How does earnings quality affect the equity market? An alternative measure and a new perspective

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1 How does earnings quality affect the equity market? An alternative measure and a new perspective Chad Larson Olin School of Business Washington University in St. Louis clarson@wustl.edu Robert J. Resutek Tuck School of Business Dartmouth robert.j.resutek@tuck.dartmouth.edu First Draft July 2011 Current Draft November 2011 Preliminary do not cite without permission Abstract We propose and empirically validate forward-looking measures of earnings quality. Our earnings quality measures directly relate to how precisely future earnings can be estimated and have two components: an accrual component and a cash flow component. Our empirical tests produce three results: (i) The forward-looking earnings quality measures are more strongly associated with the absolute magnitude of earnings forecast errors relative to time-series based earnings quality measures. (ii) There is a strong negative relation between future returns and our measures of earnings quality. This relation is strongest in the accrual component of our earnings quality measure, but also exists in the cash flow component. (iii) Variation in earnings quality is unrelated to variation in conventional measures of risk. JEL Codes: G14, M41 Key Words: Earnings quality, earnings volatility, accrual quality, earnings management Data Availability: Data is available from public sources as identified in the text. Contact author. We thank Weili Ge and workshop participants at Dartmouth, BYU s Accounting Research Symposium, and Washington University for helpful comments.

2 How does earnings quality affect the equity market? An alternative measure and a new perspective Abstract We propose and empirically validate forward-looking measures of earnings quality. Our earnings quality measures directly relate to how precisely future earnings can be estimated and have two components: an accrual component and a cash flow component. Our empirical tests produce three results: (i) The forward-looking earnings quality measures are more strongly associated with the absolute magnitude of earnings forecast errors relative to time-series based earnings quality measures. (ii) There is a strong negative relation between future returns and our measures of earnings quality. This relation is strongest in the accrual component of our earnings quality measure, but also exists in the cash flow component. (iii) Variation in earnings quality is unrelated to variation in conventional measures of risk.

3 1 Introduction This study proposes new, forward-looking estimates of earnings quality and examines the relation between these measures and future returns over the period We limit our definition of earnings quality and define it only in terms of uncertainty, namely, how precisely future earnings can be estimated. This view is consistent with SFAC No. 1 which states one of the objectives of financial reporting is to provide information that is relevant to assessing the amount, timing, and uncertainty of future cash flows. This view is also consistent with theoretical studies that model earnings quality as a reduction of the market s assessment of variance in the terminal value due to earnings (Ewert and Wagenhofer 2010) and empirical studies that define earnings quality in terms of precision (Ecker et al. 2006; Francis et al. 2008). 1 We argue that the precision with which future earnings can be estimated is a joint function of two elements of uncertainty. The first element is uncertainty in the future financial performance as measured by GAAP (economic uncertainty). The second element is uncertainty in the financial reporting and disclosure choices managers will make in reporting future performance (reporting uncertainty). Prior studies often use time-series volatility measures to proxy for earnings quality. These time-series measures jointly capture both aspects of earnings uncertainty. Our empirical approach provides a direct estimate of the economic uncertainty element of earnings quality, an element that has been largely ignored by prior studies despite its significance to variation in earnings quality (Dechow et al. 2010). The motivation for our earnings quality measures is both theoretical and practical. From a theoretical perspective, earnings quality is often proxied as a noise term that informs on how precisely future earnings can be estimated. Since change in equity value is a function of future earnings, not realized earnings, understanding how precisely future earnings can be estimated is important when assessing a firm s earnings quality. Empirical studies to date have proxied for the noise term using time-series variation in realizations of earnings and cash flows. This empirical design choice could lead to flawed earnings quality inferences if time-series variation is not a reasonable proxy for how precisely future earnings can be estimated. From a practical perspective, we note several limitations with respect to earnings quality variables derived from a time-series of realizations. First, time-series measures of earnings quality assume stationary earnings and cash flow processes. Given extensive evidence on earnings momentum and 1 We note that most empirical proxies for earnings quality are direct or derivative functions of earnings volatility. For example, earnings predictability (e.g., Francis et al. 2005), earnings smoothness (Leuz et al. 2003), and residual accrual volatility (Dechow and Dichev 2002) are each estimated from empirical proxies of volatility. 1

4 earnings reversals (Kothari 2001), the reasonableness of this assumption is questionable. Second, time-series based earnings quality variables often require a minimum 5-10 year time-series of earnings, cash flow, and accrual realizations, thereby limiting empirical inferences to those firms that have survived for at least 5-10 years. Given these limitations, we develop an empirical measure of earnings quality that requires a minimal time-series and does not impose a stationarity assumption. Our empirical design is based on the premise that a reasonable proxy for the uncertainty of future earnings and cash flows is the distribution (or volatility) surrounding expected future earnings and cash flows. In this spirit, we employ a matched-firm empirical design that matches the firm of interest to firms with similar characteristics from prior periods. From this matching process, we obtain an expectation of future earnings and cash flows. We then use the standard deviation of the matched-firm realizations as proxies for the uncertainty surrounding future earnings and cash flows. Because our uncertainty estimates are functions of the average financial performance of comparable firms as measured by GAAP, we argue that these estimates capture uncertainty in future financial performance (economic uncertainty). Likewise, we argue that the element of earnings uncertainty associated with idiosyncratic reporting choices of individual managers is not captured since these choices tend to cancel out against the choices of the other matched-firms. Given our two independently-generated estimates of earnings and cash flow uncertainty, we derive an estimate of uncertainty that is attributable to the accrual process. We then examine whether the equity market places differential weights on the two components of earnings quality: cash flow uncertainty and accrual uncertainty. An extensive literature in accounting has developed over the past ten years that examines the equity market consequences of variation in earnings quality. Given that our measures of earnings quality are forward-looking and more directly map into the precision in investor expectations of future earnings, our measures have the potential to capture value-relevant pricing dynamics that may not be evident from time-series based measures of earnings quality. Our results contribute to the earnings quality literature in four ways. First, we argue that our measures of earnings quality, the accrual and cash flow components of earnings uncertainty, capture the economic element of earnings quality. Recent reviews of the earnings quality literatures observe that although the quality of a firm s earnings is a joint function of both the firm s economic performance and the reporting choices of managers, the earnings quality literature often inadequately distinguishes between these two elements (Dechow et al. 2010). To the best of our knowledge, our study represents the first attempt to propose empirical variables that only capture the earnings quality dynamics associated with the firm s expected economic performance. This advance allows us to make stronger inferences with respect 2

