An Analysis of the Sources of Value Loss Following Financial Restatements

Keejae P. Hong†
Belk College of Business
The University of North Carolina at Charlotte
khong5@uncc.edu

Jaywon Lee
College of Business
Korea Advanced Institute of Science and Technology
jaywonlee@kaist.ac.kr

Sang-Hyun (Sam) Park
Knox School of Accountancy
Augusta University
sapark@augusta.edu

Sukesh Patro
College of BusinessNorthern Illinois University
spatro@niu.edu

November 2017_________________________________†

Corresponding Author. Keejae P. Hong is grateful for the financial support from the Childress-Klein Faculty Scholars
Program through the Belk College of Business, University of North Carolina at Charlotte. Sukesh Patro is grateful for
financial support from the Summer Research Grant Program at the College of Business, Northern Illinois University.

An Analysis of the Sources of Value Loss Following Financial Restatements
Abstract
We decompose the total value loss around firms’ announcements of financial restatements into
components arising from investors’ revisions in cash flows and discount rates. While we findsignificant contributions from both sources, the impact of revisions in the discount rate is still moresignificant, explaining over 66% of the variation in stock returns surrounding restatement
announcements. For restatements caused by financial fraud, the discount rate impact is much more
important than the cash flow impact, explaining about 88% of return variation. Similarly, thediscount rate impact is larger for firms with lower earnings persistence. Our decomposition of thevalue loss helps explain returns in the post-announcement period. Firms with a higher relative
discount rate impact experience a significant downward stock price drift after the initial
announcement-related price decline. For firms with a higher relative cash flow impact, the initial
impact of the restatement announcement is long-lasting. Our findings close gaps in the evidence
on financial restatements, extend the literature on the drivers of stock price movements and informthe research on the value relevance of earnings.

1

An Analysis of the Sources of Value Loss Following Financial Restatements
1. Introduction
This study examines the underlying sources of declines in firm value following financial
restatements, with the aim of estimating the relative contributions of value loss from such sources,
and understanding whether and how post-restatement stock returns are affected by investors’ initial
reactions to restatements. 1 The sharp rise in financial restatements in the new millennium has
shaken investor confidence in the corporate financial reporting system (GAO 2002; 2006). The
annual frequency of restatements by US companies reporting to the Securities and Exchange
Commission (SEC) peaked at nearly 1,850 in 2006, declining thereafter to around 900 in 2012
(Murphy 2014). Since the first listing of restatement firms published by the Government
Accountability Office in 2002 (GAO 2002), academic research has provided consistent evidenceof a significant negative stock price reaction associated with restatements. For instance, early workfinds that short window cumulative average abnormal returns surrounding the restatement
announcement range from -6% (Dechow et al. 1996) to -10% (GAO 2003, Palmrose et al. 2004).
In subsequent studies, researchers have examined changes in specific components of the firm
valuation model, i.e., projections of the firm’s future cash flows or the discount rate used to value
these cash flows (Hribar and Jenkins 2004). However, empirical evidence on the linkages between
these valuation components to the announcement value decline is limited.
The various factors that contribute to the value change, typically negative, to financial
restatements can be grouped into two main sources. First, restatements affect investors’ priors
about the firm’s ability to generate or sustain future cash flows. The resulting change in value

Restatements are defined “as corrections of accounting misstatements made previously by negligent, or in theextreme, opportunistic managers” (Baber et al. 2013). A restatement can be initiated by firms, auditors or regulators(SEC).
12

could be positive or negative depending on the direction of the restatement. Second, restatements
create incremental uncertainty about the quality of the firm’s earnings, which escalates thediscount rate and causes a decline in firm value.2 Here, it is more likely that the impact on value isnegative. Prior studies examine each of these causes on a standalone basis and provide someevidence that suggests they are both significant contributors to the decline in firm value. While it
is intuitive that restatements influence each of the cash flow and discount rate components of thefirm valuation function, what is missing in the literature is a joint examination of both the sourcesof stock price declines. Specifically, no prior study has examined the relative importance of thetwo sources of stock price declines at restatement announcements. In this study, we undertake suchan examination by decomposing the total restatement-related value loss that the firm experiences
into a cash flow-related component and a discount rate-related component.
Such a decomposition, we believe is important for several reasons. First, quite simply, sucha decomposition enables a direct comparison of the loss in value from each source. Not only is thisof interest to researchers, but also practitioners because the challenge to managers of effectingchanges in the cash flows of the firm is significantly different from the challenge of effectingchanges in the discount rate of the firm. Whereas the former is in large part a result of managerial
effort, the latter is heavily influenced not only by investor perception of the business risk of thefirm but also by investor perception of the quality of firm management and the risks thereof.
Second, related to the preceding point, the comparative challenge of tackling the value loss due toeach of cash flow and discount rate revisions is likely to be different for different kinds of firms. 3
Third, by addressing these questions it is also possible to shed incremental light on a fundamental

In this paper, we use the terms “discount rate”, “cost of equity”, “cost of equity capital”, “implied cost of equity”
and “cost of capital” interchangeably.
3
For example, firms with high earnings persistence will likely find it harder to recover from a restatement that results
in a bigger impact on value arising from changes in the discount rate.
23

question in the finance and accounting literature – are stock prices driven primarily by cash flow
news or discount rate news (Campbell and Shiller 1988a)? 4 Finally, one advantage of our analyses
is that we utilize a large sample of restatements to provide a comprehensive documentation of thelinks between the change in valuation of the restating firm and the extent to which it is driven bycash flow and discount rate changes. While this is an important issue, as discussed above, theexisting empirical evidence on this is limited.
To examine the variation in stock price changes surrounding financial restatement
announcements, we rely on the valuation frameworks in Chen et al. (2013) and Da et al. (2016) tofirst express a firm’s stock price as a function of its discount rate and future cash flows. We thendecompose stock price changes into components that can be attributed to cash flow revisions anddiscount flow revisions. Cash flow changes are estimated as the changes in the analyst consensus
estimate of EPS across the restatement announcement. Revisions in the discount rate are measured
by estimating the implied cost of equity from the Claus and Thomas (2001) model using analysts
EPS forecasts and stock prices, both, before and after the restatement announcement. 5 Following
Chen et al. (2013) and Da et al. (2016), we use the estimated revisions in each of the earnings
forecasts and implied cost of equity in a variance decomposition framework that decomposes thetotal change in the stock price across the restatement into components attributable to each of theearnings and cost of equity revisions. By construction, the variance decomposition constrains thetotal variation in stock prices to be apportioned to one of the two components. This variancedecomposition is, in principle, similar to the return decomposition of Campbell and Shiller (1988a;

4

See also Campbell and Shiller (1988b; 2001), Cochrane (1992; 2008), Campbell and Ammer (1993), Ang (2002)
and Vuoltennaho (2002) among many others. “News” is a commonly used term in the finance literature to refer tochanges in expectations. For example, cash flow news means changes in investor’s cash flow expectations.
5
We use the stock price and the cash flow estimate before the restatement announcement for the pre-implied cost ofequity and the corresponding values after the restatement announcement for the post-implied cost of equity.

4

1988b) and Vuolteenaho (2002).6
We use a sample of over 1,800 restatements drawn from the Audit Analytics database forour analysis. Our findings are as follows. We find that approximately 33.5% of the variation instock price changes across restatements is attributable to revisions in the future earnings of thefirm with the remaining 66.5% attributable to revisions in its implied cost of equity. Compared toonly 12.9% for this component for the entire population, on average, the importance of cash flow
news in explaining changes in valuation is much higher in the restatement sample. We also findthat the restatement type is related to the extent to which it explains the change in stock values.
We partition the restatement firms into two groups: firms whose initial (3-day) returns is negative[Negative BHAR(-1,1)] vs. positive [Positive BHAR(-1,1)] restatement subsamples. We
document that the variation in stock prices is driven by revisions in future earnings (about 30%)and by revisions in implied cost of equity (about 70%) for both Negative and Positive BHAR(-1,1)
restatement subsamples. However, two subsamples show quite different patterns in terms of themagnitude of changes in stock prices driven by each component. For example, the one-monthaverage stock returns for the Negative BHAR(-1,1) group is -4.9%, of which -1.2% is driven by
the investors’ revisions in future earnings and -3.7% is driven by the revisions in its implied costof equity. On the other hand, for the Positive BHAR(-1,1) subsample, the total stock price increaseof 3.9% is mainly attributable to expectation changes in future earnings (4.6%), but very little isdriven by changes in its implied cost of equity.
To better understand the relative importance of cash flow news versus discount rate news
implications, we partition the restatement firms based on the underlying cause of the restatement:

6

However, while the traditional return decomposition relies on vector autoregression methods to estimate market
expectations, the method adopted in this paper utilizes forecasts made by analysts as an input to a return decomposition.
See Chen and Zhao (2009) for arguments on why this is a preferred method.

