Choosing the Precision of Performance Metrics

Transcription

1 Choosing the Precision of Performance Metrics Alan D. Crane Jones Graduate School of Business Rice University Chishen Wei Nanyang Business School Nanyang Technological University Andrew Koch Katz Graduate School of Business University of Pittsburgh Abstract There is a standard trade-off in contracts between the provision of incentives and insurance. We hypothesize that this trade-off influences the precision with which firm performance is measured. We find that firm outcomes are measured less precisely when chance plays a large role in these outcomes. Further, this precision is determined through the choice of shares outstanding. This has several novel implications. Firms with low prices should have volatile cash flows, pay fixed wages, and contract on EPS less frequently. There are additional implications for stock price levels over time and at IPO. We find evidence consistent with the implications. Keywords Compensation; Performance benchmarks; Stock splits acrane@rice.edu; awkoch@pitt.edu; cswei@ntu.edu.sg;

2 1 Introduction The Olympic 100m dash is measured in hundredths of seconds even though timing technology allows the runners to be timed to the ten thousandth. The precision of timing is purposely limited because of the margin of error in the distance of the race. Differences of a few ten thousandths of a second likely reflect random variation in lane length, not true differences in ability or effort. Similar issues arise within the firm. The precision with which firm outcomes are measured can be too coarse to adequately measure CEO performance or so fine such that the measures reflect noise. Conceptually, one can think of a setting in which large differences in firm cash flows are generated by the effort or ability of management, but smaller differences are due to chance. Given the well known trade-off between the provision of incentives versus insurance (e.g. Hölmstrom (1979)), the optimal measure of firm performance should be precise enough to reflect true managerial performance, but not so precise that it rewards or penalizes the manager for noise. This issue can be particularly important in the context of CEO compensation. Per Hölmstrom (1979), the board would like to incentivize the manager without rewarding or penalizing him for good or bad luck. One simple way for boards to control the precision with which they measure the performance of the manager is to write contracts that treat specific ranges of firm outcomes the same. Contracts written on per-share performance outcomes effectively do just that. For example, the earnings-per-share (EPS) forecast for Microsoft s Q earnings is With roughly 8 billion shares outstanding, this EPS represents any total earnings between 5.40 and 5.48 billion dollar. Each penny of EPS represents an 80 2

3 million dollar range of earnings. Importantly, managers together with the board can choose this precision by choosing the number of shares. 1 If Microsoft had twice as many shares, each penny of EPS would represent a range of earnings 160 million wide. CEO contracts often contain EPS based provisions. Graham, Harvey, and Rajgopal (2005) find that EPS outcomes relative to analyst forecasts or past EPS is the single most important managerial incentive target. Cheng, Harford, and Zhang (2015) find that almost half of S&P 500 CEOs have annual incentive plans with explicit earnings-per-share (EPS) targets. By choosing the number of shares, the firm can create an EPS metric that reflects performance and not noise. Stated differently, if contracts are written on per-share metrics, firms can use the number of shares to smooth plateaus in likelihood ratios, resulting in more efficient contracts. Alternatively, managers could simply contract on ranges of EPS. Bennett et al. (2015) find evidence consistent with this, supporting the view that managers and boards are cognizant of the precision of EPS and that, in some cases, EPS can be too precise to reflect CEO performance. However, virtually all CEOs have equity positions in firms and on average will face negative wealth shocks when they fail to meet market forecasts. Importantly, these forecasts are in terms of specific EPS targets rather than ranges. Payne and Thomas (2003) and Skinner and Sloan (2002) both generally find stronger negative stock price reactions to missing earnings forecasts, consistent with survey evidence from Graham, Harvey, and Rajgopal (2005) suggesting that this is the metric managers care most about. Market participants also understands that, with higher stock price levels, such metrics are less informative, providing 1 In practice, decisions regarding shares are made by managers in concert with the board. For the purposes of exposition, we refer to both managers and boards as decision makers since agency conflicts are not the focus of this paper. 3

