Evidence from a Multi-factor Return Model
ABSTRACT: Although earnings quality has been an important part of literature in accounting and financial economics for some time, there are relatively few examples of empirical work designed to isolate the effects of variation in earnings quality on the returns to equity ownership in the marketplace. Building on the previous literature, we conduct a robust analysis of these effects by employing earnings restatements as a proxy for quality of earnings in a multi-factor return model. Our results indicate that material misstatements of earnings have persistent (long-run) impacts on equity returns.
KEYWORDS: Earnings Quality; Cost of Equity; Multi-factor Return Models
Significant manipulations of (or material omissions from) audited financial statements by public corporations can be problematic for investors and other users of a firm’s financial reports. Greater attention to the concept of earnings quality, a catch-all term for the reliability of accounting information contained in the financial statements of corporate enterprises, may represent a response to perceptions that the manipulation of financial reporting has increased. There has been relatively little work, however, on market reactions to evidence of earnings manipulation apart from the rather immediate impact of a forced earnings restatement. Specifically, while there has been an abundance of research into the prevalence and indications of earnings management, long-run market behavior regarding the quality of earnings has been under-explored in the literature.
Earnings quality can be thought of as the “ability of reported earnings to reflect true earnings, as well as the usefulness of reported earnings to predict future earnings” (Bellovary et al., 2005). The underlying rationale for measuring earnings quality is that “current earnings are useful for predicting future earnings . . . [which] are an indicator of future dividend-paying ability” (Bauman, 1996). Thus, the accounting concept of earnings quality ties directly to the economic interpretation of earnings, or, “the extent to which reported earnings faithfully represent Hicksian income, [including] the change in net economic assets other than from transactions with owners” (Schipper and Vincent, 2003). This relationship is an important one because, as reported by Healy and Whalen (1999), “investors view earnings as value-relevant data” for assessing the prospects of corporate enterprises.
Earnings quality can also be a useful indicator of the degree of earnings management, although the two related concepts are not synonymous. Schipper (1989) defines earnings management as the “purposeful intervention in the external reporting process with the intent of obtaining some private gain” (p. 92). Teets (2002) points out that the quality of earnings is affected by at least three distinct sets of decisions: (1) decisions by standard setters; (2) management choices with regard to which accounting methods should be chosen; and, (3) judgments and estimates made in order to implement the chosen alternatives. Earnings management “can affect the quality of earnings on each of the three dimensions mentioned” (Teets, 2002. p. 356). Patterns of “smoothed” earnings can be used in attempts to communicate superior earnings to investors (Tan and Jamal, 2006; Thomas and Zhang, 2002), beat analysts’ expectations (Fields and Keys, 2003), and raise stock prices (Barth et al., 1999). Bedard and Johnstone (2004) confirm that there are positive relationships between earnings management risk and planned audit hours, billing rates, and corporate governance risk. Thus, earnings management represents an important and, possibly, expensive aspect of managerial behavior that must be monitored.
As it relates specifically to earnings management, earnings quality is also an ethical issue. As pointed out by Abdelghany (2005), an organization that manages earnings “sends a message to its employees that bending the truth is an acceptable price” and risks “creating an ethical climate in which other questionable activities may occur” (p. 1002). Thus, the relationship between earnings quality and the market pricing of equity claims involves important aspects of economic theory, accounting standard setting, and business ethics.
The current paper develops an econometric model of the impact of earnings quality on measures of market returns, to explore the level of “market monitoring” of earnings quality and management. Evidence from the model suggests that market valuations adjust to perceived indicators of low earning quality by increasing the firm’s cost of capital in response to those indicators. We begin with an overview of the theoretical relationship between earnings quality and returns, and a discussion of the appropriate measures of earnings quality in this context. Next, we introduce the use of multi-factor models in examining the impact of earnings quality on long-run returns. The sections that follow present the data, methods, and results of our quantitative tests, and a discussion of the evidence produced by them. Finally, the paper concludes with some directions for further research.
