The Role of Anchoring Bias in the Equity Market

Transcription

1 The Role of Anchoring Bias in the Equity Market Ling Cen Department of Finance University of Toronto Gilles Hilary Department of Accounting HEC Paris K.C. John Wei Department of Finance HKUST Jie Zhang School of Accounting and Finance Hong Kong Polytechnic University This Draft: November 2009 A previous draft of the paper was circulated under the following title: The Cross-Sectional Anchoring of Forecasted Earnings per Share and Expected Stock Returns. We appreciate helpful comments from Kalok Chan, Louis Chan, Eric Chang, Xin Chang, Sudipto Dasgupta, John Doukas, Jie Gan, David Lesmond, Chishen Wei, Chu Zhang, and seminar participants at the Hong Kong University of Science and Technology, National Chiao-Tung University, Peking University, the 2008 Chinese International Conference of Finance, 2007 Financial Management Association meetings and the 2008 European Finance Association Annual Meeting.

2 The Role of Anchoring Bias in the Equity Market Abstract: Anchoring is the fact that, in forming numerical estimates of uncertain quantities, adjustments in assessments away from arbitrary initial values are often insufficient. We find that this cognitive bias has significant economic consequences for the efficiency of financial markets. First, analysts make optimistic (pessimistic) forecasts when the firm forecasted earnings per share (F-FEPS) is lower (higher) than the industry median FEPS. Second, firms with F-FEPS greater (lower) than the industry median experience abnormally high (low) future stock returns, particularly around the subsequent earnings announcements. Third, firms with high F-FEPS relative to the industry median are more likely to engage in stock splits. Fourth, split firms with lower (higher) F-FEPS relative to the industry median experience more (less) positive forecast revisions, higher (lower) forecast errors, and more (less) negative earnings surprises after a stock split compared to non-split firms. Key words: Anchoring, cognitive biases, analysts, earnings forecasts.

3 1. Introduction Analysts are key financial market participants. Further, researchers often use analysts earnings forecasts as proxies for market expectations and differences in opinion. In addition, analysts earnings forecasts are one of the rare settings for which researchers have a large natural data set of individuals actual decisions, while the biases in decision making can be observed and verified ex post. Not surprisingly, the activities of analysts have been a fertile ground for behavioral research and the prior literature has shown them to suffer from different biases. For example, prior literature suggests that analysts (1) make upwardly biased forecasts (e.g., DeBondt and Thaler (1990)), (2) overreact to positive information, (3) under-react to negative information (e.g., Easterwood and Nutt (1999)), and (4) are overconfident in their own skill (Hilary and Menzly (2006)). However, the implications of these potential cognitive biases for investors and, even more so, for managers are less understood. We also consider the behavior of financial market participants but from a perspective different from the prior literature. We focus on the anchoring bias, a topic that has not been extensively investigated by the prior literature in accounting and finance. Anchoring is the fact that, in forming numerical estimates of uncertain quantities, adjustments in assessments away from arbitrary initial values are often insufficient. One of the first studies of this cognitive bias is the seminal experiment by Kahneman and Tversky (1974). These authors report that the estimates of an uncertain proportion (the percentage of African nations in the United Nations) were affected by a number between 0 and 100 that was determined by spinning a wheel of 1

4 fortune in the subjects presence. Subsequent research (reviewed in Section I) has confirmed the robustness of this cognitive bias. We hypothesize that market participants such as sell side analysts and investors are also affected by the anchoring bias when they estimate the future profitability of a firm. This estimation is a complex task that involves a high degree of uncertainty. This suggests that market participants naturally anchor on salient information such as the industry median forecasted earnings per share (I-FEPS). If this conjecture is correct, this should have different implications for the behavior of analysts and investors. First, if analysts anchor on median industry FEPS, their forecasts should be too close to this number. As a consequence, analysts are likely to underestimate the future earnings growth of firms with high firm FEPS (F-FEPS) compared to the industry median FEPS. In other words, analysts give more pessimistic earnings forecasts for firms with high FEPS than for similar firms in the same industry with low FEPS. As a result, earnings forecast errors should be lower for high F-FEPS firms than for low F-FEPS firms in the same industry. Second, if investors anchor on industry median FEPS, their expectations of future profitability should be biased. Firms with an already high F-FEPS compared to their industry should suffer from low expectations regarding their future profits. Conversely, firms with a low current F- FEPS relative to their industry should enjoy high expectations regarding their future profits. If this is the case, stocks with high F-FEPS should significantly outperform similar stocks in the same industry with low F-FEPS when the true firm profitability is subsequently revealed, for example, in subsequent earnings announcements. Third, 2

5 if managers realize this phenomenon, they should manage their firm FEPS so that it remains low relative to other firms in the industry. One relatively easy way to achieve this goal is to engage in a stock split. Thus, we expect that firms with high F-FEPS should be more likely to engage in a stock split to lower their F-FEPS relative to other firms in the industry. If this strategy is successful, we expect that both analysts and investors should be affected. In particular, we expect analysts to subsequently revise their earnings forecasts upward. This effect should be stronger for firms that have a high F-FEPS relative to the industry than for firms that have a low F-FEPS. As a consequence, the signed forecast errors and earnings surprises should be reduced for these firms. Our empirical results are consistent with these hypotheses. We define a measure of cross-sectional anchoring, CAF, as the difference between the firm FEPS (F-FEPS) and the industry FEPS (I-FEPS), scaled by the absolute value of the later. First, we find that analysts earnings forecasts of firms with high CAF are more pessimistic than the forecasts for similar firms with low CAF. This result is consistent with analysts anchoring their forecasts on the industry median forecasted EPS. Second, stock returns are significantly higher for firms with high CAF than for similar firms in the same industry with low CAF. The positive relationship between firm FEPS and future stock returns cannot be explained by risk factors, the book-to-market or earnings-to-price effect, the accounting accruals effect, and price or earnings momentum. In addition, earnings surprises are more positive for firms with high CAF than for firms with low CAF. These results are consistent with investors anchoring 3

6 their forecasts on the industry median forecasted EPS. All these results are stronger when the industry FEPS is more stable and when market participants are less sophisticated. Third, we find that the likelihood of doing a stock split within a year is increasing when CAF is high. This result is consistent with the idea that managers realize the existence of anchoring in the financial markets and adjust their behavior to cater to this cognitive bias. Finally, firms with low CAF experience positive earnings forecasts revisions by analysts and positive forecast errors after a stock split than firms with high CAF do. Conversely, firms with low CAF experience more negative changes in earnings surprises after a stock split than firms with high CAF do. This study contributes to the literature in at least three ways. First, it investigates whether anchoring, an important principle in the psychology literature, affects the decision making process of individuals in an important economic setting. This large sample test complements previous research that was largely based on small sample experimental work. Although we focus on analysts earnings forecasts and price behavior in order to take advantage of a particularly rich data set, we expect the results to generalize to other settings as well. Second, the paper also enhances our understanding of the financial markets by providing new understanding of analyst and investor behaviors. Of particular importance, we show that the understanding of the behavioral principles may yield a trading strategy that generates abnormal returns. Specifically, our results suggest a hedge portfolio that goes long on firms with high CAF and short on firms with low CAF can generate abnormal returns (Alpha) of 0.75% per month. The profitability of this trading strategy remains for investment 4

7 horizons that extend to 12 months. Third, our results suggest a strategy based on stock split for manager of firms with high EPS. This strategy can mitigate undervaluation and sometime generate overvaluation by influencing analysts earnings forecasts or revisions. The rest of this paper is organized as follows. In the two next sections, we discuss the theoretical foundations of our analysis and develop our research hypotheses. In Section III, we discuss the sample and descriptive statistics. In Section VI, we present our empirical results. We conclude in Section VI. 2. Prior Research on Anchoring The prior literature (e.g., Kahneman and Tversky (1974)) suggests that individuals use cognitively tractable decisions strategies, known as heuristics, to cope with complex situations. These heuristics reduce complex inferential tasks to relatively simple cognitive operations. Although these mental short-cuts help dealing with complex situations, they may also lead to systematically skewed outcomes. The anchoring effect is one of the most studied examples of cognitive biases that lead individuals to make sub-optimal decisions. In their classical study, Kahenman and Tvesky (1974) suggest that individual frequently form estimates by starting with a given, easily available reference value and adjusting from this value. Although this approach may not be problematic per se, prior research also shows that 5

