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Analysts’ Forecast Dispersion, Analysts’ Forecast Bias and Stock Returns∗ Tingting Liu1 1 Terry College of Business, University of Georgia, Athens, GA 30602, USA June, 2014 Keywords: Divergence of Opinion, Analysts’ Forecast Dispersion, Analysts’ Forecast Bias, Stock Returns. Abstract This paper examines the relation between divergence of opinion and stock returns. I find that analyst forecast dispersion, a popular proxy for divergence of opinion, is highly correlated with forecast bias. A decomposition of forecast dispersion into bias and disagreement reveals a strong positive relation between the disagreement component and returns. Further analysis shows that the high-dispersion-low-returns relation documented in Diether et al (2002) is driven by bias which is negatively associated with returns. The results show that investors require higher returns for holding high disagreement stocks, consistent with Merton (1987)’s view that divergence of opinion proxies for risk. ∗ Tingting Liu: [email protected]. I am particularly grateful to Paul Irvine, as well as Julie Wu, Harold Mulherin, Jack (Jie) He, Lee Cohen, Alexander Barinov, Jeffry Netter, Bradley Paye, Linda S. Bamber, Kewei Hou, Anna Scherbina, Suzanne S. Lee, Wenjing Ouyang, Greg Eaton, and conference participants at the 2014 Financial Intermediation Research Society (FIRS) Conference, the 2012 Financial Management Association (FMA) Meetings, the 2012 Southern Financial Association (SFA) Meetings, and seminar participants at University of Georgia, for comments and suggestions. Analysts’ Forecast Dispersion, Analysts’ Forecast Bias and Stock Returns Abstract This paper examines the relation between divergence of opinion and stock returns. I find that analyst forecast dispersion, a popular proxy for divergence of opinion, is highly correlated with forecast bias. A decomposition of forecast dispersion into bias and disagreement reveals a strong positive relation between the disagreement component and returns. Further analysis shows that the high-dispersion-low-returns relation documented in Diether et al (2002) is driven by bias which is negatively associated with returns. The results show that investors require higher returns for holding high disagreement stocks, consistent with Merton (1987)’s view that divergence of opinion proxies for risk. Keywords: Divergence of Opinion, Analysts’ Forecast Dispersion, Analysts’ Forecast Bias, Stock Returns. June, 2014 Introduction The question of how divergence of opinion affects stock returns has drawn extensive attention in the recent literature. Prior theoretical studies provide different predictions about the relation between divergence of opinion and stock returns. Miller (1977) predicts lower future returns for high divergence of opinion stocks. Miller argues that stock prices will reflect a more optimistic valuation if pessimistic investors are kept out of the market by high short-sale costs. In contrast, Merton (1987) predicts that divergence of opinion proxies for risk. Intuitively, a high level of divergence of opinion among investors likely indicates more volatile, less predictable future earnings and investors demand a higher return to compensate for the idiosyncratic risk of the stocks they hold. Thus the greater the disagreement among investors about the value of a stock, the higher its future return. One challenge in testing these theoretical predictions is to find a reasonable proxy that captures differences of opinion among investors about stock value, since it is almost impossible to directly measure investor opinion. Empirical studies examining the relation between divergence of opinion and stock returns rely on different proxies for divergence of opinion. The most commonly used proxy is dispersion in analysts’ forecasts (e.g., Ziebart (1990), Ajinkya, Atiase, and Gift (1991), Atiase and Bamber (1994), Abarbanell, Lanen, and Verrecchia (1995), Diether, Malloy, and Scherbina (2002), Sadka and Scherbina (2007), Berkman, Dimitrov, Jain, Koch, and Tice (2009), and Barinov (2013)). Other measures that also have been used to proxy for divergence of opinion include abnormal trading volume, income volatility, and stock return volatility (e.g., Garfinkel and Sokobin (2006) and Berkman, Dimitrov, Jain, Koch, and Tice (2009)).1 Interestingly, the empirical research investigating the relation between divergence of opinion and stock returns provides contradictory results based on the use of difference proxies. Diether, Malloy, and Scherbina (2002) document a negative relation between dispersion in analysts’ forecasts and future stock returns and conclude that the results reject the interpretation of dispersion in analysts’ forecasts as a measure of risk. However, Garfinkel and Sokobin (2006) show that if a trading volume measure of opinion divergence is used instead of dispersion in 1 In a recent study by Giannini, Irvine, and Shu (2013), the authors develop a direct measure of divergence of opinion among investors using a unique dataset of Twitter posts. 1 analysts’ forecasts, the divergence of opinion is positively related to future returns, suggesting that divergence of opinion is a proxy for risk. The conflicting empirical evidence highlights need for further investigation on the proxies for divergence of opinion. In this study, I examine the validity of the most commonly used proxy (dispersion in analysts’ forecasts) for divergence of opinion. The idea to use dispersion in analysts’ forecast as a proxy for divergence of opinion is intuitively appealing: if we assume that analysts make forecasts based on their true beliefs, then dispersion in analysts’ forecasts indicates the divergence of opinion among analysts. Frederickson and Miller (2004) report evidence that analysts themselves are more sophisticated investors and are better at processing information,2 thus disagreement among analysts would be a reasonable proxy for disagreement among investors. However, the assumption that analysts make forecasts based on their best expectations has been challenged by a large body of empirical studies. Analysts have been found to be subject to a number of well-known conflicts of interest that can result in biased forecasts (Francis and Philbrick (1993), Dugar and Nathan (1995), McNichols and O’Brien (1997), Lin and McNichols (1998), Irvine (2004), Bradshaw, Richardson, and Sloan (2006)). More importantly, Ackert and Athanassakos (1997) show that the upward forecast bias could be positively related to forecast dispersion.3 In Diether, Malloy, and Scherbina (2002), the authors acknowledge that “Forecast bias increases with dispersion in the underlying forecasts. It would be interesting to isolate the importance of this effect on upward price bias.” In this paper, I argue that if analysts’ forecasts dispersion is measured with a bias component and if investors do not fully anticipate this bias, then the bias component will be correlated with subsequent stock returns, which introduces serious endogeneity problem caused by measurement error (Roberts and Whited (2012)). Thus, one should exercise caution in interpreting any results relying on forecast dispersion as a proxy since the results could be driven by either the bias component, or the actual disagreement component, or a mix of both. I start my analysis by testing the negative relation between dispersion in analysts’ forecasts and future stocks returns 2 Frederickson and Miller (2004) conducted an experiment to test whether pro forma disclosures influences analysts stock price judgments and find that analysts are not misled by pro forma disclosures. However, they find that pro forma earnings disclosures influence less sophisticated investors. 3 Ackert and Athanassakos (1997) show a higher level of optimistic forecast bias proxied by the difference between the consensus forecast and actual earnings for higher forecast dispersion quartiles. 2 documented in Diether, Malloy, and Scherbina (2002) over a longer sample period 1986 to 2012. I then study how forecast bias is associated with forecast dispersion. My goal is to decompose dispersion into a bias component and a true disagreement component. After removing the bias component, I then study how divergence of opinion affects stock returns by examining the relation between disagreement and stock returns. Consistent with Diether, Malloy, and Scherbina (2002), my results show a negative relation between dispersion in analysts’ forecasts and future stock returns over the sample period 1986 to 2012, and the asset pricing models fail to explain the negative relation. However, we need to be cautious to interpret this result, because dispersion in analysts’ forecasts is likely to be contaminated by forecast bias. To decompose dispersion into a bias component and an actual disagreement component, I first construct three measures of forecast bias following the literature. I then perform Fama and MacBeth (1973) cross-sectional regression of dispersion in analysts’ forecasts on forecast bias. I use the regression residual as the proxy for disagreement among analysts because the regression residual is the part that is not explained by bias. The results show that all three bias measures are strongly positively correlated with dispersion in analysts’ forecasts. The average R-square of Fama and MacBeth (1973) cross-sectional regression of dispersion on bias is 33%, indicating that forecast bias explains approximately one third of the observed forecast dispersion. More importantly, after removing the bias component, I provide strong evidence that disagreement is positively related to stock returns. My results show that the average monthly return increases monotonically with the increase of analyst disagreement. Merton (1987) implies that the disagreement effect (i.e. the positive relation between analyst disagreement and stock returns) should be stronger among small stocks because of incomplete information. Similarly, Barry and Brown (1984) predicts that small firms are riskier because these firms have higher information risk. To provide further evidence of how firm size influences divergence of opinion and subsequent stock returns, I sort stocks into five groups based on firm size and then sort each size group into five additional groups based on analyst disagreement. Consistent with the risk-based expectation, I find that the positive relation between disagreement and future stock returns is more pronounced among small stocks. However, the return differential is statistically significant for all size groups, indicating that the positive relation 3 between disagreement and returns also holds for large stocks. The positive relation between disagreement and stock returns implies that the observed negative relation between dispersion and returns is driven by forecast bias. Thus I expect a negative relation between bias and future stock returns and the negative relation should more than offset the positive relation between disagreement and stock returns. To further analyze this conjecture, I sort stocks into portfolios based on forecast bias. Consistent with the expectation, the results show that forecast bias is negatively associated with stock returns. I further sort stocks on size and bias and find that the negative relation between forecast bias and stock returns is most pronounced among small stocks, consistent with Lim (2001) who predicts that analysts have stronger incentives to make biased forecasts for small firms. Additional results confirm that small stocks indeed have a higher level of forecast bias. I also calculate portfolio returns for two subperiods: 1986 to 2002 and 2003 to 2012. This is motivated by the series of reforms around 2002 that were at least partially motivated by practices in the analyst community. Of particular importance is the Global Settlement, which directly targeted analysts who allegedly issued fraudulent research. If the negative relation between dispersion in analysts’ forecasts and future stock returns is driven by forecast bias, we would expect the negative relation to decrease after the reforms mainly due to the decrease in forecast bias. Consistent with this expectation, I find that forecast bias decreases by half after the Global Settlement. More importantly, the negative relation between forecast dispersion and stock returns disappears after the Global Settlement and the positive relation between disagreement and stock returns remains highly significant. The evidence presented in this paper contributes to the literature along the following dimensions. First, despite the fact that dispersion in analysts’ forecast has been widely used in the literature to proxy for different variables of interest, my results indicate that dispersion is not a good proxy since it is contaminated by forecast bias.4 More importantly, I provide evidence that forecast bias is able to explain one third of forecast dispersion, raising serious questions to an extensive literature that draw conclusions relying on forecast dispersion as a proxy. 