Data Availability: Data are available from sources identified in the paper.

The Relative Contributions of Value Relevance and Mispricing to the Pricing of Abnormal Accruals

Frank Heflin*

College of Business

Florida State University

Rovetta Business Annex

821 Academic Way

Tallahassee, Florida 32306

College of Business

Florida State University

Rovetta Business Annex

821 Academic Way

Tallahassee, Florida 32306

Keywords: discretionary accruals; abnormal accruals; value relevance; accrual anomaly;

mispricing

Data Availability: Data are available from sources identified in the paper.

We thank Allen Blay, Dave Bryan, Terry Mason, Rick Morton, Dana Wallace, and workshop participants at Florida State University and the University of Syracuse for helpful comments.

The Relative Contributions of Value Relevance and Mispricing to the Pricing of Abnormal Accruals

ABSTRACT: We examine the relative contributions of mispricing and value relevance to the pricing of abnormal accruals. Unlike prior research, we provide estimates of how much of the pricing of abnormal accruals is due to value relevance and how much is due to mispricing. Our estimates suggest approximately half of abnormal accrual valuation is due to their value relevance and half is due to mispricing. However, our estimates differ considerably by time period. Before 2002, nearly two-thirds of abnormal accruals pricing is due to mispricing, and the mispricing is not limited to extreme accruals, as prior research suggests. Post-2002, mispricing largely disappears. Further, the post-2002 reduction in mispricing is partially attributable to an improvement in the quality of accruals.

1 1. Introduction

Evidence in Subramanyam (1996) suggests investors price abnormal accruals, and evidence in both Subramanyam (1996) and Louis and Robinson (2005) suggests abnormal accruals convey information about the intrinsic value of the firm (i.e. abnormal accruals are value relevant). However, Sloan (1996) concludes that investors overvalue accruals, and Xie (2001) attributes this overvaluation primarily to the abnormal component of accruals.1 To date, researchers have focused on either one explanation or the other (value relevance or mispricing), and no research has attempted to estimate the relative contributions of mispricing and value relevance to the initial pricing of abnormal accruals.2 We develop a method of evaluating the extent to which value relevance and mispricing explain the pricing of abnormal accruals.3 The sum of the contemporaneous and future coefficients divided by the contemporaneous coefficient (we label this the “value relevance ratio”) provides a measure of the percentage of initial pricing of abnormal accruals attributable to their value relevance, and one minus that ratio represents the percentage attributable to mispricing. We then use the method to examine how the contributions of value relevance and mispricing to abnormal accruals pricing change over time.

Over our full sample period (1973-2008), we find that approximately half (at least 20%) of the pricing of abnormal accruals reverses in the three years following, meaning half (at most 80%) of the pricing of abnormal accruals is due to their value relevance. However, these estimates vary considerably

1 _{Subramanyam (1996) uses the term “discretionary accruals” while Xie (2001) uses “abnormal accruals”. We}

generally use the term, “abnormal accruals”. Whether or not discretion contributes to abnormal accruals is not crucial for our study. Consistent with Subramanyam (1996), we use the term “non-discretionary net income” when referring to operating cash flows plus normal accruals (both defined later) rather than introduce the term “non-abnormal net income”.

2

The value relevance literature often refers to the contemporaneous pricing of an accounting construct (like abnormal accruals) as indicative of value relevance. However, pricing can arise because either because (1) investors accurately assess the relation between the accounting construct and future cash flows, or (2) investors inaccurately attribute too much association between the construct and future cash flows. We refer to the former as value relevance and the latter as mispricing.

3 _{An overview of our method is as follows: We first assess the contemporaneous pricing of abnormal accruals by}

regressing stock returns on contemporaneous abnormal accruals (Subramanyam 1996). To the extent abnormal accruals are mispriced, some portion of their initial pricing should reverse within the subsequent three years (Sloan 1996). Therefore, we regress the three-year future return on current abnormal accruals (Desai et al. 2004; e.g., Cheng and Thomas 2006). The sum of the abnormal accruals coefficients from the two regressions yields the total pricing of abnormal accruals across the four years.

2 by time period. Prior to 2002 (which corresponds roughly with the implementation of the Sarbanes-Oxley Act, or SOX), mispricing explains nearly two-thirds of the pricing of abnormal accruals.4 After SOX, mispricing explains virtually none of the pricing of abnormal accruals. That is, after SOX, the pricing of abnormal accruals is due almost exclusively to their value relevance. In addition, we investigate whether the pre-2002 mispricing was limited to extreme accruals (i.e., the accruals exploited by accrual anomaly strategies) and find it was not, as the majority of abnormal accruals exhibit significant future price correction.

Our final analyses investigate why value relevance’s contribution to the pricing of abnormal accruals improves after SOX. The increase (decline) in the contribution of value relevance (mispricing) to the pricing of abnormal accruals has at least three possible explanations. First, investors in an adaptively efficient market could have changed their initial valuations of abnormal accruals such that they no longer misprice them. This explanation is consistent with Mohanram (2013), which finds information conveyed through analysts’ cash flow forecasts reduces mispricing. Second, hedge funds could rapidly arbitrage away initial mispricing, eliminating long-run price correction. This explanation is consistent with evidence in Green et al. (2011), who suggest that increased hedge-fund activity contributes to the decline of the accrual anomaly. Third, the quality of abnormal accruals may have improved. Better quality accruals can improve value relevance even if investors ‘fixate’ on reported earnings because investors are fixating on an earnings number that better reflects fundamental value. The first two explanations suggest a decrease in initial mispricing and the third explanation suggests an increase in value relevance. Any of these explanations results in an increase in the value relevance ratio.5

4 _{We use the terms ‘pre-SOX’ and ‘post-SOX’ primarily for convenience. We do not directly test whether}

provisions in SOX lead to the changes we document. As in Cohen et al. 2008, we acknowledge that several important economic changes occurred near to SOX’s implementation. We describe these changes later.

5

Arbitrage activity by hedge funds can affect the value relevance ratio because the ratio is pricing due to value relevance divided by total pricing. If hedge funds (quickly) arbitrage mispricing away, then total pricing declines, increasing the VRR.

3 Our results suggest that, in the post-SOX period, contemporaneous valuation of abnormal accruals declines slightly, suggesting some investor price adjustment, but the effect is minimal. However, we observe a significant decline in the association between abnormal accruals and future returns. Combining the lack of significant change in the initial pricing of abnormal accruals with the reduction in future price correction implies that the content, or quality, of abnormal accruals has improved. We then examine how accruals quality changes over time. We observe a steady decline in accruals quality, measured as in Dechow and Dichev (2002), until around 2001 at which point there is a sharp increase. We then regress annual relevance ratios on annual accruals quality and the hedge fund activity measure from Green et al. (2011) (and controls). We find that both accruals quality and hedge fund activity contributes significantly to the explanation of over-time variation in value relevance ratios. Thus, our evidence suggests that the increase in the contribution of value relevance to abnormal accruals pricing after SOX is explained by an increase in both accruals quality and hedge fund activity.

