (L-H) to the MDDMATCH sorted portfolios is always negative and

significant, consistent with the results in Tables 2 to 4 Moreover, as firms become more

financially constrained, the magnitude of the MDDMATCH spread increases monotonically, supporting hypothesis H 2c.17

In Panel B of Table 5, financial constraints are proxied by firm age (AGE) The variation

of the ACCBS spread, MDDERROR spread and MDDMATCH spread across the AGE spectrum is qualitatively similar to and corroborates the results in Panel A The MDDGROWTH spread

follows a similar pattern across the financially constrained terciles, except that its difference

between the extreme AGE terciles is not statistically significant Overall, the results reported in Table 5 strongly support hypotheses H 2b and H 2c while weakly support hypothesis H 2a To control for other factors that may affect stock returns in the cross-section, Table 6 employs the cross-sectional regression approach with control variables (i.e other firm characteristics capable

of predicting future returns) Regression equation (6) is run at firm level in the subsamples of

firms facing different degrees of financial constraints (as measured by TA in Panel A and by AGE in Panel B) The coefficient a 1 attached to either ACCBS or its three components is

reported Li and Zhang (2010) suggest that q-theory predicts a steeper slope of stock returns on firms’ investments as they are subject to a higher degree of financial constraints In our empirical

testing, a steeper MDDGROWTH slope (i.e a more negative MDDGROWTH coefficient)

amongst more financially constrained firms in Table 6, would corroborate the portfolio sorting

results in Table 5 and lend support to hypothesis H 2a Using the same analogue, hypotheses H 2b

and H 2c imply steeper MDDERROR and MDDMATCH slopes amongst more financially

constrained firms

17 The difference in the MDDMATCH spread between the extreme TA terciles is 0.38% per month (t=2.41)