A simple explanation for the dispersion anomaly

Transcription

1 A simple explanation for the dispersion anomaly Paul Irvine Neeley School of Business Texas Christian University Tingting Liu Heider College of Business Creighton University February, 2018 Abstract We explain the dispersion anomaly, the tendency of stocks with high analyst forecast dispersion to produce lower future returns, by testing the implied assumption that analysts bias is distributed equally when portfolios are sorted by dispersion (Johnson, 2004). We find that analysts bias is not symmetrically distributed across dispersion groups. High dispersion firms contain forecasts that are too optimistic, but the over optimism in low dispersion firms is much less. Given the well-known tendency of analysts to walk-down their forecasts over the fiscal year, this asymmetry produces future negative forecast revisions for the high dispersion firms. These negative cash flow shocks are suffi cient to completely explain the dispersion anomaly. Removing the forecast bias component from dispersion produces a conditional dispersion measure that positively predicts returns, suggesting a positive risk premium to differences of opinion in equities. Comments welcome. We thank Stan Markov and seminar participants at UT-Dallas for helpful comments. Send correspondence to p.irvine@tcu.edu

2 A simple explanation for the dispersion anomaly Abstract We explain the dispersion anomaly, the tendency of stocks with high analyst forecast dispersion to produce lower future returns, by testing the implied assumption that analysts bias is distributed equally when portfolios are sorted by dispersion (Johnson, 2004). We find that analysts bias is not symmetrically distributed across dispersion groups. High dispersion firms contain forecasts that are too optimistic, but the over optimism in low dispersion firms is much less. Given the well-known tendency of analysts to walkdown their forecasts over the fiscal year, this asymmetry produces future negative forecast revisions for the high dispersion firms. These negative cash flow shocks are suffi cient to completely explain the dispersion anomaly. Removing the forecast bias component from dispersion produces a conditional dispersion measure that positively predicts returns, suggesting a positive risk premium to differences of opinion in equities.

3 1 Introduction There is a compelling literature including Williams (1977), Mayshar (1983), Varian (1985), Merton (1987) and Epstein and Wang (1994) that considers divergence of investor s opinion a proxy for risk. Naturally, as a risk proxy divergence of opinion should be positively related to future returns, yet controversy remains as there is evidence that divergence of opinion is negatively related to equity returns. Motivated by this controversy, Carlin, Longstaff and Moterba (2014) study differences of opinion in the mortgage-backed security market and find results consistent with the theoretical conclusion that differences in opinion lead to a positive risk premium. However, their conclusions do not immediately transfer to the equity market, primarily due to the strong contrary evidence in Diether, Malloy and Scherbina (2002) who use analysts forecast dispersion as a proxy for investors differences of opinion. Diether et al. (2002) find that higher forecast dispersion in month t predicts lower returns in month t + 1 and interpret their results using Miller s (1977) theory that optimistic investors dominate the market when pessimistic investors are restricted from expressing their opinions about stock prices because of high short-sale costs. Since the mean of a truncated distribution increases with the standard deviation of the distribution; Miller (1977) implies that the higher the forecast dispersion, the more overvalued the security price in month t. Given the conflicting empirical findings between the mortgage-back security market and the equity market, we investigate the nature of analysts forecast dispersion as a measure of differences of opinion in the equity market. We find that it is a flawed measure and provide a conditional dispersion measure that reconciles the contrary equity evidence with the mainstream of thought on the risk premium to differences of opinion. 1 1 It is notable that Cragg and Malkiel (1982) using early forecast data from the 1960 s found a positive relation between dispersion and returns. This finding motivates Varian s (1985) theoretical insights. 1

4 The results in Diether et al. (2002) influenced research in two significant ways. First, they encouraged the continued use of analyst forecast dispersion as a proxy for differences of opinion despite the reservations outlined in Abarbanell, Lanen and Verrecchia (1995). 2 Secondly, they founded a literature attempting to frame the results of Diether et al. (2002) in a different context. For example, Johnson (2004) counters that forecast dispersion represents information risk. Although careful to note that his explanation is not mutually exclusive from Diether et al. (2002), Johnson (2004) contends that analyst forecast dispersion is likely to be a manifestation of idiosyncratic risk relating to the unobservability of a firm s true value. Johnson (2004) derives a Merton (1974) based model wherein raising the uncertainty about the underlying value of a levered firm, lowers its expected return. Since forecast dispersion is a measure of uncertainty, it is correlated with lower future returns. Barron, Stanford and Yu (2009) investigate the effect of two separate components of dispersion on returns using the Barron, Kim, Lin and Stevens (BKLS, 1998) decomposition of earnings forecasts. The decomposition separates forecast dispersion into a common uncertainty component and a lack of consensus component. The common uncertainty component reflects the squared errors between forecasts and actual earnings and the lack of consensus component represents the degree to which individual analysts disagree, net of the common uncertainty component. 3 When examining the effects of these components separately, Barron et al. (2009) find that the common uncertainty component is primarily responsible for the negative relation between dispersion and future returns. A conclusion consistent with Johnson s (2004) interpretation of the dispersion effect representing risk. 4 Avramov, Chordia, Jostova and Philipov (2009) find that the high dispersion-low return 2 Abarbanell, Lanen and Verrechia (1995) theoretically criticize the use of forecast dispersion as a proxy for investor beliefs. They argue that the dispersion in analysts forecasts is an incomplete measure of investor uncertainty. 3 Barron et al. (2009) contend that the lack of consensus component measures the level of information asymmetry among analysts and, by extension, among informed investors. 4 While a powerful tool, the Barron et al. (1998) decomposition is not without weaknesses. Sheng and Thevenot (2012) point out that the Barron et al. (2009) estimates use actual earnings, not known at the time of the forecast. 2