4 The literature relies on dispersion in analysts’ forecasts not only to proxy for divergence of opinion, but also to proxy for other variables of interest such as uncertainty of the firm and information risk. For example, Imhoff and Lobo (1992), Ackert and Athanassakos (1997), and Barron and Stuerke (1998) use it to proxy for uncertainty; Johnson (2004) and Officer (2004) use it as a measure of information risk; Doukas, Kim, and Pantzalis (2006) try to decompose the dispersion into uncertainty and divergence of opinion. 4 Second, I provide an explanation to the conflicting findings in Diether, Malloy, and Scherbina (2002) and Garfinkel and Sokobin (2006). I show that the negative relation between forecast dispersion and future stock returns documented in Diether, Malloy, and Scherbina (2002) is driven by forecast bias. After removing the bias component, I find strong evidence that analyst disagreement is positively associated with stock returns. The evidence provided in this paper adds to the inconclusive empirical literature on divergence of opinion and stock returns. The strong positive relation between analyst disagreement and future stock returns is consistent with the predictions that divergence of opinion represents risk ( Merton (1987)) and inconsistent with the prediction of Miller (1977).5 Finally, this paper provides additional evidence to the effects of regulatory reforms implemented around 2002. More specifically, the results show that the negative relation between forecast dispersion and stocks returns has disappeared after the Global Settlement and at the same time there is a significant decrease in forecast bias. These results further support that the observed negative relation between dispersion in analysts’ forecasts and stock returns before the Global Settlement is driven by forecast bias and the regulatory reforms reduce (although the reforms do not completely eliminate) bias in analysts’ forecast. The rest of the paper is organized as follows. Section I discusses motivation and hypotheses development. Section II describes the data. Section III presents variable construction. Section IV reports the empirical results. Section V concludes. I. Motivation and Hypotheses Development A Dispersion in Analysts’ Forecasts as a Proxy and Bias in Analysts’ Earnings Forecasts It has been well-documented that analysts tend to make upwardly biased forecasts. There are extensive studies examining the question of why analysts make biased forecasts. The explanations provided in these studies can be divided into three categories. The first explanation argues that analysts cover firms about which they have optimistic views, implying a selection bias in coverage decisions (McNichols and O’Brien (1997)). The second explanation focuses on 5 Williams (1977), Mayshar (1983), Varian (1985), and Epstein and Wang (1994) also predict that divergence of opinion proxies for risk. 5 conflicting incentives. For example, Dugar and Nathan (1995) find that analysts employed by investment banks issue more optimistic earnings forecast and recommendations; Irvine (2004) finds that forecasts that deviate more from the consensus forecast can generate more trading for the brokerage firm; Bradshaw, Richardson, and Sloan (2006) show that over-optimism in analysts’ earnings forecasts, stock recommendations, and target prices are systematically related to net corporate financing activities. The last explanation relates forecast bias to cognitive failures. Easterwood and Nutt (1999) demonstrate that analysts under-react to negative earnings news but overreact to positive news and conclude that analysts interpret new information optimistically.6 Although it is important to notice the distinction between biased forecasts driven by judgment errors as distinct from economic incentives because the latter is motive driven and the former is not, this paper focuses on examining the relation between forecast bias and forecast dispersion rather than distinguishing rational bias from irrational bias. One goal of this paper is to test the relation between forecast bias and forecast dispersion. In fact, several empirical studies imply that forecast bias could be systematically related to forecast dispersion. Das, Levine, and Sivaramakrishnan (1998a) and Ackert and Athanassakos (1997) show that companies with higher earnings variability or forecast uncertainty are associated with more optimistic bias. Similarly, Jackson (2005) conjectures that analysts, who benefit from issuing optimistic forecasts, tend to add a higher bias to their estimates because they know they will be penalized less for being wrong when earnings are uncertain. Several recent studies provide a more complete picture about analysts’ forecast bias. Matsumoto (2002) show that some firms prefer lower forecasts to avoid negative earnings surprise. Matsumoto (2002) find that on average, the last published forecast before quarterly earnings announcement is downwardly biased by one penny.7 Richardson, Teoh, and Wysocki (2004) find that analysts tend to make optimistic forecasts early in the fiscal period and walk-down the optimistic forecasts to a beatable level right before the earnings announcement.8 Cotter, Tuna, 6 De Bondt and Thaler (1990) argue that analysts have a behavior tendency to overreact and form expectations that are too extreme. Abarbanell (1991) and Klein (1990) show that analysts appear to under-react to information in past quarterly earnings and stock returns. 7 By making slightly pessimistic forecasts right before earnings announcement, analysts also gain accuracy since they would only miss the announced earnings by pennies. 8 Other papers examining forecast(expectation) management include Soffer, Thiagarajan, and Walther (2000), Kasznik (1996), Skinner and Sloan (2002), Cotter, Tuna, and Wysocki (2006), Burgstahler and Eames (2006), 6 and Wysocki (2006) find that management is more likely to guide analysts when the initial forecasts are optimistic and analysts quickly react to management guidance and are more likely to issue final beatable earnings targets. Although the empirical evidence suggests that when analysts make upward biased forecasts, the level of dispersion in forecasts is likely to be high, few studies have explicitly examined the relation between the level of forecast bias and forecast dispersion.9 To illustrate my point that forecast bias can be related to forecast dispersion, assume that, two analysts follow firm A and the true earnings per share (EPS) for firm A is $0.5. If the two analysts make earnings forecasts based on their true beliefs, they are able to make EPS forecast around the true earning. I sketch three different scenarios to illustrate the relation between bias and dispersion. Case I assumes that both analysts make unbiased forecasts. For example, one forecasts $0.4 per share and the other forecasts $0.6 per share. The mean forecast is consistent with the true earnings and the sample standard deviation is 0.141. Case II assumes that one of the two analysts makes an optimistic forecast based on misaligned incentives as suggested by the earlier literature. For example, one analyst makes a forecast of $1, and the other analyst still forecasts $0.4, the observed mean forecast is $0.7 and the sample standard deviation increases to 0.424. Case III assumes that the firm prefers pessimistic forecast right before the earnings announcement as suggested by the more recent literature. In this case, managers guide the optimistic analyst to downward revise the forecast so that the firm can beat the consensus forecast. Assume that the optimistic analyst adjusts the forecast down to $0.5, then the observed mean forecast is $0.45 and the sample standard deviation decreases to 0.07. and Das, Kim, and Patro (2011). 9 Ackert and Athanassakos (1997) show that forecast bias is higher for higher forecast dispersion stocks. However, they do not provide any further tests and their sample only includes 169 firms. 7 Case I: No Bias Analyst A: $0.4 Analyst B: $0.6 Case II: Upward Bias Analyst A: $0.4 Analyst B: $1 Case III: Downward Bias Analyst A: $0.4 Analyst B: $0.5 $0.50 $0.70 $0.45 0.141 0.424 0.071 0.282 0.606 0.157 Mean forecast: Forecast dispersion: Measured by sample stdev Measured by sample stdev scaled by mean forecast based on Diether, Malloy, and Scherbina (2002) The simple example above illustrates that if one analyst introduces upward bias in the forecast (Case II), both the observed mean forecast and forecast dispersion (measured by either standard deviation or the dispersion measure in Diether, Malloy, and Scherbina (2002)) are higher, compared to those observed in Case I where no bias is introduced. On the other hand, when one analyst adjusts the optimistic forecast to a more pessimistic level (Case III), both the mean forecast and forecast dispersion are likely to be lower. Thus, both Case II and Case III indicate a positive relation between forecast bias and forecast dispersion.10 In the Appendix, I also provide a model illustrating the positive relation between forecast bias and forecast dispersion. My first testable hypothesis predicts that dispersion in analysts’ forecast is positively related to the level of forecast bias. H1: Dispersion in analysts’ forecast and forecast bias are positively correlated. One might argue that if all analysts issue biased forecasts (of exactly the same magnitude), then dispersion should not be affected by forecast bias. Empirical evidence suggests that it is unlikely for all analysts to make biased forecasts because their career concern serves as a mechanism to control the biases in their forecasts. Jackson (2005) shows that analyst reputation strengthens with greater forecast accuracy and that reputation does play a role when analysts move to other jobs. Mikhail, Walther, and Willis (1999) show that analyst turnover is more likely as accuracy declines relative to peer performance, regardless of the profitability of the 10 One might argue that there might be a Case IV where the pessimistic analyst may revise his forecast to an even lower level. For example, if the analyst who makes the initial forecast of $0.4 revises the forecast down to -$0.5, then we observe a lower mean forecast but a higher dispersion. However, this case is not likely because Scherbina (2008) presents evidence that analysts withhold negative information. More specifically, analysts stop revising their annual earnings forecasts when analysts have bad information about firms and if firms do not want bad news to be shared. 