Background and Literature
Much of the literature on earnings quality and earnings management focuses on the extent to which earnings management can be detected from publicly-available accounting information. For example, Das, et al., (2007) address whether the pattern of quarterly earnings can potentially serve as an indicator of earnings management. Using quarterly data on COMPUSTAT firms from 1988 to 2004, along with CRSP daily returns on those firms, they compare firms with earnings reversals to a control sample of similar, non-reversal firms (based on seasonal changes in quarterly EPS, before extraordinary items). Their results indicate that reversals are frequent; that significant changes in fourth quarter cash flows and tax rates, relative to industry averages, indicate earnings manipulation rather than mean reversion and other alternative explanations; and that market participants, on average, regard reversals in earnings changes as efforts to manage earnings.
Researchers must take care, however, in utilizing restatements of accounting information to determine the existence or extent of earnings management. Hennes, et al., (2008) examine whether the power of hypothesis tests on accounting restatements could be significantly improved by either limiting the restatement sample to verified “irregularities” or by including variables that distinguish between errors and irregularities. The impetus for the idea is that expected turnover rates observed in top management in firms that restate earnings are lower than expected; the authors thought this likely a result of the fact that restatements may be due to either irregularities or errors. Generally speaking, only the former indicate earnings management that is potentially subject to log-run market discipline.
Employing data that includes all 8-K filings between 2002 and 2005, Hennes, et al., (2008) identify restatements that correct previous misapplications of GAAP using three sets of criteria. The authors determine that 24 percent of the restatements in the sample period were irregularities and 76 percent were errors. After refining the sample, they use COMPUSTAT data to find evidence of significant decreases in returns for firms who announced a restatement attributed to irregularity, while finding that firms whose restated earnings were due to an error had financial returns dip only slightly. Overall, the findings indicate that the effects of earnings restatements due to manipulation are more likely to be persistent than those due to errors in accounting procedure.
Dechow, et al., (2011) address two related questions: What causes managers to misstate their firms’ financial statements, and how best can investors, auditors, financial analysts, and regulators detect those misstatements? Their study examines 2,190 AAERs from 1982 to 2005 and identifies firms with misstated quarterly and or annual earnings, finding that the misstatement of expenses, the overstatement of revenues, and capitalization costs are the most common forms of misstatement. The study also identifies the time periods and industries in which misstatements were most common. The authors identify the characteristics of misstating firms in the constructed database using a series of variables including accrual quality, financial performance, nonfinancial performance, off-balance-sheet activities, and market related variables.
Some interesting conclusions emerge from the Dechow, et al., (2011) study. For example, at the time of misstatement, accrual quality is generally low and both financial and non-financial measures of performance deteriorate; financing activities, and related off-balance-sheet activities, are much more likely; and, managers of misstating firms were particularly sensitive to the firm’s stock price. The authors construct a composite measure of the likelihood of earnings manipulation, giving researchers a complementary measure to discretionary accruals for identifying low quality earnings. Their work also contributes to earnings management research by demonstrating that financial statement information beyond accruals is useful for identifying earnings manipulation.
Intuitively, it makes sense that measures of earnings quality, such as the overuse of accruals or the presence of “Big Bath” charges, should be linked to equity returns, since indications of earning management should be considered a risk factor in forecasting cash flows from holding equities. A unified, formal theory of this effect, however, has still not been firmly established. Bender and Wilson (2013) explore whether earnings quality should be considered an alpha signal, a true risk factor, or both, concluding from evidence of accrual-based measures that the first of these possibilities has the most support. By contrast, Ecker, et al., (2006), find that treating measures of earnings quality as a risk factor, analogous to market beta and other factor sensitivities, is supported by data on earning restatements, class action lawsuits relating to earnings, and bankruptcies. Further empirical work by Ecker, et al., (2006), Chan, et al., (2006), Perotti and Wagenhofer (2014), and Mitra (2016) has continued to explore the relationship between earnings quality and returns, generally indicating that such a relationship does exist.