5 to whether the reporting choices of mangers or the underlying economic fundamentals of the firm lead to certain empirical associations. Second, we empirically validate and compare our earnings quality variables against the conventional time-series measures used in prior studies. Across both the cross-sectional and time-series analyses, our estimates of earnings quality are more strongly associated with how precisely future earnings can be estimated compared to the conventional, time-series measures of earnings quality. Third, in contrast to recent studies which find no relation between volatility-based measures of earnings quality and realized one-year returns (Core et al. 2008; McInnis 2010), we find a strong negative relation between future returns and our forward-looking measures of earnings quality. Our results do not contradict Core et al. (2008) or McInnis (2010). Rather, we show that when the components of earnings quality are estimated on a forward-looking basis and capture only the economic elements of a firm, there is a strong negative relation between future returns and accrual components of earnings quality. Fourth, we propose an alternative equity market consequence associated with variation in earnings quality. Prior studies have posited that if earnings quality is relevant to the equity market, the consequences of this quality would manifest through variation in the firm s cost of capital (Francis et al. 2004; Easley and O Hara 2004; Lambert et al. 2007). Our evidence suggests that if earnings quality is a function of earnings uncertainty, a proposition supported by many prior studies, variation in earnings quality has an economically significant effect on investor expectations of future earnings. Our evidence does not refute or rebuff the contention that earnings quality is inversely related to cost of equity. In fact, our results say little on the effect that disclosure quality has on a firm s cost of equity, an effect that has been posited in both empirical (Botosan 1997; Botosan and Plumlee 2002) and theoretical studies (Lambert et al. 2007). Rather, our empirical evidence highlights the need to consider the effect of economic uncertainty on a firm s earnings quality when examining the relation between disclosure quality and cost of equity capital. This consideration is especially important since the financial reporting and disclosure policies of a manager are most likely correlated to uncertainty in the firm s future earnings. Our study proceeds as follows. Section 2 describes prior literature and motivates our empirical design. Section 3 describes our cross-sectional measures of uncertainty and discusses summary statistics. Section 4 empirically compares our cross-sectional measures of uncertainty against the time-series equivalents. Section 5 notes how we decompose earnings quality into an accrual and cash flow component and compares these earnings quality elements against the conventional time-series earnings quality variables. Section 6 documents the relation between our cross-sectional earnings quality variables 3

6 and future returns. Section 7 discusses robustness tests and time-series variation in our measure. Section 8 concludes. 2. Prior literature and motivation 2.1 Prior literature An underlying principle of accrual accounting is that accruals eliminate random fluctuations in cash flows resulting from the timing of cash receipts and disbursements. The elimination of random fluctuations in cash flows leads to earnings that are generally less volatile than cash flows, thereby making earnings more informative about current and future economic performance (Dechow 1994; Dechow et al. 2010). However, because the accrual process requires management discretion and estimation, it is subject to both intentional and unintentional measurement error thereby reducing the reliability of accruals relative to cash flows (Richardson et al. 2005). Herein is the tension motivating recent studies examining whether earnings quality affects firm value through cost of capital. Recent asset pricing models such as Easley and O Hara (2004), Lambert et al. (2007) suggest that firms with more precise information about future cash flows should enjoy lower costs of equity. While the mechanisms vary across these and other estimation risk models, the general empirical implications are the same. That is, to the extent that the precision that market agents can estimate a firm s future dividend stream is positively associated with the firm s earnings quality, a firm s cost of capital will negatively covary with the firm s earnings quality. Despite an extensive set of empirical studies in this area over the past 10 years, strong debate still exists as to whether a firm s earnings quality is associated with its cost of capital. Much of the debate centers on the fact that despite relations between measures of earnings quality and implied cost of equity measures that suggest that earnings quality is inversely related to systematic risk (Francis et al. 2004; 2005), realized returns are unrelated to these measures of earnings quality (Core et al. 2008; McInnis 2010). Since realized future returns are viewed as an unbiased, albeit potentially noisy, estimate of cost of equity (Lewellen 2010), the lack of a significant relation with current period measures of earnings quality leaves doubt in the minds of some researchers as to the value-relevance of earnings quality to the equity market. Perhaps overlooked in the debate on the equity market consequences of earnings quality is whether earnings quality affects investor expectations, and thereby asset price. There is a relatively extensive asset pricing literature that suggests if certain assumptions regarding the existence of homogeneous expectations, frictionless markets, influential market makers with unlimited arbitraging ability are relaxed, predictable cross-sectional variation in future returns not attributable to risk can be noted. Alternatively, even if classic asset pricing assumptions bind, if the precision of accounting 4