8 analyst’s recommendations. Hong and Kubik (2003) go a step further and show that more accurate analysts are more likely to move to more prestigious firms. These empirical studies indicate that although analysts have incentives to make biased forecasts, they have to balance the accuracy of their forecasts and forecast bias. B Divergence of Opinion and Stock Returns A large number of studies have examined the relation between divergence of opinion and future stock returns. The theoretical work of Miller (1977) predicts that high divergence of opinion stocks realize low future returns because pessimistic investors are kept out of the market when short-sale constraints bind. Miller (1977) argues that optimistic investors hold the stock because they have higher valuation compared to pessimistic investors. The larger the disagreement about a stock’s value, the higher the market price relative to its true value, and the lower the subsequent returns. Similarly, Harrison and Kreps (1978), Morris (1996), and Chen, Hong, and Stein (2002) also provide price-optimism models and predict that optimists, who have the highest valuations hold the stock and suffer losses in expectation since the best estimate of the stock price should be the average opinion. Empirical studies relying on dispersion of analysts’ forecasts as a proxy for divergence of opinion in general find a negative relation between dispersion in analysts’ forecast and future stock returns (see e.g, Diether, Malloy, and Scherbina (2002), Ackert and Athanassakos (1997), and Park (2005)). Several other studies investigate the source of the negative relation and document that the negative relation between forecast dispersion and stock returns increases with their proxy for short sale constraints (Nagel (2005) and Boehme, Danielsen, and Sorescu (2006)). Sadka and Scherbina (2007) argue that the negative relation is due to mispricing and the reason mispricing has persisted through the years is that high forecast dispersion coincides with high trading costs. Sadka and Scherbina (2007) show that in the cross-section, the less liquid stocks tend to be more severely overpriced.11 11 Several other studies explain the negative relation between forecast dispersion and stock returns from a rational perspective. Johnson (2004) interprets dispersion as a proxy for unpriced information risk arising when asset values are unobservable. Johnson shows that the negative relation increases with leverage and is absent for all-equity firms, suggesting that for levered firms, adding uncertainty increases the option value of equity. However, Sadka and Scherbina (2007) and Avramov, Chordia, Jostova, and Philipov (2009) show that the sign of the product of leverage and forecast dispersion is not robust to reasonable changes in the sample composition. Barinov (2013) also proposes a risk-based explanation for the negative relation between forecast dispersion 9 The negative relation between dispersion in analysts’ forecasts and future stock returns seems support Miller (1977)’s argument that stocks are mispriced due to short-selling constraints. However, as suggested by hypothesis I, forecast dispersion is contaminated by forecast bias, which casts serious doubts on dispersion being a valid proxy for divergence of opinion. This paper re-examines the relation between divergence of opinion and stock returns by providing a cleaner measure of divergence of opinion. More specifically, I decompose dispersion into two components: the bias component and the disagreement component. After removing the bias component, I use the disagreement component which is not contaminated by forecast bias to proxy for divergence of opinion and then test the relation between disagreement among analysts and future stock returns. If Miller (1977)’s hypothesis is correct, I still expect a negative relation between analyst disagreement and stock returns even after removing the bias component. This leads to my second testable hypothesis. H2: Based on Miller (1977), analyst disagreement should be negatively associated with stock returns. In contrast to Miller’s hypothesis, Merton (1987) suggests that divergence of opinion proxies for risk.12 Dispersion in analysts’ forecasts likely indicates more volatile, less predictable future earnings and investors who are not well diversified demand a higher return to compensate for the idiosyncratic risk of the stocks they hold. Thus stocks with higher level of divergence of opinion should earn higher future returns.13 Hypothesis 3 argues that if divergence of opinion proxies for risk, then after removing the bias component, the relation between analyst disagreement and future stock returns should be positive.14 and stock returns. Barinov (2013) shows that both aggregate volatility and forecast dispersion increase during recessions and concludes that the increase in forecast dispersion causes real options to respond to higher aggregate volatility with a lower decline in value than what the CAPM predicts. 12 Williams (1977), Mayshar (1983), Varian (1985), and Epstein and Wang (1994) also suggest that divergence of opinion proxies for risk. 13 Other studies examining this question include Diamond and Verrecchia (1987) who claim that even in the presence of short sale constraints, the constraints eliminate some informative trades, but do not bias prices upward, and Hong and Stein (2003) who introduce influential rational agents and rely on rational arbitrageurs that can eliminate mispricing. The assumption of perfectly rational arbitrageurs is challenged by Shleifer and Vishny (1997) and Chen, Hong, and Stein (2002) who provide theoretical explanations why arbitrageurs may fail to close the arbitrage opportunity. 14 Garfinkel and Sokobin (2006) using trading volume as a proxy for divergence of opinion show a positive relation between divergence of opinion and future stock returns, suggesting that divergence of opinion is a proxy for risk. Doukas, Kim, and Pantzalis (2006) also show that when the Barron, Kim, Lim, and Stevens (1998) 10 H3: Based on Merton (1987) who views divergence of opinion as a proxy for risk, analyst disagreement should be positively associated with stock returns. In summary, the first hypothesis predicts a positive association between forecast dispersion and forecast bias. The second hypothesis based on Miller (1977) predicts a negative relation between analyst disagreement and stock returns. And the third hypothesis based on Merton (1987) views divergence of opinion as a proxy for risk and predicts a positive relation between analyst disagreement and stock returns. II. Data I used several datasets that cover January 1986 to December 2012. Following Sadka and Scherbina (2007) and Scherbina (2008), analysts’ earnings forecasts data were obtained from the Institutional Brokers Estimate System (I/B/E/S) US Summary History Unadjusted dataset, which includes mean, median, and standard deviation for outstanding analysts’ annual earnings forecasts as well as the number of analysts issuing forecasts. The unadjusted dataset is used to avoid the rounding error present in the adjusted dataset, arising when historical earnings forecasts are divided by subsequent stock splits and rounded to the nearest cent. Data on realized earnings were obtained from the I/B/E/S Unadjusted Actuals file which includes realized earnings. Information on stock returns, prices, and shares outstanding were obtained from the Center for Research in Securities Prices (CRSP) Daily and Monthly stock files. I exclude stocks with less than two analysts following. The accounting data are from Compustat. Following Diether, Malloy, and Scherbina (2002) and Barinov (2013), I exclude stocks with prices less than 5 dollars per share on the portfolio formation date. My sample is composed of predominantly large stocks, because I/B/E/S only covers relatively large firms and I have to exclude firms with less than two analysts following to compute the dispersion in analysts’ forecasts. For each stock in CRSP, I set the coverage in any given month equal to the number of I/B/E/S analysts who provide fiscal year one earnings estimates that month. I use the Amihud (2002) ratio to measure liquidity, which is the average ratio of absolute return to dollar volume. measure of investor disagreement is used, the negative relation between dispersion and future returns does not hold. 11 The market to book ratio is defined as the ratio of market value of equity to book equity plus deferred taxes. I use the fiscal year end book equity for book value. Market capitalization is computed by using the number of shares outstanding times share price, both from the CRSP monthly file. III. Variable Construction Since the accounting literature provides evidence that analysts have incentives to make biased forecasts, which can also affect the dispersion in analysts’ forecasts, the first goal of this study is to decompose the observed dispersion into the bias component and the actual disagreement component. Then I try to provide evidence on the relation between the level of disagreement among analysts and stock returns. A Measuring Dispersion Following Diether, Malloy, and Scherbina (2002), I define 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 in the I/B/E/S Summary History file.15 Dispersionitm = StandardDeviationitm Abs(M eanF orecastitm ) (1) where subscripts refer to firm i, year t, and month m. B Measuring Forecast Bias In this section, I discuss my proxies for forecast bias. Following the literature, I construct three measures to capture the bias in analysts’ forecasts. B.1 Bias Measure I The first measure of forecast bias is the difference between the consensus forecast and the actual annual earnings. This is the most commonly used bias measure in the literature (e.g., Das, 15 I obtain similar results when I construct all the variables scaled by stock price. I choose to present the absolute mean forecast deflated results in order to compare to prior literature such as Diether, Malloy, and Scherbina (2002). 