4 an incentive for managers to maintain certain levels of EPS precision. 2 In this paper we test whether managers choose the number of shares to influence the precision in firm metrics. We expect that firms whose performance (e.g. cash flows) is a noisy function of the manager s decisions will have more shares than firms whose performance is less noisy. We find that, in the cross section, firms with the most noise in earnings have 3.5 times more shares than those with the least. This holds not just in the cross section, but also when shares are chosen at IPO, and when the magnitude of noise in earnings changes over time. These results are robust to a variety of different measures of noise in firm performance outcomes and are not driven by differences in firm characteristics such as size. However, it is difficult to make causal inference from these relations alone. In order to determine whether the number of shares is chosen to effect the precision of performance metrics, we take an instrumental variables (IV) approach by examining how precision changes in response to shocks to the noise in a firm s earnings outcomes. Our instrument is plausibly exogenous drops in analyst coverage (e.g. Hong and Kacperczyk (2010), Kelly and Ljungqvist (2012)). Sampling fewer analysts results in a noisier forecast which results in noisier earnings outcomes relative to that forecast. This is an ideal IV because the increase in the noise in earnings outcomes is the result of changes in statistical sampling error of forecasts and not of changes in firm fundamentals. 3 We find that shocks to earnings noise cause boards to increase shares, reducing the precision with which firm performance is measured. Specifically, a one standard deviation increase in earnings noise results in a 2 See, for example, Forbes article In addition, Dechow and You (2012) show that analysts stop attempting to forecast EPS to the penny when the firm s EPS is very precise. 3 At least two assumptions are implicit in this identification strategy. First, re-contracting is costly relative to changing precision. Second, managers must care specifically about analysts expected EPS. 4

5 one-half standard deviation decrease in the number of shares. We expect the response to this shock to be strongest among firms that contract on EPS and weaker among firms that do not. Using terminology in CEO contracts gathered from proxy filings and compensation data, we identify managers with contracts explicitly written on EPS forecasts. We find that the response to the predictability shock is strongest among firms with managers that have these EPS contractual provisions. Specifically, the change in shares among these firms is 2.5 times greater than the unconditional effect. The response is insignificant among managers whose compensation is not sensitive to EPS. 4 There are reasons why firms may not be able to fully adjust the precision of their performance metrics. In particular, firms with low stock prices may be constrained if the costs of delisting are greater than the benefits of decreasing precision. As such, firms with low stock prices may have per-share metrics that are too precise. In this case, we expect that firms close to delisting are less likely to contract on performance outcomes and instead pay more fixed wages. We find that firms with low share prices are more likely to pay a fixed wage and less likely to have explicit EPS targets in their contracts. Theoretical literature on contracting and the precision of performance metrics also argues that precise measurement in one dimension may generate gaming and distortions in other dimensions. For example, Hölmstrom and Milgrom (1991) describe how contracting on the quantity of output can lead agents to shirk on quality. In our context, contracting on a precise measure of the quantity of earnings may lead managers to distort investment or 4 In this paper, we focus on explicit contractual EPS provisions. However, we expect managers and boards to have implicit incentives to manage precision for a variety of reasons, not only because CEOs are often explicitly contracted on EPS. De Angelis and Grinstein (2015) show that roughly 50% of compensation is not explicitly delineated in the contract. This discretionary portion of compensation may also be sensitive to EPS outcomes. Managers and boards may care about analyst coverage, media attention, or the short term stock price, all of which may be sensitive to EPS outcomes. 5

6 the quality of earnings. Motivated by the literature that connects managerial incentives to investment distortions (e.g. Stein (1989)) and Roychowdhury (2006)), we examine whether these distortions change around changes in precision. We find that investment and earnings distortions decrease following decreases in precision. Our results do not imply that the precision of performance metrics is the only driver of stock splits. It is likely that other factors such as liquidity and optimal trading ranges also influence the choice for shares. However, we note that those drivers do not appear to explain our overall findings. These alternatives would need to be consistent with the broader set of empirical results we present in our paper, such as variation in industry IPO pricing, responses conditional on EPS contractual provisions, and the usage of earnings management tools around splits. Our results are also consistent with one of the primary reasons that managers give for stock splits, the desire to keep shares in some range (e.g. Baker and Gallagher, 1980)). Only when stock prices are within some reasonable range are EPS metrics representative of true firm performance rather than noise. While our findings suggest that only a portion of variation in shares is explained by EPS incentives, the friction we document can have surprisingly broad implications and is important for several reasons. We contribute to the large literature on per-share price levels. Several papers connect per-share prices to fundamentals (e.g. firm value (Baker et al. (2009)), idiosyncratic volatility (Brandt et al. (2010)), and return comovement(green and Hwang (2009))). We offer a clear reason why per-share price levels are naturally linked to the volatility of the firm s cash flows. We show that this is true in equilibrium in the cross section, as well as when the firm chooses the price level at IPO. A related strand of literature examines more explicitly how share prices relate to the 6