7 information is associated with uncertainty in future earnings or parameter uncertainty, predictable variation in future returns will be noted (Pastor and Veronesi 2003; Lewellen and Shanken 2002). Early empirical evidence suggestive that differences in investor expectations can lead to predictable future return patterns is noted by Diether et al (2002). The differences in opinion (DO) hypothesis builds on an idea put forth in Miller (1977). Specifically, Diether et al. contend that analyst forecast dispersion proxies for investor disagreement. They suggest that the negative future return pattern associated with analyst forecast dispersion is consistent with Miller s hypothesis that stock price will reflect a more optimistic valuation if pessimistic investors are kept out of the market by high short-sale costs or high arbitrage risk. Subsequent studies confirm the relation between future returns and analyst forecast dispersion, although debate Diether et al. s explanation (Johnson 2004; Barron et al. 2009). In a related stream of literature, Zhang (2006) and Jiang et al. (2005) suggest that the earnings processes of firms operating in uncertain environments are less knowable to even sophisticated investors (information uncertainty (IU) hypothesis). The IU hypothesis also focuses on variation in investor expectations of future earnings, but frames the argument from the perspective of ambiguity. Jiang et al. and Zhang each suggest that ambiguity relating to the level and distribution of future earnings amplifies behavioral pricing biases like those posited in Daniel et al. (1998; 2001). Specifically, investor overconfidence in private information leads to greater deviation in price from intrinsic value in high IU stocks since verifiable, public information is less prevalent. Consequently, high IU firms tend to realized stronger price continuation anomalies such as return momentum and post-announcement drift since price discovery takes longer. Prior studies in both the DO and IU literatures do not directly specify a primitive economic mechanism describing the cause of the disagreement or ambiguity. For example, the empirical proxies for information uncertainty of Jiang et al. (2005) include firm age, implied equity duration, and return volatility. Other proxies of value ambiguity examined in prior studies include firm size, return volatility, variation in institutional ownership, and many non-accounting based variables. Interestingly, despite theory suggesting earnings quality is positively associated with how precisely future earnings can be estimated (Ewert and Wagenhofer 2010), direct accounting-based measures of earnings quality are rarely examined in the DO and IU literature. 2 In these instances, empirical evidence suggesting that accounting-based measures of information uncertainty are associated with future returns is much weaker 2 Zhang (2006) examines cash flow volatility and analyst earnings forecast dispersion (table 2, pp. 114) and fails to find a significant relation between these measures of information uncertainty and future returns. 5

8 (or insignificant) in comparison to the non-accounting based measures such as return volatility, market capitalization, and firm age. 2.2 Motivation for forward-looking earnings quality measure As examined in prior studies, empirical estimates of earnings quality are generally derived in one of two ways. The first way uses a 5-10 year time-series of earnings, cash flow, and accrual realizations to estimate accounting-based measures of earnings quality. Common time-series based measures include derivatives of firm-specific OLS regressions (e.g., earnings persistence, earnings predictability, residual accrual volatility) as well as derivatives of firm-specific volatility estimates (e.g., earnings smoothness). The second way is to use firm characteristics not directly related to accounting realizations, but posited to affect investors perspective of future earnings. These characteristics include such things as firm age, firm size, R&D intensity, propensity to meet or beat earnings targets. Shortcomings of empirical proxies of earnings quality have been discussed at length in the literature (McNichols 2002; Dechow et al. 2010; DeFond 2010). Criticisms generally center on the fact that these measures jointly capture uncertainty attributable to financial performance and uncertainty attributable to the idiosyncratic reporting choices of managers. For example, Dechow et al. note that prior studies often inadequately distinguishes the effect on earnings quality of fundamental performance from the effect of the reporting choices managers make. 3 A less discussed, but possibly equally important criticism, relates to the specification of the earnings quality measures derived from a time-series of accounting realizations. As noted above, many earnings quality measures are either direct or derivative functions of time-series variation in the accounting realizations. For example, Francis et al. (2005) examine earnings characteristics such as earnings predictability, earnings smoothness, accruals quality, cash flow volatility, and sales volatility. Each of these characteristics is computed over rolling 10 year windows using time-series variation in accounting realizations. If these measures of earnings quality are to be relevant to the equity market, they must be informative of qualities of future earnings realizations. In other words, if historical variation is a poor proxy for future uncertainty, then earnings quality will appear empirically to be irrelevant to the equity market even if the equity market is systematically affected by earnings quality. Our study represents the first attempt to estimate only one component of earnings quality, the component associated with economic uncertainty, and do so on a forward looking basis. As noted above, we define earnings quality in terms of precision, namely how precisely can future earnings be estimated. This perspective is similar to Easley and O Hara (2004), Lambert et al. (2007), Ecker et al. (2006) who 3 A similar criticism is often leveled against the empirical models used to distinguish discretionary from non-discretionary accruals in the earnings management literature see McNichols