51) accounting rule application failures, 2) financial fraud, 3) errors, and 4) others. Because
accounting rule application failures account occur in over 90% of total restatements, the relative
importance of cash flow and discount rate components for this type of restatement is similar to thatof the full sample. However, when the restatement is a result of an error we find that the componentof value loss due to cash flow revisions is relatively higher, accounting for about 60% of the valuechange. This is consistent with the interpretation that investors indeed view such restatements as
mainly arising out of errors and imposing a smaller increase in the cost of capital of the firm. By
contrast, for restatements due to financial fraud changes in the cost of equity capital explain asignificantly larger portion of the change in value (88%). As investors’ weighting of cash flow
news (relative to news related to the firm’s discount rate) is highly dependent on the persistenceof earnings (Brav and Heaton 2002 and Francis et al. 2007), we also examine subsamples of firms
with high and low earnings persistence. We find that for subsample of firms whose earnings
persistency is lower, the discount rate related component of the value loss is significantly larger.
Thus, our results that examine the cross-section of the decomposition of the changes in value acrossfinancial restatements help quantify the relative importance of revisions in the cost of equity madeby investors and highlight the kinds of restatements where stock valuations are more susceptible
to the impact of cash flow revisions relative to the impact of discount rate revisions.
We next turn to an examination of how the relative impact of the cash flow versus cost ofequity-related components of the value loss at the announcement explains post-restatement
announcement stock returns of restating firms. On average, buy-and-hold returns adjusted for risk
following Daniel et al. (1997) show that stock prices continue to drift downward up to one year
after the restatement. More interestingly, we find that such a downward drift is more pronounced
among the firms whose stock price decline around the restatement announcement is driven more6

by discount rate revisions, but not by cash flow revisions. These firms have a mean negative buyand-hold abnormal return of approximately -4.7% in the subsequent 252-day period. By contrast,
firms with above-median cash flow-related components of value loss remain relatively stable over
the year with a mean buy-and-hold abnormal return of about 0.9% at the end of the 252-day period.
In subsample analysis, we observe the downward drift of stock prices in both Negative and Positive
BHAR (-1,1) restatement firms. These results suggest that value losses from cash flow revisions
are relatively immediate and complete compared to value losses from cost of equity revisions,which seem to be realized relatively more in the long term. Additional tests rule out the possibility
that this pattern in the post-announcement returns of restating firms is driven by firm risk, bookto-market ratios, leverage, beta, momentum or accruals.
We subject our analysis to several tests of robustness. Because our estimation of earningsand cost of equity-related components of value loss uses revisions made by analysts in theirconsensus EPS forecasts that straddle the restatement announcement, we check the robustness of
our results in this regard. Specifically, our results presented above use analyst consensus forecastsof EPS separated by approximately one month. To better account for the impact of the restatement,
we allow analysts more time to react and make sure that stale forecasts are eliminated from theconsensus by using post-restatement forecasts at least one month after the announcement, i.e.,
separated by approximately a total of two months. We find that our decomposition returns andpost-announcement return results are similar. When we drop potentially stale earnings forecasts(i.e. where the earnings forecast remains unchanged) from the sample, we find a small increase in
the value loss explained by the revision in cash flow forecasts to 38.5%. In our main analysis, we
use the valuation model from Claus and Thomas (2001), which helps mitigate measurement error
issues in estimating the implied cost of equity (Da et al. 2016). However, because our analysis

7hinges crucially on the valuation model used to estimate the implicit cost of equity and changes
thereof, we re-estimate our results with alternative valuation models from Pastor et al. (2008). We
find that our results are robust to this change in estimation.
Overall, the findings of this paper extend the research that examines financial restatementsby empirically formalizing the links between firms’ value losses around financial restatements andthe sources of such losses. While prior work has examined earnings and discount rate impacts
around restatements, the analysis of these factors has been performed separately with the resultthat evidence on their linkages to the decline in firm value is limited. Further, because substantial
seminal work in this area was undertaken soon after the GAO’s (2002) publication of the list ofrestating firms, sample sizes in these studies are relatively small compared to the explosive growthin the number of restating firms since then. This study establishes the links between the firm’s loss
in value and the sources of this loss within a unified valuation framework using a much larger
sample of restating firms.
Our findings also inform the research that examines the drivers of stock price movements.
In a summary of prior work, Cochrane (2011) concludes that much of the variation in stock prices
is driven by discount rate news. In recent work, Chen et al. (2013) document the existence of asignificant cash flow component in the drivers of stock price movements. We extend this literatureby examining significant event-related movements in stock prices – financial restatements arewidely acknowledged to affect both cash flow and discount rate aspects of valuation and are thus
ideally suited for the purpose. Consistent with Chen et al. (2013), our results suggest the existenceof a significant cash flow component that explains stock price declines around restatements.
However, also consistent with prior work, our results show that discount rate revisions are
generally the more important driver, especially over shorter horizons. Further, our results suggest8that investors make significantly larger revisions in discount rates when it is less than completely
clear that the reason for the restatement is an inadvertent error. These results contribute to theextensive and important literature that examines the value relevance of earnings.
Finally, our variance decomposition of restatement-related value declines helps explain
differences in the post-restatement stock performance of restating firms. Specifically, the results
show that the valuation impact of discount rate revisions around restatements is relatively slower
than the impact of cash flow revisions, with the latter firms experiencing a significant downward
drift in prices in the year after the restatement announcement. The resulting return difference
between these two groups is economically significant. These results help provide insight into theprocess by which investors revise their stock valuations around restatements. Combined with theproportion of announcement return variation explained by discount rate revisions, these results
help quantify the importance of investors’ risk perceptions of firms surrounding earnings
restatements.
An important caveat is in order. Our examination is a joint test of the relative importanceof cash flows versus discount rates as value drivers and the valuation model that is employed.
While we attempt to mitigate this issue by employing different valuation models, commonalities
in the features of these models naturally limit the extent to which our examination can be modelfree. To that extent, our results are to be interpreted with caution. In this regard, it is useful to notethat our tests of post-announcement returns do not depend parametrically on the decomposition.
The rest of this paper is organized as follows. Section 2 describes prior studies and develops
research questions. Section 3 discusses our variance decomposition methodology using the Claus
and Thomas (2001) valuation model. Section 4 discusses the sample formation process andpresents descriptive statistics. Section 5 presents the empirical results of the variance9decomposition and the analysis of post-restatement announcement stock returns. Section 6presents results of robustness tests and Section 7 concludes the paper.

2. Review of Related Work and Development of Empirical Expectations
2.1. The Short-Term Market Response to Restatements and Changes in Expected Cash
Flows/Discount Rates
Prior studies provide consistent evidence of a significant negative stock market reaction tofinancial restatement announcements (e.g., Dechow et al. 1996; GAO 2003; Palmrose et al. 2004).
The market’s reaction is attributable to its revisions of two main components of the firm valuation
model, i.e., projections of the firm’s future cash flows and the discount rate used to value thesecash flows (Hribar and Jenkins 2004). Because investors rely on accounting information to predict
future cash flows, they are likely to adjust the future cash flow potential of the firm
downward/upward when it restates its earnings and/or revises other related statements. Palmrose
et al. (2004) document a significant downward revision by analysts of their earnings forecasts
following restatement announcements. Akhigbe et al. (2005) also present similar findings ofdownward revisions. Although not the main focus of their study, Palmrose et al. (2004) document
the univariate correlation between the revision in EPS forecasts and the stock price reaction to therestatement announcement and find a negative association.
Financial restatements are also likely to decrease the credibility of reported earnings.
Hribar and Jenkins (2004) argue that this can happen due to “uncertainty regarding managerial
competence and integrity, and perceptions about overall earnings quality.” Consistent with the
reduced credibility of reported earnings, Anderson and Yohn (2002) and Wu (2003) show that thestock return response to earnings news is dampened, at least temporarily. More directly, Hribar

10and Jenkins (2004), find an increase of between 7% and 19% in the cost of capital of firms
following restatements. However, Hribar and Jenkins (2004) do not examine the extent to which
the change in cost of capital explains the stock price decline around restatements byeconometrically relating the two. Using a discretionary information risk factor in a Fama andFrench (1993) factor model, Kravet and Shevlin (2010) also document that the cost of capitalincreases by 86 basis points. Further, they demonstrate a positive link between the increase in thecost of capital and the value change around the restatement announcement. However, they do not
examine cash flow changes.
While the above studies demonstrate significant changes in the cash flow and discount ratecomponents of the firm valuation function individually, they do not examine the relative
importance of these two components as sources of the declines in stock at restatement
announcement. Therefore, it is difficult to gauge the extent to which the changes in stock value
associated with restatements is driven by cash flow revisions versus discount flow revisions. Priorwork on the drivers of stock price movements in general, suggests that discount rates are overall amore significant determinant than cash flows (e.g., Cochrane 2008). However, in the context offinancial restatements, investors and analysts could make significant revisions to cash flows
expectations. At the same time, restatements are also likely to lead to significant revisions in thecost of capital of the company. Therefore, it is not clear whether discount rates will remain adominant factor in explaining stock price changes surrounding the restatement announcement.
Therefore, we state our first testable hypothesis non-directionally as follows.

H1: Stock price changes surrounding restatement announcements are more affected bychanges in cash flow expectations than by changes in discount rate or vice-versa.