7 choice for the number of shares. Weld, Michaely, Thaler, and Benartzi (2009) show that share price levels have not increased with inflation. They argue that this is inconsistent with any current explanation for stock splits, leading the authors to introduce the nominal price puzzle. We argue that if shares are chosen to maintain some level of precision in performance metrics, then nominal prices should remain constant over time. 5 Therefore, our paper not only contributes to our understanding of this puzzle, but it also offers a new potential explanation for stock splits. While such an explanation is unlikely to drive splits for all firms, it is consistent with not only our findings, but with existing empirical facts about splits (e.g. Lakonishok and Lev (1987), Asquith et al. (1989)) that are difficult to reconcile with existing models. Our findings also help rationalize why metrics such as EPS receive such considerable attention and are central to managerial compensation contracts (Graham et al. (2005)). At first glance, the use of such a measure is difficult to understand, given that the firm s total earnings are observable. However, total earnings may be too precise a measure, leading to an equilibrium in which compensation contracts are written on EPS instead. Finally, our results suggest several avenues for future research. The connection between the choice of EPS precision and investment and other earnings distortions relates to the vast literature on earnings management. For example, firms can avoid the need to manage earnings by choosing a large number of shares. Similarly, firms with low stock prices might manage earnings more frequently because they cannot increase shares without being delisted. 5 EPS has been reported in penny units throughout time despite the real value of a penny changing. If the units to which EPS were reported changed with inflation, then we would expect prices to also change with inflation. 7

8 2 Data Our sample is compiled from four major databases. The primary data sample is gathered from the quarterly CRSP/COMPUSTAT Merged database and combined with analyst forecast data obtained from I/B/E/S. Our sample starts in 1984 since we require 12 previous quarters of analyst forecasts in several of our tests. Our sample ends in We include stock return data from CRSP. Only common stock with CRSP share code 10 or 11 are included. We merge in institutional ownership obtained from the Thomson Reuters 13(f) institutional holdings database. For a subset of tests, we require compensation data from ExecuComp. To distinguish between changes in shares outstanding due to stock splits, repurchases, or equity issuances, we use distribution codes from CRSP. Stock splits have a distribution code equal to We assign a change in shares to a fiscal quarter if the CRSP payment date (PAYDT) occurs after the prior earnings report date, but before the earnings report date as reported in COMPUSTAT. If the earnings report date is missing, a share change is assigned to a fiscal quarter if it occurs within the fiscal quarter begin and end dates. We gather details on CEOs bonus structures from annual proxy statements (Schedule 14A) available on the SEC website. Online electronic versions of the statements start in We match the proxy statements to firms in COMPUSTAT using match file provided by Compustat for the sample period (fiscal year). To identify EPS based compensation, we analyze the text of annual reports and proxy statements and search for specific sentences that contain the phrase earnings per share or EPS and target, bonus, incentive, award, threshold, goal, benchmark, 8

9 criteria, performance indicator, or performance metric. We perform the search using Natural Language Processing (NLP) which is a programming algorithm designed to accurately interpret semantics (Bird et al. (2009)). This allows us to perform sentence boundary disambiguation to distinguish between sentence ends and abbreviations that use punctuation marks. Parsing statements using NLP and employing the strict requirement that the phrases must be contained in same sentence increases the likelihood of accurately identifying compensation schemes that factor in EPS outcomes. A key prediction in our study centers on the link between the number of shares outstanding and the extent to which the firm s earnings reflect something other than manager effort or ability. Earnings that reflect other factors are noisy proxies for managerial effort or ability. We create three measures of the volatility of the firm s earnings. These proxies reflect how different the firm s total earnings tend to be from the expectation. If expectations of firm outcomes include expectations of a manager s ability or effort, volatility in outcomes relative to expectations should be correlated with variation in earnings that is beyond the manager s control. So, to truly reflect noise, this volatility should be measured relative to the expectation, which is unobservable. We use three proxies. Noise Naive is calculated as the standard deviation of total earnings over the past 12 quarters. This is likely correlated with the variation in earnings outside the manager s control, however it does not capture predictable, seasonal variation in the expectation. Noise Seasonal is the standard deviation of the difference between actual total earnings and a seasonally adjusted proxy for expected total earnings. Specifically, the expected total earnings is total earnings from 4 quarters prior, plus the difference between the total earnings 4 quarters and 8 quarters before. This proxy captures the variance around 9

10 a time-varying mean using a simple forecast for the mean based on seasonality and prior growth in earnings. Noise F orecast is calculated as the standard deviation of the difference between total earnings and the median IBES forecasted total earnings over the past 12 quarters. We calculate median IBES forecasted earnings as the median EPS forecast multiplied by shares outstanding. A benefit of this measure is that it relies on earnings expectations formed by professional analysts in each period. A drawback is that it requires data from IBES which reduces the sample. Our usage of historical EPS and analysts forecasts as proxies for expectations is consistent with Graham et al. (2005), who find that these are the two most important EPS benchmarks. Results are robust to using various definitions of total earnings, including Operating Income Before Depreciation as well as Income Before Extraordinary Items. Table 1 presents the summary statistics of the sample. The key dependent variable used in this study is shares outstanding (median = million, mean = million). EPS has a median of $0.19 and mean of $ Results Our analysis begins from the simple observation that per-share metrics are imprecise. This imprecision exists because the firm outcome (e.g. earnings) is scaled by shares, but the result is not reported to infinite decimal places. Generally, per-share metrics are rounded to the penny. Importantly, the precision of per-share metrics is determined by the number of shares. Each penny of EPS represents a range of total earnings that is shares 100 dollars wide. Mi- 10