What has not been adequately determined, however, is the extent to which this relationship is primarily transitory, (i.e., an alpha signal), persistent, (i.e., a priced factor) or a combination of both. While research has firmly tied earnings restatements to losses in market value (Dechow, et al., 1996; Palmrose, et al., 2004), comparatively little has examined the extent to which restatements affect discount rates and the cost of capital by increasing perceptions of risk. Hribar and Jenkins (2004) are among the few to examine the direct impact of restatements on the implied cost of capital, finding that the latter increases by 7-19% in month following a restatement, and that the effect continues to be positive, though perhaps declining, in the longer run. Francis, et al. (2004), examine the relation between cost of capital and several attributes of earnings quality, including accrual quality, persistence, predictability, and smoothness. Both studies represent attempts to measure direct impacts on the cost of capital, rather than relying on indirect evidence indicated by proxies for disclosure level and cost of capital (see, e.g., Welker, 1995; Botosan, 1997; Healy et al., 1999; Botosan and Plumlee, 2002). Our research is an attempt to better illuminate these impacts by allowing for both transitory and persistent (priced) impacts on market behavior, thus distinguishing between the earnings and risk adjustment impacts of earnings restatements.
Measures of Earnings Quality in Asset Pricing Models
Previous research suggests a firm’s earnings quality should have implications for the pricing of risks in the marketplace; see, e.g., Francis, et al. (2004, 2005). Our attempt to determine the impact of earnings management on financial returns, thus, requires that we estimate the level of earnings quality on a firm-by-firm basis. There are two types of earnings quality measurements generally mentioned in the literature: Input-based measures taken from data about financial disclosures themselves, and output-based measures that track the expected consequences of earnings management for the prediction of important financial time series. Input measures of earnings quality employ information about managerial decisions for a specific firm as reflected in the accounting statements that they publish. Some examples of input measures include the net levels of (or changes in) accrual and deferred accounts, the ratio of net operating assets to sales, and the frequency of “Big Bath” charges.
One of the more widely used input measures involves the behavior of accruals. For example, DeAngelo (1986) tests for earnings management by computing first differences in a firm’s total accruals over time, under the assumption that these first differences have an expected value of zero under the null hypothesis of no earnings management. Similar approaches are taken by Healy (1985), Jones (1991), Dechow (1994), and Dechow, et al., (1995). Indeed, Healy and Whalen (1999) report that investors discount “abnormal” accruals relative to “normal” accruals, indicating that they view abnormal accruals as more likely to reflect earnings management. Other input measures focus on the accumulation effects that earnings management would be expected to produce. Barton and Simko (2002)predict that, since the balance sheet accumulates the effects of previous accounting choices, the level of net operating assets relative to sales partly reflects the extent of previous earnings management (the “earnings surprise” indicator). Abdelghany (2005)posits that earnings are managed by overstating one-time “Big Bath” charges and then reversing the excessive reserve so that future earnings will increase.
Output measures of earnings quality focus on the ultimate results of published earnings over time, and on the relationships between those earnings and the financial fundamentals they represent. Schipper and Vincent’s (2003) review of the earnings management literature suggests three time-series constructs associated with earnings quality: persistence, predictability, and variability. Persistence refers to the sustainability of earnings effects on stock prices; i.e. the extent to which a change in the level of earnings translates into a “permanent” change in stock price. Predictability refers to the ability to use current earnings to forecast future earnings. Variability refers to the extent to which volatility in earnings reflects volatility in the underlying fundamentals of the firm, such as the free cash flow generation. Each of these constructs is employed to various degrees in the earnings management literature. For example, Penman (2001, 2003) employs the notions of predictability and variability in measuring the quality of earnings by the ratio of cash flow from operations (CFO) divided by net income. To the extent that earnings are reliable indicators of the firm’s ability to generate current and future cash flows, a smaller ratio indicates a higher quality of earnings. On the other hand, extensive use of accruals to manage earnings would show up as a consistent divergence between CFO and net income. In a similar vein, Leuz et al. (2003) suggest that the quality of earnings is measured by the relative variability of earnings, which is equal to the standard deviation of operating income divided by the standard deviation of cash flow from operations. The smaller the ratio, the lower the quality of earnings, on the logic that “true” earnings reflect the generation of current and future cash flows.