8 individuals typically fail to properly adjust their final estimate away from the salient but potential irrelevant starting point (the anchor ). The seminal example involves spinning a wheel-of-fortune in front of subjects and thus generating a number between 0 and 100. Kahneman and Tversky (1974) then ask the subjects their best estimates of the percentage of African nations in the United Nations. The obviously irrelevant random number generates systematic bias in the estimates of the percentage. For example, subjects who observe a number equal to 10 estimated on average that the percentage was 25%. In contrast, subjects who observed a random number equal to 65 estimated on average that the percentage was 45%. This basic result has been replicated in other experimental settings. For example, Kahneman and Tversky (1974) ask half of the subjects to estimate the value of 1x2x3x4x5x6x8 and asked the other half to estimate 8x7x6x5x4x3x2x1. The average answer is 512 and 2,250 in the first and second case, respectively. In a different setting, Russo and Shoemaker (1989) first provide an anchor based on a constant (varying from 400 to 1,200) plus the last three digit of the subject phone number. The two researchers then ask for an estimate of the year in which the Attila the Hun was defeated. Estimates were positively and significantly correlated with the anchor. More recently, Qu, Zhou, and Luo (2008) provide physiological evidence of the anchoring process based on event-related potential techniques (i.e., techniques that measure brain response that is directly the result of a thought or perception). The prior literature has shown that anchoring is an extremely robust phenomenon that influences many different types of decisions in many different 6

9 contexts. 1 The effect has been found in a wide range of questions such as judicial sentencing decisions (e.g., Englich and Mussweiler, (2001)), personal injury verdicts (e.g., Chapman and Bornstein (1996)), estimation of likelihood of diseases (e.g., Brewer, Chapman, Schwartz and Bergus (2007), job performance evaluation (2008) or real estate acquisitions (e.g., Northcraft and Neale (1987)). The accounting literature has also suggested situations in which anchoring leads to biased outcomes. For example, Joyce and Biddle (1981) use experimental evidence to suggest that fraud estimation and audit planning are affected by anchoring. Consistent with these findings, Kinney and Uecker (1982) indicate that analytical revenues performed by auditors and compliance testing settings are affected by the anchoring bias. In particular, unaudited values in the financial statements audit influence analytical revues. Biggs and Wild (1985) confirm the results in Kinney and Uecker (1982) but report that the bias was moderated when additional audited information was available. Butler (1986) revisits some of the issues discussed in Joyce and Biddle (1981), while Kinney and Uecker (1982) refine the understanding of the anchoring process among auditors. 1 For example, anchoring has been showed to influence intuitive numerical estimations (e.g., Wilson, Houston, Etling and Brekke (1996)), probability estimates (e.g., Plous, (1989)), estimations of a sample mean and standard deviation (e.g., Lovie (1985)), confidence interval (Block and Harper (1991)), sales predictions (e.g., Hogarth (1980)), Bayesian updating tasks (e.g., Lopes (1981)), utility assessments (e.g., Johnson and Schkade (1989)), risk assessments (e.g., Lichtenstein et al. 1978), preferences for gambles (e.g., Lichtenstein and Slovic (1971)), perception of deception and information leakage (e.g., Zuckerman, Koetsner, Colella and Alton (1984)), negotiation outcomes (e.g., Ritov (1996)) and choices between product categories (e.g., Davis, Hoch and Ragsdale, 1986). 7

10 The prior literature also suggests that it is particularly hard to debias subjects and that anchoring is robust to several conditions. For example, this auditing literature suggests that anchoring is prevalent, even among experienced professionals. Consistent with this view, Northcraft and Neale (1987) conclude (p. 95) that (1) experts are susceptible to decision bias, even in the confines of their home decision setting, and (2) experts are less likely than amateurs to admit to (or perhaps understand) their use of heuristics in producing biased judgments. Plous (1989) also shows that task familiarity is not sufficient to avoid anchoring and that the effects of anchoring are not significantly influenced by the ease with which respondents can imagine the outcome (outcome availability), by the instructions to list the most likely path to the outcome (path availability), or by casting the problem in terms of the avoidance (rather than the occurrence). He also mentions that anchoring exists even after correcting for social demand biases (i.e., the existence of expert opinion running against the initial anchor). Wright and Anderson (1989) also consider the effect of situation familiarity on anchoring. They conclude (p. 68) that the anchoring effect is so dominant that increasing situational familiarity did not result in decreased anchoring. They find that monetary incentives can reduce anchoring but the effect is statistically marginal (p<0.09). In contrast, Tversky and Kahneman (1974) find that payoffs for accuracy did not reduce the anchoring effect. Brewer, Chapman, Schwartz, and Bergus (2007) report that accountability does not reduce the anchoring bias in doctors prediction of infection. Whyte and Sebenius (1997) provide results suggesting that groups do not debias individual judgments. 8

11 However, most of the prior research is based on small sample experimental approaches and research based on large sample archival approaches is much more limited. Ginsburgh and van Ours (2003) examine the career success of pianists who compete in the Queen Elizabeth Piano Competition. The order in which competitors play both across the week of the competition and on the night they perform (two perform each night) predicts the judges ranking, even though order is chosen randomly. The authors find that subsequent career success is significantly related to the component of the competition ranking that is related to order. George and Hwang (2004) postulate that investors are reluctant to bid the price high enough, when a stock price is at or near its highest historical value. Consistent with this intuition, they find that nearness to the 52-week high has predictive power for future returns. Campbell and Sharpe (2009) show that professional forecasters anchor their predictions of macroeconomic data such as the consumer price index or non farm payroll employment on the values of previous releases, which lead to systematic and sizeable forecast errors. However, these three studies focus on the possibility of time series anchoring, but do not investigate the more general possibility of cross-sectional anchoring, the topic of our study. 3. Hypotheses development and research design 3.1 Hypotheses development Given the documented robustness of the anchoring bias, we hypothesize that market participants such as sell side analysts and investors should also be affected by 9

12 the anchoring bias when they estimate the future profitability of a firm. This estimation is a complex task that involves a high degree of uncertainty. This suggests that market participants naturally anchor on salient information. Prior research (e.g., Chapman and Johnson (2002)) suggests that anchors are most influential if they are expressed on the same response scale (dollars and dollars rather than dollars and percentages) and if they represent the same underlying dimension (width and width rather than width and length). A natural candidate in our setting is the industry median earnings per share. Since an analyst usually covers a group of firms within the same industry, this number is readily available and is naturally associated with the task on hand. For example, Zachs Investment Research states in the first line of a recent analyst report that median EPS is projected to drop 21.2%. 2 The popular website Investopedia.com notes that earnings per share is generally considered to be the single most important variable in determining a share s price. 3 The role of median values in anchoring is also consistent with the theoretical literature. For example, Tversky and Kahneman (1974) show in an experimental setting that subjects who receive the median estimates of other subjects tend to anchor on this median. If the conjecture that market participants anchor on industry median is correct, this should have different implications for the behavior of analysts, investors and managers of publicly traded companies. First, if analysts anchor on the median industry forecasted EPS, their forecasts should be too close to this number. As a consequence, analysts are likely to underestimate the future realized earnings growth

13 of firms with high F-FEPS (relative to the industry median FEPS). In other words, analysts give more optimistic earnings forecasts for stocks with low F-FEPS than similar firms in the same industry with high F-FEPS. Thus, signed earnings forecast errors are larger for low F-FEPS firms than for high F-FEPS firms in the same industry. This motivates our first hypothesis: H1: Signed forecast errors are larger for firms with low F-FEPS relative to the industry median FEPS than for firms with high F-FEPS relative to the industry median FEPS. Second, if investors anchor on median industry FEPS, their expectations of future profitability should also be biased. Firms with a high F-FEPS relative to their industry median should suffer from low expectations regarding their future profits. Conversely, firms with current low F-FEPS relative to their industry median should enjoy high expectations regarding their future profits. If this is the case, stocks with high F-FEPS should significantly outperform similar stocks in the same industry with low F-FEPS once the true profitability is revealed. This motivates our second hypothesis: H2: Controlling for risk factors, future stock returns for firms with high F-FEPS relative to the industry median FEPS are larger than for firms with low F-FEPS relative to the industry median. 11