11Prior studies document that the reasons for the restatement also affect investors’ andanalysts’ assessment of the scope and impact of restatements on firm valuation (Wu 2002;
Palmrose et al. 2004). For example, Wu (2002) documents a more negative stock price reaction torestatement news that involves admitted fraud (-23.0%) compared to restatements that do not
involve fraud (-9.9%). Holding the extent of the cash flow revision constant, it is likely that there
will be larger revisions in the firm’s cost of capital when the restatement news contributes to alarger decrease in investor confidence in the firm. To examine the impact of restatement type on
the relative importance of cash flow news and discount rate news in explaining the market’s
reaction to financial restatement announcements, we state our second hypothesis as follows:

H2: The importance of cash flow expectation changes [discount rate changes] decreases[increases] in explaining stock price changes surrounding restatement announcements
when the restatement reflects greater management weakness.

In addition to examining how the relative importance of cash flow and discount rate news
varies with the underlying reason for the restatement, as a corollary to the above hypothesis, we
examine this variation across subgroups formed on the basis of earnings persistence. Investors’
weighting of cash flow news (relative to news related to the firm’s discount rate) is highly
dependent on the persistence of earnings (see for example, Brav and Heaton 2002 and Francis etal. 2007). This characteristic of earnings is likely to be of particular salience at the time of financial
restatements which introduce investors to incremental uncertainty. In such circumstances, we
expect that investors are likely to weight cash flow news more when cash flows (earnings) are12more persistent.

2.2. The Long-Term Market Response to Restatements and Changes in Expected Cash
Flows/Discount Rates
Prior studies that examine the market’s response to financial restatements, generally findthat the short-term stock market response is negative (e.g. Chakravarthy et al. 2014; Drake et al.
2015; Files, Swanson and Tse 2009; Gordon et al. 2013; Lev, Ryan and Wu 2008; Marciukaityte
and Varma 2008; Myers et al. 2013; Palmrose, et al 2004). Under the efficient market hypothesis,
the short-term market reaction to the announcement should be complete and efficient in the usual
way, and variation in the restatement news should not affect the firm’s long-term stock returns.
However, prior studies do not provide consistent evidence on the post-announcement returns ofrestating firms. Badertscher et al. (2011) document that stock prices of restatement firms remain
stable in the 180-period after the initial negative reaction to the restatement announcement. On theother hand, Gleason et al. (2008) document a significant downward price drift in the 60 trading
day post-restatement for a sample of 380 restatements from 1990 to 2002. They report a mean
return of -10.3% from t+2 to t+60 days on top of the initial negative response of -19.8% from t-1
to t+1 days. Similarly, Desai et al. (2006) also document a downward price drift up to six months
after the restatement announcement, and find that this negative post-restatement return is
associated with the level of short interest in the firm.7

7

A couple of factors may be attributable to this inconsistent post-restatement return patterns across different studies.
First, a different sample period (or sample size) may be one factor. Gleason et al. (2008) and Desai et al. (2006) arebased on the sample compiled by Government Accountability Office, which ranges from year 1997 to 2002 while
Badertscher et al. (2011) expand the sample period to 2008. However, all these studies are still based on a limited
number of restatement firms ranging between 380 and 541. Our study is based on 1,892 restatements from year 1995
to 2013. Second, different ways of computing cumulative abnormal returns (CAR) can be also a factor.

13

We attempt to shed new light on the impact of financial restatements on long-term stock
post-announcement returns by examining differences in post-restatement returns between
subgroups formed on the basis of whether the initial stock price drop is driven relatively more bychanges in future cash flow expectations or by changes in the firm’s discount rate.
The variance decomposition framework we utilize decomposes the short-term stock pricechange into a cash flow component whose value impact is less uncertain and a discount rate impact
whose value impact is more uncertain. Thereby the decomposition framework helps us directly
address the issue of incremental uncertainty faced by investors at restatements and naturally links
to the firm’s long term returns. Based on the link between firm risk/uncertainty and thedecomposition of the change in value at restatement, we conjecture that the decomposition ofannouncement period value changes could also help explain longer term post-restatement stock
price returns. Our post-restatement return tests are similar in spirit to tests in Wilson (2008) that
document that the drop in the information content of earnings numbers following earnings
restatement is short-lived. 8 Instead of following firms’ post-restatement earnings response
coefficients, we examine post-restatement abnormal returns to better understand whether investors’
initial response to restatement announcements has been rational, and to see if a firm’s restatement
announcement has any investment value. More specifically, we examine whether there is any
difference in post-restatement returns between subgroups formed on the basis of whether the initialstock price drop is driven relatively more by changes in future cash flow expectations or bychanges in discount rate. Based on the discussion above we state our final hypothesis as follows:8

Wilson (2008) finds that the capital market penalizes accounting restating firms only for four quarters by assigninglower earnings response coefficients. After four quarters, the valuation of reported earnings goes back up to prerestatement levels.

14

H3: Post-restatement stock returns between subgroups formed on the basis of whether the
initial stock price change is driven relatively more by changes in expectation of cash flows
or by changes expectations of discount rate are different.

3. Methodology
We adopt a variance decomposition framework to quantify the impact of the main driversof the stock price movement immediately after a firm’s accounting restatement announcement:
cash flow news and discount rate news. We closely follow the method used in Chen et al. (2013)and Da et al. (2016). 9 While financial analysts’ earnings and growth forecasts can be used todevelop a proxy for investors’ cash flow expectations, the firm’s discount rate (or cost of equity
capital) is not directly observable and is therefore model-dependent. To estimate the firm’s cost ofequity capital, we first model its equity value as the present value of residual income and a terminal
value as follows:𝑇

𝑃𝑡 = 𝑏𝑣𝑝𝑠𝑡 + ∑𝑖=1

𝐸𝑡 (𝑅𝐼𝑡+𝑖 ) 𝐸𝑡 (𝑇𝑉)+
(1 + 𝑟)𝑖(1 + 𝑟)𝑇(1)

where 𝑏𝑣𝑝𝑠𝑡 is the book value of equity per share at time t, 𝑅𝐼𝑡+𝑖 is the residual income for periodt + i computed as 𝑓𝑒𝑝𝑠𝑡+𝑖 − 𝑟 ∗ 𝑏𝑣𝑝𝑠𝑡+𝑖−1 , (𝑓𝑒𝑝𝑠𝑡+𝑖 denotes the earnings per share forecast for
fiscal period t + i and r the discount rate or cost of equity capital), and 𝑇𝑉 is the terminal value.
Following Claus and Thomas (2001), we explicitly forecast future earnings per share up to t+5,
and compute the terminal value that captures all residual income beyond year t+5 assuming that

9

A more traditional method in examining the main drivers of stock price movement is through the return
decomposition, which was first developed by Campbell and Shiller (1988a). However, although the two methods are
the same in theory, Chen and Zhao (2009) empirically show that modeling cash flow news explicitly as we do in ourstudy is a better approach than modeling the discount rate news and using the residuals as cash flow news in the return
decomposition (please see the appendix in Chen et al. 2013 for details).

15

residual income growth occurs at the 10-year government bond yield less 3%. We use analyst
consensus forecasts of EPS from the I/B/E/S database for the current fiscal year (fepst) and thenext fiscal year (fepst+1), Earnings forecasts beyond year t+2 are computed as follows:
𝑓𝑒𝑝𝑠𝑡+𝑖 = 𝑓𝑒𝑝𝑠𝑡+𝑖−1 × (1 + 𝑙𝑡𝑔𝑡 ) for 𝑖 = 3, 4, & 5(2)

where (𝑙𝑡𝑔𝑡 ) is the mean long-term growth forecast, also from I/B/E/S. At time t, all other factors
except the cost of equity capital (r) are known, and r can be backed out from equation (1) above.
We next model the decomposition of the price change around earnings restatements.
From equation (1), the stock price (Pt) is a function of cash flow forecasts (cft) and the discountrate (drt):
𝑃𝑡 = 𝑓(𝑐𝑓𝑡 , 𝑑𝑟𝑡 )(3)

where cash flow forecasts (cft) are proxied by earnings forecasts (𝑓𝑒𝑝𝑠𝑡 ) and growth rate forecasts( 𝑙𝑡𝑔𝑡 ). 10 We use this equation to decompose the return (𝐷𝑃𝑡,𝑡+𝑗 ) between t and t+j into acomponent related to cash flow news (𝐶𝐹𝑁𝑡,𝑡+𝑗 ) and a component related to discount rate news
(𝐷𝑅𝑁𝑡,𝑡+𝑗 ). Specifically, 𝐶𝐹𝑁 is the change in value caused only by changes in future cash flow
expectations, and DRN is the change in value caused only by changes in discount rates. Eachcomponent is measured as follows:𝐷𝑃𝑡,𝑡+𝑗=

𝑃𝑡+𝑗− 𝑃𝑡
𝑃𝑡

(4)

=

𝑓(𝑐𝑓𝑡+𝑗 , 𝑑𝑟𝑡+𝑗 ) − 𝑓(𝑐𝑓𝑡 , 𝑑𝑟𝑡 )
𝑃𝑡

(5)

=

𝑓(𝑐𝑓𝑡+𝑗 ,𝑑𝑟𝑡+𝑗 )𝑃𝑡+[𝑓(𝑐𝑓𝑡+𝑗 ,𝑑𝑟𝑡 )−𝑓(𝑐𝑓𝑡+𝑗 ,𝑑𝑟𝑡 )+𝑓(𝑐𝑓𝑡 ,𝑑𝑟𝑡+𝑗 )−𝑓(𝑐𝑓𝑡 ,𝑑𝑟𝑡+𝑗 )]2𝑃𝑡−

𝑓(𝑐𝑓𝑡 ,𝑑𝑟𝑡 )
𝑃𝑡

(6)

10

Revisions in long-term growth forecasts is considered part of cash flow news along with earnings forecasts revisions(Campbell and Shiller 1988a and 1988b, Vuolteenaho 2002, Chen and Zhao 2009, Chen et al. 2013).