5 effect is concentrated in stocks with poor credit ratings in financial distress. After controlling for credit rating they find that implementing dispersion strategies yield profits that are economically small and statistically insignificant. Although, Avramov et al. (2009) identify a set of stocks where the negative relation between dispersion and return is most pronounced, as well as a set of stocks where the relation is insignificant, their method is unable to identify a strategy where differences of opinion, measured by forecast dispersion, produces the positive risk premium hypothesized in theory and found in the mortgage-backed security market by Carlin et al. (2014). These papers make strong contributions in identifying the dispersion anomaly, exploring the possible reasons for the anomaly, and exploring the validity of forecast dispersion as an empirical proxy for investor s beliefs. While the construct of forecast dispersion as an empirical proxy for investor beliefs is powerful, we contend dispersion is a contaminated measure of differences of opinion. As Johnson (2004) points out, one implicit assumption of Diether et al. (2002), Barron et al. (2009) and Sheng and Thevenot (2012) is that analyst bias is distributed evenly across firms and thus, can be considered relatively unimportant when comparing differences in dispersion across groups of firms. 5 We provide evidence that this assumption is invalid, and propose a simple alternative explanation for the forecast dispersion anomaly that does not require investor overoptimism, or a specific return generating process (Johnson, 2004). Nor does it require that analyst expectations be a reasonable proxy for investor beliefs, rather only that expected cash flows matter to prices and lower expected cash flows lead to lower stock prices. Notably, when we control for analyst s bias, the remaining component of forecast dispersion does appear to proxy for differences of opinion in They suggest that unanticipated events following the forecast can cause the BKLS estimate to be an impaired estimate of ex ante uncertainty at the time of the forecast. They also call into doubt the exogeneity of the actual earnings estimate, particularly in cases where management can manipulate actual earnings to meet or beat analysts forecasts. As an alternative, Sheng and Thevenot (2012) propose an alternative GARCH estimate of the variance of mean forecast errors that uses only historical data known at the time of the forecast. 5 Sheng and Thevenot (2012) in footnote 3 on page 22, note that under the assumption that forecasts are unbiased, the variance of mean forecast errors is the same as the expected squared error in the mean forecast, their Equation (2). 3

6 that this conditional dispersion measure produces a significantly positive risk premium. Before outlining this hypothesis, we identify one of its salient effects. We find that forecast dispersion is strongly correlated with the likelihood of a negative forecast revision in the upcoming month; the rank correlation between forecast dispersion in month t and earnings estimate revisions in month t + 1 is On average, month t + 1 forecast revision in the highest quintile of forecast dispersion stocks is -17% relative to the month t consensus forecast, while it is only -1% for the three lowest dispersion quintiles. Johnson (2004) raises several concerns regarding analysts forecasts as proxies for investor beliefs. These concerns include the fact that analysts forecasts are known to be biased by a number of conflicts of interest including how the choice of conforming or deviating from the consensus forecast influences career outcomes. 6 However, Johnson (2004) admits these known biases may be less of a concern in research that focuses on the differences in dispersion across stocks. This last contention implies that when forecast bias is distributed uniformly, then an analysis of the differences in forecast dispersion across stocks (Diether et al. 2002), would find that the bias nets out in a roughly equal way across dispersion groups. In this case, the differences in dispersion across stocks could represent differences in investor beliefs or risk. However, we document that forecast bias, measured as the scaled difference between the consensus forecast and actual reported earnings, is extremely asymmetric across dispersion quintiles. Over the years the mean forecast bias relative to reported earnings in the low dispersion quintile is 6%, while the mean forecast bias in the high dispersion quintile is 85%, a statistically and economically significant difference of 78% (t-stat = 27.1). Thus, high dispersion stocks contain much more forecast bias than low dispersion stocks necessitating the likelihood that analysts will 6 Deither et al. (2002) recognize a positive correlation between forecast bias and dispersion can exist when analysts self-select away from negative forecasts to protect their relationships with firm management. However, they do not consider the consequences of this relation for earnings revisions. 4