14 This prediction should be particularly true around subsequent earnings announcements. Third, if managers realize the presence of these biases among analysts and investors, they should manage their firm FEPS so that it is low relative to other firms in the industry. One fairly easy way to achieve this goal is to perform stock splits. We expect that firms with high F-FEPS should be more likely to engage a stock split to lower their EPS relative to other firms in the industry. This motivates our third hypothesis: H3: The probability of stock splits is larger for firms with high F-FEPS relative to the industry median FEPS than for firms with low F-FEPS relative to the industry median. If this strategy is successful, we also expect that both analysts and investors should be affected. In particular, we expect that firms with low F-FEPS relative to the industry FEPS before the stock splits should experience more positive earnings forecasts revisions by analysts, more positive forecast errors, and more negative changes in earnings surprises after a stock split than firms with high initial F-FEPS do. 3.2 Research design 12

15 We use two basic approaches to investigate our hypotheses: regressions and portfolio sorts. One advantage of the regression approach is that it allows us to control easily for a host of potentially confounding effects. In contrast, the portfolio approach allows us to address econometric issues (such as overlapping observations) and non-linearities more easily than in a regression framework. The portfolio approach also allows us to deal more easily with the bad model issue discussed by Fama (1998) and Mitchell and Stafford (2000) Regression analysis Our first approach is based on the estimation of the following model: DepVar i,t = α + β CAF i,t + γ k X K i,t + ε i,t DepVar i,t represents our different dependent variables for firm i in period t. To test our first hypothesis, we consider FE, the analyst forecast error, as the dependent variable. We define FE as the difference between the consensus EPS forecast (F- FEPS) and the actual EPS that is announced at the end of the fiscal year, scaled by the absolute value of the latter (we define our different variables in details in Appendix A). 4 F-FEPS is the mean of forecasted one-year-ahead earnings per share in the previous month from the I/B/E/S unadjusted summary historical file. EPS is the actual earnings per share for the next fiscal year end (reported in IBES actual file). To test our second hypothesis, we compute two dependent variables at the end of each 4 We obtain similar untabulated results if we deflate FE by the stock price at the end of month t-1. 13

16 calendar month t. The first one is BHAR 0:1, defined as the cumulative buy-and-hold raw return for firm i in the current month t. 5 Our second variable is ECAR, defined as the three-day risk-adjusted cumulative abnormal returns around the different earnings announcement days over the next twelve months after the end of calendar month t-1. If a firm experiences four earnings announcements in these twelve months, we calculate this return over 12 days. To test our third hypothesis, we define Split i,t as an indicator variable that equals one if firm i carries out a significant stock split (e.g., one share is split into 1.5 or more shares) in month t and zero otherwise. Our main treatment variable, CAF, is a measure of cross-sectional anchoring. We define CAF as the difference between the individual firm forecasted EPS (F- FEPS) and the industry cross-sectional median of FEPS (I-FEPS), scaled by the absolute value of the latter. We define the 48 industries as in Fama and French (1997). Aside from including a constant (usually not tabulated), we control for X K, a vector of K control variables. Specifically, we include the following variables (defined in greater details in the Appendix A): the logarithm of market capitalization (Size), the logarithm of book-to-market ratio (BTM), accounting accruals (Accruals), the three-day abnormal return around the most recent earnings announcement date up to the beginning of month t (ES recent ), and the time-series anchoring measure of EPS (TAF). TAF is defined as the difference between the individual F-FEPS and the most 5 We focus on a one month horizon to minimize the bad model problem discussed in Fama (1998) and Mitchell and Strafford (2000). As discussed in Section V, results hold if we extend the horizon to twelve months. 14

17 recently announced EPS, scaled by the absolute value of the latter. We use the lagged information to ensure that the value of these variables is known by investors at the beginning of month t and to avoid any look-ahead bias. We also control for past returns in our specifications. When FE, ECAR and Split are the dependent variable, we simply use the six-month buy-and hold return in the prior six months (Ret -6:0 ). However, when BHAR is the dependent variable, we control for Ret -7:-1 and Ret -1:0 because the prior literature has shown the presence of momentum and reversal (e.g., Jegadeesh and Titman (1993, 2001)). In addition, we also control for the following three additional variables when FE is the dependent variable: Experience (the natural logarithm of one plus average number of months covered by existing analysts), Breadth (the natural logarithm of average number of stocks covered by existing analysts) and Horizon (the natural logarithm of one plus the number of months before next earnings announcement). If our hypothesis H1 is correct, the coefficient of CAF should be negative when FE is the dependent variable. In essence, when F-FEPS is low relative to I-FEPS, analysts should anchor on this second number and issue relative high forecasts. This would lead to negative surprises when the true earnings are subsequently revealed. If H2 is correct, we expect that the coefficient of CAF should be positive when BHAR is the dependent variable. We also expect that the coefficient of CAF should be positive when ECAR is the dependent variable if investors realize their initial mistake when subsequent earnings are released. If H3 is correct, we expect that the coefficient of CAF should be positive when Split is the dependent variable. In essence, the 15

18 managers would reduce their EPS to avoid having to low forecasted EPS and low valuation. We use a Fama-McBeth (1973) approach when we use a continuous dependent variable (FE, BHAR, and ECAR). We also correct the standard errors for serial correlation using the Newey-West procedure. We use a logit specification when the dependent variable is binary (Split). We correct the standard errors of the estimated coefficient for heterokedasticity and simultaneous clustering of observations by firm and period (e.g., Cameron, Gelbach and Miller (2009) and Peterson (2009)) Portfolio Sorts. Our second approach is based on portfolio sorts. We rank firms in quintiles along two dimensions, size (i.e., market capitalization) and CAF. We then observe the behavior of different variables across portfolios. To test the first hypothesis, we consider FE as the dependent variable. To test the second hypothesis, we consider two variables, Alpha and ECAR, as dependent variables. Alpha is the intercept from the time-series regression based on the Fama and French (1993) thee factor plus the Carhart (1997) momentum factor model as follows: R M i, t R f, t = i + βi Mktt R f, t ) α ( + β SMB + β HML + β UMD + ε S i t H i t U i t i, t, (1) where Mkt R f, SMB and HML constitute the Fama and French market, size and value factors, and UMD denotes the Carhart (1997) momentum factor. We use the onemonth portfolio return as the dependent variable and we estimate the intercept (Alpha) for each of the 25 portfolios. To test the third hypothesis, we consider the time-series 16

19 averages of stock-split ratios (SSR). 6 In each case, we form hedge portfolios that go long in firms with high CAF values and go short in firms with low CAF values. We test for the significance of the different dependent variables (FE, Alpha, ECAR, and SSR) in the different hedge portfolios. 4. Sample and descriptive statistics. 4.1 Sample Selection Our basic sample consists of all NYSE, Amex and Nasdaq-listed common stocks in the intersection of (a) the CRSP stock file, (b) the merged Compustat annual industrial file, and (c) the Institutional Brokerage Earnings Estimates (I/B/E/S) unadjusted summary historical file for the period from January 1983 to December We obtain the data for the different systematic risk factors from Ken French s website. 8 To be included in the sample for a given month, t, a stock must satisfy the following criteria. First, its mean of analyst forecasts on the one-year-ahead (FY1) earnings per share (F-FEPS) in the previous month, t-1, should be available from the I/B/E/S unadjusted summary historical file. Second, its returns in the current month, t, and the previous six months, from t-6 to t-1, should be available from CRSP, and 6 To calculate this variable, we consider all the firms that engage in a stock split in a given period, we measure the stock split ratio (e.g., 2 for 1) and we average the ratios across all firms. Thus, SSR potentially ranges from 1 (if there is not stock split) to infinity. 7 Though I/B/E/S provides data starting from 1976, we restrict our sample period to January 1983 to December 2005 for two reasons. First, before January 1983, the coverage of stocks by I/B/E/S was limited, which would reduce the power of our tests. Second, the I/B/E/S detailed unadjusted historical file began in Hence, we can only conduct robustness checks on the results with the detailed file data after Extending the sample period to 1976 does not change our results