Another output measure is the number and/or magnitude of earnings restatements. Moriarty and Livingston (2001) report that there were 1,080 earnings restatements from 1977 to 2000, and Magrath and Weld (2002) indicate that improper revenue recognition practices were the cause of one-third of all voluntary or forced restatements of income filed with the SEC over this period. To the extent that these restatements induce market reactions, they can potentially be employed as indicators of previously-inaccurate earnings reporting subject to both short-term (transitory) and long-term (persistent) adjustments in equity prices and returns.
Multi-Factor Models and Their Application to Earnings Quality
Multi-factor return models are best known in the context of financial economics, where they are routinely used to predict and measure the required returns on portfolios of financial assets as a function of priced risk factors, which are indexes thought to be related to the risks that are relevant for pricing the portfolios. For example, a simple and well known multi-factor model of required returns is the Fama and French (1993) three-factor model. The Fama-French model suggests that the relevant risks for financial asset pricing are summarized in three indexes: One that measures the non-diversifiable market-related risk of the asset, another that adjusts the risk premium for firm size, and a third that adjusts the risk premium for the ratio of market value to book value. The rationale for such a model is that financial market participants will systematically require greater returns from riskier portfolios of assets. The three-factor model posits that those risk premiums are due to (1) non-diversifiable risks associated with the assets’ correlations with the market; (2) risks associated with firm size, where smaller firms are considered riskier; and (3) risks associated with (low) market values relative to the recorded (original) book value of the stock. This third risk factor is thought to arise from the fact that high book-to-market ratios generally indicate less confidence in the marketplace about the capability of the financial asset to “add value” in the future; thus, it is a measure of the “value” premium attached to riskier assets. Importantly, we employ this model not only because of its demonstrated value in predicting long-run returns, but also because it incorporates measures of firm size and profitability, both of which have been connected to incentives for earnings management (see, e.g., Truman and Titman, 1988) and, thus, must be controlled for in a study of earnings quality impacts on financial returns.
The Fama-French model of asset returns can be expressed in a regression equation as,
Rt – Rrf = α + b1β + b2S + b3V + et, (1)
where Rt is the one-period return on the asset in period t, Rrf is the risk-free rate, β is the market beta of the asset (defined as the sensitivity of the asset’s returns to those on the market portfolio), S is the size of the firm measured in market capitalization, V is the relative value of the firm measured by the book-to-market ratio, and et is an idiosyncratic error term in time t. To derive factor sensitivities, bi, historical data on the asset returns are regressed on measures of the relevant factors using a method such as ordinary least squares. The estimated coefficients on the factors represent the factor sensitivities. These can then be used to predict the returns required on portfolios constructed of assets with measurable factor exposures. To the extent the model holds true, the required return can be thought of as a long run prediction of tendencies in portfolio returns, and can therefore be used to determine over- or under-valuation of portfolios based on their current market prices.
The approach in this paper is to take this method which is common to financial analysis and apply it to the problem of earnings quality monitoring. There are two possible linkages between earnings quality and a firm’s market returns in our model. First, to the extent that market participants recognize earnings quality as a long-run risk factor that should be systematically discounted, firms with relatively low earnings quality will pay higher systematic returns relative to the risk-free rate. This interpretation of earnings quality discounting rests on the idea that earnings management is likely to be negatively correlated with true, underlying firm performance, and thus cyclical in its impact upon the variance in the firm’s portfolio value; i.e., it is likely that the distorting effects of earnings manipulation will be most prominent during times when performance is poor and earnings management is potentially most profitable. In this scenario, earnings quality becomes a systematic discount factor and will be assessed as part of the firm’s overall risk profile. A second possibility is that earnings quality is assessed on a period-by-period basis and, in effect, marked-to-market as part of the asset pricing process. In this alternate scenario, long run returns remain determined only by stable risk factors, but short run periodic returns vary with respect to the market’s evaluation of earnings quality on an idiosyncratic (firm-by-firm) basis. This second scenario avoids strong claims about the nature of long run asset pricing and merely asks whether periodic returns appear sensitive to changes in the level of earnings quality.