We make three important contributions: (1) we provide estimates of how much of the pricing of abnormal accruals is due to value relevance and how much is due to mispricing, (2) we document dramatic changes in these estimates before versus after SOX, and (3) we provide evidence that improvements in accruals quality after SOX contribute to the decline in the mispricing of abnormal accruals. We stress that our first contribution is not that we demonstrate that both value relevance and mispricing contribute to abnormal accrual pricing. Evidence that both contribute to abnormal accrual pricing would not be surprising given the evidence in Subramanyam (1996) and Xie (2001). Rather, our contribution is that we provide estimates of how much each (value relevance and mispricing) contribute to abnormal accrual pricing. Prior research does not provide estimates of the extent to which value relevance and mispricing contribute to the pricing of abnormal accruals. In fact, statements in both value relevance and mispricing research suggest that the explanation each investigates is pervasive. For example, Subramanyam (1996) states, “[O]n average the market attaches value to discretionary accruals, probably because the discretionary component increases the ability of earnings to reflect fundamental

4 value” (Subramanyam 1996, 252, his emphasis).6 On the other hand, Xie claims, “[T]he overpricing of abnormal accruals arises in general contexts…” (Xie 2001, 370) implying that mispricing is not limited to small segments of the population of firms, and Sloan suggests, “[S]tock prices reflect naive expectations about fundamental valuation attributes such as earnings” (Sloan 1996, 290). Both statements suggest that mispricing is not isolated.

Why are estimates of the contributions of value relevance and mispricing to abnormal accrual pricing important? Those estimates are critical for interpreting the economic meaning of abnormal accruals. If abnormal accruals are 90% mispriced and only 10% value relevant, we (academics, regulators, etc.) would conclude that abnormal accruals largely mislead investors and in this sense do more harm than good. In contrast, if abnormal accruals are 90% value relevant, we would conclude abnormal accruals provide investors with important, value-relevant information. This point is articulated in terms of relevance and reliability in Barth et al. (2001). They note that pricing (i.e. value relevance) tests are generally tests of relevance and reliability. Researchers infer an accounting construct is both relevant and reliable if it is associated with price. However, mispricing by investors undermines such an inference. Finally, abnormal accruals models continue to be used extensively in the literature, so understanding the nature of their valuation by investors is vital to understanding and synthesizing results of abnormal accruals based research.7

We also stress that the contribution of our time-series analyses (our second and third contributions) make is not that we document a decline in the mispricing of accruals, as that evidence is provided by (Green et al. 2011; Mohanram 2013; Richardson et al. 2010). Rather, the contribution of our time-series analyses is that (1) we provide estimates of how much of abnormal accrual pricing is due to value relevance versus mispricing before and after the change, and (2) more importantly, we provide

6 _{See additional arguments supporting value relevance as the primary explanation for abnormal accrual pricing on}

pages 251-252 of Subramanyam (1996).

7 _{Since 2008, Google scholar reports over 2,800 citations of Jones (1991), indicating the continued prevalence of}

5 evidence that part of the change in the pricing of abnormal accrual quality is due to a change in the quality of accruals, and not just because of an increase in hedge fund activity.

Finally, our results have potential practical implications for investors and standard setters. In order to achieve market efficiency, “capital market participants [must] actively trade on useful information…” (Richardson et al. 2010, 449; Grossman and Stiglitz 1980). We enhance investor understanding of what constitutes useful information by quantifying the degree to which abnormal accruals enhance the value relevance of earnings. Further, value relevance research, such as our study, “provide[s] evidence to accounting standard setters that can update their prior beliefs about how accounting amounts are reflected in share prices and, thus, can be informative to their deliberations on accounting standards” (Barth et al. 2001, 88–89). Our results illustrate how the quality of accounting estimates (abnormal accruals) affects the degree of investor mispricing.

The remainder of the paper proceeds as follows: Section 2 discusses background literature and the motivations for our study; Section 3 describes variable measurement and empirical design; Section 4 presents our empirical results; Section 5 presents our analysis of determinants of value relevance ratios; Section 6 reports results from sensitivity analyses, and Section 7 concludes.

2. Related Literature and Motivation

2.1 Value Relevance and Mispricing of Abnormal Accruals

The value relevance of accruals is one of the most fundamental questions in accounting. Dechow (1994) argues that earnings should be superior to cash flows for explaining firm value because accruals correct timing and matching problems inherent to cash flows. Consistent with her conjecture, she finds earnings explain contemporaneous stock returns better than cash flows, and the superiority of earnings over cash flows increases with the length of the operating cycle. Dechow’s (1994) results imply that accruals are value relevant and contribute to the value relevance of earnings. Unresolved in Dechow (1994), however, is whether managerial discretion contributes to, or detracts from, the value relevance of

6 accruals. Two streams of subsequent research provide evidence on the effect of managerial discretion on accruals’ value relevance. We discuss each next.

One stream suggests managerial discretion contributes to the value relevance of accruals. Subramanyam (1996) finds that abnormal (or discretionary) accruals contribute to the explanation of stock returns beyond the explanatory power provided by operating cash flows and normal accruals. His results suggest abnormal accruals are either value relevant (i.e. contribute to the value relevance of accruals in general) or value irrelevant, but investors err and misprice them. Consistent with the former explanation, he finds that abnormal accruals are associated with future dividend increases, implying abnormal accruals contain value relevant information. Similarly, evidence in Louis and Robinson (2005) suggests abnormal accruals contain value relevant information. They conclude that managers use abnormal accruals to signal future stock splits, as abnormal accruals in the period preceding a stock split are positively related to split-announcement returns. Results in Beaver and Engel (1996) also support the value relevance of abnormal accruals, albeit in a more specific setting. They find that the market prices both the normal and abnormal components of banks’ loan loss reserves. Bowen et al. (2008) find accounting discretion (measured in part by abnormal accruals) that is associated with low corporate governance leads to better future financial performance. They interpret their evidence as consistent with the notion that shareholders benefit from earnings management.

The second stream investigates investor mispricing of accruals. Sloan’s (1996) results suggest investors fixate on the earnings number as a whole and ignore the differential persistence of cash flows (more persistent) and accruals (less persistent). Consequently, investors overestimate accrual persistence and underestimate cash flow persistence.8 Sloan’s (1996) analyses do not separately consider abnormal and normal accrual components, but his results raise the possibility that the pricing of abnormal accruals is because they are mispriced rather than because they contain value relevant information. Xie (2001)

8

We recognize there are other explanations for the mispricing of accruals, including investors’ failure to understand accruals’ implications for growth (Fairfield et al. 2003) and, relatedly, diminishing return on investments (Zhang 2007; Dechow et al. 2008). The underlying reason for initial mispricing is inconsequential in our setting.

7 tests this notion more directly. Xie (2001) decomposes accruals into abnormal and normal components and finds that the accrual mispricing documented by Sloan (1996) is attributable primarily to the abnormal component of accruals. Xie’s (2001) results strengthen the notion that abnormal accruals pricing is due to mispricing.

Subsequent studies lend additional support to the mispricing of accruals. Collins and Hribar (2000) find evidence of the accrual anomaly in quarterly data and show that trading strategies based on extreme accruals are distinct from those exploiting post-earnings announcement drift (PEAD). They find that a combined accruals-PEAD strategy earns larger hedge returns than single-anomaly strategies. Collins et al. (2003) show that accruals mispricing dissipates for firms with higher transient institutional ownership, presumably because such institutions arbitrage away this mispricing. Their results support the assertion that the accrual anomaly does not represent a priced risk factor. Finally, Desai et al. (2004) and Cheng and Thomas (2006) show that firm characteristics associated with the value glamour anomaly do not fully explain accrual anomaly abnormal returns.

In summary, existing research provides evidence that abnormal accruals are priced because of their value relevance and because they are mispriced. Prior research does not attempt to estimate the relative contributions of value relevance and mispricing to the pricing of abnormal accruals. Estimating the relative contributions of value relevance and mispricing to abnormal accrual pricing is important because the magnitudes of those estimates determine whether we can conclude abnormal accruals are mostly value relevant and therefore relevant and reliable (Barth et al. 2001). This leads us to our first research question.

RQ1: How much of the pricing of abnormal accruals is attributable to value relevance versus mispricing?