16

= 𝐶𝐹𝑁𝑡,𝑡+𝑗 + 𝐷𝑅𝑁𝑡,𝑡+𝑗

(7)

where
𝐶𝐹𝑁𝑡,𝑡+𝑗𝑓(𝑐𝑓𝑡+𝑗 , 𝑑𝑟𝑡+𝑗 ) − 𝑓(𝑐𝑓𝑡 , 𝑑𝑟𝑡+𝑗 ) 𝑓(𝑐𝑓𝑡+𝑗 , 𝑑𝑟𝑡 ) − 𝑓(𝑐𝑓𝑡 , 𝑑𝑟𝑡 )
+
)⁄
𝑃𝑡
𝑃𝑡
=
2

(8)

𝐷𝑅𝑁𝑡,𝑡+𝑗𝑓(𝑐𝑓𝑡 , 𝑑𝑟𝑡+𝑗 ) − 𝑓(𝑐𝑓𝑡 , 𝑑𝑟𝑡 ) 𝑓(𝑐𝑓𝑡+𝑗 , 𝑑𝑟𝑡+𝑗 ) − 𝑓(𝑐𝑓𝑡+𝑗 , 𝑑𝑟𝑡 )
+
)⁄
𝑃𝑡
𝑃𝑡
=
2

(9)

(

(

This decomposition approach enables us to estimate the changes in stock prices due to therevision in one component by allowing the component to vary over time while holding the othercomponent fixed. Thus, cash flow news (𝐶𝐹𝑁𝑡,𝑡+𝑗 ) is computed by holding the discount rate
constant, and it captures the price change driven solely by changing cash flow expectations from t
to t+ j. Likewise, discount rate news (𝐷𝑅𝑁𝑡,𝑡+𝑗 ) is computed by holding the cash flow expectation
constant, and it captures the price change driven solely by changing discount rate expectations
from t to t+ j. The decomposition equation (7) provides a convenient way to express the varianceof stock price changes (or stock returns) as the sum of the two covariances:
Var(𝐷𝑃) = Cov[𝐷𝑃, 𝐶𝐹𝑁] + Cov[𝐷𝑃, 𝐷𝑅𝑁]11(10)

Dividing both sides of equation (10) by Var(𝐷𝑃), we obtain:
1=

Cov[𝐷𝑃,𝐶𝐹𝑁]
Var(𝐷𝑃)+Cov[𝐷𝑃,𝐷𝑅𝑁]
Var(𝐷𝑃).

(11)

Each term on the right-hand side of equation (11) can be estimated by regressing 𝐶𝐹𝑁 and 𝐷𝑅𝑁,
respectively, on 𝐷𝑃. The slope coefficient of each regression is interpreted as the proportion of
the total variation in price changes that is explained by variation in revisions of each component.
By construction, the coefficients from each regression sum to one.

11

We drop the time (t) and the firm (i) subscripts for notational simplicity.

174. Data and Summary Statistics
We obtain restatement data from Audit Analytics, earnings and long-term growth rate
forecasts from I/B/E/S, stock price data from CRSP, and accounting data from Compustat. For an
accounting restatement announced at time t, the measurement dates for all the inputs to Equation(1) are as follows. We use the most recent consensus forecasts of annual EPS (fepst) and longterm earnings growth rate (𝑙𝑡𝑔𝑡 ) available from I/B/E/S before the announcement date to estimate
the pre-announcement implied cost of equity. The corresponding forecasts that are available
most immediately after the announcement are used to estimate the post-announcement implied
cost of equity. We choose these forecast dates to ensure that we reliably attribute the change inthe earnings forecast to the restatement. Accounting data are taken from the most recent quarterly
statement in Compustat before the accounting restatement date t. Stock prices (Pt, Pt+1) fromCRSP are taken two days after the date of the computation of the consensus earnings forecast(fepst, fepst+1) to ensure that information in the forecast is impounded in the price.
We identify a total of 4,186 restatement announcements from Audit Analytics with nonmissing stock price from CRSP between 1995 and 2013. When this initial sample is merged with
Compustat with the imposition of minimum data requirements, the sample decreases to 3,884.
With the imposition of non-missing analysts’ earnings and long-term growth forecasts from
I/B/E/S, we obtain a final dataset that consists of 1,849 observations. Table 1 reports summary
statistics for the full sample and subsamples based on the restatement’s initial impact on stock
prices. If the 3-day returns surrounding restatement announcement date is positive [negative], werefer to those firms as the “Positive [Negative] restatement subsample”.12

In Tables, we also use “Positive [or Negative] BHAR(-1,1)” to referred to positive [or negative] restatement
subsample.
1218

Statistics for the full sample show that restating firms are on average quite large with amean (median) market capitalization of $4.95 ($1.07) billion. Firms are reasonably wellperforming with an average return on assets of 7.9%, book-to-market ratio of 0.557 (BP) and longterm growth forecasts of 15.7%. Firm characteristics of the two restatement subsamples, Positive
and Negative BHAR(-1,1), are not very different when measured at the median (i.e. book-tomarket ratios, market capitalization, return on assets, and long-term growth expectations).13
Table 1 also reports the revisions in EPS forecasts and the model-derived implied cost ofequity capital, and stock returns surrounding the restatement announcement. On average, financial
analysts revise earnings, our proxy for future cash flow expectations, downward by about 1.6 cents(DFEPS), while the cost of equity capital increases by 20 basis points (DCOE). The combined
effect of the decrease in earnings and an increase in the cost of equity capital is that restating firms
experience an average price decline of 1.3% (DP) in the one-month window (t-1 to t+1 month)surrounding the restatement announcement.
This negative return is mainly attributable to changes in cost of equity capital, i.e., holding
revisions in earnings and earnings growth forecasts constant, the average price change due tochanges in cost of equity capital (i.e., DP DRN) is -2.5%. While the analysts revise earnings
downward on average, the impact of earnings downward revisions seems to have a slight positive
impact on price changes (DP CFN = 1.1%) on average. Expectedly, the two subsamples show
significantly different earnings revisions – the positive subsample has a mean revision of 6.1 cents
upwards compared to a mean downward revision of 1.4 cents in the negative subsample, and they
are statistically different at 1% level although at the median, they are not much different. However,the change in the cost of equity capital is more comparable across the two subsamples – an average

13

The claim is based on z-statistics that are omitted from the table for the sake of brevity.

19

(median) upward move of 30 (20) basis points for the negative restatement subsample and 0.0 (0.0)
basis points for the positive restatement subsample. The net impact of restatements for the negative
subsample is a decline in stock prices (DP = -4.9%) compared to an increase in stock prices forthe positive subsample (DP = 3.9%) (different at 10% level). The total stock price changes
attributable to discount rate revisions (DP DRN = -3.7%) is larger than those attributable to future
earnings expectations (DP CFN = -1.2%) for the negative subsample. On the other hand, for the
positive subsample, the stock price changes surrounding the restatements are mainly driven bychanges in future earnings expectations (DP CFN = 4.6%), but very little by discount rate revisions(DP DRN = -0.6%).
Overall, these descriptive statistics show that the decrease in stock price following
accounting restatement announcements is on average caused more by an increase in the cost ofequity capital than by revisions in expectations of future cash flows, but for the positive subsample,
the stock price increase is mainly driven by the revisions in expectations of future cash flows. In
the following section, to understand the drivers of stock price changes surrounding the restatement
announcement in a relative sense, we adopt the variance decomposition framework.
Table 1 about here.

5. Results
4.1. Variance Decomposition - Full Sample Analysis
To examine the main drivers of stock price movements around accounting restatements,
we adopt the variance decomposition framework as detailed in Section 3. The coefficient from a
regression of cash flow news (CFNi,t) on the stock price change across the restatement
announcement (DPi,t) measures the proportion of returns driven by changes in investors’ cash flow

20

expectations. Likewise, the coefficient from a regression of discount rate news (DRNi,t) on stock
price changes (DPi,t) measures the proportion of returns that is attributable to the market’s changes
in the cost of equity capital of the firm. We report the results of these cross-sectional regressions
in Table 2.
We measure changes in price, earnings and earnings growth forecasts and cost of equity
capital, i.e., the main inputs to our variance decomposition equation, between the closest I/B/E/S
consensus forecast date right before (t-1) and after (t+1) the accounting restatement
announcement date (t). Since I/B/E/S consensus forecasts are available on a monthly basis, thetime interval between t-1 and t+1 is, on average, about 30 days, and the accounting restatement
falls somewhere between the t-1 and t+1 consensus forecast dates. 14 Table 2 reports the
proportion of total price variation, Var(DPi,t), that is explained by the covariance between DPi,tand CFNi,t (or DRNi,t), which is estimated as

Cov[𝐷𝑃,𝐶𝐹𝑁]
Var(𝐷𝑃)andCov[𝐷𝑃,𝐷𝑅𝑁]
Var(𝐷𝑃), respectively. As abaseline case, we first conduct the variance decomposition exercise with the intersection of theentire universe of CRSP, IBES and Compustat firms during the same sample period surrounding
pseudo-restatement dates. For the entire population, using a one-month revision interval (i.e.
between t-1 and t+1 dates surrounding pseudo-restatement announcement dates), cash flow news
explains 12.9% of stock price movements, and discount rate news explains the remaining 87.1%(Table 2). The relatively small proportion of cash flow news is in line with the notion that, in the
short term, stock prices can move with investors’ sentiments not related to changes in expectations
regarding future cash flows, and is consistent with prior studies. In addition, we also conduct thevariance decomposition exercise with the matching sample surrounding pseudo-restatement dates.