7 walk down their earnings forecasts in the upcoming months, a pattern that was first discerned in Chopra (1998). Chopra (1998) charts analyst optimism and forecast dispersion through the calendar year and shows the general pattern of less optimistic forecasts as the year progresses as well as the mechanical consequence of declining dispersion. Chopra s (1998) evidence of a mechanical relation between forecast optimism and dispersion is for the S&P 500 index, and although it makes clear the relation between bias and dispersion, we are the first to recognize the asymmetry of forecast bias across stocks and the resulting effects on the dispersion anomaly. With asymmetric bias, the high level of optimistic forecast bias in the high dispersion quintile drives analysts to downwardly revise their earnings forecasts in the upcoming month. Downward revisions lower expected cash flows to the firm and therefore, lower investors valuations. These lower valuations produce lower returns for the high dispersion portfolio in month t + 1. The main contention in this paper is that these large negative revisions in the high dispersion portfolio account for the low returns to this portfolio and thus, the forecast dispersion anomaly. The only assumptions required for us to make this conclusion are that some investors use analysts forecasts as an input into their stock valuations and that the lower expected cash flows revealed by the negative revision lead investors to lower their valuations. Our results are challenging to fit into the existing explanations of the dispersion anomaly. At first glance our findings seem to generally align with Diether et al. s (2002) theories based on Miller s (1977) optimists. We show that for high dispersion stocks analysts forecasts are too optimistic and must be negatively revised in the upcoming months. Just because analysts are optimistic does not imply that optimistic investors dominate the price-setting mechanism for these stocks, but if optimistic investors tend to believe the analysts forecasts then our results would be consistent with 5

8 Miller (1977). What we do provide that is new is the crucially important, and often overlooked, catalyst, namely the future downward revisions in analysts earnings forecasts. This catalyst is a necessary condition in Miller s (1977) hypothesis. To affect returns, something must occur to get the optimistic investors to lower their optimistic valuations. The future downward revisions that we document are a particularly suitable catalyst. However, we show that earnings forecast revisions are predictable. We build a simple regression model of expected forecast revision and find that dispersion in month t is the most important predictor of negative forecast revisions in month t + 1. We use the regression estimates of actual forecast revisions to construct a measure of expected revisions, and find that our model of expected forecast revisions effectively predicts future forecast revisions. Further, when we sort stocks into portfolios based on the expected forecast revision there is a 0.89% difference between the returns to the low expected revision portfolio and returns to the high expected revision portfolio. The magnitude of this difference is larger than that of the dispersion anomaly (0.53%) and thus, suggests that negative forecast revisions produce return differences that are large enough to completely explain the dispersion anomaly. In other words, the component of dispersion that is related to expected forecast revisions is the component predicting negative future returns. When we orthogonalize dispersion by removing the component that predicts forecast revisions, we find the remainder is associated with positive, not negative, returns. This finding, that higher conditional dispersion is positively associated with future returns, is diffi cult to integrate into the Miller (1977) model or any model that predicts a negative risk premium for differences in opinion. The finding that dispersion contains two distinct elements, one that predicts negative returns and another that predicts positive returns, could be the reason that the dispersion anomaly has generated such controversy. This result has important 6

9 implications for research using forecast dispersion as a proxy for divergence of opinion. This proxy is common in finance and accounting research and has been used to examine trading volume (Ziebart, 1990; Ajinkya, Atiase and Gift, 1991; Atiase and Bamber, 1994), mergers and acquisitions (Moeller, Schlingemann and Stulz, 2007), earnings announcement returns (Berkman, Dimitrov, Jain, Koch and Tice, 2009), and aggregate volatility (Barinov, 2013). Our findings are also diffi cult to put into the context of the Johnson (2004) or Barron et al. (2009) alternatives. We first note that our paper claims that forecast dispersion is a poor proxy for differences of opinion, and since we show that forecast dispersion is strongly correlated with analyst optimism. We show that forecast optimism tends to decline over the course of the fiscal year, and conclude that the dispersion anomaly does not represent a negative risk premium for differences of opinion. Forecast dispersion could still be a proxy for information risk, as in Johnson (2004), or its components could be a proxy for uncertainty and information asymmetry, as in Barron et al. (2009). 7 However, fitting our findings into the Johnson (2004) and Barron et al. (2009) hypotheses seems a diffi cult task. Essentially, both the Johnson (2004) and Barron et al. (2009) conclude that dispersion primarily reflects risk, a risk that leads to lower future returns. Since we show that analyst optimism is the largest component of dispersion, any risk-based explanation requires that the risk be correlated with analyst optimism; a linkage that is not immediately clear. However, as Johnson (2004) points out his information risk theory is not mutually exclusive from Miller (1977). We only argue that neither is required to explain the dispersion anomaly. The papers proceeds as follows. Section 2 briefly outlines the relation between bias and dispersion. Section 3 details the data used in the paper and the formulas for our calculations of forecast dispersion, forecast revision and forecast bias. Section 4 presents a preliminary investigation of 7 Imhoff and Lobo (1992), Ackert and Athanassakos (1997) and Offi cer (2004) also use forecast dispersion as a proxy for uncertainty. 7