2.2 Changes in Abnormal Accrual Pricing and Mispricing Over Time

Several factors lead us to suspect that the nature of accrual pricing has changed significantly over time. First, widespread circulation and publication of both Sloan (1996) and Xie (2001) informed investors of the anomaly. Semi-strong form market efficiency suggests that dissemination of this research

8 should have increased arbitrage activity and reduced mispricing. Consistent with this notion, Green et al. (2011) find that, beginning in the early 2000s, neither raw nor size-adjusted hedge returns based on total-accrual trading strategies are reliably positive. They attribute the majority of the total-accrual anomaly’s demise to increased investment of capital by hedge funds.9 The former explanation (an increase in hedge fund investment) is consistent with sophisticated investors adjusting the pricing of abnormal accruals, while the latter suggests the content of accruals may have changed.10

Second, several events in the early 2000s may have affected accrual pricing and, more specifically, abnormal accruals pricing. Perhaps the most significant regulatory change since the Securities Acts of the 1930s is the passage of SOX in 2002. Additionally, major accounting scandals in the early 2000s (e.g. WorldCom and Enron) may have raised public attention to opportunistic accounting and motivated managers to report less opportunistically (Cohen et al. 2008). Also, the United States Securities and Exchange Commission (SEC), the New York Stock Exchange (NYSE), and the National Association of Securities Dealers reached a legal settlement (i.e., the “Global Settlement”) with the ten largest U.S. investment banking firms, which may have also motivated less accounting opportunism. Additionally, existing research supports a change in financial reporting in the early 2000s, including more conservative earnings (Lobo and Zhou 2006) and less accruals-based earnings management (Cohen et al. 2008). Finally, research suggests an overall decline in earnings’ value relevance (e.g., Balachandran and Mohanram 2010; Brown et al. 1999; Collins et al. 1997). A decline in earnings’ value relevance could be due, in part, to a decline in the value relevance of abnormal accruals, or by less mispricing of abnormal accruals.

9 _{Green et al. (2011) also discuss a less powerful accruals “signal,” evidenced by a lower difference in persistence}

between cash flows and accruals and less extreme accruals; as an additional explanation for the accrual anomaly’s demise. However, as they note, their evidence regarding a change in the accruals signal is weak, particularly in their time-series analyses where the accruals signal variable does not attain statistical significance.

10 _{Richardson et al. (2010) also document a decline in accrual-anomaly based hedge returns. Specifically, intercepts}

in the Fama-French three-factor model are not reliably positive after 2002. Mohanram (2013) also documents a decline, though no elimination, of accrual anomaly returns in recent periods. He attributes the decline to an increasing number of analysts providing cash flow forecasts. This explanation is consistent with investors altering initial pricing of accruals given better information.

9 Given the evidence suggesting both a change in the value relevance of earnings (which includes abnormal accruals) and a decline in abnormal returns attributable to total accruals, we examine how the initial valuation and future price reversals of abnormal accruals vary over time.11 While the evidence in prior research suggests a decline in the negative association between current accruals and future returns (Green et al. 2011; Richardson et al. 2010; Mohanram 2013), their evidence does not answer whether (1) abnormal accrual pricing remains, and more importantly, (2) whether the relative contributions of mispricing and value relevance to the pricing of investors have changed. This is our second research question:

RQ2: How has the pricing of abnormal accruals and the contributions of value relevance and mispricing to the pricing of abnormal accruals changed over time?

We again stress that the evidence in Green et al. (2011), Richardson et al. (2010), and Mohanram (2013) does not answer this question. Prior research does not address whether investors alter initial pricing of accruals, whether the value relevance of abnormal accruals changes over time, or whether abnormal accruals remain priced at all. Regarding whether abnormal accruals remain priced at all, if (1) the mispricing of total accruals was due entirely (or mostly) to mispricing of abnormal accruals, (2) the pricing of abnormal accruals was due entirely (or mostly) to mispricing, and (3) mispricing of total accruals has dissipated, it is possible abnormal accruals are no longer priced at all. Our analyses can answer this (and other) questions.

We next explain how we measure the relative contributions of value relevance and mispricing to the pricing of abnormal accruals.

3. Measuring the Relative Contributions of Value Relevance and Mispricing

At the core of our approach is the simple notion that if abnormal accruals are initially mispriced, they will be related to future returns due to subsequent price correction. More specifically, prior research

11 _{We again stress that the results of this question are not obvious given evidence in Green et al. (2011), Richardson}

et al. (2010), or Mohanram (2013). While we are likely to find a reduction in the negative association between current abnormal accruals and future returns, the question of whether investors alter initial pricing, the value relevance of abnormal accruals changes, or any mispricing still exists remain unanswered.

10 suggests that accruals are initially overpriced (Sloan 1996; Xie 2001). That is, investors place too much pricing weight on accruals. For example, for each dollar of positive accruals, investors increase their estimates of future cash flows too much and consequently bid-up the price of the stock too far. Over time, as new information becomes available, investors slowly realize the price is too high and the price declines. Higher (more positive) accruals in period t lead to more contemporaneous stock overpricing and thus more price reversal in period t+s, where s is the period over which the price correction occurs. Therefore, if abnormal accruals are mispriced, we expect abnormal accruals in period t to be positively related to stock returns in period t and negatively related to stock returns in period t+s. We refer to the relation between period t abnormal accruals and period t stock returns as the ‘contemporaneous pricing’ of abnormal accruals, and we refer to the relation between period t abnormal accruals and period t+s stock returns as the ‘subsequent pricing’ of abnormal accruals.

Following extensive prior research (e.g., Subramanyam 1996; Xie 2001) we decompose earnings before extraordinary items (IBi,t) into cash flows from operations (OCFi,t) and accruals (ACCRi,t), and

accruals into normal accruals (NACi,t), and abnormal accruals (AACi,t). We obtain operating cash flows

from the statement of cash flows for post 1988-observations and estimate it from the balance sheet for periods prior to SFAS 95 (Hribar and Collins 2002). Total accruals is the difference between IBi,t and

OCFi,t. To estimate the normal and abnormal components of accruals, we follow Xie (2001) and use the

cross-sectional version of the Jones (1991) model, estimated within each year-industry combination with more than 12 observations, where industry is defined by two-digit SIC designation.12

12 _{The use of the Jones (1991) model to identify “discretionary” accruals is the subject of much debate. However,}

these debates most often focus on biases in earnings management tests (see, for example, Dechow et al. 2010). Whether we capture earnings management per se is not germane to our study. Rather, our intent is only to capture the component of accruals that is most mispriced as suggested by Xie (2001), and, given our results in Table 4, the Jones model successfully identifies this component.

11 To assess the contemporaneous pricing of abnormal accruals, we follow Subramanyam (1996). We regress (pooled time-series and cross-sectional) firm i's year t size-adjusted returns (SARi,t) on its year

t operating cash flows (OCFi,t), normal accruals (NACi,t), and abnormal accruals (AACi,t), as follows:

13

𝑆𝐴𝑅𝑖,𝑡= 𝛽0+ 𝛽1𝑂𝐶𝐹𝑖,𝑡+ 𝛽2𝑁𝐴𝐶𝑖,𝑡+ 𝛽3𝐴𝐴𝐶𝑖,𝑡+ 𝜖𝑖,𝑡 ₍₁₎

To measure firm i's period t returns, we compound monthly returns over the 12 months ending three months following the firm’s fiscal year end.14 To compute size-adjusted returns (SARi,t), we subtract

from firm i's raw return the return earned on the value-weighted portfolio consisting of the firms from the size decile to which firm i belongs. Size-decile assignments are based on CRSP designations at the beginning of the calendar year in which the return period begins.