14-1 or +1 in the time subscript simply indicates the most recent consensus forecasts before (-1) or after (1) the
restatement, and does not refer to month -1 or + 1.

21

Firms in the matching sample are non-restatement firms in the same industry and that have firm
characteristics similar to those of restatement firms. The matching sample is constructed based on thepropensity score from a logistic prediction model of restatement vs. non-restatement firms using
determinant variables that include the book-to-market ratio, market capitalization, profitability (return on
assets) and momentum (past twelve month returns) measures. For the matching sample, cash flow news

explains 21.8% of stock price movements, and discount rate news explains the remaining 78.2%.
Table 2 about here.
For restating firms, cash flow news explains 33.5% of the stock price change surrounding
accounting restatements while discount rate news explains the remaining 66.5%. Compared to theentire population (or matching sample), the proportion of cash flow news explaining stock pricevariation is much higher for the restatement sample. This difference captures the significance of
the immediate impact of a firm’s restatement on investors’ expectations regarding future cash
flows relative to investors’ assessment of the firm’s risk reflected in its cost of equity capital.
We partition our sample on the basis of the initial 3-day stock returns surrounding
restatement announcements: Negative BHAR(-1,1) and Positive BHAR(-1,1) subsamples.
Negative restatements are more common (60%) than positive restatements (40%) during oursample period. Interestingly, unlike the relative magnitude of stock price changes at therestatement announcement which shows a quite different pattern for the positive and negative
restatement subsamples, these two subsamples are quite similar in the importance of CFN and
DRN in explaining stock price changes. CFN [DRN] in the negative sample explains 30.2%[69.8%] of stock price changes, which is very similar in magnitude to the results for the positive
sample. Overall, the results in Table 2 support our first hypotheses.

4.2. Variance Decomposition and Types of Restatements
22

Audit Analytics documents over 60 different reasons for firms to restate their financial
statements. These can be grouped into four broad categories: Restatements due to 1) Accounting
rule application failures (ARAF), 2) Errors, 3) Financial fraud (Fraud), and 4) Others.15 In Panel
A of Table 3 we report how different types of restatements affect the variance decomposition
results differently. Accounting rule application failures occur in over 93% (1,725) of total
restatements, Errors in about 6.9% (128), Financial Fraud 2.5% (47), and Others 10.9% (202) inour sample.16 Because ARAF includes over 90% of total restatements, the relative importance of
CFN (31.4%) or DRN (68.6%) in explaining stock return variation is very similar to that of thefull sample. We also find that restatements that fall into the “Others” category show a similar
pattern to that of the overall restatement sample. However, when errors (“Errors”) lead to financial
restatements, changes in stock value are driven to a larger extent by future cash flow expectations(CFN coefficient = 0.606) than changes in discount rate (DRN coefficient = 0.394) (and the highest
proportion of cash flow news-related variation across various samples examined in the study). Thisis consistent with investors viewing such restatements as being less indicative of management
weakness than other types of restatements. On the other hand, when restatements are associatedwith financial fraud (“Fraud” group), stock price changes are mainly driven by changes in discountrate – for this subsample discount rate revisions explain 88.0% of the total stock return variation.
This suggests that when investors’ confidence in a firm’s financial reporting system is shaken, thecost of equity (or discount rate) explains more of the return variation than revisions in the firm’s
expected cash flows. The results of Table 3 support our second hypothesis that for restatements

15This classification is provided by the Audit Analytics database, and is consistent with prior studies. A few examples
in the “Others” category include restatements associated with footnote and segment reporting information,
irregularities associated with material weakness reporting, and disclosure failure issues associated with loan covenantviolations.
16
Since many firms disclose multiple reasons for their restatements, the sum of total restatements is over 100%.

23

that are more indicative of management weakness the change in value is driven to a greater extent
by revisions in the discount rate of the firm.
Table 3 about here.
In Panel B of Table 3, we examine how our decomposition varies across subgroups formedon the basis of earnings persistence. Brav and Heaton (2002) and Francis et al. (2007) argue that
Bayesian investors will place more weight on less uncertain earnings information. Therefore, we
conjecture that investors will place more weight on earnings information for firms with higher
earnings persistence. Our aim here is to extend the evidence of the rational variation in thedecomposition results of Panel A above. For this test, we drop restatements with no earnings
impact and split the sample on the basis of subsample median value of earnings persistence.
Earnings persistence is measured as the coefficient b1 from the time-series regression ROA(t) =b0 + b1*ROA(t-1) + ε at the firm level using past six years of ROA with a minimum of four yearsof data, where ROA is measured as net income divided by total assets. As the results in Panel B of
Table 3 show, firms with low persistence have 26.5% of the change in value explained by cash
flow news whereas for firms with high earnings persistence this is 42.0%. This result supports ourconjecture that investors weight earnings information more when earnings information is lessuncertain.

4.3. Post-Restatement Announcement Stock Returns
We next turn to an examination of how the variance decomposition of stock price changes
around the restatement announcement informs post-announcement stock returns. Table 4 reports
post-announcement abnormal returns for the full sample and by restatement type: High versus Low
CFN/DP restatements, where the High [Low] CFN/DP restatement group has above median values

24

of CFN/DP , i.e., where the initial restatement stock price change is driven more by changes infuture cash flow changes [changes in discount rate]. As a baseline case, we report raw returns inPanel A. Consistent with some prior studies (discussed in Section 2), we find that postannouncement returns are significantly positive for the whole sample as well as for each of the
Low and High subgroups. Further, we find that the High subgroup has significantly higher returns
than the Low subgroup in the 63-, 126- and 252-day trading periods.
To compute abnormal returns, we subtract characteristics-based benchmark portfolio
returns from raw returns following Daniel et al. (1997). These results are reported in Panel B of
Table 4. After adjusting for risk and other pricing factors we find that restating firms show adownward stock price drift that lasts up to one year (252 trading days) after the restatement
announcement. The mean buy-and-hold abnormal return after a year for the full sample is -1.9%(t+2, t+252). However, while both the High and Low CFN/DP restatement subsamples have an
initial negative return similar to that of the full sample, post-announcement returns of the two
subsamples show marked differences. The Low CFN/DP restatement firms continue to drift
downward, and their mean buy-and-hold abnormal return is -4.7% 252 days after the restatement
announcement date. On the other hand, the average buy-and-hold return for the High CFN/DP
restatement subgroup remains relatively stable - one year after the restatement, the buy-and-holdabnormal return is 0.9% (insignificant) with no significant peaks or dips in the intervening period.
The one-year buy-and-hold abnormal return difference between the High and Low CFN/DP
restatement subsamples is 5.5%, and is statistically significant (p < 0.05).
Table 4 about here.
In Table 5, we replicate Table 4 post-restatement buy-and-hold abnormal returns for
subsamples of negative (Panel A) and positive (Panel B) restatements. The return pattern for25

negative restatement firms (Panel A) are very similar to those in Table 4. For example, the mean
buy-and-hold abnormal return after a year for this subgroup is -2.1% (t+2, t+252). The Low
CFN/DP restatement firms continue to drift downward, and their mean buy-and-hold abnormal
return is -4.9% 252 days after the restatement announcement date. On the other hand, the intial
reaction to restatement seems complete for High CFN/DP restatement firms. The average buyand-hold return remains relatively stable - one year after the restatement, the buy-and-holdabnormal return is 0.6% (insignificant). The one-year buy-and-hold abnormal return difference
between the High and Low CFN/DP restatement subsamples is still 5.5%, and is statisticallysignificant (p < 0.05).
Panels B of Table 5 examine the positive restatement subsamples. While the initial 3-day
return is positive for two subgroups (i.e., High and Low CFN/DP), the post-restatement returns
show quite different patterns. Like the negative subsample case (Panel A, Table 5), the intial
reactions to restatement annoucements seem complete for High CFN/DP restatement firms.
However, the positive initial 3-day returns for the Low CFN/DP restatement firms (3.8%) reverses
and their mean buy-and-hold abnormal return becomes -4.8% in a year.
By documenting that variation in the initial stock price reaction to restatements (cash flow
revisions versus discount rate revisions) helps explain patterns in post-announcement returns, theresults in Table 5 provide several insights. At a descriptive level, we find that post-announcement
returns are consistent with an average under-reaction to restatement announcements. More
importantly, the extent of underreaction is significantly more pronounced when the initial stock
return reaction is driven to a greater extent by changes in investors’ cost of equity expectations.
For restatements characterized by a larger content of cash flow news, post-restatement returns
suggest the immediate market reaction is relatively complete and therefore efficient. These26

regularities are consistent with the argument that investors are able to estimate the value impact ofshocks to earnings relatively quicker than the value impact of changes in the firm’s discount rate.
Thus, by tying long-term returns to the drivers of short-term stock price movements, our results
provide a more comprehensive analysis of the investor reaction to restatement announcements.
Table 5 about here.