11 crosoft has roughly 8 billion shares. Therefore, each penny of EPS represents an 80 million dollar range of total earnings. This imprecision means that Microsoft s management will meet a given EPS forecast by producing total earnings within ± 40 million of the amount of total earnings implied by the forecast (E[EP S] shares). In relative terms, the range is ±( 1 shares )( )( 1 ) = 1 %. The average firm E[EP S] shares 2 E[EP S] in our sample has EPS of $0.20. As such, the average firm will meet the forecast by producing total earnings within ± = ±2.5% of expected total earnings. If, as in the Olympics, it is costly to measure outcomes too precisely, then firms may choose to contract on per-share metrics and, at the same time, manage the precision by adjusting the number of shares. A doubling of shares doubles the range of earnings reflected by a penny s worth of EPS. If the average firm in our sample doubled the number of shares outstanding, the forecasted EPS would mechanically drop to $0.10, and the relative range would increase to ±5%. The analysis that follows examines if the noise in firm earnings (relative to the impact of managerial effort or ability) describes the cross-sectional and time-series distributions of the number of shares outstanding. We then examine several novel and wide-ranging implications. 3.1 The Relation Between Noise and Precision Our main cross-sectional hypothesis is that managers of firms with noisy earnings will choose higher levels of shares outstanding. We use one of the three measures of earnings noise described in Section 2. For a stable, predictable firm, small deviations in earnings can be informative of ability/effort. In contrast, for a firm with volatile, unpredictable, noisy 11

12 earnings, the deviation from expectations needs to be larger to be a meaningful indicator of effort/ability. Because it is costly to reward or penalize the manager for things outside his control, boards and managers may optimally choose more precise measures (fewer shares) for stable, predictable firms, and less precision (more shares) for noisy, unpredictable firms. We briefly examine this using multivariate sorts. Figure 1 presents the average median shares outstanding across deciles of Noise Naive in Panel A. 6 In order to compare firms with similar earnings levels, in each quarter we first sort the sample into 20 groups based on the level of total earnings. Then within each group we sort into deciles based on Noise Naive. We plot median shares (bar height) across Noise Naive. We also report median net income (line) to confirm that we are comparing firms of similar size. We find a strong association between shares outstanding and Noise Naive. Shares outstanding is monotonically increasing across Noise Naive deciles. The average level of total earnings (line) is stable across the decile ranks, indicating that the pattern is not due to differences in the magnitudes of firms earnings. While the extreme deciles have similar total earnings, the top Noise Naive decile has nearly 3.5 times as many shares outstanding (in thousands) than its bottom decile counterpart 34,147 vs. 11,153, p-value < While our sorts control for the overall level of firm earnings, they do not control for differences in other firm characteristics that may relate to the number of shares. Table 2 presents pooled OLS regression models of shares outstanding as a function of firm characteristics measured in the prior quarter. Regression coefficients are standardized to represent standard deviation effects in shares outstanding for a one standard deviation difference in a given covariate. All specifications include firm size, stock illiquidity as defined in Amihud 6 In unreported results, we find that the patterns in both Panels A and B are stronger using averages. 12

13 (2002), and the fraction of the firm owned by institutions, as independent variables. Previous research finds that these characteristics are associated with changes in shares outstanding (i.e. stock splits) and, as such, we expect them to be related to the level of shares outstanding. Additional control variables are the market to book ratio, past stock return, and return volatility. The key dependent variable in column 1 is Noise Naive,t 1, and columns 2 and 3 use Noise Seasonal,t 1 and Noise F orecast,t 1 respectively. The results in column 1 indicate a positive relation between Noise Naive,t 1 and the number of shares outstanding. The coefficient estimate is highly significant, both economically and statistically. A firm with a value of Noise Naive,t 1 one standard deviation above the mean has 0.21 standard deviations more shares outstanding. The association is consistent across columns 1 through 3 using different proxies of earnings predictability. The effect is largest using Noise F orecast,t 1. One standard deviation higher Noise F orecast,t 1 is associated with 0.30 standard deviations more shares. These findings suggest that the association between the noise in firm cash flows and the number of shares outstanding is economically large. Of the dependent variables, only market capitalization has a larger association with shares outstanding. A one standard deviation change in market capitalization is associated with 0.84 standard deviations more shares outstanding (column 1). A one standard deviation greater illiquidity is associated with a small, but statistically significant lower number of shares outstanding (0.05 of a standard deviation, column 1). The number of shares is positively related to return volatility and negatively related to the level of net income, and the relations with market to book and institutional ownership are economically small. 13