Based on Subramanyam (1996), we expect β3 to be positive, implying that investors price

abnormal accruals.15 However, investors could price abnormal accruals in part because abnormal accruals provide value relevant information and in part because investors overvalue, i.e. misprice, them. If investors overvalue abnormal accruals, such overvaluation should reverse in future periods as new information becomes available. That is, overvaluation of abnormal accruals implies both a positive relation between current abnormal accruals and current returns, and a negative relation between future returns and current abnormal accruals. To assess the association between future returns and current abnormal accruals, we estimate the following pooled, cross-sectional regression:

𝑆𝐴𝑅𝑖,𝑡+𝑠= 𝜙0+ 𝜙1𝑂𝐶𝐹𝑖,𝑡+ 𝜙2𝑁𝐴𝐶𝑖,𝑡+ 𝜙3𝐴𝐴𝐶𝑖,𝑡+ 𝜏𝑖,𝑡 (2)

13 _{One departure from Subramanyam (1996) is that we use size adjusted returns while he uses raw returns. We use}

size adjusted returns because most accrual mispricing research (Xie 2001; e.g., Desai et al. 2004; Green et al. 2011), which post-dates Subramanyam (1996), uses size-adjusted returns when analyzing relations between current accruals and future returns. As we describe next, the relation between contemporaneous earnings and future returns is an important aspect of our design.

14 _{A 12-month return window is often used in both the value relevance literature (i.e. Subramanyam 1996) and}

accrual anomaly literature (i.e. Sloan 1996; Xie 2001).

15 _{To the extent investors form expectations about earnings prior to the start of our return accumulation period, our}

pricing coefficients, including β3, are biased towards zero. However, our return accumulation period (12 months

starting three months after the firms year t-1 fiscal year end) follows prior value relevance (i.e. Subramanyam 1996) and accrual anomaly research (i.e. Sloan 1996; Xie 2001). Further, our primary interest is in abnormal accruals, which are presumably devoid of an expected component. Nevertheless, we address the possibility of an expected component in abnormal accruals in Section 6.

12 SARi,t+s is the size-adjusted return for firm i over the one, two, or three year-period following year

t. If investors initially overvalue abnormal accruals and then reverse that pricing over the subsequent one to three years, we expect φ3 to be negative. Evidence from Sloan (1996) suggests initial mispricing is

corrected within three years. Therefore, we limit our subsequent return period to the three years following year t, but we also analyze subsequent periods of one and two years in case most of the initial mispricing reverses in less than three subsequent years. We estimate equations (1) and (2) as a stacked regression, which allows construction of value relevance ratios, discussed next.16

β3 measures the percent contemporaneous return per asset-scaled dollar of abnormal accruals, and

φ3 measures the reversal of that return through the period t+s.

17

Thus, the magnitudes of β3 and φ3 are

comparable. If the pricing of abnormal accruals is due entirely to mispricing, then φ3 should be equal in

magnitude (but of the opposite sign) to β3. If the pricing of abnormal accruals is due entirely to their

value relevance, then φ3 should be zero. Thus, (β3 + ϕ3)/β3 measures the percentage of abnormal accruals

pricing due to value relevance.18 We refer to this as the ‘value relevance ratio’, or the VRR. One minus the VRR measures the percentage of abnormal accruals pricing due to mispricing.

The VRR is a point estimate and, as such, has a variance (or second moment). However, the VRR is a nonlinear combination of two asymptotically normal random variables, and moments of nonlinear combinations of random variables often cannot be found via conventional methods because closed form solutions of their integrals and moment generating functions do not exist. However, provided finite moments exist and the sample size is sufficiently large, expected values and variances can be estimated via the delta-method.19 Estimates of the VRR’s expected value and variance allow us to test

16 _{Estimating the two models as a stacked regression yields identical coefficient and standard error estimates as}

estimating each equation independently.

17 _{Recall, we define s as the period over which price reversal occurs. Empirically, we assess returns in the one, two,}

and three year periods following the end of year t.

18 _{The VRR is undefined if the estimate of β}

3 is zero. However, given results from Subramanyam (1996), there is

little likelihood β3 is zero (or very close to zero), at least in the pre-SOX period. Nevertheless, we consider an

alternate method for assessing the significance of VRRs in Section 6.

13 whether the VRR is greater than zero and, separately, whether it is less than one. If it is significantly greater than zero, then we can conclude that the pricing of abnormal accruals is driven at least in part by communication of value relevant information. If the VRR is significantly less than one, then we can conclude that mispricing also contributes to the pricing of abnormal accruals. Additionally, an estimate of the VRR’s variance allows us to construct its confidence interval. We use the confidence interval to construct ‘conservative’ estimates of abnormal accruals pricing due to value relevance versus mispricing. If the left-hand side of the α-percent confidence interval for the VRR is L, we can conclude that the pricing of abnormal accruals is at least L percent due to their value relevance with 1-[(1-α)/2] percent confidence. This is a conservative estimate because the actual percentage of abnormal accruals pricing due to value relevance could be as high as the right-hand side of the confidence interval (with 1-[(1-α)/2] percent confidence). We construct conservative estimates of the percentage of abnormal accruals pricing due to mispricing analogously using the right-hand side of the VRR’s confidence interval. We set α equal to 0.8, which provides 90 percent confidence for our conservative estimates.20

For most of our analyses (exception explained below), we replace the earnings components in equations (1) and (2) with their predicted values from rank regressions. The procedure involves two stages. In the first stage, for each year, we rank each earnings component into 20 quantiles (i.e., vingtiles) and then regress each earnings component on its vingtile-rank (i.e., three regressions per year).21 We then obtain the predicted values from these regressions, denoted as OCF_Ri,t, NAC_Ri,t, and AAC_Ri,t. In the

second stage, we replace OCFi,t, NACi,t, and AACi,t with OCF_Ri,t, NAC_Ri,t, and AAC_Ri,t respectively, in

equations (1) and (2). We perform this transformation for two reasons. First, much of the mispricing literature analyzes future returns for portfolios formed based on accrual quantiles. Associating transformed-ranks with future returns as outlined in equation (2) parallels this approach. Second, using

20_{An α level of 0.80 leaves 0.10 in each tail of the distribution. Therefore, at the low (high) estimate of the VRR,}

we can conclude that 90 percent of the distribution is greater than (less than) this value.

21 _R2_{s from these regressions are generally above 80 percent. Increasing the number of quantiles beyond 20}

14 ranks instead of raw values mitigates the consequences of measurement error in our independent variables in equations (1) and (2) and reduces the influence of outliers, both of which are common issues in abnormal accrual estimation. While we winsorize variables used in abnormal accrual estimation, our ranking procedure further reduces the likelihood that outer tails of earnings component distributions unduly influence coefficient estimates. Using the predicted values (from regressions of the earnings components on their ranks) allows the coefficients in equations (1) and (2) to retain the same economic meaning as if one uses the original variables.22 Using separate yearly regressions (as opposed to a single pooled, cross-sectional regression) to obtain the predicted values retains some of the yearly variation in the distribution of each earnings component.

To assess changes in value relevance ratios over time, we consider two separate time periods. The first, 1973 to 2001, represents the pre-SOX period. The latter portion of our sample period, 2002 to 2008, captures the post-SOX period. As mentioned previously, we use the designations pre- and post-SOX for expositional convenience. As we explain previously, other important events occur near in time to SOX. While there are reasons to suspect that SOX plays a role in potential changes in abnormal accruals pricing, we recognize SOX is likely only a contributing factor. We estimate VRRs in both periods and provide pre- and post-SOX estimates of the pricing of abnormal accruals due to value relevance versus mispricing.23 To test for changes in mispricing from before SOX to after, we add an indicator, POSTt to

our equations, as well as an interaction between POSTt and each of the three earnings components. POSTt

equals one for observations from 2002 and later and zero otherwise. Specifically, we estimate the following equations as a stacked regression24:

22

See Biddle and Lindahl (1982).