9 each interpret precision as a proxy for earnings (or information) quality. Further, to the extent that earnings precision is relevant to equity investors and informative of the future earnings process of the firm, our definition of earnings quality also dovetails into the broad definition for earnings quality of Dechow et al. (2010). Our empirical design rests on the premise that an estimate of the second moment of a random variable (e.g., earnings volatility or precision) is only as valid as the estimate of the first moment of that random variable (e.g., the earnings expectation). Accordingly, we build from the empirical designs of Barber and Lyon (1996), Blouin et al. (2010) and Donelson and Resutek (2011) and form expectations of future earnings and cash flows based on a matched-firm approach. We then use the distributions of the matched firms earnings and cash flow realizations to derive our estimates of earnings quality which, by default, relate directly to how precisely future earnings can be estimated. Further, because the idiosyncratic financial reporting choices of managers tend to cancel out when aggregated across multiple firms, we argue that variation in our earnings quality measures is attributable to economic uncertainty, not uncertainty in how managers will choose to report in the future. 3 Sample, variable measurement, and descriptive statistics 3.1 Cross-sectional volatility measurement (CSEV and CSCFV) Our earnings quality measures are based on the uncertainties (or volatilities) surrounding the expectations of future earnings and cash flows. To derive empirical estimates of these volatilities, we begin by first estimating future earnings and cash flows in the spirit of Barber and Lyon (1996). 4 We match each firm i, at time t, on three characteristics. First, we match by firm size based on NYSE average total asset deciles. Each year, firms are allocated to one of three asset-based portfolios based on prior year breakpoints. The first portfolio comprises the smallest NYSE size decile (this is roughly 50% of the sample). The remaining two portfolios are constructed by combining the first through fourth NYSE deciles and the fifth through tenth NYSE deciles. We then match each firm i to firms within the respective size portfolio with comparable earnings characteristics in year t-1. Specifically, for a firm i in fiscal year t, we utilize as matches all firms within the same size portfolio whose earnings level and one year earnings change at fiscal year end t-1 (Earnings t-1 -Earnings t-2 ) are between 70% and 130% of firm i's earnings level and one-year earnings change at fiscal year end t. This matching process yields, for each firm i, a set of firms with comparable expected performance that is observable at the time t. For each matched-firm, we then compute the change in earnings between t-1 and t. To reduce the 4 For brevity, we discuss the construction of our cross-sectional measure of earnings volatility in section 3.1. The construction of our cross-sectional measure of cash flow volatility (CSCFV) follows the exact same steps as CSEV, but we substitute cash flow from operations for earnings. 7

10 mechanical effect that an extreme earnings change in a matched-firm has on estimates of earnings volatility, we discard matched-firms with extreme performance, defined as earnings changes less than -50% or greater than 50%. We use the median change in earnings across matched-firms (between t-1 and t) as an expectation of firm i's expected earnings change between t and t+1. We use the standard deviation in the expected earnings of firm i as a measure of firm i's earnings volatility around its t+1 earnings expectation. We require at least two matches for each firm to compute this characteristic. When at least two matches are not available in year t-1 (the minimum number of observations to derive a standard deviation), we extend the matching process back to year t-2. If at least two matches are not available across t-1 and t-2, we extend it back to t-3. We repeat this process for unmatched-firms back 5 years. 5 To summarize, for each firm i at time t, we require an earnings realization (Earn i,t ) and a change in earnings over the last fiscal year (Earn i,t -Earn i,t-1 ). We then group all firms j with earnings realizations (Earn j,t ) and change in earnings (Earn j,t-1 -Earn j,t-2 ) between 70% and 130% of firm i. That is, to be included in firm i s matched-firms, firm j must meet the following criteria: 0.70(Earn i,t ) ( Earn j,t-τ ) 1.30(Earn i,t ) and 0.70(Earn i,t -Earn i,t-1 ) ( Earn j,t- τ -Earn j,t- τ-1 ) 1.30(Earn i,t -Earn i,t-1 ), where Earn j,t- τ -Earn j,t- τ-1 <0.50 Formally, we define the earnings expectation and earnings volatility as follows: E i,t [Earn i,t+1 ] = median(earn i,t + δearn j,t ) CSEV i,t = n n (Earn i,t 1 - Earn i,t 1 ) n-1 (δearn ) n-1 j i 1 i 1 To construct our cross-sectional cash flow volatility measure (CSCFV), we follow the same empirical matching process as discussed above for CSEV, but substitute cash flow from operations for earnings. That is, firms are grouped into portfolios based on size, level of cash flows, and change in cash flows and a cash flow expectation and volatility estimate are derived. 5 We account for fiscal year end month in our matching process to ensure that the matched firms (firms j) earnings realizations are available to form the earnings estimate and volatility estimate of firm i at time t. 8