6. Robustness Tests
We conduct additional tests to verify whether our results documented above are sensitive
to key aspects of our test design. There are at least two reasons that, we believe, could lead to an
overestimation of the portion of stock price variation explained by discount rate news. First, thediscount rate is unobservable and is estimated on the basis of a catch-all measure. Specifically,
because the discount rate is derived from the stock price and earnings and earnings growthforecasts, noise in the stock price or biases in earnings and earnings growth forecasts are also likely
to be captured in the discount rate and innovations thereof. This is unlike innovations in cash flows
which are estimated more directly from analyst consensus forecasts. Second, our valuation model(1) and variance decomposition (7) are based on the assumption that analysts’ earnings forecasts
accurately reflect investors’ expectations of earnings in a timely fashion. However, analysts’
delayed revisions of earnings forecasts can lead to an underestimation of the impact of cash flow
news contained in the financial restatement.
To address this issue and to reduce the likelihood of stale forecasts in the postannouncement period, we first extend the measurement of cash flow expectations after therestatement announcement by another month (so to t+2). We report the results based on this27

alternative measurement in Panel A of Table 6. Second, we delete any observations that haveearnings forecast revisions of zero value and report the results in Table 6, Panel B.

6.1. Extension of the Consensus Forecast Revision Period
When we extend the revision period to two months to mitigate the stale forecast issue, forthe overall population (baseline case) the importance of CFN in explaining stock price variation
increases from 12.9% to 22.4%. This is consistent with the notion that while in the short-term stock
price changes can be driven relatively more by sentiment or other factors unrelated to firm
fundamentals, over the longer term stock returns will eventually be more closely tied to expectedchanges in future cash flows (Easton et al. 1992; Chen et al. 2013; Da et al. 2016). However, in
the restatement sample, we do not observe an increase in the coefficient on CFN, rather it decreases
slightly. For the whole sample, cash flow news explains only 28.0% of return variation comparedto 33.5% with the one-month forecast revision. The pattern of results for the negative, positive andno-impact subgroups is qualitatively similar to that reported in Table 2. Overall, the results inPanel A, Table 6 suggest that our proxy of cash flow news (earnings forecast revision) does not
suffer from a significant timing issue.
Table 6 about here.

6.2. Removal of Potentially Stale Forecasts
There are 499 observations for which the revision in the consensus analyst forecast from t1 to t+1 is zero. All else equal, these are observations that are more likely susceptible to the stale
forecast issue. In Panel B of Table 6, we report our main variance decomposition results after
dropping these observations from the analysis. Compared to the results in Table 2, when we drop

28

the stale forecasts the proportion of CFN explaining stock price variation is higher. For example,
in the full sample, the coefficient for CFN is 38.5% compared to 33.5% in Table 2. However, theCFN coefficients for the negative and positive restatement samples are also similar in magnitude.
These results suggest that while stale forecasts have the effect of inflating the impact of DRN in
explaining stock price variation, our conclusions are not driven by this effect.

6.3. Alternative Equity Valuation ModelIn estimating the cost of equity capital (or discount rate) and conducting variancedecomposition, we rely on the valuation model proposed by Claus and Thomas (2001). To test if
our results are sensitive to our choice of the valuation model, we adopt an alternative valuation
model used in Pastor et al. (2008) as follows.17
𝐸 (𝑅𝐼

)

𝐸 (𝑇𝑉)

𝑡𝑡+𝑖
𝑃𝑡 = ∑𝑇𝑖=1 𝑡(1+𝑟)𝑖 + (1+𝑟)𝑇(12)

where all variables are defined as in equation (1) except that Pastor et al. (2008) use a 15-year
horizon (T=15).
Panel C of Table 6 reports our main analysis based on this alternative valuation model. The
results are qualitatively very similar to our main findings reported in Table 2. For example, thecoefficient on CFN for the restatement sample is 31.1% with the model used in Pastor et al. (2008)
compared to 33.5% with our main model.18

6.4. Restatements with Large versus Small Income Impacts

17
18This model is used in Chen et al. (2013) as well.
The sample size increase slightly due to different input variables used.

29

In this sub-section, we examine whether the magnitude of the restatement affects therelative importance of how much each component contributes to the stock price variation acrossthe restatement announcement. We partition our sample on the basis of the absolute impact of therestatement on cumulative past net income. If the impact of the restatement on the firm’s equity is
above [below] the median of the entire sample each year, we classify the restatement into the large[small] restatement subgroup. Panel D of Table 6 reports the results. We find that CFN [DRN] in
the large restatement sample explains 35.7% [64.3%] of stock price changes surrounding therestatement. For the small restatement sample, in contrast, the importance of CFN decreases to
29.9%. Thus, when a firm makes a restatement announcement that has a large impact on pastearnings (i.e., large restatement firms), the restatement related stock price change is driven moreby investor’s changes in confidence in the firm’s ability to generate future cash flows than changes
in the firm’s cost of capital.

6.5. Exclusion of Restatement Announcements Bundled with Earnings Announcements
There are 139 restatement announcements made within the three-day window around an
earnings announcement. Because this may affect our variance decomposition results, in Panel Eof Table 6 we report our main variance decomposition results after dropping these restatements.
Excluding these observations, does not yield a major difference in the proportion of CFN
explaining stock price variation. For example, the coefficient for CFN in this subsample is 32.9%
compared to 33.5% in Table 2.

6.6. Post-restatement Announcement Returns after Controlling for Additional Risk Factors

30Here, we conduct a test that helps rule out the possibility that the difference in postannouncement returns between the two subsamples documented in Table 4 is driven by otherknown risk factors including book-to-market ratios, leverage, beta, momentum, and accruals. We
use the following regression model:
𝑅𝑒𝑡𝑖,𝑡 = 𝛽0 + 𝛽1 ∗ 𝐿𝑜𝑤𝐶𝐹𝑁_𝐷𝑃𝑖,𝑡 + 𝛽2 ∗ 𝐵𝑒𝑡𝑎𝑖,𝑡−1 + 𝛽3 ∗ 𝑇𝐴𝐶𝑖,𝑡−1 + 𝛽4 ∗ 𝐵𝑃𝑖,𝑡−1+𝛽5 ∗ 𝐿𝑒𝑣𝑒𝑟𝑎𝑔𝑒𝑖,𝑡−1 + 𝛽6 ∗ 𝑀𝑜𝑚𝑒𝑛𝑡𝑢𝑚𝑖,𝑡−1 + 𝜀𝑖,𝑡(13)𝑅𝑒𝑡𝑖,𝑡 is the one year buy-and-hold return (or raw return) from one day after the restatement
announcement date to 252 trading days after. 𝐿𝑜𝑤𝐶𝐹𝑁_𝐷𝑃𝑖,𝑡 takes a value of one if a firm’s cash
flow news (CFN) relative to stock price changes (DP) surrounding the restatement announcement
date is below the crossectional median CFN/DP each year, zero otherwise. All other independent
variables are used using the most recent publicly available data before the restatement
announcements.19 𝐵𝑒𝑡𝑎𝑖,𝑡−1 is computed using 60 monthly returns based on the market model.
𝑇𝐴𝐶𝑖,𝑡−1 is total accruals, computed as earnings before extraordinary income minus cash flow fromoperating income, scaled by average total assets. 𝐵𝑃𝑖,𝑡−1 is the book-to-market ratio, defined as
the ratio of book value of equity to market capitalization. 𝐿𝑒𝑣𝑒𝑟𝑎𝑔𝑒𝑖,𝑡−1 is measured as total
liabilities divided by total assets. 𝑀𝑜𝑚𝑒𝑛𝑡𝑢𝑚𝑖,𝑡−1is the twelve-month raw return from month t 12 to month t - 1.
Table 7 reports estimation results for equation (13). The coefficient on 𝐿𝑜𝑤𝐶𝐹𝑁_𝐷𝑃𝑖,𝑡 (𝛽1 )is -0.052 (t = -2.34) indicating the one-year post-restatement announcement date BHAR return
difference between the High vs. Low CFN/DP subsamples is 5.2%. This is consistent with our

19

The time subscript t-1 is used to denote that independent variables are known to the market before the restatement
announcement date.

31

findings in Table 4 and suggests that other known risk factors do not drive our results. We find asimilar result when we use raw returns instead of BHAR returns as the dependent variable.