23 _{In an untabulated analysis, we included a third time-period—the years between the publication of Sloan (1996)}

and the passage of SOX. We find no significant differences in either initial value relevance or future price correction for this period relative to the pre- Sloan (1996) period. Therefore, we limit further discussion to comparisons of the pre- and post-SOX periods.

24 _{While our interest is limited to the change in pricing of abnormal accruals, we include interactions with other}

15 𝑆𝐴𝑅𝑖,𝑡= 𝛽0+ 𝛽1𝑃𝑂𝑆𝑇𝑖,𝑡+ 𝛽2𝑂𝐶𝐹_𝑅𝑖,𝑡+ 𝛽3𝑃𝑂𝑆𝑇 × 𝑂𝐶𝐹_𝑅𝑖,𝑡+ 𝛽4𝑁𝐴𝐶_𝑅 𝑖,𝑡+ 𝛽5𝑃𝑂𝑆𝑇 ×

𝑁𝐴𝐶_𝑅𝑖,𝑡+ 𝛽6𝐴𝐴𝐶_𝑅𝑖,𝑡+ 𝛽7 𝑃𝑂𝑆𝑇 × 𝐴𝐴𝐶_𝑅𝑖,𝑡+ 𝜖𝑖,𝑡 (3)

𝑆𝐴𝑅𝑖,𝑡+𝑠= 𝜙0+ 𝜙1𝑃𝑂𝑆𝑇𝑖,𝑡+ 𝜙2𝑂𝐶𝐹_𝑅 𝑖,𝑡+ 𝜙3𝑃𝑂𝑆𝑇 × 𝑂𝐶𝐹_𝑅𝑖,𝑡+ 𝜙4𝑁𝐴𝐶_𝑅 𝑖,𝑡+

𝜙5𝑃𝑂𝑆𝑇 × 𝑁𝐴𝐶_𝑅 𝑖,𝑡+ 𝜙6𝐴𝐴𝐶_𝑅 𝑖,𝑡+ 𝜙7 𝑃𝑂𝑆𝑇 × 𝐴𝐴𝐶_𝑅 𝑖,𝑡+ 𝜏𝑖,𝑡 (4) A significant coefficient on the POSTi,t×AAC_Ri,t interaction (β7) in equation (5) implies a change

in initial valuation of abnormal accruals, while a significant interaction coefficient (ϕ7) in equation (6)

implies a change in price correction related to abnormal accruals. We compute the VRR for the pre-SOX period as described above, i.e. (β6 + φ6) / (β6). We compute the VRR for the post-SOX period as (β6 + β7 + φ6 + φ7) / (β6 + β7). The numerator represents the net effect of abnormal accruals on stock price persisting past year t+s in the post-SOX period, and the denominator captures the initial valuation. One benefit of our research design is that it simultaneously tests for both a change in initial valuation (β6) of abnormal accruals and for future price adjustment (φ6). Adjustments to contemporaneous valuation (β7)

suggest investor adjustment of abnormal accrual value relevance, which will also result in a change in price correction (φ7) since initial mispricing is reduced. Conversely, changes in the relation between

abnormal accruals and future returns (φ7) absent a change in contemporaneous valuation (β7) suggest a

change in the content of the accruals. In other words, if investors price abnormal accruals in the same way, but the initial pricing does not reverse, then abnormal accruals’ value relevance has improved.25 The results in Table 5 suggest that the value relevance of abnormal accruals has declined in the post-SOX period, which suggests β7 will be negative. Further, if the reduced value relevance of abnormal accruals leads to less mispricing, φ7 will be positive.

4. Empirical Results

4.1 Sample and Descriptive Statistics

To construct our sample, we collect returns data from the Center for Research in Security Prices (CRSP) from 1973 through 2011 and financial statement data from Compustat from 1973 through 2008.

16 We require sufficient balance sheet data to estimate the Jones model and consecutive returns for the 24-month period beginning nine 24-months prior to the fiscal year end. To reduce the number of extreme returns, we drop firms with stock prices less than one dollar, and, to avoid small denominator problems in deflated earnings components, we drop observations with less than five million dollars in total assets. Like Subramanyam (1996), we delete any observations more than three standard deviations away from the mean of any continuous variable to avoid undue influence from outliers in regressions. Consistent with the value relevance and accrual anomaly literature, we also drop firms in SIC codes 6000-6999 (financial services) and 4800-4999 (utilities). These data requirements and sample screens leave us with a sample of 62,280 firm-year observations comprised of 7,809 unique firms.

Table 1 reports descriptive statistics for our sample. In general, our sample firms are profitable, though mean earnings is slightly lower than that reported by Xie (2001) and Subramanyam (1996). Cash flows are virtually identical, and accruals are slightly more negative for our sample. Given our sample covers a more recent period than Xie (2001) and Subramanyam (1996), these results are not surprising. Over time, average Compustat firm size has declined, leading to a higher incidence of losses and thus lower earnings (Collins et al. 1997). The mean size-adjusted return for all windows is slightly negative. Finally, the time-period indicator variable reveals that approximately 74% of our sample is from prior to 2003 and 26% is from 2003 or later.

Table 2 contains select correlations of returns and earnings components. Consistent with prior research, we observe a negative correlation between accruals (both normal and abnormal) and operating cash flows (Dechow 1994; Desai et al. 2004). We also observe that cash flows are positively related to both current and future size-adjusted returns, while accruals are negatively related. We suspect the negative relation between normal and abnormal accruals and contemporaneous returns is primarily driven by the negative correlation between cash flows and accruals, highlighting the importance of including both earnings components in regressions of returns on earnings components.

17 4.2 Replication of Subramanyam (1996)

Before quantifying the relative contributions of value relevance and mispricing to the pricing of abnormal accruals, we first verify that we can replicate Subramanyam’s (1996) inferences. This replication is important because of some departures we employ relative to Subramanyam’s (1996) analysis. First, we use size-adjusted returns as our dependent variable to be consistent with the accrual anomaly literature, whereas Subramanyam (1996) uses raw returns.26 Second, we report standard errors clustered by firm and year (in this and all regressions) to correct for time-series and cross-sectional correlation in residuals (Petersen 2009; Cameron et al. 2011; Thompson 2011), whereas Subramanyam (1996) adjusts only for heteroscedastisity. As a result, our t-statistics tend to be lower than those in Subramanyam (1996). Third, our sample period extends through 2008, while Subramanyam’s (1996) sample period ends in 1993. Note that for the purposes of this replication, we follow Subramanyam (1996) and use the raw values of the earnings components instead of their rank-regression predicted values (i.e., we use OCFi,t, NACi,t, and AACi,t instead of OCF_Ri,t, NAC_Rit, and AAC_Ri,t).

Table 3 reports our replication of Subramanyam (1996) for our sample period. Consistent with prior research (Dechow 1994; Subramanyam 1996), comparing column 2 to column 1 suggests that earnings (IBi,t) are superior to cash flows at explaining contemporaneous returns (Z=5.47, p<0.001).

27 Non-discretionary net income (i.e., operating cash flows plus normal accruals, or NDNIi,t) also

outperforms cash flows (column 3 vs. 1; Z=9.43, p<0.001), though unlike in Subramanyam (1996), total earnings does not explain returns better than non-discretionary net income (column 2 vs. 3; Z=0.80, p=0.42). Adding accruals to cash flows adds significant explanatory power to operating cash flows (column 4 vs. 1; Z=11.98, p<0.001), and adding abnormal accruals to non-discretionary net income also yields significant improvement (column 6 vs. 3; Z=9.00, p<0.001). Finally, abnormal accruals add explanatory power beyond operating cash flows and normal accruals (column 7 vs. 5; Z=9.00, p<0.001).