11 Table 1 Variable Construction and Summary Statistics This table reports derivation of the cross-sectional volatility estimates (Panel A) and cross-sectional summary statistics (Panel B). Specifically, Panel B reports the time-series average of the annual cross-sectional mean (Avg.), standard deviation (Std.), 1 st percentile (Min.), 50 th percentile (Med.), 99 th percentile (Max.), and number of observations (Obs.). The sample spans firms with fiscal year ends between 1973:06 and 2010:12. All variables are scaled by average total assets with the exception of LogB/M t and are annually winsorized at the 1 st and 99 th percentile. Panel A: Derivation of cross-sectional volatility estimates Full Compustat sample 1/1/ /31/ , ,763 Compustat sample where -1.0 Earn t (CFO t ) 1.0 and Earn t-1 (CFO t-1 ) is not missing 301, ,323 Firms with at least 2 matches going back: 1 year 266, ,020 2 years 10,084 5,948 3 years 2,226 1,224 4 years years , ,396 NYSE/AMEX/Nasdaq firms (CRSP exchange code 1, 2, or 3), fiscal years ending 6/73 12/10 and CRSP share code 10 or 11: w/non-missing CSEV or TSEV (CSCFV or TSCFV) 166, ,086 w/non-missing Earn t and CFO t and 1 volatility vars. (CSEV or TSEV or CSCFV or TSCFV) 141, ,608 Earn t CFO t Panel B: Summary Statistics Variable Description Avg. Std. Min. Med. Max. Obs. Earn t Earnings before X-ordinary ,726.5 CFO t Cash flow from operations ,726.5 dnwc t Change in NWC ,726.5 OthAcc t Other operating accruals ,726.5 CSEV t Cross-sectional earnings volatility ,563.1 TSEV t Time-series earnings volatility ,989.6 CSCFV t Cross-sectional cash flow volatility ,242.3 TSCFV t Time-series cash flow volatility ,594.3 dsales t One year change in Sales ,723.7 LogB/M t Book-to-market ,584.0 Earn t Earnings before extraordinary items (IB) scaled by average total assets (AT) CFO t Earn t + OthAcc t - dnwc t dnwc t One year change net working capital. Net working capital is defined as current assets (ACT) minus cash (CHE) minus current liabilities (LCT) plus short term debt (DLCC). Short term debt is set to zero if missing. OthAcc t Non-working capital accruals from the Statement of Cash Flow to adjust Earn t to cash flow from operations. CSEV t Cross-sectional earnings volatility as defined in section 3.1 TSEV t Time-series earnings volatility computed as the standard deviation of Earn t between t-4 and t. CSCFV t Cross-sectional cash flow volatility as defined in section 3.1 TSCFV t Time-series cash flow volatility computed as the standard deviation of CFO t between t-4 and t. dsales t One year change in sales (Sale) between t-1 and t LogB/M t Natural log of book to market. To compute book value of equity we take, when not missing, shareholder s equity (SEQ), or common equity plus preferred stock (CEQ+PSTK), or total assets minus total liabilities (AT-LT) in that order. From shareholders equity, we subtract preferred stock value, where we use either redemption value (PSTKRV) or liquidating value (PSTKL), in that order. Finally, if not missing we add to book value the balance sheet value of deferred taxes (TXDITC). Market equity is per CRSP as of the last day of fiscal year t. 9

12 3.2 Sample Selection Our primary sample is drawn from the population of all firms listed in the Compustat Annual Industrial and Research files with fiscal year ends between 1973:06 and 2010:12. The sample begins in 1973 because the first year Compustat reports flow of funds data, which we use to compute cash flow from operations, is 1971 and we need at least three years of data to perform our matching process (two years for firm i, one year to match against). Since we are interested in examining how the earnings estimates of analysts and investors are affected by earnings and cash flow volatility, we require a cross-sectional or time-series volatility estimate for either earnings or cash flows. We further reduce the sample size to those domestic firms traded on the NYSE, AMEX, and NASDAQ (CRSP exchange code 1, 2, 3 and CRSP share codes 10 and 11). Our primary sample is comprised of all firms that meet the above criteria, yielding 141,608 observations see panel A of table 1 for sample construction detail. We annually winsorize all current-year summary statistics. To prevent summary statistics from being overly influenced by the increase in observations in the latter years of the sample and to report results that more closely correlate to the average time-series regression slopes examined in later tests, summary statistics are time series means (an average of each annual statistic). 3.3 Descriptive Statistics Panel B of table 1 provides descriptive statistics for all firms in our primary sample. Summary statistics are largely in line with those reported in prior studies. However, several characteristics are worth noting. First, our cross-sectional measures of earnings and cash flow volatility capture roughly 20% more observations than the respective time-series variables. Second, there is considerably less dispersion in the cross-sectional volatility estimates compared to the time-series volatility estimates. For example, the standard deviation of CSEV t (0.058) is roughly 30% lower than the standard deviation of TSEV t (0.081). Finally, the cross-sectional earnings volatility estimate (0.077) is marginally higher than the time-series estimate of earnings volatility (0.068), although considerably less right skewed. Table 2 provides a correlation matrix for key variables, and results again are largely in line with prior studies. Volatility measures derived using both time-series and cross-sectional empirical designs are negatively associated with firm size and book-to-market. Also worth noting is the fact that correlations between the time-series and cross-sectional volatility variables are positive, but are not highly collinear (0.40<ρ<0.60). This suggests that the volatility variables capture similar economic variation, but are distinct enough that we should be able to attribute unique effects to the time-series and cross-sectional volatility characteristics. 10

13 Table 2 Time-series means of annual correlations This table reports the time-series average of the annual cross-sectional correlations, with Pearson product moment correlations reported above the diagonal, and Spearman rank correlations reported below the diagonal. The sample spans firms with fiscal year ends between 1973:06 and 2010:12. LogSize t is the natural log of the market value of equity (in $millions) per CRSP as of fiscal year end t. All other variables are defined in table 1. Earn t CFO t dnwc t CSEV t TSEV t CSCFV t TSCFV t dsales t LogSize t LogBM t Earn t CFO t dnwc t CSEV t TSEV t CSCFV t TSCFV t dsales t LogSize t LogB/M t Time-series patterns the cross-sectional volatility measures Academic research has noted an increase in stock return and earnings volatility since the early 1960 s (Campbell et al. 2001; Wei and Zhang 2006). Further, recent accounting studies have noted a decline in earnings quality over the same time period (Rajgopal and Venkatachalam 2011). As a final descriptive exercise, we plot the median firm s earnings and cash flow volatility for each year in our sample. Firms are classified as tiny, small, or large, based on the total asset portfolios in which they are classified in the matching process. Several interesting patterns are noted. Cross-sectional earnings volatility (CSEV) Tiny ( ); Small (---); Large ( ) Time-series earnings volatility (TSEV) Tiny ( ); Small (---); Large ( ) 11