12 Levine, and Sivaramakrishnan (1998b), Gu and Wu (2003), Lim (2001), Ackert and Athanassakos (1997), Hong and Kubik (2003), Diether, Malloy, and Scherbina (2002) and Doukas, Kim, and Pantzalis (2006)). BiasAitm = Ait − Fitm Abs(M eanF orecastitm ) (2) where subscripts refer to firm i, year t, and month m, and Ait = the annual earnings realization (EPS), Fitm = the consensus analyst forecast obtained from I/B/E/S, M eanF orecastitm = the mean analyst forecast obtained from I/B/E/S. A positive value of BiasA indicates average optimism for a particular firm and a negative value indicates average pessimism. I scale the bias by the absolute value of mean forecast to make it consistent with the construction of the dispersion measure. B.2 Bias Measure II Following Scherbina (2008), the second measure of analysts’ forecast bias is the skewness in the forecast distribution. It is defined as the difference between mean and the median forecast scaled by the absolute value of the mean forecast. Skewnessitm = M eanitm − M edianitm Abs(M eanF orecastitm ) (3) where subscripts refer to firm i, year t, and month m. This measure is motivated by the argument that if analysts’ private signals are symmetrically distributed around the true future earnings, reported forecasts should also be symmetrically distributed. Scherbina (2008) argue that when negative opinions are withheld, the forecast distribution is right-skewed. If investors do not adjust their valuations based on the shape of the reported distribution, the stock price would be overvalued. B.3 Bias Measure III Matsumoto (2002) develops a model to compute unexpected forecast (forecast bias). Matsumoto first constructs a measure of expected forecast, then computes the forecast bias as the 13 difference between consensus analyst forecast and the expected forecast. Following Matsumoto (2002), I construct the third measure of forecast bias (BiasM) by first computing the expected change in earnings per share (EPS) using the model below: ∆EP Sijt−1 ∆EP Sijt = αjtm + β1jtm + β2jtm CRETijtm + εijtm Pijtm−12 Pijtm−24 (4) The expected forecast change is then computed using the following equation: E[∆EP Sijtm ] = [α̂jtm−1 + β̂1jtm−1 ∆EP Sijt−1 + β̂2jtm−1 CRETijtm ] × Pijtm−12 Pijtm−24 (5) The forecast bias (unexpected forecast) is computed as: BiasMijtm = Fijtm − (EP Sijt−1 + E[∆EP Sijtm ]) Abs(M eanF orecastitm ) (6) where subscripts refer to firm i, four digit SIC code j, year t, month m, and Fijtm = the consensus analyst forecast obtained from I/B/E/S, ∆EP Sijt = the annual earnings per share change between the current year and previous year, Pijtm = price per share at the end of month m, CRETijtm = cumulative monthly excess returns in the past 12 month (-12 month to -1 month relative to the current month m). Following Matsumoto (2002), I estimate equation (3) using OLS regression for each fourdigit SIC industry and year and use the lagged estimated coefficients in equation (4) to get the expected forecast. The forecast bias for each firm in each month is then calculated as the difference between the consensus forecast and the expected forecast. Unlike in Matsumoto (2002), who focuses on quarterly earnings and obtains expected quarterly forecasts, my analysis focuses annual forecasts. Consequently, I use change in annual earnings per share instead of change in quarterly earning per share. Similar to Matsumoto (2002), the cumulative returns over the previous 12 months is included to capture additional value-relevant information that analyst might use to estimate earnings. 14 IV. Results The results of the study are presented below. I first examine the relation between stock returns and analysts’ forecast dispersion as in Diether, Malloy, and Scherbina (2002) over the sample period 1986 to 2012. I then study the relation between forecast bias and forecast dispersion, followed by decomposing dispersion in analysts’ forecasts into two components: the bias component and the disagreement component. Removing the bias component allows me to test the true relation between stock returns and a non-contaminated measure of disagreement among analysts. Lastly, I conduct subperiod analyses for the subperiods 1986 to 2002 and 2003 to 2012. A Forecast Dispersion and Stock Returns A.1 Descriptive Statistics Table I presents descriptive statistics for the firms sorted on dispersion in analysts’ earnings forecasts. Following the literature (e.g., Diether, Malloy, and Scherbina (2002) and Barinov (2013)), all firms are sorted into five groups based on dispersion in analysts’ earnings forecasts using NYSE breakpoints. NYSE firms are defined as the firms for which the exchange code listing indicator from the CRSP events file equals 1 at portfolio formation. I report both mean and median summary statistics for each dispersion portfolio (median is reported under the mean). The last column of Table I reports the mean difference between the highest and lowest dispersion quintile and the corresponding t-statistic is reported in the parenthesis. Return is the average one month holding return based on the sorting of analyst forecast dispersion. Dispersion is measured as the standard deviation of all outstanding earnings-pershare forecasts for the current fiscal year scaled by the absolute value of the mean forecast (with zero-mean-forecast observations excluded from the sample). All three bias measures are defined in Section III. MktCap is shares outstanding times price from the CRSP monthly returns file. Market-to-Book is defined as market value of equity divided by book equity plus deferred taxes. Illiquidity is the average ratio of absolute return to dollar volume. The ratio is computed daily and averaged within each firm-year-month. StockPrice is from CRSP monthly file. AnalystFollowing is the number of outstanding forecasts from I/B/E/S file. Stocks with 15 price less than $5 are excluded on the date of portfolio formation. For expositional convenience, Skewness is multiplied by 100 and MktCap is reported in millions. The first row of Table I shows that, consistent with the findings of Diether, Malloy, and Scherbina (2002), the analysts’ dispersion effect survives over a longer period and with a larger sample. The high dispersion stocks earn lower future returns than the low dispersion stocks. The return difference is 0.473% monthly and is statistically significant (with a return of 5.67% annually).16 The results show that all three measures of forecast bias increase as dispersion in analysts’ forecast increases. The differences for all three bias measures between the lowest and the highest dispersion portfolios are highly significant. Figure 1 confirms the positive relationship between analysts’ forecast bias and forecast dispersion, with the highest dispersion stocks having the highest level of all three forecast bias measures. Another observation is that high dispersion stocks are almost four times smaller in size than low dispersion stocks. The size difference between these two groups is 4,275 million, with a t-value of 25.81. This seems to contradict the size premium effect. The average marketto-book shows a U-shape, with the lowest dispersion quintile firms having the highest average market-to-book value. The difference of the Amihud illiquidity ratio between the high dispersion stocks and the low dispersion stocks is 0.152 with a t-value of 12.81. The price impact is 20.4 basis points per $1 million trade for the low dispersion stocks and is 35.6 basis points per $1 million trade for the high dispersion stocks. The average price of high dispersion stocks is much smaller. High dispersion stocks also have a lower average number of analyst following. The highest dispersion quintile firms have an average of 7.7 analysts covering and the lowest dispersion quintile firms have an average of 9.2 analysts following. The difference is statistically significant. Overall, the results in Table I show clear evidence that dispersion in analysts’ forecasts is positively related to forecast bias. High dispersion stocks are also relatively smaller stocks with less information available and have higher forecast bias. Besides, they also have high price impact and low stock price, which makes it relatively difficult to short.17 These results are 16 The monthly return difference reported here is smaller than the monthly return difference reported in Diether, Malloy, and Scherbina (2002) (0.79% monthly). As shown in the subperiod analyses, the smaller return over the longer sample period is mainly driven by the subperiod after 2002. 17 It is worth noting that even though on average, the high dispersion stocks are relatively smaller, they are not typically small firms. This is because analysts usually do not cover small firms, and to be included in my 16 consistent with those of Das, Levine, and Sivaramakrishnan (1998b) who show that analysts make relatively optimistic forecasts when earnings are least predictable in order to obtain better information from managers and with those of Lim (2001) who documents that company size and analyst coverage are inversely related to forecast bias. A.2 Regression Analysis In this section, I employ Fama and French (1996) three factor (FF3) and four factor (FF4) models to examine whether these asset pricing models can capture the return patterns observed in Table I. The momentum factor is included in the regression to capture the the medium-term continuation of returns documented in Jegadeesh and Titman (1993).18 The stocks are sorted monthly into portfolios based on previous month’s dispersion in analysts’ forecasts. Table II reports average monthly risk-adjusted returns on five equal-weighted portfolios formed on dispersion in analysts’ forecasts for the period January 1986 to December 2012. Similar to Diether, Malloy, and Scherbina (2002) and Sadka and Scherbina (2007), the results show that average portfolio alphas decline monotonically with analysts’ forecast dispersion and the risk-adjusted returns of the long-short portfolio (long the low dispersion stocks and short the high dispersion stocks) is 0.7% using FF3 and 0.6% using FF4 Model. The risk-adjusted returns of high-dispersion portfolios are negative and statistically significant. Diether, Malloy, and Scherbina (2002) argue that the negative relation between dispersion and stock returns is consistent with Miller (1977) because high dispersion stocks are overpriced if investors face high short sale constraints. Indeed, the highest dispersion quintile stocks have significantly negative risk-adjusted returns (alpha = -0.41% and t statistic = -3.81 using FF3 and alpha = -0.36% and t statistic = -3.31 using FF4). However, another interesting observation is that the risk-adjusted returns of the low-dispersion portfolio are positive and significant. If short sell constraints are able to explain the negative alpha for the high dispersion quintile stocks, it does not explain the positive alpha for the low dispersion quintile stocks because investors do not face any ‘long constraints’. In fact, about 40% of the returns of the long-short portfolio comes from the long side (alpha = 0.29% and sample, the firm has to have at least two analysts following. 18 I also computed alpha using CAPM Model and the results are very similar. 