26 _{Results (not tabulated) are nearly identical using raw returns.}

18 Additionally, column 7’s results reveal why total earnings do not explain returns better than non-discretionary net income (column 2 vs. 3). The valuation coefficients on normal accruals and operating cash flows are not significantly different from one another (untabulated F=0.26, p=0.61), but the coefficient on abnormal accruals is significantly less than that of operating cash flows and normal accruals. Therefore, although abnormal accruals are value relevant, their relevance is lower than the other two earnings components.28

In summary, we find abnormal accruals are priced in our sample and sample period, although we find pricing coefficients that are somewhat lower than in Subramanyam (1996). Therefore, we next attempt to quantify the relative contributions of value relevance and investor mispricing to the value relevance of abnormal accruals.

4.3 How Much of the Pricing of Abnormal Accruals is Due to Value Relevance and How much is due to Mispricing?

Table 4, Panel A reports results of estimating equations (1) and (2) simultaneously as a stacked regression. Columns 1 and 2 report coefficient estimates for the sample with one-year-ahead returns. Columns 3 and 4 (5 and 6) report estimates for observations with two-year-ahead (three-year-ahead) returns. Consistent with the results in Table 3, the scaled-ranks of each earnings component are positive and highly significant in all three contemporaneous returns models (columns 1, 3, and 5). Turning to the even-numbered columns, we find that abnormal accruals load negatively in two of three horizons. In the one-year ahead sample, the abnormal accruals coefficient (ϕ3) is negative, though insignificantly different

from zero (p=0.13). In the two-year ahead (three-year head) horizon, ϕ3 is significantly negative at the

p<0.05 (p<0.01) level. Therefore, it appears that at least a portion of the pricing of abnormal accruals can be attributed to investor fixation on earnings, leading to abnormal accrual mispricing.

28

We repeated the analysis in Table 3 after eliminating all observations from 1998 and later, so as to more closely correspond to Subramanyam’s (1996) sample period. These results (not tabulated) correspond even more closely to Subramanyam’s (1996). We discuss over-time changes in the pricing of accruals later.

19 Panel B of Table 4 reports VRRs for abnormal accruals for each of the three time horizons. In the one-year horizon, 76 percent of initial valuation persists and 24 percent reverses. As we extend the time horizon, the mispricing percentage increases to 37 percent for the two-year horizon, and 50 percent for the three-year horizon. However, standard errors for all three of these estimates are high, leading to relatively wide confidence intervals. Therefore, as mentioned previously, we test whether each ratio is significantly different from zero and from one.29 In all three horizons, we find that the VRR is significantly greater than zero (p<0.01), suggesting that at least some of the pricing of abnormal accruals is due to their value relevance. We also find that all three VRRs are less than one (p=0.11, p=0.01, and p<0.01 for one-, two-, and three-year), suggesting mispricing also plays a significant role in abnormal accruals pricing. In summary, our evidence suggests that, for our sample period as a whole, the pricing of abnormal accruals is due to both value relevance and mispricing. Based on the three-year horizon, it appears value relevance and mispricing play roughly equal roles.

Turning briefly to the other earnings components, we find that normal accruals are generally not associated with future returns, consistent with the hedge return results in Xie (2001). Conversely, operating cash flows load significantly positively in all three future return horizons suggesting cash flow underpricing, consistent with evidence in Sloan (1996) and Xie (2001). While we include cash flows in all remaining analyses to avoid a correlated omitted variable problem (cash flows are correlated with both normal and abnormal accruals), we refrain from further discussion of operating cash flow mispricing.

In summary, our full sample-period results suggest that the pricing of abnormal accruals is due partly to their value relevance and partly to mispricing. More importantly, our point estimates (based on a three-year future return horizon) suggest that the relative contributions of value relevance and mispricing are approximately equal. These results suggest that mispricing identified in Xie (2001) plays a significant role in abnormal accruals ability to improve upon non-discretionary earnings as a measure of firm value

20 (Subramanyam 1996). However, as we show in the next section, these point estimates vary considerable by time-period.

4.4 Changes in Value Relevance Ratios over Time

Before assessing how VRRs change over time, we first repeat Subramanyam’s (1996) analysis on the post-SOX period (2002-2008) to determine whether abnormal accruals remain priced in the period associated with the demise of the accrual anomaly (Green et al. 2011; Richardson et al. 2010). If abnormal accruals were previously priced primarily because of mispricing (we note our earlier evidence suggests about 50 percent of abnormal accruals pricing due to mispricing) and the accrual anomaly is mostly driven by abnormal accruals (Xie 2001), the demise of the accrual anomaly could imply abnormal accruals are no longer priced at levels that are statistically detectable. Table 5 presents these results. Unlike in Table 3, the univariate models (columns 1 through 3) generally reveal modest to insignificant differences in explanatory power of cash flows, earnings, or non-discretionary earnings. However, the final four columns in Table 5 show that allowing the valuation coefficients of each earnings component to vary yields significant improvements in explanatory power, suggesting that all three earnings components are value relevant, albeit at lower levels than in earlier periods, and that these components are differentially priced by investors. Most importantly, adding abnormal accruals to non-discretionary net income significantly improves explanatory power, as the difference between columns 3 and 6 is significant (Z=3.850, p<0.01). Similarly, adding abnormal accruals to the separate components of non-discretionary net income (cash flows and normal accruals) yields a significant increase in explanatory power (column 7 versus 5; Z=3.702, p<0.01).

Given abnormal accruals remain value relevant, we next examine how abnormal accrual mispricing varies over time. Table 6 presents results from estimating equations (3) and (4). As in Table 4, the coefficient on AAC_Ri,t is significantly positive. We find limited evidence that the association

21 marginally significant (the largest t-statistic in magnitude is -1.29 in the 2-year horizon). Therefore, we find little evidence of a change in abnormal accruals pricing from pre- to post-SOX.

In contrast, the subsequent pricing models, reported in columns 2, 4, and 6 in Table 6 provide rather compelling evidence that mispricing changes after SOX. As in Table 4, the coefficient on AAC_Ri,t

is highly significant in the two- and three-year ahead horizons. Furthermore, the coefficient on the interaction term POSTi,t×AAC_Ri,t (ϕ7) is positive and highly significant in both the two- and three-year

ahead horizons, suggesting a reduction in price correction following SOX. In addition, in an untabulated test, we are unable to reject the hypothesis that φ6 + φ7 equals zero in any horizon (p>0.10). In other words, we find little if any evidence of abnormal accrual mispricing post-SOX.

In panel B of Table 6, we compute VRRs for the pre- and post-SOX periods. Point estimates for the pre-SOX VRRs for all three horizons are lower than their Table 4 counterparts. In fact, by the end of year t+3, 63 percent (1-0.37) of abnormal accruals valuation reverses, suggesting the majority of pre-SOX abnormal accruals pricing is attributable to mispricing. In addition to reporting point estimates for the pre-SOX VRRs, we also report conservative estimates, computed as described in Section 3. For the three-year horizon, the conservative VRR estimate is 0.584.30 Recall that the conservative estimate reflects the 90th percentile of the underlying pre-SOX VRR distribution. In other words, we conclude with 90 percent confidence that no more than 58 percent of pre-SOX abnormal accruals pricing results from value relevance. We also test whether the pre-SOX VRR is significantly different from zero and one for each of the three return horizons. As in Table 4, we reject the null in all cases, suggesting that value relevance does play a role in pre-SOX abnormal accruals pricing, albeit less so than our earlier, full-sample-period results implied.