14 3.2 Identification Results in the previous section indicate that firms with stable, predictable earnings have fewer share, and hence more precise measures of per-share metrics relative to their counterparts whose earnings are noisy. We show that this association is robust to controlling for a variety of characteristics that may also relate to the number of shares. However, to the extent that firms have unobserved characteristics that determine share structure, earnings noise, and managerial incentives, these pooled OLS estimates will be biased and inconsistent. The first step we take to mitigate these issues is to examine a first difference model in which we estimate the relation between changes in firm characteristics and changes in shares outstanding. Focusing on changes allows us to control for the effect of observable firm characteristics that change over time as well as unobservable, time-invariant firm characteristics. In Table 3, we present three specifications, one for each of the proxies for earnings noise. Consistent with prior results, the noise in the firm s total earnings is an important determinant of shares outstanding. In this case, a one standard deviation change in noise is associated with a 0.03 to 0.07 standard deviation changes in shares outstanding. This effect is statistically significant at the 1% level and is still economically large when considering it is an estimate of changes. While the results in Table 3 help rule out the effects of unobservable, time-invariant heterogeneity, they do not rule out the possibility that unobserved changes in the firm (e.g. changes to investment opportunities) are driving both the differences in earnings noise as well as changes in shares. To identify a causal relation, we use plausibly exogenous variation in earnings noise. 14

15 In Table 4 we use an instrumental variable approach for the first difference model described above. We instrument for the first difference of Noise F orecast by using exogenous drops in analyst coverage. Our identification strategy is similar to those used in Hong and Kacperczyk (2010), Kelly and Ljungqvist (2012), and Derrien and Kecskés (2013) who find that the consolidation of analyst coverage following brokerage house mergers leads to exogenous drops in overall coverage. When brokerage houses merge, the combined house will often have more than one analyst covering a stock. As brokerages reduce coverage to eliminate this duplication of effort, the total number of analysts following certain stocks drops. To implement this test, we follow the strategy employed by Degeorge et al. (2012). We use drops in analyst coverage based on analysts that leave the IBES database permanently in that period. As shown in Degeorge et al. (2012), these drops match the distribution of those from brokerage mergers. A drop in analyst coverage is a useful instrument for our purpose for two important reasons. First, it acts as a shock to the noise in the forecast. After a drop in analyst coverage, the consensus forecasts will be noisier because it is formed over a smaller sampling of analysts. Stated differently, the variance of the sample mean increases when the sample size drops. Second, firm fundamentals, in particular earnings, remains unchanged. Previous studies show that drops in analyst coverage are unrelated to firm fundamentals (Hong and Kacperczyk (2010)). Therefore, we use this change in the noise of the forecast as an exogenous shock to Noise F orecast. In Table 4, we show results from the first and second stage of a 2SLS regression using drops in analyst coverage as an instrument for Noise F orecast,t 1. Our instrument is both relevant to earnings noise and satisfies the exclusion restriction required for a good instrument. Column 15

16 1 reports the first stage results of the IV estimate. In the first stage regression, the t-statistic on the instrument is > 5 and the F-statistic is > 17, both well above the benchmarks established in Stock et al. (2002), alleviating concerns due to weak instrument problems. Using the instrumental variable approach, we find a strong causal relation between changes in earnings noise and the number of shares outstanding. Column 2 shows that a one standard deviation increase in Noise F orecast,t 1 is associated with a 0.53 standard deviation increase in the number of shares outstanding. This is an economically large effect, as one standard deviation is measured over the entire cross sectional distribution of shares outstanding. Given the exogenous nature of the instrument, our evidence is consistent with the view that noise in the firm s earnings cause managers to choose the number of shares outstanding. Compared to the coefficient estimates in Table 3, the effect is much larger. This difference is consistent with an endogenous relation between these variables, and shows the importance of using the exogenous shock in measuring economic magnitudes. We also find clearer relations with respect to other variables and share structures. Share increases are associated with increases in net income, institutional ownership, market capitalization, and return volatility, and decreases in stock illiquidity. Overall, we find that changes in the predictability of total earnings cause changes in shares. This evidence supports our main cross-sectional prediction that the amount of noise in performance causes managers to choose the precision of those metrics. In columns 3 and 4 we distinguish between the various sources of changes in shares outstanding. Stock splits (or reverse splits) represent instances in which the board explicitly chooses the number of shares. As such, we expect to find a strong relation between splitdriven share changes and changes in Noise F orecast. Other actions, such as stock issuances or 16