10 forecast bias across different groups of firms sorted on analysts forecast dispersion. Section 5 presents further empirical results and Section 6 concludes. 2 Bias and dispersion Rational optimistic forecast bias (Lim, 2001) We generalize Lim s (2011) rational bias model to show how forecast bias contributes to the crosssectional standard deviation of analysts forecasts. Lim (2001) proposes a quadratic-loss utility function to the decision problem of an analyst formulating an earnings forecast. To generalize, assume N analysts indexed by j, each observe a private signal I j of earnings earnings X N(0, τ 0 ), where τ 0.is the precision or inverse of the variance of true earnings X. A common way to parameterize the cross section of analysts forecasts is to assume I j = X + ɛ j where ɛ j is a normal random variable with mean 0. Each analyst s information set contains a true estimate of upcoming earnings plus some idiosyncratic noise. In Lim (2001), this noise has a precision τ(b), where b is the conditional bias of the forecast. The analyst can increase this precision (reduce the variance) of her forecast if she improves access to company management by biasing her reported forecast. The analyst then issues a forecast F j, where F j E[X I j ] is the level of induced bias (b j ) in her forecast. The analyst chooses b j, and thus F j by minimizing the conditional expected squared error, which can be decomposed into a squared bias term and a variance term: Min F E[(F j X) 2 I] = Min b b 2 j + Var(X I j ) (1) Under the assumption made in Lim (2001) that the analyst can generate more precise private information about the company s earnings by publishing a positively biased forecast, τ(b) is a 8

11 positive, concave function of forecast bias b. The analyst s quadratic-loss utility function is then given by: Min b b 2 j + 1 τ 0 + τ(b j ) (2) The first-order condition that minimizes the conditional expected squared error is: b j = τ (b j ) > 0, (3) 2(τ 0 + τ(b j )) 2 since τ (b j ) is greater than 0, Equation (3) implies that analysts forecasts will contain some level of bias. 8 Further, since Lim (2001) points out b j / τ 0 < 0, the higher the uncertainty surrounding the firm s true earnings, the higher the level of optimal bias in the forecast. Generalizing the decision rule for F j across all analysts yields the consensus forecast: F consensus = 1 N N (F j + b j ) = F + b (4) j=1 where F is the consensus unbiased forecast and b is the average optimistic bias introduced by all analysts. Variance of observed analysts forecasts can be written as V ar(f consensus ) = V ar(f + b) = V ar(f j ) + V ar(b j ) + 2Cov(F j, b j ) (5) Equation (5) implies that observed forecast variance is affected by divergence of opinion among 8 This setup is flexible enough to accomodate manager s time-varying preferences for bias, if as in Richardson, Teoh, and Wysocki (2004) and Ke and Yu (2006) managers usually prefer positive bias, but wish analysts to walk their forecasts down to beatable targets before the earnings release date. This desire implies that right before earnings τ (b j) would be < 0. 9

12 analysts, the cross-sectional variance of bias and a covariance term. Consistent with Lim s (2001) proposition 1, we expect that when public information about the company s earnings prospects is less readily available, both forecast dispersion and forecast bias will be higher because analysts benefit more when trading off positive bias to gain management access. This implies that consensus forecast and forecast dispersion are higher earlier in the year because the uncertainty of the company s earnings prospects is relatively high at that time. Lim s (2001) proposition 2 predicts and finds cross-sectional variation in forecast bias. Lim (2001) shows that when τ (b j ) varies across analysts due to brokerage resource constraints or differences in experience, forecast bias contributes to the dispersion of the consensus forecast. Together, these propositions theoretically ground our contention that forecast bias can be a significant component of analysts forecast dispersion. If sorting analysts forecast by forecast dispersion produces portfolio sorts that are unequal in forecast bias, then reductions in forecast bias as the year progresses produces differences in the level of forecast revision across portfolios. 3 Data Following Sadka and Scherbina (2007) and Scherbina (2008) we obtain analysts earnings forecasts data from the IBES US Summary History Unadjusted data set. We use the unadjusted IBES data to avoid the rounding error arising when historical earnings forecasts are affected by subsequent stock splits and rounded to the nearest cent. We also obtain individual analysts forecasts from the Detail History file that contains individual forecasts organized by the consensus forecast release date. We choose the time period of 1982 to 2015 because Diether, Malloy and Scherbina (2002) show that IBES coverage is very limited for stocks followed by two or more analysts prior to Calculating analyst forecast dispersion requires firms be covered by at least 10

13 two analysts. Our final sample covers 372 months from We merge the IBES sample with the Center for Research in Securities Prices (CRSP) stock files to get information on stock returns. 10 We exclude stocks with prices less than $5 per share on the portfolio formation date to ensure that the results are not driven by small, illiquid stocks. Our CRSP-IBES sample includes 11,208 unique firms, with an average coverage of 2,636 firms per year Variable construction Measuring forecast dispersion Following Diether, Malloy and Scherbina (2002), we define forecast dispersion as the standard deviation of analysts current fiscal year annual earnings-per-share forecasts scaled by the absolute value of the mean earnings forecast, reported as the consensus mean in the IBES Summary History file. 12 Dispersion is defined as: F orecast dispersion t = Standard deviation t Abs(Consensus forecast t ) (6) Measuring forecast revision To calculate the consensus forecast revision in each firm-month, we first calculate the difference between the current month t consensus forecast and the previous month, t 1, consensus forecast, then scale by the absolute value of the previous month s consensus forecast. Forecast revision is 9 We use 36 months of historical data to estimate some of our equations. To report a consistent common period across all the tables in the paper, we disregard observations from even when they can be calculated. 10 We use the IBES-CRSP linking program provided on WRDS to merge IBES with CRSP. The link tables match the IBES unique identifier (IBES TICKER) with CRSP PERMNO. 11 The maximum number of firms covered in a year is 3,729, and minimum number of firms covered in a year is 1, We obtain similar results when constructing all the variables scaled by stock price or asset per share. We choose to present the absolute mean forecast deflated results in order to compare to the Diether, Malloy and Scherbina (2002) results in the literature. 11