20 sufficient data should be available to obtain market capitalization and stock prices in the previous month, t-1. Third, sufficient data from CRSP and Compustat should be available to compute the Fama and French (1993) book-to-market ratio as of December of the previous year. In addition, stocks with share prices lower than five dollars at the end of the previous month, t-1, are excluded, as are the stocks with negative reported Compustat book values of stockholders equity (Item #60) as of the previous month, t-1. This screening process yields 712,563 stock-month observations or an average of 2,699 stocks per month. 9 Before presenting our empirical results, we would like to emphasize the importance of using the I/B/E/S unadjusted data rather than the I/B/E/S adjusted data. The unadjusted FEPS is the actual reported value, while the adjusted FEPS has been adjusted for stock splits and stock issuance on the basis of the number of shares outstanding as of the latest data release day. Consequently, when we perform trading strategies based on FEPS, the results are only valid when the unadjusted FEPS is used because this measure reflects the actual value that investors had historically perceived or observed at that time. The results are not valid when the adjusted FEPS is used because this measure contains ex post information reflecting stock splits, which could induce severe selection biases. The importance of using unadjusted I/B/E/S data has been recognized by many previous researchers, such as Diether, Malloy and 9 Following previous literature (e.g., Jegadeesh and Titman, 2001), we remove stocks with prices under $5 because these stocks not only have few analysts covering them, but they also incur large transaction costs due to their poor market liquidity (thin trading and large bid-ask spreads), which could distort the feasibility of any trading strategy. We remove the stocks with negative book value of stockholders equity simply to make some measures meaningful (e.g., returns on equity). Including these observations leads to (untabulated) results that are economically and statistically more significant. 18

21 Scherbina (2002), and it has become the standard treatment in studying analysts forecast behaviors. 4.2 Sample Characteristics Table 1 provides summary descriptive statistics of our sample. All the variables mentioned above are either lagged by one month or computed based on public information as of the previous month, t-1, in order to guarantee that they are already known by investors at the beginning of each month and can be used to execute our trading strategies. Panel A of Table 1 reports the time-series averages of the crosssectional means, medians, standard deviations and other statistics of the above variables. As shown in Panel A, all variables exhibit substantial variation, suggesting that the portfolio sorting strategies using these characteristics should offer reasonable statistical power for our tests. The mean and median of firm size (Size) are $2.04 billion and $0.35 billion, respectively, which are much larger than the corresponding values for all CRSP stocks (untabulated result). This reflects the fact that the sample of firms covered by I/B/E/S omits many small stocks. Since the return anomaly reported in this study is stronger for small stocks, the sample selection criteria bias our analysis against finding support for our. [Insert Table 1 Here] 19

22 Table 2 reports the correlation coefficients among these variables. CAF is negatively correlated with FE and positively with BHAR, ECAR and Split (although insignificantly so). The correlations between the different control variables are low, suggesting that multicollinearity is not an important issue in our setting. [Insert Table 2 Here] 5. Empirical results 5.1 Anchoring and forecast errors We first investigate if H1 is true. Results from our regressions are reported in Panel A of Table 3. We consider three different models with an increasing number of control variables. In the first column, we control for Size, BTM and RET -6:0. In the second column, we also control for Accruals and ES recent. Finally, in the last column, we also control for E/P and TAF and for the three variables specific to the FE regressions (Experience, Breath and Horizon). Consistent with H1, CAF is significantly negative in all three models. The effect is economically significant. For example, an increase of CAF by one standard deviation increases FE by approximately 13.2% of its mean. 10 The effect is also statistically significant with t- statistics ranging from to As robustness checks, we consider two alternative dependent variables in our regressions. In the first alternative specification, we use the consensus long-term 10 The effect = (from Table 3) * (from Table 1)/ (from Table 1)= 13.2% 20

23 growth rate forecasts (LTG) as reported in the IBES unadjusted summary file. In the second one, we use the revision of long-term growth rate (RLTG). RLTG is estimated as the slope coefficient (t i ) in the time-series simple regression of LTG i,t = a i + t i Time t + ε i,t over the next twenty-five months beginning from the previous month (at least twelve months), which measures the monthly movement of LTG. Consistent with the resulted tabulated in Panel A of Table 3, CAF is significantly negative in the first case (with a t-statistic equal to ) and positive in the second case (with a t-statistic of 2.77). In other words, the results in Table 3 show that analysts anchor on I-FEPS when they forecast earnings and thus are optimistic for firms with low F-FEPS. These additional untabulated results show that analysts are subject to a similar phenomenon when they forecast long term earnings and that they gradually correct their initial forecast errors over time. [Insert Table 3 Here] Panel B of Table 3 provides the results of the portfolio sorts, based on size (from G1 to G5) and on CAF (from E1 to E5). The last column of the table reports the results of the partitions based on CAF for firms of all sizes pooled together. As we go from E1 (portfolio of firms with the lowest CAF) to E5 (portfolio of firms with the highest CAF), the average value of FE is monotonically decreasing. The difference between the average value of FE in E5 and E1 is statistically significant with a t-statistic equal to The other five columns report the mean FE for the 21

24 different portfolios based on size and CAF. For all levels of CAF, FE is increasing as firm size is decreasing. The effect is monotonic in virtually all cases (except between G4 and G5 for E4). More importantly for our purpose, FE is decreasing for all levels of size when CAF is increasing. However, both the magnitude and the statistical significance of the difference between firms with high and low CAF is decreasing when the firm size is increasing. For example, the magnitude of the difference is decreasing in absolute value from to Similarly, the t-statistic of the difference is decreasing in absolute value from to from G1 to G5. Untabulated results indicate that we reach similar conclusions if we use a similar procedure to sort LTG and RLTG based on size and on CAF. The results from the sorts and double-sorts are therefore consistent with H Anchoring and one-month ahead BHAR We then investigate if H2 is true. Panel A of Table 4 presents the results of a regression of a one-month ahead BHAR on CAF and our different control variables. For all three models, CAF is significantly positive with t-statistics ranging from 3.14 to The economic effect is such that increasing CAF by one standard deviation increases BHAR by approximately 18.6% of the mean value of BHAR. 11 [Insert Table 4 Here] 11 The effect = (from Table 4) * (from Table 1) / (from Table 1) =

25 Panel B of Table 4 provides the results of the portfolio sorts, based on size (from G1 to G5) and based on CAF (from E1 to E5). For each portfolio, we estimate a time-series regression based on the Fama-French and Carhart four-factor model for each portfolio. We report the intercepts, Alphas, of the different portfolios in Panel B of Table 4. The last column of the table reports the results of the partitions based on CAF for firms of all sizes pooled together. As we go from E1 (portfolio of firms with low CAF) to E5 (portfolio of firms with high CAF), the values of Alphas are monotonically increasing. The difference between the values of Alpha in E5 and E1 is statistically significant with a t-statistic equal to The value of Alpha for the hedge portfolio monthly returns (long E5 and short E1 at the same time) is 0.7%. The other five columns report the intercept for the different hedge portfolios based on size and CAF. The average values of the abnormal returns (Alpha) are significantly positive for all levels of size. However, both the magnitude and the statistical significance are decreasing when the firm size is increasing. For example, the t- statistic of the difference is decreasing from 5.39 to 2.10 from G1 to G5. Similarly, the magnitude of the difference is decreasing in absolute value from to Untabulated results indicate that we obtain similar results if we use either valueweighed or equal-weighted portfolio returns instead of the intercepts of the timeseries regression (Alpha). The tabulated results are based on dependent sorts of the firms based on Size and CAF. These dependent sorts ensure that the number of firms is the same in all portfolios. Untabulated tests indicate that we find similar, if not stronger, results, when we use independent sorts and allow for the number of 23