We focus on an econometric design that incorporates both interpretations. The systematic discounting of earnings of low quality should provide the strongest evidence that markets select among equity offerings based on quantitative and/or qualitative assessments of earnings risk. We note, however, that there is already considerable evidence of the weaker linkage in the literature; see, e. g., Palmrose, et al., (2004). Our attempt can be viewed as an extension of this framework to the long-term impacts of earnings management on asset returns, which according to financial theory should be displayed in increased required returns to equities which show systematic evidence of earnings management and/or low earnings quality.
Data and Methods
Twenty years of data on annual returns of the S&P 500 stocks for the period December 1995-December 2014 from were obtained from Mergent Online. We designate the average value of these returns by firm as our dependent variable to explore the impact of earnings quality measures on the long run return to S&P 500 stocks. Observations without complete data are dropped from the sample. Following a common technique illustrated by Barnett and Salomon (2006), we decompose the return into its systematic and idiosyncratic components,
Ri = a + bXi+ ui, (2)
where Ri is the average annual return to firm i, Xi is the vector of independent variables that determine returns to the firm, and ui is an idiosyncratic error term. Our control variables include the period averages for the firm’s 10-year (2005-14) equity beta (BETA), size in terms of market capitalization (MARKET CAP), book value per share (BVPS), and the number of shares outstanding (SHARES O/S), as suggested by the Fama-French three-factor model. We also employ the firm’s average price-earnings ratio (P/E) as an alternative measure for capturing the growth and value components of the Fama-French model. All data for our controls are acquired from the Mergent Online database. Descriptive statistics are presented in Table 1 below. The mean values indicate that returns averaged around 20.5% per annum for S&P equities, average beta was 1.167, and just under 23% of firms had at least one earnings restatement during the period. Missing data were dropped from the sample, so that only observations with complete data for all variables was employed.
[Insert Table 1 here]
Our primary interest is in using these data to uncover the impact of earnings quality assessments on the risk premium required on equities. To measure earnings quality, we employ the Government Accounting Office (GAO) dataset of financial restatement announcements to determine whether a restatement occurred for the firm over the period 1995-2014. RESTATEMENT is a binomial variable equal to either one or zero, depending on whether a restatement is recorded for the period. We make no attempt to parse the data into “irregularities” and “errors” in the manner suggested by Hennes, et al., (2008); thus, our measure of earnings quality does not speak to earnings management or intentional manipulation directly. Instead, we rely on the design of the empirical model to produce differential effects that might be indicative of distinctions between transitory and persistent impacts dictated by market behavior.
Financial theory suggests that, for cases where earnings are thought to have been actively manipulated, there should be a persistent effect on the risk premium applied to equity returns; evidence of earnings manipulation should result in a systematic increase in the minimum return required on equity financing subject to this risk. If this is the case, then restatement events can be employed as a proxy for non-diversifiable risks that would permanently increase equity risk premia for firms where the restatements reflect “irregularities” as opposed to “errors” in the sense of Hennes, et al. (2008). Therefore, we extend Equation (2) above to include an interactive term that relates restatements to increases in non-diversifiable risk:
where d is the coefficient on the interactive term between our earnings quality measure (RESTATEMENT) and firm-specific, non-diversifiable risk (BETA). This interaction implies that earnings quality is a priced risk factor that makes a firm’s returns more variable with respect to the market and, thus, systematic in nature. A positive sign for c would indicate a re-evaluation of systematic risk for the equity whose earnings have been subject to perceived manipulation. We note that, in the absence of a risk-free rate among the independent variables, the risk-free return (Rrf) will be unidentified and, thus, incorporated into the constant, a; the constant term is not, therefore, analogous to a measure of alpha (α) or excess systematic return.
The above specification only accounts for increases in systematic (i.e. priced) risk-adjustments to returns that occur as investors learn that past earnings have been misleading. However, as mentioned earlier, there is theory and evidence that certain types of restatements, i.e., those resulting from error rather than irregularities, are likely to have only transitory effects on returns; while restatements due to an unintentional accounting error may be problematic, their effects are confined to a one-time adjustment in present values. Since this is a possibility, our model should be amended to reflect these transitory effects on return.