14 defined as: F orecast revision t = Consensus forecast t Consensus forecast t 1 Abs(Consensus forecast t 1 ) (7) Measuring forecast bias We follow the commonly used bias measure in the literature (Barron et al., 1998) and calculate forecast bias as the difference between the consensus forecast and the realized earnings, scaled by the absolute value of the mean forecast. Forecast bias is defined as: F orecast bias t = Consensus forecast t Actual earnings Abs(Consensus forecast t ) (8) Measuring individual analyst forecast optimism To measure how optimistic an individual analyst s forecast is relative to her peers, we develop a scale for forecast optimism ranging from 0 to 100. Our measure of relative analyst optimism is similar to the constructs in the literature measuring relative forecast accuracy (Hong and Kubik, 2003; Ke and Yu, 2006). For each firm-month we first rank individual analyst s forecasts according to how optimistic they are relative to the other analysts forecasting for that firm. In this calculation we use the most recent individual analyst s forecast prior to the consensus forecast publication date. We deem the highest forecast for annual earnings in the upcoming year as the most optimistic forecast, so that after ranking all reporting analysts the highest forecast receives an Optimism rank of 1. We then calculate relative forecast optimism as: F orecast optimism ijt = 100 Optimism rank ijt (9) Analyst coverage jt 1 12

15 where subscripts refer to firm j, analyst i, and month t. Analyst coverage is calculated as the number of forecasting analysts IBES reports who contribute to the consensus estimate for a particular firm-month. 13 Based on Equation (9), the most optimistic forecast (Optimism rank = 1) has a F orecast optimism score of of 100 and the most pessimistic forecast has a score of Measuring individual analyst revision optimism In a similar way, we construct a score for forecast revision optimism by ranking each individual analyst on the change in their earnings forecast from month t 1 to month t. Specifically, for each firm-month we rank individual forecast revisions based on the change in each analysts forecast revision, with the most optimistic revision receiving a Revision rank of 1. We then calculate the score of Revision optimism based on the following equation: Revision optimism ijt = 100 Revision rank ijt (10) Analyst coverage jt 1 where subscripts refer to firm j, analyst i, and month t. The most positive revision (Revision rank =1) receives a score of 100 and the most negative revision receives a score of Sample Panel A of Table 1 presents summary statistics on the CRSP-IBES joint data set. Mean forecast dispersion is 0.17, but the sample is highly right-skewed with a median of only The high skewness present in dispersion is the first fact suggesting that when dispersion is sorted into quintiles, dispersion will be asymmetrically distributed and dispersion in the highest quintile will be considerably larger than dispersion in the other quintiles. Mean reported annual earnings per share is $2.75 and mean analyst forecast is slightly optimistic relative to actual earnings at $2.77 per 13 IBES includes only forecasts made within the previous 90 days in their calculation of the consensus forecast. Given this reporting standard, stale forecasts should not influence our results. 13

16 share. Both of these numbers also exhibit right-skewness with medians less than half the size of the means. Panel B of Table 1 sorts the sample into quintiles by the level of forecast dispersion to directly examine the variables in the quintile portfolios. Forecast dispersion in the low dispersion quintile is This average slowly rises to 0.08 in quintile 4 and then jumps to 0.70 in the high dispersion quintile. Market capitalization monotonically declines across dispersion quintiles from $6.44 billion in the low dispersion quintile to $1.53 billion in the high dispersion quintile. Analyst following also declines as dispersion increases, but the decline is more modest than market capitalization and not monotonic. Earnings per share is relatively constant across the four lowest quintiles, ranging from a low of $3.05 per share in quintile 2 to a high of $3.81 per share in quintile 3. However, mean earnings per share is markedly lower for the high dispersion quintile firms at only $0.15 per share. This difference in mean earnings per share likely contributes to the high dispersion values in this quintile, since using the Diether et al. (2002) method of calculating dispersion (Equation 6) uses the consensus forecast as the denominator. 4 A Preliminary Investigation of Dispersion and Bias To clearly illustrate our core idea, we update figures similar in spirit to those in Chopra (1998) that chart forecast bias and forecast dispersion throughout the calendar year. Chopra (1998) presents a calendar-year graph of the S&P Index aggregate earnings forecast versus actual earnings supplied by IBES for the years Since we are interested in the differences across firms and do not restrict our sample to only S&P 500 stocks, we need to recreate a figure that captures Chopra s (1998) calendar-year S&P 500 pattern for all individual stocks. We begin by calculating forecast dispersion as in Diether et al. (2002) from Equation (6) for all firms in the sample with a December 14