26 observations to vary across portfolios. 12 Following Zhang (2006), we also replace Size with alternative proxies that may be correlated with information uncertainty, such as firm age, share price, analyst coverage, and institutional holdings. We find similar (untabulated) results as those reported in Table 4. Table 4 focuses on the one-month-ahead return. However, the effect of CAF is not limited to one month ahead. Figure 1 plots the average cumulative raw returns at the monthly intervals of the hedging strategy by buying the highest CAF decile portfolio and selling the lowest CAF decile portfolio. It reveals that the hedging portfolio returns to the CAF strategy grow consistently within at least the first six months after portfolio formation. To investigate this possibility, we re-estimate a model similar to the one reported in the last column of Panel A of Table 4 but we use returns cumulated over 3, 6 and 12 month, respectively. The (untabulated) intercepts are equal to 0.121, and with t-statistics of 1.96, 2.13 and 2.21, respectively. Although the cumulated abnormal returns grow at a decreasing rate, they do not show any reversal over the next thirty-six months. This distinguishes the FEPS anomaly from the momentum anomaly, for which Jegadeesh and Titman (2001) find a dramatic reversal of returns to the momentum strategy after one year. 5.3 Anchoring and market reaction around earnings announcements 12 Results (untabulated) are also robust if we use three way sorts based on Size, Momentum and CAF; Size, Book-to-market and CAF; Size, earnings surprises and CAF; Size, forecasted E/P ratio and CAF; Size, Accruals and CAF; Size, V/P and CAF or Size, FE scaled by price and CAF. 24

27 Having found that future returns and CAF are positively related, we focus next on returns around earnings announcements. Panel A of Table 5 presents the results of a regression of the earnings announcement on CAF and our different control variables. For all three models, CAF is significantly positive with t-statistics ranging from 4.08 to The economic effect is such that increasing CAF by one standard deviation increases ECAR by approximately 100% of the mean value of ECAR. 13 [Insert Table 5 Here] Panel B of Table 5 provides the results of earnings surprises from portfolio sorts, based on size (from G1 to G5) and based on CAF (from E1 to E5). For each portfolio, we estimate the average market reaction around the earnings announcements. The last column of the table reports the results of the partitions based on CAF for firms of all sizes pooled together. As we go from E1 (portfolio of firms with low CAF) to E5 (portfolio of firms with high CAF), the average value of earnings surprises is increasing. The difference in the value of earnings surprises between E5 and E1 is statistically significant with a t-statistic equal to The return of the hedge portfolio is 0.4% over the three day period. The other five columns report the intercept for the different portfolios based on size and CAF. The returns of the hedge portfolios are positive for all levels of size. However, both the magnitude and the statistical significance are decreasing when the firm size is 13 The effect = (from Table 5) * (from Table 1) / (from Table 1) = 99.7% 25

28 increasing. For example, the magnitude of the difference in earnings surprises is decreasing from to Similarly, the t-statistic of the difference is decreasing from 5.07 to 1.16 from G1 to G5. Overall, the returns surrounding earnings announcements of the hedge portfolios are significant for the three smallest size quintiles and in the pooled sample. 5.4 Anchoring and stock splits We next investigate if H3 is true. But before doing so, we examine the time-series behavior of forecasted earnings per share (FEPS) and aggregate earnings. Figure 2 indicates the existence of a stable pattern in the cross-sectional distribution of nominal forecasted EPS (FEPS). Untabulated results also indicate that this phenomenon also exists in the nominal realized earnings per share (EPS). The cross-sectional median of FEPS rarely deviates away from a small range bounded by $1.5 and $2 in our sample period from 1983 to In contrast, the median of forecasted total earnings (TFE) in the cross-section almost tripled from US$14 million to US$37 million during the same time period. [Insert Graph 1 Here] This provides an indirect test of this hypothesis. These differences in times series are consistent with the idea that firms manage their nominal earnings per share around an optimal level. Panel A of Table 6 presents the results of logit regressions of Split 26

29 on CAF and our different control variables. For all three models, CAF is significantly positive with t-statistics ranging from 2.59 to The economic effect is such that increasing CAF by one standard deviation increases the odd ratio of a stock split by approximately 5.0%. [Insert Table 6 Here] Panel B of Table 6 provides the results of the portfolio sorts, based on size (from G1 to G5) and on CAF (from E1 to E5). For each portfolio, we estimate the average stock split ratio (SSR). The last column of the table reports the results of the partitions based on CAF for firms of all sizes pooled together. As we go from E1 (portfolio of firms with low CAF) to E5 (portfolio of firms with high CAF), the average value of SSR is monotonically increasing. The difference between the average value of SSR in E5 and E1 is statistically significant with a t-statistic equal to 8.48 in the pooled sample. Results also indicate that for each value of CAF, the stock split ratio is increasing monotonically with the firm size. More importantly for our purpose, the difference in SSR between E1 and E5 is significant in all size groups. However, both the magnitude and the statistical significance of this result are decreasing when the firm size is increasing. For example, the magnitude of the difference is decreasing from to Similarly, the t-statistic of the difference in SSR is decreasing from 9.31 to 4.87 from G1 to G5. We reach a similar 27

30 conclusion if we use the number of stock split instead of SSR as a dependent variable (untabulated). 5.5 Consequences of the stock splits Having considered the causes of the stock splits, we next examine some of their consequences for analyst forecast revisions (Panel A of Table 7), analyst forecast errors (Panel B) and earnings surprises (Panel C). To do so, we use a difference in difference approach. We first identify firms that carry out significant stock splits (e.g., one share is split into 1.5 or more shares) in each month. In Panels A and B, we match these firms with firms that do not engage in a stock split and have similar size, book-to-market ratio, forecast errors and CAF (we use the value for the month prior to the stock split to match firms). We then compute the differences in forecast errors (Panel A) and in forecast revisions (Panel B) between the firms that engage in a stock split and the median value of the matched firms that do not engage in a stock split. In Panel C, for each firm and each month, we compute the change in ex post and ex ante earnings surprises (ES). We match firms that engage in a stock-split with firms that do not by size, book-to-market ratio and CAF. We report the difference in changes in earnings surprises between the firms that engage in a stock-split and the median value of the matched firms that do not. We next repeat our procedure of double sort based on size and CAF. [Insert Table 7 Here] 28

31 Panel A of Table 7 shows that there is a positive change in forecast revisions for firms after a stock split compared to firms that did not engage in a stock split. In 28 out 30 cells, the difference is positive. More importantly for our purpose, the effect is more significant for firms with low CAF than for firms with high CAF. For example, the difference is (with a t-statistic of 16.78) between the extreme portfolios based on CAF when firms of all sizes are considered. The difference is also significant across all five size groups with t-statistics ranging from 4.55 to Panel B show that there is a more positive forecast errors for firms after a stock split compared to firms that did not engage in a stock split. This is true for most firms but the effect is less positive as the CAF is increasing. The effect is even negative for portfolios in which CAF is the highest (E5). The difference between the portfolios of high and low CAF is significant when firms of all sizes are considered (the t-statistic is 5.53) and in four out of five size groups (the t-statistic is 1.54 in the second smallest size group). Panel C shows that there is a negative change in earnings surprises after the split compared to firms that did not engage in a stock split. In 29 out 30 cells, the difference is negative. More importantly for our purpose, the effect is more significant for firms with low CAF than for firms with high CAF. For example, the difference is (with a t-statistic of 13.04) between the extreme portfolios based on CAF when firms of all sizes are considered. The difference is also significant across all five size groups with t-statistics ranging from to

32 5.6 Cross-sectional partitions. Our results are consistent with our different hypotheses. On average, we find that analysts and investors tend to anchor on the industry median FEPS. Before concluding the study, we investigate two additional issues. The first one is that we expect that the anchoring effect should be stronger when the anchor is more stable. To test this conjecture, we re-estimate our different models from Panel A of Tables 3 to 6 but we split the sample between two sub-groups based on the stability of the anchor. We use the full specification reported in the last column of each table. The stability of the anchor is measured by the coefficients of variation (CV) of I-FEPS corresponding to a period of previous 24 months (lower CVs indicate more stable anchors). Results are reported in Table 8 (the different control variables are included but not tabulated). In all subsamples, CAF has the predicted sign and is significant at the 5% level or better (except when FE is the dependent variable and the anchor is unstable, in which case the significance is at the 10% level). More importantly for our purpose, CAF is economically and statistically more significant in the subsamples in which the anchor is stable. In fact, the difference in coefficients between the stable and unstable samples is significant at the 5% or better in all cases. [Insert Table 8 Here] 30