14 Cross-sectional cash flow volatility (CSCFV) Tiny ( ); Small (---); Large ( ) Time-series cash flow volatility (TSCFV) Tiny ( ); Small (---); Large ( ) Fig. 1: Time-series variation in the median volatility measures, This figure plots the median earnings and cash flow volatility estimates by year. Volatilities are reported by size portfolios, where portfolio classification is based on NYSE total asset breakpoints. Tiny firms ( ) have average total assets less than the 10 th NYSE total asset percentile; Small firms (---) have average total assets between the 10 th and 40 th NYSE total asset percentile; Large firms ( ) have average total assets greater than the 40 th NYSE total asset percentile. First, both cross-sectional earnings volatility and time-series earnings volatility have increased over time. However, the increase in volatility is much sharper in the cross-sectional estimates compared to the time-series estimates. Second, the cross-sectional earnings volatility estimates are highest at the peak of the dotcom bull market (2000) and during the financial crisis (2009). Both years correspond to periods of high uncertainty in the market as measured by either return volatility or the VIX index. Third, cash flow volatility has been relatively constant over time whereas earnings volatility has increased. This suggests that earnings uncertainty attributable to the accrual process has increased significantly over the time, consistent with the tenor of prior studies (Rajgopal and Venkatachalam 2011). 4 Empirical tests of the cross-sectional volatility measures In this section, we empirically compare our cross-sectional volatility measures against the more conventional time-series volatility measures. There are two purposes for this analysis. First, since the empirical validity of our earnings quality measures depends on how well our volatility estimates proxy for uncertainty, we want to empirically confirm whether our cross-sectional estimates of earnings and cash flow volatility better proxy for actual earnings and cash flow volatility on average across the full sample. Second, we want to examine time-series trends in the volatility estimates to determine if the volatility estimates are getting better or worse over the sample period. 4.1 Cross-sectional comparison of the volatility measures To assess how well our cross-sectional estimates of volatility proxy for actual volatility at time t, we annually regress realized volatility against the volatility estimates. Specifically, in table 3 we report the time-series average slopes from annual regressions of realized volatility regressed on the empirical 12

15 volatility estimates. We define realized volatility as the absolute value of the difference between realized earnings (cash flows) and expected earnings (expected cash flows). 6 Formally, Real_CSEV = Earn t+1 - E Match t [Earn t+1 ] (1a) Real_TSEV = Earn t+1 - Earn t (1b) Real_CSCFV = CFO t+1 - E Match t [CFO t+1 ] (1c) Real_TSCFV = CFO t+1 - CFO t (1d) In panel A of table 3, we report the results of annual regressions of the realized volatility variables (1a-1d) on their respective volatility estimates. The closer the slope (γ i ) is to 1.0, the better the respective variable proxies for actual volatility at time t. Real_CSEV t+1 = α 1 + γ 1 CSEV t + e Real_TSEV t+1 = α 2 + γ 2 TSEV t + e Real_CSCFV t+1 = α 3 + γ 3 CSCFV t + e Real_TSCFV t+1 = α 4 + γ 4 TSCFV t + e (2a) (2b) (2c) (2d) In addition, since estimates of earnings and cash flow volatility are direct functions of expected future earnings and expected future cash flows, we also report the time-series average of the annual cross-sectional slopes (β i ) of actual earnings and cash flows regressed on expected earnings and cash flows in panel B of table 3. Earn t+1 = a 1 + β 1 E Match t [Earn t+1 ] + e Earn t+1 = a 2 + β 2 Earn t + e CFO t+1 = a 3 + β 3 E Match t [CFO t+1 ] + e CFO t+1 = a 4 + β 4 CFO t + e Both sets of t-statistics are based on the variability in the time-series slope estimates and (3a) (3b) (3c) (3d) incorporate a Newey-West (1987) correction with five lags to control for possible autocorrelation in the slope estimates. Panel A of table 3 notes the average slopes (γ) on both cross-sectional volatility measures (models 1 and 3) are significantly higher than the time-series volatility measures (models 2 and 4). This pattern holds in the full sample and in the overlapping sample and suggests that the cross-sectional volatility estimates better proxy for actual volatility compared to the conventional time-series measures. Second, the average slopes (β) on the earnings and cash flow expectations in panel B suggest that expectations derived from the matched-firm approach yields better estimates of future earnings and cash flows compared to the random-walk expectation model. Thus, our matched-firm expectation model appears to produce better estimates of future earnings and cash flows compared to the random-walk expectation model. 6 Note that if the earnings expectation model is well-specified, unexpected earnings should be approximately zero and the expected volatility of earnings (proxied by TSEV t-4,t or CSEV t ) will equal E[(Earn t 1 - E t[earn t 1 ]) ] E[((Earn t 1 - E t [Earn t 1 ]) 0) ] (unexpected earnings) Earn t 1 - E t Earn t 1 13