17 fiscal year end. 14 We then sort all firms with suffi cient data into five dispersion quintiles. Panel A of Figure 1 presents the calendar-time plots of forecast bias and forecast dispersion for firms in the highest dispersion quintile. Panel B plots the corresponding variables for the low dispersion quintile. Panel C plots the average forecast bias each month for the high dispersion and low dispersion groups to directly compare the scale of the bias across the two groups. Both Panel A and Panel B show similar calendar-year patterns. In Chopra (1998), the level of forecast bias and dispersion for the S&P 500 peaked in February and declined monotonically throughout the year. In our graphs of high and low dispersion quintiles, the level of bias, and thus dispersion, grows for a month or two and reaches a peak in April then declines monotonically until January. 15 These figures illustrate two important points. First, for the bulk of the year forecast bias and forecast dispersion decline from month-to-month. Second, there is a large difference in the level of optimistic forecast bias between the high dispersion group and the low dispersion group. If forecast bias were uncorrelated with dispersion, the level of forecast bias should not be related to the level of forecast dispersion and therefore, should be roughly equal across dispersion groups. Clearly, forecast bias is not equal across forecast dispersion quintiles. The striking difference in magnitude is apparent in Panel C which plots the level of forecast bias in the high dispersion group against that of the low dispersion group. For example, in July, the average forecast dispersion of the high dispersion group is over eighty percent of the absolute value of the mean forecast, while the average forecast bias for the low dispersion group is under ten percent. 14 We only restrict the sample to December fiscal year firms for comparison with Chopra s (1998) calendar-year figures. All other tests in the paper use firms with all fiscal year end dates. 15 There are several potential reasons why our February dispersion is not as high as that in Chopra (1998). We include an additional 19 years of data and the pattern might have changed. We also include firms outside the S&P that are smaller and have lower analyst coverage. Earnings estimates could be sparsely reported for these firms. Most likely, Chopra (1998) uses a February rollover of IBES S&P 500 data that includes some forecasts made before February. These older forecasts could be particularly optimistic. As we use only recent forecasts, our method would not use these older forecasts in our estimation of forecast bias and dispersion. 15

18 Given the well-known property that analysts forecasts tend to converge to reported earnings during the fiscal year (Matsumoto 2002; Richardson, Wysocki and Teoh, 2004; Cotter, Tuna and Wysocki, 2006), the conclusion from these graphs is straightforward. Forecast bias for both the high and low dispersion groups falls throughout the year, but the magnitude the forecasts must fall is markedly larger for the high dispersion quintile. The only way that forecast optimism can decline so that forecasts better approximate actual earnings is for the forecasts to be revised downwards over time. The magnitude of these downward revisions must be significantly larger in the high dispersion quintile than in the low dispersion quintile. As a consequence, high dispersion firms are more likely to suffer significant negative forecast revisions in the upcoming months. As these negative revisions are, quite naturally, taken as negative shocks to future cash flows, stock prices fall in the upcoming month. We investigate the consequences of these negative forecast revisions on the dispersion anomaly in the following section. 5 Results 5.1 Main result In Panel A of Table 2 we replicate the main evidence for the dispersion anomaly in Diether et al. (2002) by sorting firms into quintiles by the level of forecast dispersion in month t and calculating returns for each quintile in month t + 1. As in Diether et al. (2002) upcoming month returns decline as dispersion increases; returns in the low dispersion quintile average 1.30% in month t + 1 but only 0.77% in the high dispersion quintile. The difference is 0.53% (t-stat = 2.84). This difference is somewhat smaller than the 0.79% (t-stat = 2.88) quintile spread reported in Diether et al. (2002) using data. Our smaller dispersion anomaly estimate is consistent with the findings of McLean and Pontiff (2016) who find many anomalies decrease in size following academic 16

19 publication. Panel B of Table 2 directly examines the underlying assumption in Diether et al. (2002) noted by Johnson (2004) that forecast bias, or analyst optimism as the bias is usually positive, is roughly equal across the five dispersion quintiles. Inspection of Panel B reveals that this assumption does not hold. Mean analyst optimism is 0.06 in the low dispersion quintile, but jumps considerably to 0.85 for the high dispersion quintile. The difference of 0.78 is statistically significant with a t-statistic of The consequences of the violation of this assumption were outlined in Section 3. Given that the average analyst s forecast is optimistic relative to reported earnings and the fact that this optimism declines as the earnings report date approaches, we predict that all analysts forecasts will exhibit negative revisions in the upcoming months. Since Panel B demonstrates that the high dispersion quintile forecasts are the most optimistic, we predict that the forecasts in the high dispersion quintile must fall the most. This is precisely the pattern we find in Panel C which reports mean forecast revision in month t + 1. The four lowest forecast dispersion quintiles all show modest negative earnings revisions in month t + 1, for quintiles 1, 2, and 3 and for quintile 4. In contrast, the negative revision of mean earnings in month t + 1 for the high dispersion quintile is The difference in mean revision between the low dispersion and the high dispersion portfolios is -0.16, the difference is statistically significant with a t-statistic of The main contention in this paper is that it is these large negative revisions in the high dispersion portfolio that account for the low returns to this portfolio and thus, the forecast dispersion anomaly. The only assumptions required for us to make this conclusion are that some investors use analysts forecasts as an input into their stock valuations and that the lower expected cash flows revealed by the negative revision lead investors to lower their valuations. 17