33 Finally, we examine the effect of the sophistication on the degree of anchoring. To do so, we split the sample based on the sophistication of the market participants. For analysts, we consider the size of the employer. The prior literature (e.g., Hong and Kubik (2003)) has suggested that analysts working for large employers produce more informative forecasts. For investors, we consider the percentage of institutional ownership. The prior literature has also suggested that institutional are more sophisticated than retail investors (Bartov, Radhakrishnan, and Krinsky (2000), and Bhusan (1994)). Results indicate that the effect of anchoring is weaker when market participants are sophisticated than when they are not. The effect is economically and statistically more significant in the sub-samples of unsophisticated participants than in the sample of sophisticated participants. The difference between the coefficients across the subsamples is significant at the 5% level or better for the institutional investors. The difference is significant at the 10% level for the analysts. VI. Conclusion We consider the effect of the anchoring bias on market participants such as sell side analysts and investors, a topic that has not been extensively investigated by the prior literature in accounting and finance. We hypothesize that market participants are affected by the anchoring bias when they estimate the future profitability of a firm. Our empirical results are consistent with this hypothesis. First, we find that analysts earnings forecasts of firms with low forecasted EPS relative to 31

34 the median industry forecasted EPS are more optimistic than the forecasts for similar firms with high forecasted EPS relative to the median industry forecasted EPS. This result is consistent with analysts anchoring their forecasts on the industry median forecasted EPS. Second, stock returns are significantly higher for firms with high forecasted EPS relative to the median industry forecasted EPS than for similar firms in the same industry with low forecasted EPS relative to the median industry forecasted EPS. The positive relationship between firm FEPS and future stock returns cannot be explained by risk factors, the book-to-market or earnings-to-price effect, price or earnings momentum, or the accounting accruals effect. In addition, earnings surprises are more positive for firms with high forecasted EPS relative to the median industry forecasted EPS than for firms with low forecasted EPS relative to the median industry forecasted EPS. Third, we find that the likelihood of doing a stock split within a year is increasing when forecasted EPS relative to the median industry forecasted EPS is high. All these results are stronger when the industry medians are stable and when market participants are not sophisticated. Finally, stock split firms with low forecasted EPS relative to the median industry forecasted EPS experience more positive earnings forecasts revisions by analysts, more positive forecast errors than they do for their non-stock-split firms and more negative changes in earnings surprises after a stock split than firms with high forecasted EPS relative to the median industry forecasted EPS do. 32

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40 Appendix 1: Definitions of Major Dependent and Independent Variables Variable CAF: F-FEPS: TFE: Definition and data source The industry cross-sectional anchoring measure of FEPS, which is defined as the difference between the individual firm FEPS (F-FEPS in this paper) and the industry cross-sectional median of FEPS (I-FEPS in this paper), scaled by the absolute value of the latter. The 48 industries are defined as in Fama and French (1997); Mean of forecasted one-year-ahead earnings per share in the previous month from the I/B/E/S unadjusted summary historical file; Total forecasted earnings = FEPS Number of Shares Outstanding; Log(Size): The natural logarithm of market value of equity at the end of the previous month, as retrieved from CRSP; Log(BTM): The natural logarithm of the Fama and French (1993) book-to-market ratio, where the value for July of year y to June of year y+1 is computed using the book value of equity for the fiscal-year-end in calendar year y-1 from Compustat and the market value of equity at the end of December of year y-1 from CRSP; FE: ECAR Forecast error, which is defined as the difference between the FEPS and the actual EPS that will be announced at the end of the fiscal year, scaled by the absolute value of the latter; The cumulative abnormal return relative to the CRSP value-weighted index, cumulated from one day before to one day after the date of the most forthcoming earnings announcement over the next twelve months; Stock_Split: A dummy variable that equals 1 if this firm carries out a significant stock split (e.g., one share is split into 1.5 or more shares) in the month and 0 otherwise; BHAR 0:1 : Ret -6:0 : Cumulative (buy-and-hold) return of this month as of the previous month computed from CRSP; Cumulative (buy-and-hold) return over the past six months as of the previous month computed from CRSP; Accrual: Total accruals scaled by average total assets = ((ΔCA - ΔCash) - (ΔCL - ΔSTD - ΔTP) Dep)/TA, as defined in Sloan (1996), where ΔCA = change in current assets (Compustat Item #4), ΔCash = change in cash and cash equivalents (Compustat Item #1), ΔCL = change in current liabilities (Compustat Item #5), ΔSTD = change in debt included in current liabilities (Compustat Item #34), ΔTP = change in income taxes payable (Compustat Item #71), Dep = depreciation and amortization expense (Compustat Item #14) and TA is the average of the beginning and end of year book value of total assets (Compustat Item #6). E/P t 1 : Net income before extraordinary items (Compustat Item 237) for the recently announced fiscal-year-end (I/B/E/S Item FY0EDATS) is divided by the number of shares outstanding on the corresponding date of the I/B/E/S statistical period to obtain the historical earnings per share (E) for month t 1. E is divided by the stock price (P) on the same day as E to obtain E/P t 1. ES recent : The three-day abnormal return around the most recent earnings announcement date up to the beginning of month t; 38

41 TAF: Experience Breadth Horizon The time-series anchoring measure of FEPS, which is defined as the difference between the individual FEPS and most recently announced EPS, scaled by the absolute value of the latter; The natural logarithm of one plus average number of months covered by existing analysts; The natural logarithm of average number of stocks covered by existing analysts; The natural logarithm of one plus the number of months before next earnings announcement; Inst_holding The percentage of institutional ownership at the end of last quarter; 39

42 Table 1: Summary Statistics This table reports the descriptive statistics for our final sample during the period from January 1983 to December The sample includes all stocks listed on NYSE, AMEX and Nasdaq, excluding stocks with prices less than $5 at the end of the previous month. Additionally, a stock is eligible to be included in the sample if it has sufficient data in CRSP, Compustat and I/B/E/S for the firm characteristic variables defined in Appendix 1. The time-series averages of common statistics for major dependent and independent variables in this paper are reported in this table. Variables Mean Median Standard deviation Skewness Percentile 10% Percentile 90% CAF F-FEPS ($) FE BHAR 0:1 (%) ECAR Stock_Split Size ($B) BTM Ret -6:0 (%) Accrual ES recent (%) E/P t TAF

43 Table 2: Correlation Table This table reports the correlation coefficients between major dependent and independent variables. Our final sample starts from January 1983 and ends at December The sample includes all stocks listed on NYSE, AMEX and Nasdaq, excluding stocks with prices less than $5 at the end of the previous month. Additionally, a stock is eligible to be included in the sample if it has sufficient data in CRSP, Compustat and I/B/E/S for the firm characteristic variables defined in Appendix 1. The time-series averages of correlation coefficients are reported in this table. a,b,c indicate that the time-series average p-value of the correlation coefficient is below 1%, 5% and 10% levels, respectively. Variables CAF F-FEPS FE BHAR ECAR Stock_Split Size ($B) BTM Ret -6:0 (%) Accrual ES recent E/P t 1 TAF CAF F-FEPS ($) a FE BHAR 0:1 (%) ECAR b Stock_Split c Size ($B) a a BTM b Ret -6:0 (%) c b b Accrual c c ES recent (%) a E/P t a a c a TAF c b a