7. Conclusion
This paper examines the fundamental drivers of stock price changes around financial
restatements – investors’ revisions in the firm’s cash flow expectations and implied cost of equity
capital. Despite extensive research on earnings restatements, the evidence on the links between
these drivers of price movements and the price decline around restatements is relatively sparse.
Our findings address this gap in the literature by undertaking a joint analysis of these drivers within
a single valuation model.
Using a variance decomposition framework, consistent with stock price movements ingeneral, revisions in the discount rate are generally a bigger driver of the short-term price reaction
to financial restatements. This is true for restatements irrespective of whether they have a positiveor negative initial market reactions. However, financial restatements do present a context where
the proportion of stock price variation explained by cash flow news is higher than for the crosssection of the population or in a propensity score matched sample. Consistent with a financial
reporting risk argument, we find that discount rate news explains more of the variation in thechange in value when the underlying reason for the restatement is fraud, whereas cash flow news
is more important when errors are the reason for the restatement. These results make contributions
to the literature on earnings restatements as well as to the literature on the drivers of stock pricemovements.
Our decomposition also informs post-announcement stock returns. For restatements where
the proportion of announcement price changes explained by discount rate changes is relatively

32higher we find a significant negative drift in stock prices. Otherwise, the short-term reaction seems
to be relatively efficient, and no drift pattern obtains for restatements whose announcement pricechanges are mainly explained by revision in future earnings. The difference in returns is
economically significant. These findings help shed additional light on the link between investors’
revaluation of stocks around restatements and suggest that revisions in the financial reporting riskof the company are relatively long-lived.

33

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36

TABLE 1
Descriptive statistics

Variables

N

Full Sample

Negative BHAR (-1,1)

Positive BHAR (-1,1)

Mean

N

N

MedianMeanMedianMeanMedian

BP
1849
0.557
0.485
1107
0.544
0.478
742
0.577
0.497
MktCaP
1849
4954
1070
1107
5164
1104
742
4640
1005
MOM
1849
0.195
0.078
1107
0.186
0.071
742
0.210
0.087
ROA
1849
0.079
0.067
1107
0.077
0.066
742
0.082
0.068
LTG
1849
0.157
0.150
1107
0.155
0.150
742
0.159
0.150
RestateSize
1849
0.100
0.007
1107
0.132
0.009
742
0.051
0.005
DFEPS
1849
0.016
0.000
1107 -0.014
0.000
742
0.061
0.000
DCOE
1849
0.002
0.001
1107
0.003
0.002
742
0.000
0.000
DP
1849 -1.3%
-0.6%
1107
-4.9%
-3.0%
742
3.9%
3.2%
DPCFN
1849
1.1%
0.4%
1107
-1.2%
0.1%
742
4.6%
0.8%
DPDRN
1849 -2.5%
-1.3%
1107
-3.7%
-2.5%
742
-0.6%
1.0%
The table reports summary statistics for the firms with restatement announcements from Audit Analytics database during 1995 to 2013. The Negative[Positive] BHAR(-1,1) restatement sample includes any restatement announcement whose 3-day market reaction is negative [positive].Variables aredefined as follows. Book-to-market (BP) is the ratio of the book value of equity to market capitalization at each quarter-end. Market capitalization(MktCap) is the market capitalization in millions. The past return or momentum (MOM) is the 12-month cumulative return from month t – 12 tomonth t – 1. Return on assets (ROA) is quarterly earnings before extraordinary items divided by the total assets at the beginning of each quarter.
Long-term growth rate (LTG) is analysts’ monthly consensus long-term earnings forecasts from I/B/E/S. RestateSize is total cumulative changes in
net income divided by the book value of equity in absolute terms. Revisions in earnings forecasts (DFEPS) is measured between t-1 and t+1 dates,
where t-1 is the most recent earnings forecast consensus date right before the restatement announcement date, and t+1 is the most immediate earnings
forecast consensus date right after the restatement announcement date. Changes in cost of equity capital estimates (DCOE) is measured between thesame t-1 and t+1 dates surrounding restatement announcements used in measuring DFEPS. Cost of equity capital measure is based on the method
used in Clause and Thomas (2001). Stock price change (DP) is a log returns between the same t-1 and t+1 dates surrounding restatement
announcements used in measuring DFEPS. Cash flow news (DPCFN) is the stock return driven solely by changes in cash flow expectations from t-1
to t+1 surrounding restatement announcements. Discount rate news (DPDRN) is the stock return driven solely by changes in cost of equity capitalfrom t-1 to t+1 surrounding restatement announcements.

37

TABLE 2
The Drivers of Stock Price Changes Following Accounting Restatement:
Cash Flow News vs. Discount Rate News
Coefficients
Obs

CFN

DRN

Population

821,3950.129(2.72)

0.871(18.36)

Matching Sample

1,849

0.218
(7.44)

0.782(26.74)

Restatement –Full Sample

1,849

0.335
(8.78)

0.665(17.44)

Negative BHAR(-1,1)

1,107

0.302
(6.04)

0.698(13.98)

Positive BHAR(-1,1)

742

0.318
(4.86)

0.682(10.43)

The table reports the proportion of stock returns variation that is explained by cash flow news (CFN) anddiscount rate news (DRN) following accounting restatements. Population includes all the firms from theintersection of CRSP, I/B/E/S and Compustat universe from year 1995 to 2014. The Matching Sample
includes non-restatement firms that have similar firm characteristics to those of restatement firms in thesame industry. The matching sample was constructed based on the propensity score measured by the logistic
prediction model of restatement vs. non-restatement firms using determinant variables of the book-tomarket, market capitalization, profitability (return on assets) and momentum (past twelve month returns)
measures. Restatement – Full Sample includes all the firms with restatement announcements from Audit
Analytics database during 1995 to 2013. The Negative [Positive] BHAR(-1,1) restatement sample includes
any restatement announcement whose 3-day market reaction is negative [positive]. Obs is the total numberof observations. Cash flow news (CFN) is the stock return driven solely by changes in cash flow
expectations from t-1 to t+1 surrounding restatement announcements. Discount rate news (DRN) is thestock return driven solely by changes in cost of equity capital from t-1 to t+1 surrounding restatement
Cov[𝑑𝑝,𝐶𝐹𝑁]
announcements. The CFN coefficient is estimated as Var(𝑑𝑝) , where DP is the log return from the samet-1 to t+1 period surrounding the restatement announcements. Likewise, the CRN coefficient is estimatedCov[𝑑𝑝,𝐷𝑅𝑁]
as Var(𝑑𝑝) . t-statistics are reported in parentheses.

38TABLE 3
The Drivers of Stock Price Changes Following Accounting Restatement
By Restatement Types
Panel A: Audit Analytics-based reasons for the restatement
Coefficients
Obs

CFN

DRN

Restatement –Full Sample

1,849

0.335
(8.78)

0.665(17.44)

Accounting Rule
Application Failure

1,725

0.314
(7.83)

0.686(17.12)Errors128

0.606(3.62)

0.394(2.36)

Financial Fraud

47

0.120
(0.27)

0.880(1.96)

Others202

0.378(3.25)

0.622(5.35)

Panel B: Restatements based on firms’ earnings persistence
Coefficients
Obs

CFN

DRN

Restatement –Full Sample

1,849

0.335
(8.78)

0.665(17.44)

Low Persistence

589

0.265
(3.51)

0.736(9.75)

0.420
0.580(5.66)(7.82)The table reports the proportion of stock returns variation that is explained by cash flow news (CFN) anddiscount rate news (DRN) following accounting restatement by restatement types (Panel A) and by earnings
persistence (Panel B). Restatement – Full Sample includes all the firms with restatement announcementsfrom Audit Analytics database during 1995 to 2013. Accounting Rule Application Failures is a subsampleof firms whose restatement is due to misapplication of accounting rules. Financial Fraud is a subsample offirms whose restatement is caused by financial fraud. Errors is a subsample of firms whose restatement isdue to a simple error. Others include all other restatements. Obs is the total number of observations. Cashflow news (CFN) is the stock return driven solely by changes in cash flow expectations from t-1 to t+1
surrounding restatement announcements. Discount rate news (DRN) is the stock return driven solely bychanges in cost of equity capital from t-1 to t+1 surrounding restatement announcements. The CFN
coefficient is estimated as Cov[𝑑𝑝,𝐶𝐹𝑁], where DP is the log return from the same t-1 to t+1 period surrounding
Var(𝑑𝑝)High Persistence589

the restatement announcements. Likewise, the CRN coefficient is estimated as Cov[𝑑𝑝,𝐷𝑅𝑁]. t-statistics are
Var(𝑑𝑝)reported in parentheses. Earnings persistence is measured as the coefficient b1 from a time-series regressionof ROA(t) = b0 + b1*ROA(t-1) at the firm level using past six years of ROA with a minimum of four yearsof data where ROA is measure net income divided by total assets.

39

TABLE 4
Post-Restatement Buy and Hold Return on Full Sample
Panel A: Raw Returns
Return Periods

Full Sample

Low CFN/DP
Restatement

High CFN/DP
Restatement

High-Low

Raw Ret (-1,1)-0.015***-0.017***-0.014***0.002

Raw Ret (2,63)

0.033***

0.023**

0.044***

0.021*

Raw Ret (2,126)

0.053***

0.036***

0.069***

0.034*

Raw Ret (2,252)

0.123***

0.092***

0.154***

0.063**

Panel B: Abnormal Returns (Raw returns – DGTW (1997) Characteristics Portfolio Returns)
Return Periods

Full Sample

Low CFN/DP
Restatement

High CFN/DP
Restatement

High-Low

BHAR (-1,1)-0.018***-0.018***-0.017***0.001

BHAR (2,63)-0.001-0.009

0.007

0.016

BHAR (2,126)-0.014*-0.028**-0.0010.027*

BHAR (2,252)-0.019-0.047***0.009
0.055**The table reports raw returns in Panel A, and buy-and-hold abnormal returns (BHAR) in Panel B from one
day before the restatement date to 252 trading days after the restatement by the magnitude of cash flow
news (CFN) relative to stock price changes (High vs. Low) in quarterly intervals. The High [Low] CFN/DP
sample includes any restatement firms with high [below] the median of CFN/DP between t-1 to t+1 dates,
where t-1 is the most recent earnings forecast consensus date right before the restatement announcement
date, and t+1 is the most immediate earnings forecast consensus date right after the restatement
announcement date. BHARs are calculated during each trading period we choose by subtracting thecorresponding 125 characteristics based benchmark portfolio returns based on the size, book-to-market
ratio and momentum portfolio following Daniel et al. (1997) from the raw returns. High – Low column
reports the difference in BHAR between the High and Low CFN/DP samples. *, **, and *** represent thesignificance levels at 5%, 1%, and 0.1%, respectively.