20 5.2 Optimistic analysts and pessimistic revisions We next present a simple regression to demonstrate that optimistic analysts tend to downwardly revise their forecasts more than pessimistic analysts. Using Equation (9), we identify how optimistic an analyst is relative to her peers. For each firm-month we rank all analysts from the highest earnings forecast to the lowest earnings forecast. The analysts rank is then divided by the number of analysts issuing forecasts for that firm-month. The resulting F orecast optimism measure takes on a percentile value between 0 and 100. We then calculate Revision optimism from Equation (10) by looking at all forecast revisions in a particular firm-month and ranking them from the most positive (or optimistic) revision to the most pessimistic. We then divide this Revision rank by the total number of analysts issuing forecasts for that month. In Equations (9) and (10) both F orecast optimism and Revision optimism are multiplied by 100 to allow for interpretation of the coeffi cients in percent. We then regress Revision optimism in month t on F orecast optimism in month t 1. The results are presented in Table 3. We find the intercept in this regression to be 77.4%. Since the average Revision Rank is 50% by construction, the coeffi cient the rank of forecast optimism must be negative. We find that forecast optimism in month t 1 significantly predicts revision activity in month t. For every 1 percent increase ranked forecast optimism in month t 1, the analysts revision will be -0.28% more pessimistic in month t. This result confirms that optimistic analysts, those with high forecast bias, tend to be the analysts issuing pessimistic revisions in the upcoming month. 5.3 A model of forecast revisions Forecast revisions are predictable. In fact, our main hypothesis is that dispersion predicts negative revisions and the negative cash flow shocks resulting from these revisions can explain the 18

21 dispersion anomaly. Our next empirical analysis examines whether dispersion can predict negative revisions when other predictive variables are included in the regression specification. Chen, Narayanamoorthy, Sougiannis, and Zhou (2015) construct a model of individual analyst forecast revisions to examine analyst underreaction as a contributing factor in a momentum strategy that goes long in stocks with the most optimistic individual analyst revisions and short in stocks with the most pessimistic revisions. Several of their independent variables can be adapted to forecast the consensus forecast revisions we study in this paper. Chen et al. (2015) find that individual analyst forecast revisions contain a significant AR(1) component. To test whether this finding also applies to consensus revisions we include the consensus revision from the prior month in our regression specification. Recent earnings surprises should be important in predicting forecast revisions as analysts update their forecasts based on recent firm results. We control for recent earnings surprises by including the most recent standardized unexpected earnings (SU E). Following Chen et al. (2015) we also control for firm size, measured by market capitalization. Barth and Hutton (2004) find that the level of firm accruals is significantly correlated with the first forecast revision after the prior year s earnings are reported. Since accruals appear to be correlated with forecast revisions at this point in time, we include accruals to examine its ability to predict forecast revisions in other forecast months. Thus, our regression specification is modelled as: F orecast revision j,t = β 0 + β 1 Dispersion j,t 1 + β 2 F orecast revision j,t 1 + β 3 Accruals j,t 1 +β 4 LOGMV t 1 + +β 5 SUE j,t 1 + ɛ j.t, (11) where LOGMV is the log of firm market capitalization and firm Accruals is defined as the 19

22 change in current assets (Compustat item ACT - Lag ACT) plus the change in debt in current liabilities (Compustat item DLC - Lag DLC) minus the change in cash and short-term investments (Compustat item CHE - Lag CHE), and minus the change in current liabilities (Compustat item LCT - Lag LCT), all scaled by the number of shares outstanding to get an accruals per share calculation that matches the earnings per share basis of the forecast revision. Table 3 shows that forecast optimism (bias) can predict upcoming revisions. However, there are two reasons why we omit this variable from the specification in Equation (11). First, Figure 1 and Panel B of Table 2 show that forecast optimism (bias) is strongly correlated with dispersion. Therefore, to avoid a multicollinearity problem and to focus on our explanation for the dispersion anomaly, we only include dispersion in our specification. Second, forecast optimism (bias), calculated the standard way as in Equation (8) uses actual earnings which are not known until the end of the fiscal year, a point in time after our month t regressions. Thus, omitting forecast bias from Equation (11) avoids using information that is not yet known to market participants in month t of the forecast year. Table 4 presents the results of five separate univariate specifications using each of the regressors in Columns (1) to (5) and a joint model of Equation (11) in Column (6). Fama and MacBeth (1973) monthly regressions are run for every month from January 1985 to December 2015 using only observations from the previous 3 years, specifically month t 36 through month t 1. This rolling estimation method ensures that we only use historical information in each regression. The results reveal that dispersion is clearly the most important variable in predicting consensus forecast revisions in the upcoming month. The average coeffi cient on Dispersion is negative and significant (t-statistic = -36.7) and by itself Dispersion produces an average R 2 value of 14.7%. Each of the other four variables included in Equation (11) is a significant predictor of forecast 20