44 Table 3: Forecast Errors This table reports the Fama-MacBeth regression tests for the incremental role of CAF in explaining the cross section of forecast errors. The dependent variable, the forecast error, is defined as the difference between the FEPS in the previous month and the corresponding actual earnings per share (Actual) deflated by the absolute value of Actual. That is, FE = (FEPS Actual)/ Actual. The explanatory variables include a constant (not reported), the logarithm of market capitalization at t 1 (Size), the logarithm of book-to-market ratio (BTM), the past six-month return (Ret -6:-0 ), accounting accruals (Accruals), the experience of analysts (Experience), the breadth of analysts (Breadth), the logarithm of time gap between the forecasts and actual earnings announcements (Horizon), the most recent earnings announcement effect (ES recent ), the E/P ratio based on last announced EPS (E/P t 1 ), the time-series anchoring measure (TAF) and the cross-sectional anchoring measure (CAF). Their detailed definitions are provided in the Appendix 1. In Panel A, Fama and Macbeth (1973) cross-sectional regressions are estimated each month from February 1983 to December 2005, and the means of the monthly estimates are reported. Stocks with a price less than $5 are excluded from the sample. For all dependent and explanatory variables, values greater than the fractile or less than the fractile are set to equal to the and fractile values, respectively. Panel B of this table reports the time-series averages of forecast errors (FE) for 5 5 Size- and CAFsorted portfolios. The portfolios are constructed as follows: at the beginning of each month, all stocks are sorted into five groups (G1 to G5) based on the level of market capitalization (Size) at the end of the previous month; stocks in each Size group are further sorted into five additional quintiles (E1 to E5) based on their CAF in the previous month. The t-statistics (in parentheses) in both Panel A and B are adjusted for serial correlations using the Newey and West (1987) procedure. a,b,c indicate significance at the 1%, 5% and 10% levels, respectively. 42

45 Panel A: Fama-MacBeth Regressions (1) (2) (3) CAF b b a (-2.42) (-2.54) (-4.97) Log(Size) a a a (-24.06) (-23.48) (-18.28) Log(BTM) a a a (6.43) (7.22) (6.72) Ret -6, a a a (-16.34) (-15.56) (-16.71) Accrual a a (3.92) (4.57) ES recent a a (-7.51) (-8.15) E/P t a (4.94) TAF a (13.12) Experience a (2.71) Breadth a (-4.59) Horizon a (22.88) Average Adj. R Avg. N/Year Panel B: Forecast Errors in Size-CAF Groups Size quintiles CAF quintiles G1 (Small) G2 G3 G4 G5 (Large) All stocks E1 (Low) E E E E5 (High) E5 E a a a a c a t-statistic (-5.82) (-5.65) (-5.40) (-4.81) (-1.92) (-5.28) 43

46 Table 4: the Cross Section of Individual Stock Returns Panel A of this table reports the Fama-MacBeth regression tests for the incremental role of CAF in explaining the cross section of individual stock returns. The dependent variable is the one-month raw returns (BHAR 0:1 ) in the current month t. The explanatory variables include a constant (not reported), the logarithm of market capitalization at t 1 (Size), the logarithm of the book-to-market ratio (B/M), a one-month lag of the past six-month return (Ret -7:-1 ), the past one-month return (Ret -1:0 ), the three-day abnormal return surrounding the most recent earnings announcement date up to the beginning of month t (ES recent ), the historical earnings-to-price ratios (E/P t 1 ), the time-series anchoring measure (TAF) and the cross-sectional anchoring measure (CAF). The values of Book-to-market ratio from July of year y to June of year y+1 are calculated using the book value of equity and the net income before extraordinary items for the fiscal-year-end falling in calendar year y 1 and the market value of equity at the end of December of year y 1. E/P t 1 is calculated as follows. First, net income before extraordinary items (Compustat Item 237) for the recently announced fiscal-year-end (I/B/E/S Item FY0EDATS) is divided by the number of shares outstanding on the corresponding date of the I/B/E/S statistical period to obtain the historical earnings per share (E) for month t 1. Next, E is divided by the stock price (P) on the same day as E to obtain E/P t 1. Panel B reports the risk-adjusted returns for equal-weighted portfolios based on Size and CAF, Alpha, which is the intercept term from the time-series regression based on Carhart s four factor model (1997).returns on CAF-sorted portfolios within each of five Size groups. The portfolios are constructed as follows: at the beginning of each month, stocks are sorted into five groups (G1 to G5) based on the level of their market capitalization (Size) at the end of the previous month; stocks in each Size group are further sorted into five additional quintiles (E1 to E5) based on their CAF levels in the previous month. The sample starts at February 1983 and ends at December Stocks with a price less than $5 are excluded from the sample. For all dependent and explanatory variables (except for all stock returns), values greater than the fractile or less than the fractile are set to equal to the and fractile values, respectively. The t-statistics (in parentheses) are adjusted for serial correlations using the Newey and West (1987) procedure. a,b,c indicate significance at the 1%, 5% and 10% levels, respectively. 44

47 Panel A: Fama-MacBeth Regressions (1) (2) (3) CAF a a a (3.43) (3.59) (3.14) Log(Size) Log(BTM) Ret -7:-1 Ret -1:0 Accrual ES recent E/P t 1 TAF (-0.95) (-1.39) (-1.28) c (1.92) (1.51) (1.45) a a a (3.65) (2.67) (2.70) a a a (-4.78) (-5.94) (-6.03) a a (-6.38) (-7.17) a a (12.55) (12.74) a (3.19) c (1.76) 2 Avg. Adj. R Avg. N/Year Panel B: Portfolio Alphas Based on Carhart s Four-factor in Size-CAF Groups Size quintiles CAF quintiles G1 (Small) G2 G3 G4 G5 (Large) All stocks E1 (Low) E E E E5 (High) E5 E a a a b b a t-statistic (5.39) (3.08) (2.82) (2.14) (2.10) (3.89) 45

48 Table 5: Ex-post Earnings Announcement Effects Panel A of this table reports the Fama-MacBeth regression tests for the incremental role of CAF in explaining the cross section of ex post earnings announcement effects. The dependent variable is earnings surprise (ECAR), which is defined as the cumulative abnormal return relative to the CRSP value-weighted index, cumulated from one day before to one day after the date of the most forthcoming earnings announcement over the next twelve months. The explanatory variables include a constant (not reported), the logarithm of market capitalization at t 1 (Size), the logarithm of the book-to-market ratio (B/M), the past six-month return (Ret -6:-0 ), the three-day abnormal return surrounding the most recent earnings announcement date up to the beginning of month t (ES recent ), the historical earnings-to-price ratios (E/P t 1 ), the time-series anchoring measure (TAF) and the cross-sectional anchoring measure (CAF). The values of Book-to-market ratio from July of year y to June of year y+1 are calculated using the book value of equity and the net income before extraordinary items for the fiscal-year-end falling in calendar year y 1 and the market value of equity at the end of December of year y 1. E/P t 1 is calculated as follows. First, net income before extraordinary items (Compustat Item 237) for the recently announced fiscal-year-end (I/B/E/S Item FY0EDATS) is divided by the number of shares outstanding on the corresponding date of the I/B/E/S statistical period to obtain the historical earnings per share (E) for month t 1. Next, E is divided by the stock price (P) on the same day as E to obtain E/P t 1. For all dependent and explanatory variables (except for all stock returns), values greater than the fractile or less than the fractile are set to equal to the and fractile values, respectively. The t-statistics (in parentheses) are adjusted for serial correlations using the Newey and West (1987) procedure. Panel B of this table reports the time-series averages of the means of earnings surprises (ES next ) for 5 5 Size- and CAF-sorted portfolios. At the beginning of each month, all stocks are sorted into five groups (G1 to G5) based on the level of market capitalization (Size) at the end of the previous month. Stocks in each Size group are further sorted into five additional quintiles (E1 to E5) based on their CAF in the previous month. The portfolios are held for twelve months after formation. The sample starts at February 1983 and ends at December Stocks with a price less than $5 are excluded from the sample. a,b,c indicate significance at the 1%, 5% and 10% levels, respectively. 46