16 Table 3 Analysis of predictive volatility slopes, This table reports the time-series average slopes of annual cross-sectional regressions (intercepts are included in all regressions but omitted from the panels). Panel A reports the average annual slopes from regressing realized earnings volatility and realized cash flow volatility from t+1on estimates of earnings and cash flow volatility at time t. Panel B reports the average annual slopes from regressing earnings and cash flow realizations from t+1 on their respective expectations at time t. All variables are scaled by average total assets and annually winsorized at the 1 st and 99 th percentile. The t-statistics are based on the time-series variation in the annual slopes and incorporate a Newey-West adjustment (5- lags) to adjust for possible autocorrelation in the slope estimates. The cross-sectional earnings and cash flow estimates (E t [Earn t+1 ] and E t [CFO t+1 ] are described in section 3.1. All other variables are described in table 1. Panel A: Annual regressions of realized volatility regressed on expected volatility (1) Real_CSEV i,t+1 = α 1 + γ 1 CSEV i,t + e i,t ; where Real_CSEV t+1 = Earn t+1 E t [Earn t+1 ] (2) Real_TSEV i,t+1 = α 2 + γ 2 TSEV i,t + e i,t ; where Real_TSEV t+1 = Earn t+1 Earn t (3) Real_CSCFV i,t+1 = α 3 + γ 3 CSCFV i,t + e i,t ; where Real_CSCFV t+1 = CFO t+1 E t [CFO t+1 ] (4) Real_TSCFV i,t+1 = α 4 + γ 4 TSCFV i,t + e i,t ; where Real_TSCFV t+1 = CFO t+1 CFO t+1 Earnings Cash Flows (1) (2) (3) (4) Full Sample Overlapping Sample FM Slope FMNW t-stat (13.66) (15.19) (11.54) (24.48) Obs. 3, , , ,572.2 FM Slope FMNW t-stat (12.49) (15.36) (13.72) (24.61) Obs. 2, , , ,442.2 Panel B: Annual regressions of realized earnings and cash flow regressed on expected earnings and cash flows (1) Earn i,t+1 = a 1 + β 1 E t [Earn i,t+1 ] + e i,t (2) Earn i,t+1 = a 2 + β 2 Earn i,t + e i,t (3) CFO i,t+1 = a 3 + β 3 E t [CFO i,t+1 ] + e i,t (4) CFO i,t+1 = a 4 + β 4 CFO i,t + e i,t Earnings Cash Flows (1) (2) (3) (4) Full Sample Overlapping Sample FM Slope FMNW t-stat (84.10) (48.15) (12.31) (6.99) Obs. 3, , , ,572.2 FM Slope FMNW t-stat (62.12) (46.04) (12.33) (6.89) Obs. 2, , , , Time-series comparison of the volatility estimates The t-statistics on the volatility estimates reported in panel A of table 3 tend to be lower for the cross-sectional estimates compared to the time-series estimates. Since the t-statistics capture time-series variation in the slopes over the entire 38 year sample, extreme slope outliers could inflate the standard errors. Of particular interest is where the slope outliers reside. That is, are the slopes trending toward or 14

17 away from 1.0 in the latter part of the sample? In figure 2, we plot the five year rolling average of the annual slopes (γ) for regressions 2a 2d. The time-series variation in slopes noted in Figure 2 shows why the cross-sectional volatility estimates tend to have lower t-statistics relative to the time-series measures. Early period estimates tend to be poorly specified, leading to lower average slopes (γ) and hence larger standard errors. However, by the mid-1980s, the average predictive slopes on the cross-sectional volatility estimates are significantly larger than those on the time-series volatility estimates. Further, the cross-sectional estimates tend to be more stable in the post-1980 period. 7 Earnings Volatility Cash flow volatility Fig. 2: Rolling 5 year average predictive slopes, This figure reports the 5 year rolling average slopes (γ) from the annual cross-sectional regressions specified in equations 2a 2d. In sum, the evidence reported in table 3 and figures 2a and 2b suggests that our matching process produces reasonable estimates of earnings and cash flow volatility that appear to dominate those estimates derived from a time-series variation. Further, our cross-sectional estimates appear to perform considerably better in the latter part of the sample. 5. The relative importance of the accrual and cash flow component of earnings quality In this section, we build from the analysis in table 3 and investigate the extent to which our cross-sectional measures of earnings quality explain the precision with which future earnings can be estimated incremental to other accounting-based and market-based measures of earnings quality. The purpose of this analysis is twofold. First, there is an extensive literature positing different characteristics as proxies for earnings quality see Dechow et al We control for the accounting-based measures of earnings quality examined by Francis et al. (2005) which represent the modal measures of earnings quality examined in the accounting literature. The measures are earnings predictability (Pred.), earnings persistence (Pers.), earnings smoothness (Smooth), and residual accrual volatility (AQ). Using these variables as established measures of earnings quality, we investigate whether our cross-sectional 7 In unreported analysis, we examine the second half of the sample (i.e., we exclude years ). Results from this 19 year subsample yields average slopes on CSEV t and CSCFV t of (NW t-stat 24.0) and (NW t-stat 51.3), respectively. 15

18 measures of earnings quality are incrementally informative. Second, other firm characteristics such as firm size, book-to-market, accruals, and return momentum are known to be associated with future returns and earnings quality. Accordingly, since our ultimate interest is to understand if future returns are associated with our cross-sectional measures of earnings quality, we also examine whether our cross-sectional measures of earnings quality explain variation in earnings precision incremental to these characteristics. 5.1 The accrual-components of cross-sectional earnings quality We propose two measures of earnings quality derived from our cross-sectional estimates of earnings and cash flow volatility. Our first measure is simply the difference between earnings volatility and cash flow volatility. Formally, CSAccV = CSEV - CSCFV (4a) The intuition supporting this measure follows from the fact that earnings are comprised of a cash flow component and an accrual component. Cash flow volatility captures fundamental uncertainty plus uncertainty attributable to the timing of cash receipts and disbursements. The accrual process should dampen uncertainty attributable to timing issues; thus, CSAccV should be negative in the average firm (evidence in table 1 confirms this hypothesis). However, CSAccV also captures elements of fundamental uncertainty unrelated to uncertainty in future economic benefits captured by cash flows. Indeed, positive values of CSAccV imply that the uncertainty in accrual-based earnings leads to earnings uncertainty estimates greater than that captured by cash flow uncertainty. Assuming the accrual process is homogenous across all firms in a given year and using CSCFV as the baseline fundamental uncertainty estimate prior to the accrual process, variation in CSAccV can be interpreted as the extent to which accruals amplify or attenuate earnings uncertainty relative to the baseline uncertainty attributable to cash flows. Prior studies in the discretionary accrual literature acknowledge that variation in accrual processes across firms is likely correlated to industry-specific dynamics. To account for this possibility, our second measure relaxes the assumption that the accrual and cash flow processes are homogeneous across time and across industries. Specifically, we account for possible differences in the accrual processes across industries via annual cross-sectional industry regressions. Our empirical implementation and intuition is consistent with that applied in the discretionary accrual literature (Xie 2001) and the 16