17 t statistic = 3.32 using FF3 and alpha = 0.24% and t statistic = 2.74 using FF4).19 The summary statistics reported in Table I show that the lowest dispersion stocks have the largest average firm size, higher analyst coverage, and higher stock price, indicating that these firms should have lower risk and more information available. The lower risk is hard to reconcile with the observed positive abnormal returns. Interestingly, the summary statistics reported in Table I also show that the low dispersion stocks have low forecast bias for all three bias measures. The results reported in Table I and Table II suggest that forecast bias could drive the observed negative relation between forecast dispersion and stock returns. In the presence of upward forecast bias, if investors follow the mean forecast which is also upward biased, the stocks are mispriced and would experience low subsequent returns. B Analyst Disagreement and Stock Returns In this section, I first study the relation between forecast bias and forecast dispersion, followed by decomposing forecast dispersion into the bias component and the disagreement component. After removing the bias component from the dispersion in analysts’ forecast, I then study the relation between analyst disagreement and stock returns. B.1 Association between Dispersion and Forecast Bias Table III Panel A presents summary statistics for three bias measures (BiasA, Skewness, and BiasM are defined in Section III). Consistent with prior literature, the results show that on average, analysts’ forecasts are optimistically biased. All three bias measures are positive and statistically significant. Panel B of Table III shows the correlations between the bias measures. The results show that BiasA and BiasM are positively correlated (coefficient=0.163 and p value <.0001). Interestingly, skewness is negatively correlated with the other two bias measures, indicating that the three measures could be seen as complementary indicators of forecast bias. 19 Barinov (2013), Diether, Malloy, and Scherbina (2002) and Sadka and Scherbina (2007) also find significantly positive abnormal returns for the low-dispersion portfolios. More specifically, Barinov (2013) reports a monthly return of 0.383% (t statistic = 2.37) and 0.281% (t statistic = 2.48) for the lowest dispersion quintile portfolio using CAPM model and FF3 factor model, respectively; Diether, Malloy, and Scherbina (2002) report 0.27% (t statistic = 2.14) using FF4 model; Sadka and Scherbina (2007) report 0.36% (t statistic = 2.65) and 0.44% (t statistic = 3.16) for the lowest dispersion portfolio using FF3 and FF4 models, respectively. 18 Panel C of Table III reports results of Fama and MacBeth (1973) cross-sectional regressions of dispersion in analysts’ forecasts on three measures of forecast bias. For each year each month, regression coefficients are obtained from the cross-sectional regression. The regression coefficients are then averaged across months. The regression equation is as follows: Dispersionitm = β̂0 + β̂1 BiasAitm + β̂2 Skewnessitm + β̂3 BiasMitm + εitm (7) To minimize the possibility of a small number of outliers driving the results, I winsorize all variables at 1% and 99%. I also adjust the t-statistics using the Newey and West (1986) correction for heteroskedasticity and autocorrelation. Consistent with hypothesis I, the results show that dispersion in analysts’ forecasts is strongly positively related to all three measures of forecast bias. All coefficients are positive and highly significant. More importantly, the average R2 of the cross-sectional regression is 33% (median R2 = 31.7%), indicating that forecast bias explains approximately one third of the observed forecast dispersion. Although I find a strong positive relation between forecast bias and forecast dispersion, I do not claim a casual effect of forecast bias on forecast dispersion. It is true that when some analysts make biased forecasts, the bias component could drive the dispersion higher. However, the reverse causation is also possible. Jackson (2005) find that analysts could add a higher bias to their estimates when earnings are uncertain, because of less penalty for being wrong, indicating a reverse causation. My objective in this study is not to claim causality between forecast bias and forecast dispersion, but to analyze whether dispersion is a good proxy for divergence of opinion by testing whether dispersion is correlated with bias. More importantly, I try to isolate the analyst disagreement component. For each firm, each year-month, I use the regression residual (the part of dispersion that is not explained by the bias component) as my proxy for disagreement among analysts. In the next section, I test the relation between analyst disagreement and stock returns. B.2 Portfolio Returns Sorted on Analyst Disagreement In this section, I assign stocks to portfolios based on analyst disagreement. Analyst disagreement is the regression residual reported in Table III. Each month, stocks are assigned into five 19 quintiles based on analyst disagreement as of the previous month. Following the literature, stocks with share price lower than five dollars are excluded in order to ensure that the results are not driven by penny stocks. It is important to notice that the purpose of studying the relation between analyst disagreement and stock returns is not to design a strategy for making profits, but to address an important scientific question of whether divergence of opinion proxies for risk. Although the bias measures require ex post data, which makes the trading strategy not implementable, the relation between the disagreement (which is not contaminated by bias) and stock returns provides us important evidence to understand how divergence of opinion is related to stock returns. Panel A of Table IV reports the average monthly portfolio returns and Panel B of Table IV reports the risk-adjusted returns for each portfolio. Again, I use Fama and French (1996) three factor (FF3) and four factor (FF4) models to compute portfolio alphas and betas. In sharp contrast to the results based on dispersion in analysts’ forecast, the results based on analyst disagreement show a strong positive relation between average stock returns and disagreement. The average return increases monotonically with the increases of analyst disagreement. The raw average return for the lowest analyst disagreement quintile is negative 0.39% and the average raw return for the highest analyst disagreement quintile is 1.78%. The difference is 2.17% and is statistically significant at 1% level. Neither FF3 factor model nor FF4 factor model explains the high(low) average return for the lowest(highest) analyst disagreement stocks. The lowest analyst disagreement stocks have significantly negative FF3 and FF4 alphas and the highest analyst disagreement stocks have significantly positive FF3 and FF4 alphas. The evidence that high disagreement stocks earn higher returns and low disagreement stocks earn lower return seems to be consistent with hypothesis 3 (which predicts that analyst disagreement is a proxy for risk), it is premature to draw this conclusion. Analyst disagreement is proxied by a regression residual, so there are two possibilities of why a stock could have a low regression residual: 1), the original dispersion in analysts’ forecasts is low, naturally leading to a low residual; 2), the original dispersion level in analysts’ forecast is high and the forecast bias is also high, thus the regression residual could also be low because a big portion of the dispersion is explained by forecast bias. If the first scenario is true, then the positive relation between disagreement and stock returns is consistent with hypothesis 3. However, if the second scenario 20 is true then we need to exercise caution in interpreting the positive relation because the forecast bias (rather than low disagreement) could cause the low returns to the low disagreement stocks. Table V reports descriptive statistics for quintile portfolios of stocks sorted on analyst disagreement. The results on the high analyst disagreement portfolio is relatively straightforward. Table IV shows that on average, the high disagreement stocks earn higher returns. Table V provides evidence that they are also smaller, less liquid, have lower stock price, and have less analysts following, suggesting a higher level of risk. Thus, the evidence from the high disagreement stock is consistent with the risk explanation. The results on the low analyst disagreement portfolio seem less clear. Two out of three bias measures (BiasM and BiasA) are the highest for the lowest analyst disagreement quintile stocks, indicating that the low returns to this quintile stocks could be driven by forecast bias. To further investigate the relation between analyst disagreement and stocks returns, I perform a two by two sort on dispersion in analysts’ forecasts and analyst disagreement. Each month, stocks are sorted in five groups based on the level of dispersion in analysts’ forecast of the previous month. Stocks in each dispersion group are then sorted into five additional groups based on analyst disagreement. The two-way cuts controlling for the dispersion level provide clearer evidence of the relation between analyst disagreement and stock returns. Table VI Panel A shows that the positive relation between analyst disagreement and stock returns holds for all dispersion quintiles. The return difference between the lowest and highest disagreement quintile portfolios statistically significant for all dispersion quntiles. Panel B of Table VI reports that within each dispersion group, the average dispersion for each disagreement quintile is very similar, indicating that the dispersion level is reasonably controlled. The positive relation between analyst disagreement and stock returns within each dispersion quintile reported in Table VI provides a more convicting evidence that analyst disagreement is positively related to stock returns. B.3 Portfolio Returns Sorted on Size and Analyst Disagreement In this section, I perform a two by two sort on firm size and analyst disagreement. Merton (1987) implies that the disagreement effect should be stronger among small stocks because of incomplete information. Barry and Brown (1984) argue that small firms are riskier because 21 there is less information available. Easley and O’hara (2004) also predict higher returns for firms with limited information. Consistent with the notion that smaller firms are less predictable, the descriptive statistics reported in Table V show that the highest analyst disagreement portfolio contains the smallest firms. If smaller firms have less information available (higher information risk) and analyst disagreement is indeed a proxy for risk, we would expect that the positive relation between analyst disagreement and stock returns to be stronger among smaller firms. Table VII Panel A presents average returns for portfolios sorted on size and analyst disagreement and Panel B reports the average disagreement for each portfolio. Size is computed using shares outstanding times price from the CRSP monthly returns file. Each month, stocks are sorted in five groups based on the firm size of the previous month. Stocks in each size group are then sorted into five additional groups based on analyst disagreement. As expected, Panel B of Table VII shows that the average disagreement is higher for smaller firms, indicating a higher level of divergence of opinion among these stocks. More specifically, the difference between the low disagreement and high disagreement in the smallest size quintile is 0.476, compared to a difference of 0.173 among the largest size group. The difference between high and low disagreement in each size group decreases monotonically as the size increases. Panel A of Table VII reports that the average stock returns experience a similar pattern. The return difference between high disagreement stocks and low disagreement stocks is the largest in the smallest size group. The average return difference decreases monotonically with