The post-SOX VRRs reveal a strikingly different picture. Point estimates range from 0.965 to 1.424, the latter of which suggests abnormal accruals are actually underpriced. However, in all three

30 _{The conservative estimate equals 0.371+1.288*0.165, where 0.371 is the point estimate of the pre-SOX VRR,}

22 horizons we cannot conclude that the post-SOX VRRs are significantly different from one (p-values are between 0.94 and 0.34). In other words, our evidence suggests that, post-SOX, abnormal accruals pricing is entirely due to their value relevance, and there is no contribution from mispricing. Panel B of Table 6 also displays conservative VRR estimates for the post-SOX period. Because our evidence suggests post-SOX abnormal accruals pricing is driven mostly by value relevance, we construct our conservative estimates so that they reflect the minimum percentage value relevance. These conservative estimates are 0.40, 0.93, and 0.85 for one-, two-, and three-year future returns, respectively.31 For example, based on the three-year future returns, we can conclude with 90 percent confidence that mispricing accounts for no more than 15 percent of abnormal accruals pricing in the post-SOX period.32 Finally, for each horizon we test whether the pre-SOX VRR is significantly different than the post-SOX VRR. For the two- (three-) year ahead models, we reject the hypothesis that the two VRRs are equal at the p=0.02 (p=0.03) level.33 In summary, our evidence suggests that until 2002, a large percentage, in fact a majority, of abnormal accruals valuation was due to mispricing. However, in the post-SOX era, nearly all mispricing of abnormal accruals dissipates, and we cannot reject the hypothesis that value relevance accounts for all of abnormal accruals pricing.

Our Table 6 results complement evidence in Green et al. (2011), Richardson et al. (2010), and Mohanram (2013) suggesting a decline in total accrual mispricing. We extend this evidence to abnormal accruals. The combination of a decline in total accrual mispricing and evidence that abnormal accruals

31 _{Compared to their pre-SOX counterparts, standard errors for post-SOX VRRs are notably higher. Some of this}

increase may be due to the fact that we cluster standard errors by year (and firm), and there are only 7 clusters in the post-SOX period (years 2002 to 2008). Clustering standard errors yields unbiased standard error estimates only when there are a sufficient number of clusters (Petersen 2009; Thompson 2011). Since there are only 7 years (clusters) in the post-SOX period, clustering may actually inflate standard errors. In untabulated analysis, we re-estimate Table 6 clustering by firm only and find more stable re-estimates. Using this standard error correction, post-SOX conservative VRR estimates are 79.5 percent, 108.4 percent, and 102.5 percent for one-, two-, and three-year ahead horizons, respectively.

32 _{The post-SOX conservative estimates reflect the tenth percentile of the VRR distribution. For example, the}

three-year conservative estimate of 0.851 equals 1.424-1.288*0.445.

33

We find no significant difference in pre- and post-SOX VRRs in the one-year horizon. This result is not surprising given the fact that the main effect of AAC_R is insignificant in the one-year ahead horizon in Table 4 and Table 6.

23 were mispriced (Xie 2001) suggests the possibility that abnormal accruals are no longer priced. However, we find that abnormal accruals are still priced. More importantly, we conclude that the post-SOX pricing of abnormal accruals is due mainly to value relevance, while their pre-SOX pricing was due mainly to mispricing. Further, because we find little or no change in the initial pricing of abnormal accruals combined with little reversal in that pricing, our results are consistent with the notion that abnormal accruals are more value relevant after SOX. We explore this topic further in the next section.

5. Explanations for the Increased Contribution of Value Relevance to Abnormal Accrual Pricing In our next analyses, we explore why mispricing contributes less, and value relevance more, to the pricing of abnormal accruals post-SOX. A shift in the contributions of value relevance and mispricing can occur for at least three reasons. First, investors may have changed the way they initially value abnormal accruals, placing less valuation weight on them so that there is less correction in future periods. We note that Tables 6 and 7 address the first possibility. For example, in Panel A of Table 6, the coefficient on POSTi,t ×AAC_Ri,t is negative, though insignificantly different from zero, when

contemporaneous return is the dependent variable (column (1)). This suggests minimal change in the initial valuation of abnormal accruals from the pre- to the post-SOX period. Thus, our evidence is not consistent with the notion that the decline in the contribution of mispricing to the pricing of abnormal accruals is due to a change in investors’ initial valuation of abnormal accruals.

A second, and closely related, potential explanation is that the initial mispricing is (relatively) quickly arbitraged away.34 Green et al. (2011) find that returns to extreme accruals portfolios decline as hedge fund activity increases over time. They conclude that hedge funds have arbitraged away the accrual anomaly. Arbitrage activity by hedge funds could explain the increase in VRRs we document if hedge funds arbitrage away initial mispricing before the beginning of our future return period (four

34 _{In the limit, the arbitrage explanation is identical to a change in how investors initially price abnormal accruals.}

In other words, an instantaneous arbitrage-induced correction is no different than no mispricing. We describe them separately because the correction is not necessarily instantaneous and because the arbitrage explanation is explicitly discussed and measured in prior research (Green et al. 2011).

24 months after the fiscal year end). Specifically, arbitrage activity would reduce contemporaneous abnormal accrual pricing, which is the denominator of the VRR.

Finally, the quality of abnormal accruals may have improved such that investors’ initial valuations are closer to “correct”. That is, perhaps abnormal accruals map better to past, present, and future cash flows. To test this conjecture, we estimate a yearly measure of accruals quality based on two common proxies for accruals quality—the Dechow-Dichev model from Dechow and Dichev (2002), and the Dechow-Dichev model as modified by McNichols (2002). Specifically, we estimate these two models within each year and 2-digit SIC industry with at least 15 observations and obtain residuals for each firm-year observation. We then compute the standard deviation of residuals for each firm-year in our sample and use this as a measure of average accruals quality.

Panel A of Figure 1 plots the standard deviation of residuals of both the original and modified Dechow-Dichev models over our sample period. Note that our measure of accruals quality is inversely measured—that is, years with higher standard deviations reflect poorer accruals quality, as less of the accruals in that year are explained by past, current, and future cash flows. This plot suggests that accruals quality declines from the beginning of our sample period until 2001 to 2002, where there is a sharp improvement. This improvement lasts for several years until the financial crisis in 2008.

Interestingly, while accruals quality improves post-SOX, it is still not as good as in the earliest years of our sample period. Both measures of accruals quality suggest that the post-SOX level is roughly equivalent to accruals quality in the mid to late 1980s, a period that exhibits significant accrual anomaly hedge returns. However, prior research (e.g., Francis et al. 2005) suggests cash flow volatility and Dechow-Dichev accrual quality are related.35 Therefore, we control for the change in cash flow volatility over time by regressing the yearly accruals quality measures on the standard deviation of operating cash flows for that year. For both accrual quality measures, we find that cash flow volatility explains 80 to

35 _{Specifically, Francis et al. (2005) include firm-specific cash flow volatility when estimating the innate component}

25 90% of variation in annual accruals quality. We then obtain the residual from this regression and use that as a measure of average accrual quality purged of the effects of cash flow volatility. Positive (negative) residuals imply accruals quality is poorer (better) than expected given cash flow volatility.