19 residual accrual volatility literature (Dechow and Dichev 2002). 8 Formally, Ind CSEV i,t = a j,t + b 1 CSCFV j,t +e t, where e t CSAccV t (4b) Similar to 4a, we take the perspective that cash flow volatility represents a baseline measure of earnings uncertainty (prior to the effect of accrual accounting). We interpret variation in the residual as informative of how much the accrual process increases or decreases earnings uncertainty relative to the average effect the accrual process has in the industry. 5.2 The relation between the accrual and cash flow components of earnings quality and realized expectation errors Table 4 reports the results from annual cross-sectional regressions of realized earnings volatility (Real_CSEV t+1 ) and the absolute value of realized analyst forecast errors ( FE t+1 ) regressed on our cross-sectional measures of earnings quality (CSCFV, CSAccV, and CSAccV Ind ) and other firm characteristics. The goal of these regressions is to establish whether variation in our measures of earnings quality explain realized deviations from expected earnings incremental to other firm characteristics associated with earnings quality (models 2 and 4) and firm characteristics associated with future returns (models 3 and 5). Remember, we view the precision that future earnings can be estimated as a summary Ind indicator of earnings quality. Thus, significant positive slopes on CSCFV t, CSAccV t, and CSAccV t would suggest that our cross-sectional measures are incrementally contributive to existing earnings quality measures. Results in table 4 highlight several key results. First, both components of earnings quality, the cash flow component (CSCFV) and the accrual components (CSAccV and CSAccV Ind ) are strongly associated with both measures of realized forecast errors. The slopes on the components of earnings quality are positive and between four and fifteen standard errors from zero. Further, the magnitudes of their respective slopes suggest that both the accrual component and cash flow components are incrementally associated with how precisely future earnings can be estimated. Second, the cross-sectional estimates of earnings quality are much more strongly associated with the measures of realized volatility than the time-series estimates of earnings quality. Indeed, the time-series earnings quality characteristics are only marginally associated with the absolute value of analyst forecast error ( FE t+1 ). Further, with the exception of earnings predictability (Pred.), the other measures of earnings quality (AQ, Pers., and Smooth) are much noisier estimates of earnings quality compared to CSCFV t, CSAccV t, and CSAccV Ind t. 8 We classify firms into industry using Ken French s 49 industry classification system, available on his website ( Consistent with prior studies, we require at least 20 firms per industry-year to be included in the industry-adjusted sample. Results are not sensitive to this threshold. 17

20 Table 4 Cross-sectional regressions of forecast errors on earnings quality characteristics, This table reports the time-series average of annual cross-sectional regressions of realized forecast errors regressed on the components of earnings volatility and other firm characteristics. All variables are scaled by average total assets and annually winsorized at the 1 st and 99 th percentile. AQ, Pers., Pred., and Smooth are defined below; all other variables are defined in previous tables. The t-statistics are based on the time-series variation in the annual slopes and incorporate a Newey-West adjustment (5-lags) to adjust for possible autocorrelation in the slope estimates. Dependent Variable: Real_CSEV t+1 Dependent Variable: FE t+1 (1) (2) (3) (4) (5) (1) (2) (3) (4) (5) Intercept (-2.27) (-2.15) (6.60) (0.28) (10.15) (2.49) (2.67) (10.37) (4.09) (8.68) CSCFV t (10.91) (8.74) (9.02) (4.89) (5.11) (5.57) (6.52) (4.42) (7.13) (6.63) CSAccV t (14.65) (11.94) (12.84) (4.85) (6.64) (4.81) CSAccV t Ind (13.21) (13.56) (7.65) (7.19) AQ (5.64) (5.48) (1.51) (1.59) Pers (-4.20) (-3.70) (-1.65) (-1.50) Pred (12.56) (20.98) (2.11) (2.01) Smooth (3.99) (5.69) (1.95) (2.22) LogB/M t (-4.23) (-4.68) (6.44) (6.23) LogSize t (-9.95) (-8.93) (-11.88) (-10.03) dnwc t (-4.08) (-4.63) (-4.43) (-4.49) Avg. Obs. 2,924 2,152 2,915 2,038 2,767 1,716 1,284 1,716 1,227 1,644 Avg. R AQ Std. dev. of regression residuals over 5 year period, lagged 1 year see Dechow and Dichev (2002) Acc t = α + β 1 CFO t+1 + β 2 CFO t + β 3 CFO t-1 + μ 2 Pers. Slope (β) from regression over trailing 5 year period, lagged 1 year. Earn t+1 = α + βearn t + μ 3 Pred. Std. dev. of regression residuals (μ) over trailing 5 year period, lagged 1 year. Earn t+1 = α + β Earn t + μ 4 Smooth Time-series earnings volatility (TSEV) divided by time-series cash flow volatility (TSCFV) Third, models 3 and 5 note that book-to-market is negatively associated with Real_CSEV t+1 (-0.015) but positively associated with the absolute value of analyst forecast error (0.022), both with t-statistics greater than 4.50 in absolute terms. The positive relation between book-to-market and absolute forecast errors is consistent with that noted in Diether et al. (2002) and Johnson (2004). The negative 18

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