We accomplish this by including our earnings quality proxy as a separate independent variable that does not interact with market risk. Modifying Equation (3) with the addition of our non-interacted measure yields,
Ri = a + bXi + cRESTATEMENT*BETAi + dRESTATEMENTi + ui. (4)
Thus, our empirical design allows for a distinction between a transitory shock due to restatements that may be due to accounting errors or unintentional omissions, and irregularities that indicate evidence of aggressive accounting and earnings manipulation, where restatements are viewed as a proxy for an increased risk profile. One would expect market participants to systematically discount the equities of companies that appear to engage in the latter, while not for the former. Our expectations are that the coefficient estimate for c should be negative, indicating one-time downward adjustments due to new information about earnings, while the estimate for d should be positive, as an indication of permanent discounting. Essentially, our two coefficients c and d represent impacts on alpha (unsystematic return) and beta (risk), respectively.
Finally, there is some concern about the use of the standard Fama-French factors on a data set that consists essentially of only large firms with considerable market and book values. The Fama-French size and value terms are meant to be measured relative to a set of complete portfolio options, and do not necessarily apply in a large firm setting. Due to the extensive evidence of both “value” and “growth” premia across equity markets, we can employ the firm’s average price-earnings (P/E) ratio as an alternative indicator of these premia. Our regression estimates, therefore, include two versions of Equations (3) and (4), one each with the standard Fama-French measures for size and value, and one each with P/E as a single indicator of value and growth impacts on long-run returns.
Results and Interpretation
The regression results are presented in Table 2 below. Pooled Ordinary Least Squares with unadjusted standard errors is used to estimate the parameters a, b, c, and d. Standard errors and t-statistics are presented for ease of interpretation. Among the control variables, only market beta (BETA) shows a statistically significant, positive effect. This suggests that a simpler model like CAPM may be appropriate for measuring required returns to S&P 500 stocks. F-statistics and log likelihood ratios suggest significance for the overall regression at well within the standard 5% probability level.
[Insert Table 2 here]
We begin with our equation for the basic Fama-French model with an interaction term for increases in perceived risk. Our variable of interest, the risk-assessment effect of restatements, shows a significant positive impact on the average annual return to S&P 500 stocks, in accordance with expectations. The coefficient on the interactive term, RESTATEMENT*BETA, is large, positive, and statistically significant, suggesting that, to the extent that investors consider restatements an indicator of earnings manipulation, investors adjust their long-term required returns on the affected equities. According to these results, an instance of restatement causes an increase in required return of 3.8% for each measured unit of beta. To illustrate the impact, consider a stock with average risk (BETA=1) that is subject to a restatement of earnings. Ignoring the minimal impact of the Fama-French coefficients for market cap, book value per share, and number of shares, the stock’s predicted required return from the model would be about r* = .074 + .101 + .038 = .213, which represents a 37.6% increase in the risk premium and a 21.7% increase in required return compared to an equity with no instance of restatement.
Of course, our theoretical discussion suggests that this is an average over all instances of restatements, including those that are judged as errors as well as irregularities. The average is, thus, being generated only by the subset of restatements that indicate irregularities which, according to Hennes et al., comprise only about a quarter of all restatements. The second estimated equation can provide a more accurate illustration by including both the transitory effect of revaluation of earnings (alpha) and the persistent effect on perceived risk (beta). The coefficient on the binomial RESTATEMENT variable represents an immediate, one-time revaluation of the equity based on a new set of expected cash flows. Although not a statistically-significant estimate, the coefficient is negative as expected, indicating the possibility of a sudden decrease of about 6% of market value caused by adjustments to new expectations concerning values of future cash flows.
The results of our second estimation of the variable of interest are more telling than those of the first. The coefficient on the interactive term is more than double that of the first estimation without the transitory alpha term included. Given that only a fraction of restatements actually indicate accounting irregularities, this is to be expected. Recall that while every restatement is subject to a one-time readjustment of return based on revaluation, each stock has only about a 1-in-4 chance of necessitating an increase in required return due to an irregularity. Assuming the 3-to-1 ratio of errors to irregularities holds, the second equation is likely to provide a much better estimate for long-term reactions for earnings manipulation in cases where actors see evidence of its occurrence.