17 repurchases, can also affect the number of shares. However, these actions also have important economic effects, such as changes to the firm s capital structure. Therefore, if managers and boards are actively adjusting precision in response to changes in earnings noise, we expect the relation to be stronger among split-driven share changes, and weaker among share changes that result from other economic decisions. Column 3 reports the effect of changes in characteristics on changes in shares from all sources other than stock splits. The effect of Noise F orecast,t 1 is small and statistically indistinguishable from zero. In contrast, column 4 shows a large and significant increase in shares in response to an increase in Noise F orecast,t 1 as a result of stock splits (including reverse splits, although these are rare). These results suggest that stock splits are the primary method by which boards adjust the precision of performance metrics. These results are consistent with the view that boards use stock splits to adjust the precision of performance metrics. 3.3 Incentives to Manage Precision We expect that the precision of performance metrics may be more important for some firms more than others. For example, the performance of some firms may not be highly sensitive to managerial effort and ability. As a result, these firms may choose shares for reasons unrelated to the precision of performance metrics. One simple way to distinguish firms that value optimally precise performance metrics is to examine which firms have compensation contracts that are sensitive to firm performance. We do this in two ways. First, we use managerial incentive compensation, which equals 17

18 the fraction of total compensation that is not fixed, (1 salary ). This measure is totalcompensation designed to capture both explicit EPS incentives (through bonuses) and implicit incentives including sensitivity to market reactions due to unexpected earnings (through grants and options). Second, we use textual analysis of SEC filings to identify firms that explicitly contract on EPS (as described in Section 2). The existence or usage of these contractual features are not exogenous, and are likely jointly determined along with the precision of performance metrics and other firm and manager characteristics. Therefore, we examine if the response to shocks to Noise F orecast is stronger in firms whose managers have compensation more sensitive to per-share performance metrics. In Table 5 we report estimates from a 2SLS specification similar to those in column 4 in Table 4. In order to compare across columns, we use standardized independent variables and unstandardized measures for changes in shares outstanding. This allows us to interpret the coefficients as the number of shares changed due to a one standard deviation change in a given independent variable. We do this to compare across different samples which have different cross sectional distributions of shares outstanding. We expect a stronger effect of shocks to noise on changes in shares among firms with managers that have high incentive compensation (Column 2) and firms with explicit EPS contractual incentives (Column 4). Among managers with high incentive compensation, a one standard deviation increase in noise causes an increase in shares of over two standard deviations. The coefficient on Noise F orecast,t 1 is over four times that of the managers with low incentive compensation (column 1). The estimate for the low incentive compensation group is statistically insignificant. 18

19 Next, we separate firms with explicit EPS contractual components from those without. We find that roughly 41% of firm-quarter observations in our sample have managers with EPS contractual components. 7 Column 3 (4) reports results using the sample of firms without (with) explicit EPS components. We find a significant effect among both samples, although the relation among firms with EPS components is stronger economically than the relation among firms without. Specifically, for firms without EPS contracts a one standard deviation increase in noise increases shares by 1.14 standard deviations. The estimate is 0.3 standard deviations higher for firms with EPS components, although the difference in estimates is not significant at conventional levels. The significant relation among firms without explicit EPS contractual components is consistent with the view that managers value the precision of performance metrics even if they are not explicitly contracted on EPS. This is not surprising, as implicit EPS incentives are likely to exist. For example, most CEOs will have substantial ownership in their firms and stocks prices on average react to EPS outcomes relative to expectations. Furthermore, the precision of EPS metrics may be important simply because EPS is widely followed by the media, analysts, and market participants in general. These findings are unlikely to be explained by liquidity-based theories for stock splits. 3.4 Constraints on Managing Precision In certain cases, the board may find it too costly to respond to shocks to earnings noise. In particular, the board of a firm with a low stock price may find de-listing costs to be more important than the precision of performance metrics. For these constrained firms, some 7 This is similar to Cheng et al. (2015), which estimate that 49% have explicit EPS incentives. 19

20 would benefit from an increase in the number of shares for precision reasons but choose not to for de-listing reasons. As a result, performance metrics of these firms remain too precise. In Table 6 we examine whether de-listing risk effects the response to shocks to Noise F orecast,t 1. Column 1 shows that when the share price is closer to de-listing (price below 20 dollars), managers do not increase the number of shares in response to exogenous shocks to earnings noise. The effect is only significant among firms with share price above 20 dollars, shown in Column 2. If firms with low stock prices are constrained and would otherwise prefer less precision, then these firms may adjust in other ways. In particular, if constraints prevent firms from choosing shares to optimize precision, firms may be less likely to contract on EPS. In our sample, firms with persistently low stock prices are dramatically less likely to explicitly contract on EPS. In Figure 2 we show that the use of performance based compensation is related to share price levels. Panel A shows that firms with persistently low share price have a lower probability of contracting on explicit EPS incentives. Firms in bottom decile of average share price are persistently close to de-listing (average price over the last two years less than $5). There is a significantly lower usage of EPS in the CEO contracts of these firms. Similarly, Panel B shows that lower priced stocks are associated with less incentive compensation. While these results are merely associations, to our knowledge no compensation theory predicts such contractual differences across variation in stock price levels. 20