Panel B of Figure 1 plots these residuals. Before SOX, the plot oscillates between positive and negative values with no apparent pattern, though the residuals from the early 80s to late 90s are mostly positive, suggesting accruals quality in that period was worse than expected based on cash flow volatility. Around the passage of SOX, the plot drops and remains negative until 2008-2009. The series of negative residuals suggests that accruals quality is better in the post-SOX period than expected given cash flow volatility. To assess the significance of this improvement, we test whether the mean of post-SOX residuals is less (more negative) than the pre-SOX mean. Despite the small sample size, we reject the null hypothesis that the two period means are equal at the p<0.01 level. Overall, our evidence suggests an improvement in accruals quality post-SOX.

These trends indirectly suggest that accruals quality improvement plays a role in the decline in abnormal accrual mispricing. To provide direct evidence regarding a potential association between the increase in accruals quality and the decline in abnormal accruals mispricing, we utilize a regression approach similar to Green et al. (2011). Specifically, we estimate equations (1) and (2) as a stacked regression for each year in our sample to obtain yearly estimates of VRRs. These yearly VRR estimates are somewhat volatile, so we rank them from one to 36. We then estimate various iterations of the following equation:

𝑉𝑅𝑅_𝑅𝑎𝑛𝑘𝑡= 𝛽0+ 𝛽1𝑇𝑅𝐸𝑁𝐷𝑡+ 𝛽2𝐴𝑄𝑡+ 𝛽3𝐶𝐹𝑂𝑉𝑂𝐿𝑡+ 𝛽4𝐴𝑈𝑀𝑡

+𝛽5𝑃𝑅𝐼𝐶𝐸𝑡+ 𝜖𝑡 (5)

VRR_Rankt is the rank of the annual VRR estimate. Higher values indicate a higher contribution

of value relevance relative to mispricing. TRENDt is defined as year minus 1973 and controls for the

over-time trend in VRRs suggested by results in Tables 6 and 7. We expect β1 to be positive. AQt is the

cross-sectional standard deviation of firm residuals obtained from the modified Dechow-Dichev model of accruals quality estimated by year and industry. AQt corresponds to the values plotted in Figure 1. We

26 multiply AQt by negative one so that it is increasing in quality. CFOVOLt is the standard deviation of

operating cash flows scaled by assets for each year in our sample.36 We standardize all independent variables to have means (standard deviations) of zero (one) to facilitate the comparison of coefficients. This standardization allows us to interpret coefficients as the change in VRR-rank attributable to a one-standard deviation change in each independent variable.

Green et al. (2011) find that hedge fund activity and share price levels help explain the decline in future returns that can be earned via the accrual anomaly. Accordingly, we include AUMt and PRICEt in

equation (5). AUM is the natural log of assets under management by hedge funds employing a long-short strategy. We obtain AUMt from Figure 3 in Green et al. (2011). Note that this hedge fund data is only

available after 1988. However, hedge fund activity was relatively non-existent prior to this year (Fung and Hsieh 1999). Therefore, we set AUMt to zero for these years, but we also estimate equation (5) using

only post-1988 years to ensure missing data does not affect our results. Results in Green et al. (2011) suggest that AUMt should be positively associated with VRR_Rankt. PRICEt is the natural log of the

average price of stocks in the outer two deciles of the abnormal accrual distribution. PRICEt inversely

proxies for transaction costs, as these costs are lower on a per trade basis for higher priced stocks.37 Opposite their predictions, Green et al. (2011) find PRICEt is positively associated with accrual-anomaly

returns, suggesting it should be negatively associated with VRR_Rankt.

38

Panel A of Table 7 reports results from estimating various iterations of equation (5) for the full sample period (1973 to 2008). The positive and significant (p<0.01) TRENDt coefficient in Column (1)

36

We include CFOVOL as a separate control variable rather than use the residual from regressing yearly accruals quality on cash flow volatility, as plotted in Panel B of Figure 1 for two reasons. First, it is more econometrically efficient. Second, this approach controls for any correlation between CFOVOL and other independent variables.

37 _{We do not consider the strength of the accruals signal as a third factor because Green et al. (2011) fail to find their}

proxy for the accruals signal has significant explanatory power in their time-series analysis. Their time-series analysis is analogous to our analysis.

38 _{Mohanram (2013) suggests that increasing levels of cash flow forecasting by analysts also contributes to the}

weakening of accrual anomaly returns. In untabulated analysis, we include the natural log of the number of cash flow forecasts issued per year, obtained from Panel A of Table 2 of his paper. This variable fails to produce a statistically significant positive test statistic in any specification and does not have any material impact on the results discussed here.

27 confirms the positive trend in VRRs. Column (2) of Table 8 introduces the variables from Green et al. (2011) that help explain returns earned via the accrual anomaly. Coefficients on both AUMt and PRICEt

are insignificantly different from zero (p>0.10). In column (3), we replace AUMtand PRICEt with AQt

and CFOVOLt. We find a significantly positive coefficient on AQt (p<0.01), suggesting changes in

accruals quality help explain the increase in value relevance ratio. In column (4), we include all four determinants (AQt, CFOVOLt, AUMt, and PRICEt) and TRENDt. AQt remains significantly positive

(p<0.01), though none of the other variables produce coefficients different from zero. We test the difference between the coefficient on AQt(β2) and AUMt (β4) and find the AQt coefficient is marginally

(p=0.07) greater than the AUMt coefficient. However, given the strong over-time trends in all four

variables, we examine variance inflation factors (VIFs), and find that the VIF on TRENDt is over 25. This

elevated VIF could lead to inflated standard errors, leading to a loss in significance on AUMt (and other

variables). Consistent with this possibility, we find that, after dropping TRENDt (column 5), the

coefficient on AUMt is significantly positive, and the difference between AQt and AUMt is no longer

significant (p>0.10). In sum, our results suggest that the quality of accruals plays an important role in the increase in the contribution of value relevance to abnormal accrual pricing over time, and that this role is at least as important as increases in hedge fund activity.

Panel B of Table 7 reports results analogous to Panel A, but we limit the sample to 1988-2008 (years with non-zero AUMt values). W re-rank the VRRs for the 1988-2008 period so that VRR_Rankt

varies between one and 21. In general, results are similar to Panel A. Both AQt and AUMt significantly

contribute to the increase in the degree to which value relevance explains abnormal accrual pricing. However, in column 9, we find that the magnitude of the coefficient on AUMt (β4=21.79) far exceeds the magnitude on AQt’s coefficient (β2=3.32), and this difference is highly significant (p<0.01). However, the coefficient on AUMt should be interpreted with caution, as we again observe very high multi-collinearity

(VIFs exceeding 50), likely due to the fact that AUMt and TRENDt exhibit near perfect collinearity

28 we remove TRENDt and find the coefficient on AUMt (β4) drops to 6.54 but it is still significantly greater than the AQt coefficient.(p=0.05).

While the results in Panel B of Table 8 suggest that AUMt may be more important than AQin

explaining the post-2001 increase in the contribution of value relevance to abnormal accruals pricing, we note a research design choice that potentially affects this inference. As mentioned previously, we follow Green et al. (2011) and use the natural log of hedge fund assets under management. The natural log transformation corrects for skewness in non-normal random variables but also reduces the magnitude of variation in the variable. In other words, the likelihood of observing a one-standard-deviation shift in the logged version of AUMt is much lower than observing the same shift in the unlogged version. Consistent

with this notion, we find that the average, absolute change from t-1 to t in AUMt is less than 14 percent of

one standard deviation.39 Conversely, the absolute change in AQt from t-1 to t averages nearly 60 percent

of one standard deviation.40 In other words, the observed year-over-year variation within the distribution of AQt exceeds that of AUMt by a factor of four. Further, and consistent with the idea that logging assets

under management attenuates variation, we find AQt is at least as important as AUMt in explaining

over-time change in VRRs when we use the unlogged version of AUMt in the 1988-2008 sample period

(untabulated).