49 Panel A: Fama-MacBeth Regressions (1) (2) (3) CAF a a a (4.20) (4.36) (4.08) Log(Size) a b b (2.78) (2.30) (2.42) Log(BTM) a a a (6.69) (6.23) (6.27) Ret -6: a a a (5.61) (4.81) (4.75) Accrual a a (-4.23) (-4.39) ES recent a a (5.75) (5.70) E/P t (0.61) TAF b (2.13) Avg. Adj. R Avg. N/Year Panel B: Ex-post Earning Announcement Effects in Size-CAF Groups Size quintiles CAF quintiles G1 (Small) G2 G3 G4 G5 (Large) All stocks E1 (Low) E E E E5 (High) E5 E a a a a t-statistic (5.07) (5.13) (3.21) (1.42) (1.16) (6.71) 47

50 Table 6: Stock Splits Panel A of this table reports the logit regression tests in explaining the likelihood of stock splits. The dependent variable is a dummy variable that equals one if a firm carries out a significant stock split (e.g., one share is split into 1.5 or more shares) in this month and zero otherwise. The explanatory variables include a constant (not reported), the logarithm of market capitalization at t 1 (Size), the logarithm of the book-to-market ratio (B/M), the past six-month return (Ret -6:0 ), the three-day abnormal return surrounding the most recent earnings announcement date up to the beginning of month t (ES recent ), the historical earnings-to-price ratios (E/P t 1 ), the time-series anchoring measure (TAF) and the cross-sectional anchoring measure (CAF). The values of Book-to-market ratio from July of year y to June of year y+1 are calculated using the book value of equity and the net income before extraordinary items for the fiscal-year-end falling in calendar year y 1 and the market value of equity at the end of December of year y 1. E/P t 1 is calculated as follows. First, net income before extraordinary items (Compustat Item 237) for the recently announced fiscal-year-end (I/B/E/S Item FY0EDATS) is divided by the number of shares outstanding on the corresponding date of the I/B/E/S statistical period to obtain the historical earnings per share (E) for month t 1. Next, E is divided by the stock price (P) on the same day as E to obtain E/P t 1. The z-statistics reported in parentheses have been adjusted for the clustered standard errors at both firm level and time level (as proposed by Petersen, 2009). Panel B of this table reports the time-series averages of stock-split ratios (SSR) for 5 5 Size- and CAFsorted portfolios. At the beginning of each month, stocks are sorted into five groups (G1 to G5) based on the level of market capitalization (Size) at the end of the previous month. Stocks in each Size group are further sorted into five additional quintiles (E1 to E5) based on their CAF in the previous month. The portfolios are held for twelve months after formation. The stock-split ratio is defined as the cumulative stock-split-driven (with CRSP Item DISTCD s first digit equals 5) changes of the factor to adjust shares outstanding (CRSP Item FACSHR) in the following twelve months. The t-statistics reported in Panel B are adjusted for serial correlations using the Newey and West (1987). The sample starts at February 1983 and ends at December Stocks with a price less than $5 are excluded from the sample. a,b,c indicate significance at the 1%, 5% and 10% levels, respectively. 48

51 Panel A: Likelihood of Stock Splits (1) (2) (3) CAF a a b (2.86) (2.76) (2.59) Log(Size) a a a (4.15) (5.49) (4.54) Log(BTM) a a a (-8.78) (-9.46) (-9.91) Ret -6: a a a (6.67) (6.21) (6.06) ES recent a a (9.55) (9.97) Accrual a a (6.73) (5.29) E/P t a (8.03) TAF (0.65) Pseudo R Panel B: Stock Split Ratios (SSR) in Size-CAF Groups Size quintiles CAF quintiles G1 (Small) G2 G3 G4 G5 (Large) All stocks E1 (Low) E E E E5 (High) E5 E1 t-statistic a a a a a a (9.31) (11.23) (10.43) (7.69) (4.87) (8.48) 49

52 Table 7: Earnings Forecast Revisions, Forecast Errors, and Changes in Earnings Surprises after Stock Splits in Different Size and CAF Groups This table examines the difference in the earnings forecast revisions (Panel A), forecast errors (Panel B) and the changes in abnormal returns surrounding the earnings announcement date (Panel C) between stock-split firms and matching non-stock-split firms. We first identify stocks that carry out significant stock splits (e.g., one share is split into 1.5 or more shares) in each month. In the tests reported in Panels A and B, we match these stock-split firms with non-stock-split firms that have similar levels of size, book-to-market ratio and forecast errors before stock splits and CAF. We compute differences in forecast errors and in forecast revisions between stock-split firms and the median level of matching non-stock-split firms. In Panel C, for each firm and each month, we compute the change in ex post and ex ante abnormal returns surrounding earnings announcement date (ES next - ES recent ). Stock-split firms are matched by non-stock-split firms by size, the book-to-market ratio and CAF before stock splits. We report the difference in (ES next -ES recent ) between stock-split firms and the median of their matching non-stock-split firms. The sample starts at February 1983 and ends at December Stocks with a price less than $5 are excluded from the sample. a,b,c indicate significance at the 1%, 5% and 10% levels, respectively. Size quintiles CAF quintiles G1 (Small) G2 G3 G4 G5 (Large) All stocks Panel A: Difference in ex post average forecast revisions between stock-split firms and non-stock-split firms E1 (Low) E E E E5 (High) All stocks a a a a a a t-statistic (4.55) (6.21) (8.79) (8.90) (8.30) (16.78) Panel B: Difference in ex post forecast errors (FE) between stock-split firms and non-stock-split firms E1 (Low) E E E E5 (High) All stocks b b a a a t-statistic (1.96) (1.54) (2.04) (3.65) (3.13) (5.53) Panel C: Difference in ex post earning surprises (ES) between stock-split firms and non-stock-split firms E1 (Low) E E E E5 (High) All stocks a a a a a a t-statistic (-6.23) (-6.80) (-5.48) (-6.01) (-5.54) (-13.04) 50

53 Table 8: Robustness Checks within Sub-groups Regression tests in Panel As of Table 3, Table 4 and Table 5 are repeated in sub-groups and the results are presented from Panel A to Panel C in this table. In each month, the entire sample is divided into two even sub-groups based on the stability of the anchor, the average size of analyst-affiliated brokers and the institutional holdings. The anchor of earnings forecasts in this paper is defined as the median forecasted earnings per share (I-FEPS) within each Fama-French 48 industries. The stability of the anchor is measured by the CVs (coefficients of variation) of I-FEPS corresponding to a period of previous 24 months (lower CVs indicate more stable anchors). The broker size is measured by the number of active analysts affiliated to the broker at the end of last month. The institutional holding is measured by the percentage of institutional ownership at the end of last quarter (Inst_holding). Detailed definitions of these measures are provided in Appendix 1. The sample for sub-groups based on the stability of anchor starts at February 1985 and ends at December Samples for other sub-group tests start at February 1983 and ends at December Stocks with their prices less than $5 are excluded from the sample. We only report the coefficients and t-statistics of CAF while those for the control variables (as shown in Table 3-6) are suppressed for simplicity. We also report the differences of coefficients and their t-statistics between two subgroups. All t-statistics reported in this table are adjusted for serial correlations using the Newey and West (1987). a,b,c indicate significance at the 1%, 5% and 10% levels, respectively. Panel A: Forecast Error (FE) Stable Anchor Unstable Anchor Small Brokers Large Brokers CAF a c a a T-stat (-8.40) (-1.67) (-3.69) (3.57) Difference a c T-stat (-5.61) (-1.78) Panel B: Future Return (BHAR 0,1 ) Stable Anchor Unstable Anchor Low Inst. Holding High Inst. Holding CAF b b a c T-stat (2.36) (2.45) (4.24) (1.67) Difference b a T-stat (1.97) (4.03) Panel C: Ex post Earning Announcement Effects (ECAR) Stable Anchor Unstable Anchor Low Inst. Holding High Inst. Holding CAF a a a a T-stat (3.96) (2.89) (3.61) (1.99) Difference b b T-stat (2.27) (2.44) 51

54 Cross-sectional Median of FEPS ($) Figure 1. The time-series of the median forecasted earnings per share (F-FEPS) and the median forecasted total earnings (TFE) in the cross section. The solid line is the median of F-FEPS ($) in the cross section and the shadowed line is the median of forecasted total earnings (TFE, in million $) from February 1983 to December The value of TFE is presented by the right-hand side of the y-axis. 52