the increase of firm size, consistent with the explanation that larger firms have more information available and a lower level of analyst disagreement. It is important to notice that even within the largest size group, the relation between analyst disagreement and stock returns is still positive and the return difference is statistically significant, indicating that the positive relation holds for even large stocks. In summary, the results reported in this section show that high analyst disagreement stocks earn higher returns and they also tend to have higher risk. The positive relation between analyst disagreement and future stock returns holds after controlling for the level of dispersion and firm size. These results are consistent with Merton (1987) who predicts divergence of opinion is a proxy for risk and investors requires a higher return by bearing this extra risk. 22 C Portfolio Returns Sorted on Bias In this section, I conduct additional analyses to provide further evidence about the relation between divergence of opinion and stock returns. I have provided evidence that if we sort on dispersion in analysts’ forecast, the relation between dispersion and future stock returns is negative. However, if we decompose dispersion into bias and disagreement, we observe a positive relation between analyst disagreement and future stock returns. These results suggest that the observed negative relation between dispersion and future stock returns is driven by forecast bias. Thus, we expect forecast bias to be negatively associated with future stock returns. Lim (2001) proposes a quadratic-loss utility function to characterize earnings forecasting and show that companies with more uncertain information environments and analysts for whom building management access is more important are predicted to be associated with more biased forecasts. More specifically, Lim (2001) argues that firm size and forecast bias should be inversely related. If analysts make more biased forecasts for small firms, then I expect that the negative relation between forecast bias and future returns to be stronger among small stocks. Table VIII presents average portfolio returns sorted on analysts’ forecast bias and average returns sorted on size and forecast bias. Size is computed by using shares outstanding times price from the CRSP monthly returns file. Forecast bias is the difference between dispersion and the regression residual from Table III. Each month, stocks are sorted in five groups based on the firm size of the previous month. Stocks in each size group are then sorted into five additional groups based on analysts’ forecast bias. Column 2 to 6 reports the average returns for the two way sorts and the last column reports the average returns for one way sort on forecast bias. Consistent with the expectation, the last column of Table VIII Panel A shows that forecast bias is negatively associated with stock returns. The average monthly return decreases monotonically with the increase of forecast bias. The return difference decreases as the size increases. Panel B of Table VIII provides evidence that small stocks indeed have a higher level of forecast bias. The results reported in Table VIII confirm that it is the negative relation between forecast bias and stock returns that drives the negative relation between forecast dispersion and returns reported in Diether, Malloy, and Scherbina (2002). Figure 2 shows that if we simply sort stocks 23 based on forecast dispersion, we observe a negative relation between forecast dispersion and stock returns. However, Figure 3 shows that if we decompose forecast dispersion into bias and disagreement, we observe a positive relation between disagreement and returns and a negative relation between bias and returns. It is important to note that the negative relation between analysts’ forecast bias and future stock returns is distinct from Miller (1977)’s prediction that stocks with higher divergence of opinion earn low future returns. Miller (1977) predicts that when investors disagree with each other, stock prices will reflect a more optimistic valuation if pessimistic investors are kept out of the market by high short-sale costs. However, the negative relation between forecast bias and future returns suggests that investors do not fully consider the bias in analysts’ forecast and are misled by the biased forecasts. Prior studies show that although analysts have incentives to make optimistic forecasts, they also tend to make pessimistic forecasts right before the earnings release so that firms can meet or beat the forecast benchmark, indicating that the bias could be either positive or negative. The negative relation between forecast bias and stock returns here is not caused by divergence of opinion, rather, it reflects that investors do not fully anticipate the forecast bias and overvalue (undervalue) the positive (negative) biased stocks, resulting in the negative relation between bias and stock returns. The evidence provided in this section shows that dispersion in analysts forecasts does not fully reflect the true level of analyst disagreement and is contaminated with a bias component. More importantly, forecast bias is negatively related to stock returns. Thus, the reliance on dispersion in analysts’ forecasts in empirical research may lead to problematic or even incorrect inference. D Subperiod Analyses In this section, I calculate average monthly returns for the portfolio for the subperiods 1986 to 2002 and 2003 to 2012. This is motivated by the fact that regulators implemented a series of reforms to address the behavior of financial analysts issuing biased research.20 Of particular 20 In May 2002, the U.S. SEC approved the amendments to New York Stock Exchange Rule 351 (reporting requirements) and Rule 472 (communications with the public) and the National Association of Securities Dealers new Rule 2711 (Research Analysts and Research Reports). In July 2002, the U.S. Congress passed the SarbanesOxley Act; section 501 of the Act addresses security analysts conflicts of interest. In December 2002, the SEC proposed enforcement actions against ten of the top U.S. investment banks. 24 importance is the Global Settlement, which directly targeted analysts who allegedly issued fraudulent research reports in violation of various sections of the Securities Exchange Act of 1934. On April 28, 2003, the Securities and Exchange Commission (SEC) announced an historic agreement with ten of the largest investment banks.21 This agreement is known as the Global Research Analyst Settlements. It was the culmination of extensive investigations by Congress, New York Attorney General Elliot Spitzer, the SEC, and other regulators, into potential conflicts of interest among security analysts employed by investment banking firms. Alleging numerous incidents where analysts compromised the integrity of their research in order to generate investment banking business, the agreement required the ten firms to pay $1.4 billion.22 In addition to these payments, the investment banks are required to separate their investment banking and research departments and add a number of specific disclosures to their research reports. The banks are also required to contract with no fewer than three independent research firms that will make available independent research to the firm’s customers. Several studies have examined the economic consequences of these reforms. After the reforms, evidence suggests that analysts have been less upwardly biased about their forecasts and recommendations (Kadan, Madureira, Wang, and Zach (2009), Barber, Lehavy, McNichols, and Trueman (2006), Mola and Guidolin (2009), and Guan, Lu, and Wong (2012)). Other studies show that investors have become more skeptical about firms that often meet or beat analysts’ forecasts (Koh, Matsumoto, and Rajgopal (2008) and Keung, Lin, and Shih (2010)). If the negative relation between dispersion in analysts’ forecasts and future stock returns is driven by forecast bias, we would expect the negative relation to decrease after the reforms due to the decrease in forecast bias and (or) the increase of investor skepticism. 21 Those are Bear Stearns & Co. LLC, Salomon Smith Barney, Inc., Credit Suisse First Boston Corp, Deutsche Bank, Goldman Sachs, J.P. Morgan & Co., Lehman Brothers, Inc., Merrill Lynch & Co., Inc, Morgan Stanley, UBS Warburg LLC. 22 The payments include $875 million in penalties and disgorgement of profits, $80 million for investor education, and $432.5 million to fund independent research. 25 D.1 Portfolio Returns Sorted on Size and Forecast Dispersion before and after the Global Settlement Table IX presents average returns for portfolios sorted on size and forecast dispersion before and after the Global Settlement. Panel A of Table IX reports the average returns and average bias for the portfolio before the Global Settlement. The column ‘All Stocks’ reports the results for one way sort on dispersion. The results show that the monthly return difference between high and low dispersion stocks is 0.73% before the Global Settlement. This result is very close to Diether, Malloy, and Scherbina (2002) who find a monthly return difference of 0.79% between high and low dispersion stocks. The results also show that, even before the Global Settlement, the dispersion effect is only significant among the smallest size portfolio (return difference = 0.93% and t-statistic = 3.55), indicating the observed negative relation between dispersion and returns is mainly driven by small stocks. Another observation is that the high dispersion stocks in the smallest size group have high forecast bias. Forecast bias increases as dispersion increases, confirming the positive relation between forecast bias and forecast dispersion. The bias difference between the high and low dispersion stocks in the smallest size group is the highest. The bias difference decreases as firm size increases, consistent with Lim (2001)’s prediction that size is inversely related forecast bias. Panel B of Table IX reports the average returns and average bias after the Global Settlement. Interestingly, the results show that the negative relation between forecast dispersion and stock returns is only observed in the smallest size group and is not statistically significant (return difference = 0.35% and t statistic = 1.37). For the other four size groups, high dispersion stocks actually have higher future returns, compared to the low dispersion stocks. However, the difference is not significant. Consistent with the expectation that forecast bias decreases after the Global Settlement, Panel B of Table IX reports that the average bias difference reduces almost by half after the Global Settlement (the bias difference between high and low dispersion stocks is 0.15 before the Global Settlement and the bias difference is 0.08 after the Global Settlement). The bias difference between the high and low dispersion stocks in the smallest size group reduces by 42%, and the bias difference for other size groups reduces by 54%, 64%, 41%, and 67%, respectively. The evidence provided in Table IX supports the hypothesis that the negative relation between 26 forecast dispersion and stock returns decrease due to decrease in forecast bias. D.2 Portfolio Returns Sorted on Size and Analyst Disagreement before and after the Global Settlement To provide further evidence to support