21 4 Additional Results and Implications Our cross-sectional evidence thus far is consistent with the view that firms with noisy earnings choose more shares. We estimate this causal effect by examining how firms change shares in response to analyst drops. While this variation is useful for identification purposes, it does not, in our estimation, describe why changes in shares (i.e. stock splits) are so common. In this section we examine time series variation within the firm. We begin with the initial choice for shares at IPO, and describe how we expect firms to change shares over time. We then examine how the choice for shares within the cross-section and time-series should relate to variation in stock price levels. 4.1 Choosing the Number of Shares at IPO We first examine the choice for the number of shares at IPO. Because we do not have data on firms prior to IPO, we proxy for firm characteristics using firms in the same industry. We expect that firms in industries in which earnings are a noisy representation of the manager s true performance will issue more shares at IPO relative to other industries. In Figure 3 we present median shares outstanding (Panel A) and share price (Panel B) at IPO across deciles sorted on industry average Noise Naive. In each figure, we also plot median total market capitalization (line-plot, in millions) at the end of the first month after IPO to show that we are comparing firms of the same size. Firms are first sorted each quarter into 20 groups based on market capitalization. Then within each group they are sorted into deciles based on Fama-French 49 industry average Noise Naive. Median shares outstanding or share price is represented on the left axis (bar height) and median market capitalization 21

22 is on the right. These figures show a clear pattern that is consistent with our cross-sectional evidence. At IPO, firms in industries with highly volatile cash flows choose to issue more shares, even after controlling for market capitalization. Panel B shows that this is reflects a lower share price. This is, to our knowledge, a prediction unique to a precision-based explanation for the number of shares, and contributes to our understanding of what drives firms choice of IPO price. 4.2 Choosing the Number of Shares over Time We expect that much of the within-firm variation in the number of shares is driven not by exogenous shocks to earnings noise or managerial incentives, but simply because, on average, the magnitude of noise in earnings increases as the scale of the firm grows. For a small firm, a swing in earnings of 1 million dollars is likely meaningful and indicative of firm health and performance. For a large firm, this amount may be trivial and not a relevant signal of the firm s true health and performance, simply because it is operating on a larger scale. We offer a simple way to quantify precision relative to firm size; the firm needs to produce total earnings within ± 0.5 % of expected total earnings to meet expected EPS. Therefore E[ EP S ] as the firm s total earnings grow, the denominator increases and the relative precision of the firm s performance metrics increases. If the number of shares stays constant, the firm s realized earnings will need to be closer to expectations in percentage terms, as the firm s total earnings grows. This simple connection between earnings growth and the relative size of the precision 22

23 of performance metrics leads to the prediction that managers will increase shares following long term, permanent earnings growth. Furthermore, an increase in shares following growth should signal to the market that the growth is permanent. Empirically, it is known that firms increase shares following earnings growth (e.g. Lakonishok and Lev (1987) and Asquith et al. (1989)) and that the market responds positively to these increases. Our evidence supports a previously unidentified explanation for these empirical relations. Therefore, we offer a potential new explanation for stock splits that is consistent with the empirical evidence in the existing literature. 4.3 The Precision in Performance Metrics and Earnings Distortions Theoretical literature on contracting and the precision of performance metrics shows that measuring precisely in one dimension can generate gaming and distortions in others (e.g. Hölmstrom and Milgrom (1991)). For example, if a worker is measured more precisely on quantity relative to quality, the worker may have the incentive to skimp on quality. Similar reasoning may apply in our context as well. As firms earnings grow, the EPS metric becomes more precise, which may lead to distortions in the quality of earnings. For example, firms may distort capital expenditures, production costs, or accounting accruals. Ultimately, the firm should respond to growth by increasing the number of shares, which relaxes the precision and also the incentives to distort performance. Therefore, we expect distortions to increase over time, but decrease following increases in shares. To test this, we compare distortions in decisions that affect firm earnings before and after 23

24 share increases. We present these results in Table 7. First we distinguish firms that have increased shares significantly through stocks splits over the fiscal year t from those that have not. We then compare distortions measured over the fourth quarter of fiscal years t 1 and t + 1. We define a significant increase as at least a 5-for-4 stock split. We present difference-in-difference estimates of distortions, comparing the post-pre difference among firms that did not experience a share increase over t, to the difference among those that did. The first measure of earnings distortions is accounting earnings management, which we estimate as the residual from an industry total accruals regression that includes performance controls following Ecker et al. (2011). We find that the growth in accounting earnings management among firms that do not increase shares is significantly different from the drop in accounting earnings management among firms that did increase shares. This is consistent with Hölmstrom and Milgrom (1991) and the view that increases(decreases) in one dimension are associated with increases(decreases) in distortions along other dimensions. We find similar results using measures of real earnings management. These are estimated from production costs and expenditures following the methodology in Roychowdhury (2006). Results show firms that experience a significant increase in the number of shares over t, have a drop in expenditure distortions that is significantly different from the difference among firms that do not increase shares over t. We also find a significant difference-in-difference in production cost distortions. At the bottom of Table 7, we report results using capital expenditures. Stein (1989) shows theoretically that managers may distort investment to affect firm earnings by underinvesting in equilibrium. Therefore, a drop in distortion should be evidenced by an increase in capital expenditures. To test this, we compute abnormal capital expenditures following 24