40

TABLE 5
Post-Restatement Buy and Hold Return by Restatement Types
Panel A: Negative BHAR(-1,1) Sample DGTW Abnormal Returns

Return Periods

Full Sample

Low CFN/DP
Restatement

High CFN/DP
Restatement

High-Low

BHAR (-1,1)-0.057***-0.053***-0.060***-0.007

BHAR (2,63)-0.006-0.015

0.002

0.016

BHAR (2,126)-0.023*-0.044***-0.0020.041*

BHAR (2,252)-0.021-0.049**0.006

0.055*

Panel B: Positive BHAR(-1,1) Sample DGTW Abnormal Returns
Return Periods

Full Sample

Low CFN/DP
Restatement

High CFN/DP
Restatement

High-Low

BHAR (-1,1)

0.041***

0.038***

0.043***

0.005

BHAR (2,63)

0.007

0.000

0.013

0.013

BHAR (2,126)-0.001-0.008

0.005

0.014

BHAR (2,252)-0.015-0.048*0.018

0.067*The table reports raw returns, and buy-and-hold abnormal returns (BHAR) from one day before therestatement date to 252 trading days after the restatement by the magnitude of cash flow news (CFN)
relative to stock price changes (High vs. Low) in quarterly intervals for the negative restatement subsample(Panel A), and the positive restatement subsample (Panel B).The Negative [Positive] BHAR(-1,1)
restatement sample includes any restatement announcement whose 3-day market reaction is negative[positive]. The High [Low] CFN/DP sample includes any restatement firms with high [below] the medianof CFN/DP between t-1 to t+1 dates, where t-1 is the most recent earnings forecast consensus date rightbefore the restatement announcement date, and t+1 is the most immediate earnings forecast consensus dateright after the restatement announcement date. BHAR are calculated during each trading period we choose
by subtracting the corresponding 125 characteristics based benchmark portfolio returns based on the size,
book-to-market ratio and momentum portfolio following Daniel et al. (1997) from the raw returns. High –Low column reports the difference in BHAR between the High and Low CFN/DP samples. *, **, and ***represent the significance levels at 5%, 1%, and 0.1%, respectively.

41

TABLE 6
The Drivers of Stock Price Changes Following Accounting Restatement:
Cash Flow News vs. Discount Rate News – Additional Tests
Panel A: The revision horizon t-1 to t+2
Coefficients
Obs

CFN

DRN

Restatement –Full Sample

1,786

0.280
(8.30)

0.720(21.35)

Negative BHAR(-1,1)

1,064

0.269
(6.69)

0.732(18.22)

Positive BHAR(-1,1)

722

0.249
(4.00)

0.751(12.06)

Panel B: Non-zero forecast revisions
Coefficients
Obs

CFN

DRN

Restatement –Full Sample

1,350

0.385
(7.97)

0.615(12.74)

Negative BHAR(-1,1)

796

0.353
(5.48)

0.647(10.04)

Positive BHAR(-1,1)

554

0.341
(4.15)

0.659(8.01)

Panel C: Alternative Valuation Model (Pastor, Sinha, and Swaminathan 2008)
Coefficients
Obs

CFN

DRN

Restatement –Full Sample

1,828

0.311
(6.10)

0.689(13.51)

Negative BHAR(-1,1)

1,094

0.287
(4.04)

0.713(10.06)

Positive BHAR(-1,1)

734

0.296
(3.73)

0.704(8.88)

42

Panel D: Subsample Partitioned by the Large and Small Restatement
Coefficients
Obs

CFN

DRN

Large Restatement

924

0.357
(6.39)

0.643(11.48)Small Restatement

925

0.299
(5.70)

0.701(13.35)

Panel E: Restatements Announcements within (t-1, t+1) days of Earnings Announcements Date
Coefficients
Obs

CFN

DRN

Restatements Without
Earnings Announcements

1,716

0.329
(8.32)

0.671(16.98)

Restatements With
Earnings Announcements

133

0.445
(3.03)

0.555(3.78)The table reports the proportion of stock returns variation that is explained by cash flow news (CFN) anddiscount rate news (DRN) following accounting restatement. Panel A reports the results with extended
revision horizon from t-1 to t+2. Panel B reports the results after deleting firms whose earnings forecaststhat financial analysts do not revise following accounting restatements. Panel C reports the results based on
the valuation model used in Pastor et al. (2008). Panel D reports the results of subsample analysis partitionedby the size of restatement. A firm is classified into the Large [Small] Restatement subsample when the
cumulative effect of restatement on changes in net income is above [below] the median of the full sample.
Panel E reports results of subsample analysis portioned by the restatements that are made with and without
earnings announcements. Population includes all the firms from the intersection of CRSP, I/B/E/S and
Compustat universe from year 1995 to 2013. Restatement – Full Sample includes all the firms withrestatement announcements from Audit Analytics database during 1995 to 2013. The Negative [Positive]
BHAR(-1,1) restatement sample includes any restatement announcement whose 3-day market reaction isnegative [positive]. Obs is the total number of observations. Cash flow news (CFN) is the stock return
driven solely by changes in cash flow expectations from t-1 to t+1 [or t+2] surrounding restatement
announcements. Discount rate news (DRN) is the stock return driven solely by changes in cost of equity
capital from t-1 to t+1 [or t+2] surrounding restatement announcements. The CFN coefficient is estimatedCov[𝑑𝑝,𝐶𝐹𝑁]
as Var(𝑑𝑝) , where DP is the log return from the same t-1 to t+1 period surrounding the restatement
announcements. Likewise, the CRN coefficient is estimated as

Cov[𝑑𝑝,𝐷𝑅𝑁]
Var(𝑑𝑝). t-statistics are reported inparentheses.

43TABLE 7
Post-restatement announcement returns after controlling for additional risk factors
Dependent Variable
Intercept
𝐿𝑜𝑤𝐶𝐹𝑁_𝐷𝑃𝑖,𝑡𝐵𝑒𝑡𝑎𝑖,𝑡−1
𝑇𝐴𝐶𝑖,𝑡−1
𝐵𝑃𝑖,𝑡−1
𝐿𝑒𝑣𝑒𝑟𝑎𝑔𝑒𝑖,𝑡−1
𝑀𝑜𝑚𝑒𝑛𝑡𝑢𝑚𝑖,𝑡−1
Adj R2# of Obs.

𝑅𝑒𝑡𝑖,𝑡

𝐵𝐻𝐴𝑅𝑖,𝑡0.010[0.22]-0.054*[-2.30]0.010[0.75]
0.165*[2.43]
0.183***[6.32]
0.025[0.50]
0.016[1.03]
0.028
1,623-0.054[-1.30]-0.052*[-2.34]0.003[0.27]
0.137[1.73]
0.059*[2.02]-0.005[-0.10]0.012[0.83]
0.007
1,211

The table reports regression results of equation (13). 𝑅𝑒𝑡𝑖,𝑡 is the one year buy-and-hold return from one day before
the restatement announcement date to 252 trading days after. 𝐵𝐻𝐴𝑅𝑖,𝑡 is the one year buy-and-hold abnormal returnfrom one day before the restatement announcement date to 252 trading days after. 𝐿𝑜𝑤𝐶𝐹𝑁_𝐷𝑃𝑖,𝑡 takes a value of
one if a firm’s cash flow news (CFN) relative to stock price changes (DP) surrounding the restatement announcement
date is below the crossectional median CFN/DP each year, otherwise zero. 𝐵𝑒𝑡𝑎𝑖,𝑡−1 is CAPM beta computed using
60 monthly returns based on the market model. 𝑇𝐴𝐶𝑖,𝑡−1 is total accruals, computed as earnings before extraordinary
income minus cash flow from operating income, scaled by the average total assets. 𝐵𝑃𝑖,𝑡−1 is the book-to-market ratio,
defined as the ratio of book value of equity to market capitalization. 𝐿𝑒𝑣𝑒𝑟𝑎𝑔𝑒𝑖,𝑡−1 is measured by total liabilities
divided by total assets. 𝑀𝑜𝑚𝑒𝑛𝑡𝑢𝑚𝑖,𝑡−1 is the twelve-month raw return from month t - 12 to month t - 1. t-statistics
reported in brackets are adjusted for heteroskedasticity and firm-level clustering. ***, **, and * indicate statisticalsignificance at the 1%, 5%, and 10% level for two-tailed test, respectively.

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