that divergence of opinion proxies for risk, I compute the portfolio returns based on analyst disagreement before and after the Global Settlement. As shown in the previous section, the Global Settlement reduces bias in analysts’ forecast. However, it should not significantly affect analyst disagreement. Analyst disagreement may decrease due to better information available in more recent period, but if disagreement indeed proxies for risk and investors require higher returns to compensate the risk, we would expect the positive relation between analyst disagreement and future stock returns still hold after the Global Settlement. Table X presents average returns for portfolios sorted on size and analyst disagreement before and after the Global Settlement. As before, each month, stocks are sorted in five groups based on the firm size of the previous month. Stocks in each size group are then sorted into five additional groups based on analyst disagreement. Consistent with the expectation, the positive relation between analyst disagreement and stock returns holds for all size quintiles, both before and after the Global Settlement. The disagreement difference reduces only by 12% after the Global Settlement (from 0.339 before the Global Settlement to 0.296 after the Global Settlement), possibly due to more information available after the Global Settlement. The results reported in Table X provide further support that divergence of opinion is positively associated with stock returns. These results are consistent with Merton (1987) who views that divergence of opinion proxies for risk and inconsistent with the prediction of Miller (1977). D.3 Regression Analysis before and after the Global Settlement In this section, I repeat the Fama and MacBeth (1973) Regression of dispersion in analysts’ forecasts on bias measures (reported in Table III) before and after the Global Settlement. Again, for each year each month, regression coefficients are obtained from the cross-sectional regression. The regression coefficients are then averaged across months. If the Global settlement indeed helps to reduce bias in analysts’ forecast, then I expected both the magnitude of the coefficients 27 and the average R2 of the cross-sectional regression to decrease after the Global Settlement. Table XI reports the average coefficients of Fama and MacBeth (1973) cross-sectional regressions before and after the Global Settlement. As expected, except for the BiasM measure, the magnitude of the other two bias measures and average R2 decrease after the Global Settlement. The column “Wilcoxon” reports the one-tail p-values of the two-sample Wilcoxon Rank-sum tests comparing coefficients before and after the Global Settlement. The average R2 before the Global Settlement is 37.5% and the average average R2 after the Global Settlement declines to 25.0%, the Wilcoxon Rank-sum test shows that the difference is highly significant at 1% level. The results reported in Table XI indicate that after the Global Settlement, dispersion in analysts’ forecasts contains a smaller component of bias, although bias is still positively related to forecast dispersion. V. Summary and Conclusions In this paper, I examine how divergence of opinion affects asset prices. My study is motivated by the conflicting empirical findings about the relation between divergence of opinion and stock returns. Prior studies mainly use dispersion in analysts’ forecasts as a proxy for divergence of opinion among investors. However, my results show that forecast dispersion is a poor proxy for divergence of opinion because it is contaminated by forecast bias. I find strong evidence that dispersion in analysts’ forecasts is positively related to forecast bias. More specifically, forecast bias explains approximately one third of forecast dispersion. My results cast serious doubt to the reliance on dispersion in analysts’ forecasts as a proxy in empirical research. Consistent with Diether, Malloy, and Scherbina (2002), I find a negative relation between forecast dispersion and stock returns. However, we should exercise caution in interpreting this negative relation because dispersion is correlated with forecast bias, thus it is not a good proxy for divergence of opinion. To provide cleaner evidence on the relation between divergence of opinion and stock returns, I decompose dispersion in analysts’ forecast into a bias component and a disagreement component. After removing the bias component, I find a strong positive relation between stock 28 returns and disagreement. The positive relation is most pronounced among small stocks but holds for all size groups. My findings also show that forecast bias is negatively associated with stock returns. One potential explanation is that investors do not fully anticipate forecast bias and overvalue stocks with positive bias and undervalue stocks with negative bias, resulting a negative relation between forecast bias and stock returns. Moreover, my findings suggest that the empirical results of Diether, Malloy, and Scherbina (2002) that show a negative relation between dispersion and future stock returns are driven by forecast bias. Finally, I document that the negative relation between dispersion and stock returns disappears after the Global Settlement because of the decrease in forecast bias. However, the positive relation between analyst disagreement and stock returns is still highly significant after the Global Settlement. The evidence provided in this paper is consistent with Merton (1987) who predicts that divergence of opinion should be viewed as a source of risk. 29 Appendix A The Relation Between Forecast Bias and Forecast Dispersion In this appendix, I develop a simple model to intuitively illustrate the relation between forecast bias and forecast dispersion. Consider a firm for which N financial analysts forecast annual earnings for the coming year. Assume the earnings that analysts forecast is Y and Y is normally distributed with mean Ȳ and standard deviation Yε . Case I: All analysts make independent and unbiased earnings forecasts for this firm. The forecast made by analyst j is defined as: Fj = Ȳ + εj (8) where Ȳ is common information available to all analysts and εj is analyst j’s personal opinion or private information about the earnings of the coming year. The error terms εj are assumed independently and normally distributed with a mean of zero. In this case, the mean forecast would be Ȳ and the standard deviation of observed analysts’ forecasts is: N Stdunbiased = 1 X 2 εj = V ar(εj ) N −1 (9) j=1 Assuming that analysts making unbiased forecasts, then the observed dispersion completely captures the level of disagreement among analysts. However, as suggested in the literature, if analysts have incentives to make biased forecasts, then both the observed average forecast and dispersion in the forecasts contain a bias component. Case II: Assume that not all analysts make independent and unbiased earnings forecasts for this firm and some analysts introduce a bias in their forecasts. The forecast made by analyst j is defined as: Fj = Ȳ + εj + bj (10) where bj is the bias component introduced by analyst j. If the analyst makes a unbiased forecast, then bj equals zero. In this case, the observed mean forecast is: µbiased = N 1 X (Ȳ + εj + bj ) = Ȳ + b̄ N (11) j=1 and the observed dispersion in analysts’ forecasts is: Stdbiased = N N j=1 j=1 1 X 1 X (Fj − µbiased )2 = (εj +bj −b̄)2 = V ar(bj )+V ar(εj )+2Cov(bj , εj ) N −1 N −1 (12) The difference between biased dispersion and unbiased dispersion is: 30 Stdbiased − Stdunbiased = V ar(bj ) + 2Cov(bj , εj ) (13) The above equation shows that the dispersion is the sum of three components if at least some of the analysts introduce bias in their forecasts: variance of analysts true personal opinions, variance of the biases and the covariance of biases and personal opinions. It is not likely that the variance of bias is zero unless all analysts making biased forecasts by exactly the same amount. 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NYSE firms are defined as the firms for which the exchange code listing indicator from the CRSP events file equals 1 at portfolio formation. Dispersion is measured as the standard deviation of all outstanding earnings-per-share forecasts for the current fiscal year scaled by the absolute value of the mean forecast (with zero-mean-forecast observations excluded from the sample). BiasA is defined as the difference between the consensus forecast and the actual annual earnings, scaled by the absolute value of the mean forecast. Skewness is defined as the difference between mean and the median forecast scaled by the absolute value of the mean forecast. BiasM is defined as the difference between the consensus forecast and the expected forecast defined in Table I, scaled by the absolute value of the mean forecast. For expositional convenience, Skewness is multiplied by 100. 37 % Portfolio Returns Sorted on Dispersion in Analysts' Forecasts 1.20 1.10 1.00 0.90 0.80 0.70 0.60 Port 1 Port 2 Port 3 Port 4 Port 5 Portfolio Returns Sorted on Dispersion Figure 2: Mean Portfolio Returns Sorted on Dispersion in Analysts’ Forecasts This figure illustrates the negative relation between stock returns and dispersion in analysts’ forecasts. All firms are sorted into five groups based on dispersion in analyst earnings forecasts using NYSE breakpoints. Then the average one month holding return based on the sorting of analyst forecast dispersion is computed. NYSE firms are defined as the firms for which the exchange code listing indicator from the CRSP events file equals 1 at portfolio formation. Dispersion is measured as the standard deviation of all outstanding earnings-per-share forecasts for the current fiscal year scaled by the absolute value of the mean forecast (with zero-mean-forecast observations excluded from the sample). Port 1 is the portfolio that has the lowest average dispersion in analysts’ forecasts and Port 5 is the portfolio that has the highest average dispersion in analysts’ forecasts. 38 % Portfolios Returns Sorted on Analyst Disagreement and Forecast Bias 2.40 1.90 1.40 0.90 0.40 -0.10 Port 1 Port 2 Port 3 Port 4 Port 5 -0.60 Portfolio Returns Sorted on Disagreement Portfolio Returns Sorted on Bias Figure 3: Mean Portfolio Returns Sorted on Analyst Disagreement and Forecast Bias This figure illustrates the relation between stock returns and analyst disagreement and forecast bias. All firms are sorted into five groups based on analyst disagreement (forecast bias) using NYSE breakpoints. Then the average one month holding return based on the sorting of analyst disagreement (forecast bias) is computed. NYSE firms are defined as the firms for which the exchange code listing indicator from the CRSP events file equals 1 at portfolio formation. Analyst disagreement is the regression residual reported in Table III. Analyst forecast bias is the difference between dispersion and analyst disagreement. Dispersion is measured as the standard deviation of all outstanding earnings-per-share forecasts for the current fiscal year scaled by the absolute value of the mean forecast (with zero-mean-forecast observations excluded from the sample). Port 1 is the portfolio that has the lowest average analyst disagreement (forecast bias) and Port 5 is the portfolio that has the highest average analyst disagreement (forecast bias). 