Our results indicate two possible effects on the returns of equities subject to an earnings restatement: A transitory decrease in the expected value (market price) of the stock based on revaluations of the cash flows expected from holding the equity claim, and a long-term increase in the equity cost of capital due to a reassessment of the risk associated with earnings estimates based on the firm’s financial reports. We reason that the first of these effects has little to do with earnings manipulation, but that the second is solid evidence that investors incorporate evidence of earnings manipulation into their assessments of financial risks associated with holding equities. Based on our estimations, the effect of perceived manipulation on an equity with average measured risk is between 3.8% and 9.9%, with models that include a transitory impact on equity alpha yielding much higher risk-adjustment impacts than those without.
Care must be taken in interpreting the coefficient estimates from our regressions; we have employed a limited data set and failed to control for numerous firm level effects that undoubtedly influence long run returns. The results, however, provide reasonable support to conclusions already explored in the literature. Our estimates for the market risk premium, our coefficient b, range from 8.9% to 10.1%, well within the range of normal estimates. Our estimates of the transitory impact of earnings restatements also fit well within established estimates. For example, Palmrose, et al., (2004) suggest that the periodic “penalty” on firms that restate earnings is in the range of 6%-20% of the firm’s beginning equity value. Since these control parameters appear reasonable, our estimates may provide a solid basis for exploring further long-run implications of earnings quality on the market pricing and required returns of equity offerings.
To add robustness to the results, we employed some alternative specifications that could address unobserved statistical issues. Pooled OLS with White heteroskedasticity-consistent standard errors should produce similar coefficient estimates with reduced statistical significance. Low statistical significance and magnitudes on our controls for market capitalization (MKT CAP) and book value (BVPS*SHARES O/S) suggest that these variables could be employed as instruments to control for omitted variable bias in the form of endogeneity between our independent variables and average annual returns. Finally, the actual number of restatements (RESTATE NUM) could be used as an alternate proxy for the transitory (short-run) effects of accounting “errors” that lead to restatements, although it would be inappropriate as a long-run indicator of earnings quality. Results presented in Table 3 below are derived from these alternate specifications. Regression results are obtained employing (1) a pooled least squares version with White-adjusted error terms and (2) two-stage least squares using the Fama-French variables as instruments. Each of the two sets includes one model where the transitory effect of restatements (RESTATE NUM) is excluded and one with it included. Unsurprisingly, significance levels fall for earnings quality in the case of the pooled OLS model with corrected errors, meaning that the OLS model might be particularly sensitive to heteroskedasticity. The 2SLS model, on the other hand, exhibits roughly the same signs and significance levels as our previous models; probability levels for our variable of interest remain in the standard ranges for statistical relevance. Therefore, we are confident that our results are at least somewhat robust to alternative methodologies for estimating the impact of restatements on expected returns.
[Insert Table 3 here]
Our results suggest that perceptions of earnings quality are an important component of risk differentiation among S&P 500 equities. In fact, although most of the systematic variation in equity returns that we would normally ascribe to market risk (BETA) is captured by that term, additional interaction with restatement activity contributes an additional impact of anywhere from 400 to 1000 basis points to the required return on an average-risk stock, with most estimates near the lower end of the spectrum. Reasonable efforts to account for endogeneity do not alter these relationships much. Most importantly, the results confirm our priors by indicating a distinct impact of restatement activity on long-run returns apart from the transitory effect that lowers (penalizes) the firm’s market value—an interactive impact with market beta that increases the minimum required long-run return on the equity. We interpret this to indicate evidence of a systematic discounting of prices on equities where accounting irregularities suggest the presence of aggressive accounting and/or earnings manipulation.
We have conducted a series of empirical tests of the relationship between accounting restatements and long-run returns to S&P 500 stocks. The results strongly support our hypothesis that long-run returns are sensitive to perceptions of earnings manipulation as indicated by earnings restatements. However, limitations inherent in this study suggest avenues for further development. First, a larger sample of equities from the NYSE, NASDAQ, or other (including non-U.S.) exchanges would allow for additional controls as well as fixed and/or random effect models. Additional input and output measures earnings quality could also provide useful variation and give a better idea of how markets do and do not interpret firm level data on earnings quality assessments. We have utilized a fairly simple measure of long run returns: average annual returns based on a 20-year time series. Alternatives would include using actual monthly returns in a panel data set, employing required returns produced from a more complex model like Arbitrage Pricing Theory (APT), or foregoing return data altogether and opting instead for price-driven data like Price/Earnings, Price/Cash Flow, EV/EBITDA or other multiples. Rates of discount from market or industry norms could be examined in this context as possible indications of market assessment of earnings quality. Finally, adding firm and industry level controls, as well as parsing “irregularities” from “errors” in accounting restatements, could add explanatory power to our generalized format. We believe, nonetheless, that the research contained herein represents an important first step toward a better understanding of earnings quality assessment in financial markets.