25 Baker et al. (2003). We find that capital expenditures are increase significantly more among firms that increase shares over t relative to those that do not. Overall, we find that decreases in the precision of performance metrics are associated with fewer distortions. Specifically, we find less accounting and real earnings management and less under-investment. 8 These relations are consistent with Hölmstrom and Milgrom (1991). 4.4 The Cross-Section of Share Price Levels Panel A of Figure 1 shows a positive association between the number of shares and the noise in earnings after controlling for the level of earnings. These strong patterns likely imply that per-share stock prices also vary with the noise in earnings. In Panel B of Figure 1, we report the median level of share price across Noise Naive deciles. We find that firms with noisy earnings have lower per-share prices relative to their counterparts. This suggests that the desire to influence the precision of performance metrics may help explain why some firms tend to trade at high stock prices levels and others at low price levels. The shares-precision relation we document may also help us better understand the importance of share price levels previously documented in the literature. Brandt et al. (2010) document that lower priced stocks are associated with higher idiosyncratic return volatility. One interpretation of this relation is that low priced stocks have higher idiosyncratic volatility because they have a low price, and that this is a result of a retail trader clientle effect. Brandt et al. (2010) find evidence consistent with this interpretation. 8 In untabulated tests, we find that firms meet earnings forecasts more frequently following increases in shares. This suggests that changes in distortion are not enough to perfectly offset the effect of the share change on precision. 25

26 Our results suggest that the relation between idiosyncratic volatility and share price may partially be explained by managers earnings incentives. Under this mechanism, the causality may also run in the opposite direction. Our hypothesis is that noisy earnings will cause firms to choose high levels of shares, resulting in low share prices. To the extent that earnings noise and idiosyncratic volatility are correlated, we would expect to see similar empirical outcomes as in Brandt et al. (2010), but through a different channel. Figure 4 reports noise in earnings (left axis) and average idiosyncratic volatility (right axis) across deciles sorted on stock price each quarter. Not surprisingly, earnings noise and idiosyncratic volatility are highly correlated. The figure shows that both are decreasing in share price. Idiosyncratic volatility is nearly 50% lower in the high price deciles compared to the low price decile, while earnings noise is 30% lower in the high price deciles relative to the low price decile. 9 The relation between the volatility of fundamental cash flows and share price levels suggests that there is more to the idiosyncratic volatility - share price relation than just retail trading. Overall, these findings suggests that one potential link between share price levels and idiosyncratic volatility may be through the volatility of fundamental cash flow in addition to the effects of retail trader clienteles. Moreover, this highlights a potential implication of firms endogenous adjustment of performance metric precision that is beyond financial reporting and EPS outcomes. 9 To ensure that these patterns are not due to differences in net income, we adjusted for net income by first sorting the sample firms into 50 groups based on net income each quarter, and then sorting into deciles based on stock price. 26

27 4.5 The Time-Series of Share Price Levels Weld et al. (2009) document that nominal per-share stock prices have remained remarkably constant across time ( ). This is surprising given significant inflation over the same period. The authors estimate that if real stock prices had remained constant over this period, prices today would average around $450. Furthermore, the authors observe that existing theories of stock splits fail to predict constant nominal share prices. We argue that the relation between the number of shares and EPS precision is one potential explanation. EPS has been, and continues to be, reported to the penny. This remains true despite the penny declining in real value over time. Moreover, Irvine and Pontiff (2009) show that idiosyncratic volatility of firm fundamentals has remained relatively stable over our time period. Therefore, if earnings noise and incentives to meet earnings targets have remained fairly constant in aggregate over time, and managers choose the number of shares outstanding to maintain the precision of EPS, then nominal price levels should remain constant over time. 10 In each quarter, we compute the median price-per-share and median earnings-per-share. We plot these median values over time in Figure 5. Due to Compustat earnings data limitations, we start the sample after Weld et al. (2009) argue that managers choose shares outstanding to keep prices constant, whereas we argue that managers choose the number of shares outstanding to keep the precision of EPS constant. The figure shows that, not surprisingly, prices and earnings levels are strongly related. It is also evident that there is variation in both price-per-share and earnings-per-share medians. 10 We would expect nominal stock prices to increase with inflation only if the unit measurement of EPS also increased with inflation. 27