23 revisions. Consensus revisions are positively autocorrelated, and they are positively related to Accruals as in Barth and Hutton (2004). Forecast revisions are also positively correlated with firm size and the most recent standardized earnings surprise reported by the firm. However, none of these other predictive variables produces an average R 2 of over 1%. The full model is estimated in Column (6) and we find that all variables maintain their significance, however, the average coeffi cient on Accruals switches from positive to negative in the joint model. 5.4 Expected forecast revisions Given that forecast revisions are to some degree predictable, we use the average coeffi cients from the model in Column (6) of Table 4 to estimate an expected forecast revision: Expected revision j,t+1 = β 0 + β 1 Dispersion j,t + β 2 F orecast revision j,t + β 3 Accruals j,t + β 4 LOGMV t + β 5 SUE j,t. (12) Using the estimate for expected revision from Equation (12), in each month t we sort stocks based on the expected revision in month t + 1 into five quintiles ranging from the lowest expected revision to the highest expected revision. The expected revision in month t + 1 is calculated using the average coeffi cients in Equation (12) and month t data so that the expected revision is a month t prediction for a month t + 1 value. Panel A of Table 5 reports the average realized consensus revision for each quintile to examine the ability of Equation (12) to predict realized revisions in analysts annual earnings forecasts. We find that the model of expected forecast revisions sorts realized revisions into quintiles quite well. The low expected revision quintile has a mean revision of -18.3%, the lowest value in any quintile. The means of the realized revisions increase monotonically in expected forecast revision from -2.1% in quintile 2 through -0.4% in the highest expected revision quintile. Means and medians in all 21

24 five quintiles are less than zero consistent with the time series patterns observed in Figure 1 where consensus forecasts tend to decline throughout the year. Given that the realized earnings forecasts decline the most for the lower expected revision quintiles, we next examine whether returns react to this negative cash flow shock. Panel B of Table 5 presents average stock returns in month t + 1 for each expected revision quintile. Unsurprisingly, the low expected revision quintile, which also suffers the largest realized forecast declines, has the lowest average stock returns at 0.66%. Average returns increase monotonically in expected revision to a peak of 1.54% for the high expected revision quintile. Forming a portfolio that goes long in the high expected revision quintile stocks and shorts the low expected revision stocks produces average returns of 0.89% that are statistically significant (t-stat = 5.18). In fact, the quintile spread for the high-low expected revision portfolio returns is larger than the 0.53% spread using dispersion alone reported in Table 2. We interpret the results from these tests to indicate the fact that forecast revisions can produce returns that are large enough to explain the dispersion anomaly Expected earnings revisions, credit ratings and the dispersion anomaly While the returns to our expected revision model appear large enough to completely explain the dispersion anomaly, we don t yet know if they subsume the predictable power of forecast dispersion for future returns. We examine this contention in Table 6 that presents average coeffi cients for Fama-Macbeth regressions that include as the primary explanatory variables, expected revisions, forecast dispersion and firm credit rating, the latter being the explanation for the dispersion anomaly hypothesized by Avramov et al. (2009). Each regression in Table 6 presents average coeffi cients of monthly regressions from January 1985 to December 2015 of monthly returns regressed against combinations of forecast dispersion, credit rating and expected earnings forecast revisions from Equation (12). Following Avramov et al. (2009) all regressions use only the subsample of firms 22

25 that have credit ratings on Compustat. This restriction does not affect the number of months in the regressions but lowers the average number of firms in a month from 1,428 in Table 5 to 572. Column (1) of Table 6 includes only forecast dispersion as an explanatory variable and we find, as expected, that higher forecast dispersion is significantly associated with lower returns. Column (2) tests the ability of credit rating to subsume the forecast dispersion anomaly. Column (3) includes forecast dispersion and expected earnings revision. In this specification, the significantly positive coeffi cient indicates that the lower the expected revision to earnings forecasts, the lower future month returns. Forecast dispersion, as a competing explanatory variable has a coeffi cient that is now positive and insignificant. This result indicates that the crucial information in dispersion for predicting negative future returns is contained in the expected revision component of dispersion. The Column (4) and (5) specifications reveal that the firm s credit rating is likewise not a significant predictor of abnormal returns in the presence of expected revision. A similar result is presented in Column (6) a specification that also includes several controls specified in Avramov et al. (2009) for Beta, Size, Book to market ratio, Leverage, Illiquidity, idiosyncratic volatility (IdioV ol), and past monthly returns (Ret). 16 Credit rating uses a 1 to 22 score as in Avramov et al. (2009). Leverage is the book value of debt divided by the book value of assets. Illiquidity is calculated as the average ratio of absolute return to dollar volume, and IdioV ol is the standard deviation of the residuals from estimation of the Fama-French 3-factor model using daily returns in each month. Ret1 is the stock return over the previous month, Ret2-3 is the cumulative return over the two months ending at the beginning of the previous month. Ret4-6 is the cumulative return over the three months ending three months previously, and Ret7-12 is the cumulative return over the six months ending six months previously. In the joint specification presented in Column (6) the coeffi cients for expected revision, firm 16 Avramov et al. (2009) Table 5, page