Table 1. Descriptive Statistics for Dependent and Independent Variables
|Variable||Mean||Median||Std. Dev.||Valid Obs.|
|MARKET CAP||$215 million||$8.1 million||$1.4 billion||486|
|SHARES O/S||6.72 million||244,027||44.1 million||493|
Table 2: Pooled OLS Results for Earnings Quality Impact on Average Annual Returns, 1995-2014. Unadjusted standard errors.
|Variable||Coef. (S. E.)||Coef. (S. E.)||Coef. (S. E.)||Coef. (S. E.)|
|CONSTANT||0.074 (0.024)**||0.089 (0.028)**||0.054 (0.024)**||0.069 (0.028)**|
|BETA||0.101 (0.020)**||0.089 (0.022)**||0.093 (0.021)**||0.083 (0.023)**|
|MARKET CAP||2.52e-11 (1.2e-11)||1.53e-11 (1.2e-11)|
|BVPS*SHARES O/S||-7.06e-11 (4.5e-11)||-2.84e-11 (4.5e-11)|
|P/E||0.001 (0.0001)**||0.001 (0.0001)**|
|RESTATEMENT*BETA||0.038 (0.019)**||0.087 (0.047)*||0.053 (0.019)**||0.099 (0.048)**|
|RESTATMENT||-0.065 (0.057)||-0.060 (0.057)|
|Mean of dep. variable||0.1987||0.1987||0.1963||0.1963|
*, ** indicate significance at the 10% and 5% levels, respectively
Table 3: Pooled OLS (White-adjusted standard errors) and Two-Stage Least Squares Results for Earnings Quality Impact on Average Annual Returns, 1995-2014.
|Pooled OLS||Pooled OLS||2SLS||2SLS|
|Variable||Coef. (S. E.)||Coef. (S. E.)||Coef. (S. E.)||Coef. (S. E.)|
|CONSTANT||0.054 (0.033)*||0.059 (0.032)*||0.054 (0.025)**||0.059 (0.025)**|
|BETA||0.093 (0.016)**||0.094 (0.016)**||0.094 (0.021)**||0.095 (0.021)**|
|P/E||0.001 (0.001)||0.0001 (0.0001)||0.001 (0.0001)**||0.001 (0.0001)**|
|RESTATEMENT*BETA||0.053 (0.043)||0.052 (0.043)||0.051 (0.020)**||0.051 (0.020)**|
|RESTATE NUM||-0.017 (0.007)**||-0.017 (0.012)|
|Mean of dep. variable||0.1963||0.1963||0.1954||0.1954|
*, ** indicate significance at the 10% and 5% levels, respectively
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 See, e. g., Easley and O’Hara (2005), Francis, et al. (2005), and Lambert, et al. (2005), for examples of work relating to the treatment of earnings quality as a priced risk factor. Thomas and Zhang (2002) also explore the theoretical relationship between earnings quality and future returns.
 Dechow, et al. (2010), provide a comprehensive overview of issues relating to earnings quality measurement. Much of the discussion in this section is derived from Dempster (2008).
 An alternative would have been to employ something like the five-factor Fama-French (2015) model that explicitly includes profitability. However, since our econometric design incorporates book value as an independent variable, additions to asset value via profitability are accounted for as directly as is necessary for our purposes.
 Multiplying Shares Outstanding and BVPS converts the two independent terms into the numerator of the value term of the Fama-French model. The denominator, market capitalization, is already included in the equation. We employ this decomposition to ensure that both firm size and profitability are independently controlled for in the model.