39 Table I: Descriptive Statistics for Quintile Portfolios of Firms Sorted on Dispersion in Analysts’ Forecasts This table presents summary statistics for firms in different dispersion quintile portfolios. Median value is reported under the mean. The last column reports the mean difference between the highest and lowest quintile and the corresponding t-statistic is reported in the parenthesis. All firms are sorted into five groups based on dispersion in analysts’ earnings forecasts using NYSE breakpoints. NYSE firms are defined as the firms for which the exchange code listing indicator from the CRSP events file equals 1 at portfolio formation. Return is the average one month holding return based on the sorting of analyst forecast dispersion. Dispersion is measured as the standard deviation of all outstanding earnings-per-share forecasts for the current fiscal year scaled by the absolute value of the mean forecast (with zero-mean-forecast observations excluded from the sample). BiasA is defined as the difference between the consensus forecast and the actual annual earnings, scaled by the absolute value of the mean forecast. Skewness is defined as the difference between mean and the median forecast scaled by the absolute value of the mean forecast. Following Matsumoto (2002), BiasM is the difference of the consensus forecast and the expected forecast which is constructed using the model below: ∆EP Sijt /Pijtm−12 = αjtm + β1jtm × (∆EP Sijt−1 /Pijtm−24 ) + β2jtm × CRETijtm + εijtm (14) , and BiasM is computed using the following equations: E[∆EP Sijtm ] = [α̂jtm−1 + β̂1jtm−1 × ∆EP Sijt−1 /Pijtm−24 } + β̂2jtm−1 × CRETijtm ] × Pijtm−12 BiasMijtm = (Fijtm − (EP Sijt−1 + E[∆EP Sijtm ]))/Abs(M eanF orecast)itm (15) (16) Following Matsumoto (2002), equation (14) is estimated using OLS regression for each four-digit SIC industry and year and the lagged estimated coefficients are used in equation (15) to get the expected forecast. The forecast bias for each firm in each month is then calculated as the difference between the consensus forecast and the expected forecast, scaled by the absolute value of the mean forecast. MktCap is shares outstanding times price from the CRSP monthly returns file. Market-to-Book is defined as market value of equity divided by book equity plus deferred taxes. Illiquidity is the average ratio of absolute return to dollar volume. The ratio is computed daily and averaged within each firm-year-month. StockPrice is from CRSP monthly file. AnalystFollowing is the number of outstanding forecasts from I/B/E/S file. Stocks with price less than $5 are excluded on the date of portfolio formation. For expositional convenience, Skewness is multiplied by 100 and MktCap is reported in millions. Return Dispersion BiasA Skewness BiasM MktCap Market-to-Book Illiquidity StockPrice AnalystFollowing Low Disp Disp2 Disp3 Disp4 High Disp High-Low 1.167 1.801 0.010 0.008 0.060 0.052 -0.002 -0.003 0.052 0.036 5,890 5,026 3.430 3.446 0.204 0.150 50.783 33.459 9.255 8.998 1.020 1.733 0.022 0.020 0.055 0.044 -0.003 -0.009 0.059 0.036 4,536 4,478 3.241 3.175 0.153 0.099 47.239 32.014 10.012 9.643 1.029 1.575 0.039 0.033 0.075 0.065 -0.001 -0.010 0.092 0.067 3,405 3,256 3.066 2.967 0.184 0.125 57.720 29.416 9.258 8.942 0.945 1.641 0.074 0.064 0.131 0.108 0.024 0.010 0.185 0.150 2,917 2,652 3.042 2.857 0.250 0.164 61.712 26.170 8.560 8.450 0.694 1.487 0.444 0.407 0.715 0.580 0.628 0.571 0.770 0.573 1,615 1,783 3.831 3.331 0.356 0.254 29.580 18.214 7.749 7.685 -0.473 (-2.3) 0.434 (46.55) 0.655 (25.92) 0.630 (10.17) 0.718 (14.60) -4,275 (-25.81) 0.402 (3.83) 0.152 (12.81) -21.204 (-4.94) -1.505 (-27.02) 40 41 Observations R-squared Constant MOM HML SMB Rm-Rf (2) 324 0.889 0.289*** (3.32) 0.917*** (34.16) 0.377*** (8.26) 0.216*** (5.05) 324 0.893 0.928*** (37.23) 0.396*** (8.08) 0.226*** (5.64) 0.065** (2.41) 0.244*** (2.74) Port1 (Low Disp) (1) 324 0.928 0.093 (1.28) (4) 324 0.928 0.994*** (44.56) 0.415*** (8.78) 0.238*** (6.24) -0.001 (-0.03) 0.094 (1.23) Port2 0.994*** (46.66) 0.416*** (8.69) 0.238*** (6.26) (3) 324 0.938 0.075 (1.12) (6) 324 0.938 1.055*** (39.72) 0.478*** (7.13) 0.231*** (5.17) -0.017 (-0.55) 0.088 (1.23) Port3 1.059*** (45.38) 0.483*** (6.84) 0.234*** (5.43) (5) 324 0.930 -0.084 (-1.12) (8) 324 0.930 1.164*** (30.75) 0.540*** (5.85) 0.280*** (4.56) -0.031 (-0.76) -0.062 (-0.80) Port4 1.169*** (36.25) 0.549*** (5.54) 0.285*** (5.10) (7) 324 0.880 -0.412*** (-3.81) (10) 324 0.882 1.292*** (20.97) 0.676*** (4.41) 0.318*** (3.25) -0.069 (-1.03) -0.363*** (-3.31) Port5 1.304*** (25.35) 0.696*** (4.25) 0.328*** (3.72) (9) (12) 324 0.332 0.701*** (4.59) -0.387*** (-6.56) -0.318** (-2.03) -0.113 (-1.14) 324 0.360 -0.364*** (-5.52) -0.280* (-1.81) -0.092 (-0.87) 0.133* (1.82) 0.607*** (4.00) Port1-Port5 (11) This table reports monthly risk-adjusted returns for portfolios sorted by dispersion in analysts’ forecasts. Dispersion is defined as the standard deviation of analysts’ current-fiscal-year annual earnings per share forecasts scaled by the absolute value of the mean earnings forecast (with zero-mean-forecast observations excluded from the sample). The Fama-French three factor and four factor (Fama-French three factors plus a momentum factor) models are used for measuring the alphas and betas. The stocks are sorted monthly into portfolios based on previous month’s dispersion in analysts’ forecasts. The sample period is from January 1986 to December 2012. Stocks with price less than five dollars are excluded on the portfolio formation date. Standard errors are adjusted for heteroskedasticity and autocorrelation. T-statistics are reported in parentheses. *, **, *** indicate significance at the 10%, 5%, and 1% levels, respectively. Table II: Time-series Tests of Three- and Four-Factor Models for Portfolios Based on Analysts’ Forecast Dispersion Table III: Fama and MacBeth (1973) Regression of Dispersion in Analysts’ Forecasts on Forecast Bias This table reports the relation between forecast bias and forecast dispersion. Panel A reports descriptive statistics on three bias measures. Panel B reports correlation of bias measures and Panel C results of Fama and MacBeth (1973) cross-sectional regressions of dispersion in analysts’ forecasts on three measures of forecast bias. Dispersionitm = β̂0 + β̂1 BiasAitm + β̂2 Skewnessitm + β̂3 BiasMitm + εitm (17) For each year each month, regression coefficients are obtained from the cross-sectional regression. The regression coefficients are then averaged across months. Average R2 of the cross-sectional regressions are reported. Dispersion is defined as the standard deviation of analysts’ current-fiscal-year annual earnings per share forecasts scaled by the absolute value of the mean earnings forecast (with zero-mean-forecast observations excluded from the sample). BiasA is defined as the difference between the consensus forecast and the actual annual earnings, scaled by the absolute value of the mean forecast. Skewness is defined as the difference between mean and the median forecast scaled by the absolute value of the mean forecast. BiasM is defined as the difference between the consensus forecast and the expected forecast defined in Table I, scaled by the absolute value of the mean forecast. The sample period is from January 1986 to December 2012. The t-statistics reported in Panel C use the Newey and West (1986) correction for heteroskedasticity and autocorrelation. Panel A: Descriptive Statistics on Bias Measures BiasA skewness BiasM Mean Standard Deviation 1st Quartile Median 3rd Quartile t 0.270 0.001 0.295 1.281 0.059 2.587 -0.044 -0.005 -0.209 0.016 0.000 0.063 0.200 0.005 0.387 53.80 3.05 24.71 Panel B: Correlations between Bias Measures BiasA BiasA Skewness BiasM 1 -0.003 0.004 0.163 <.0001 1 -0.020 <.0001 Skewness BiasM 1 Panel C: Fama and MacBeth (1973) Regression Coefficients Intercept BiasA Skewness BiasM R-squared Mean t-statistic 1st Quartile Median 3rd Quartile 0.093 0.134 0.197 0.027 0.330 24.57 28.05 2.92 10.98 42.80 0.073 0.101 -0.406 0.007 0.247 0.085 0.136 0.310 0.026 0.317 0.105 0.164 0.802 0.046 0.397 42 43 Observations R-squared Constant MOM HML SMB Rm-Rf 324 0.896 -1.402*** (-14.33) 1.099*** (35.79) 0.505*** (5.51) 0.328*** (6.18) -0.390 -1.24 0.872 3.29 Disagree2 1.325 4.83 Disagree3 1.610 5.35 Disagree4 1.786 4.88 High Disagree (2) 324 0.898 1.091*** (31.74) 0.492*** (5.56) 0.321*** (5.67) -0.045 (-1.17) -1.370*** (-14.03) 324 0.902 -0.052 (-0.63) (4) 324 0.902 0.937*** (37.87) 0.384*** (8.79) 0.298*** (6.70) -0.021 (-0.84) -0.037 (-0.44) Port2 0.940*** (39.45) 0.390*** (9.70) 0.301*** (6.66) (3) 324 0.924 0.382*** (5.15) (6) 324 0.924 0.981*** (43.03) 0.406*** (8.51) 0.291*** (7.10) -0.010 (-0.42) 0.389*** (4.96) Port3 0.983*** (44.66) 0.409*** (8.68) 0.292*** (7.09) (5) 324 0.932 0.614*** (8.21) (8) 324 0.933 1.072*** (41.10) 0.450*** (7.55) 0.300*** (6.32) -0.037 (-1.18) 0.640*** (8.11) Port4 1.078*** (47.35) 0.461*** (7.49) 0.305*** (6.61) (7) (10) 2.176 15.85 High-Low 324 0.889 0.688*** (6.72) 1.258*** (27.81) 0.618*** (4.24) 0.351*** (4.45) 324 0.890 1.251*** (23.46) 0.607*** (4.49) 0.345*** (4.00) -0.038 (-0.66) 0.715*** (6.72) High Disagree (9) Panel B: FF3 and FF4 Models for Portfolios Based on Analyst Disagreement Low Disagree (1) Return t-statistic Low Disagree Panel A: Portfolio Returns by Analyst Disagreement (12) 324 0.120 2.090*** (15.55) 0.159*** (3.99) 0.112 (1.35) 0.023 (0.32) 324 0.120 0.160*** (3.87) 0.115 (1.47) 0.024 (0.33) 0.007 (0.15) 2.085*** (15.02) Port5-Port1 (11) This table reports stock returns for portfolios sorted by analyst disagreement. Analyst disagreement is the regression residual reported in Table III. Panel A reports the average raw returns for portfolios sorted by analyst agreement and Panel B reports risk-adjusted returns for each portfolio. The Fama-French three factor and four factor (Fama-French three factors plus a momentum factor) models are used for measuring the alphas and betas. The stocks are sorted monthly into portfolios based on previous month’s analyst disagreement. The sample period is from January 1986 to December 2012. Stocks with price less than five dollars are excluded on the portfolio formation date. Standard errors are adjusted for heteroskedasticity and autocorrelation. T-statistics are reported in parentheses. *, **, *** indicate significance at the 10%, 5%, and 1% levels, respectively. Table IV: Analyst Disagreement and Stock Returns Table V: Descriptive Statistics for Quintile Portfolios of Firms Sorted on Analyst Disagreement This table presents summary statistics for firms in different analyst disagreement quintiles. Median value is reported under the mean. All firms are sorted into five groups based on analyst disagreement using NYSE breakpoints. NYSE firms are defined as the firms for which the exchange code listing indicator from the CRSP events file equals 1 at portfolio formation. The last column reports the mean difference between the highest and lowest quintile and the corresponding t-statistic. Analyst Disagreement is regression residual reported in Table III. Dispersion is measured as the standard deviation of all outstanding earnings-per-share forecasts for the current fiscal year scaled by the absolute value of the mean forecast (with zero-mean-forecast observations excluded from the sample). BiasA is defined as the difference between the consensus forecast and the actual annual earnings, scaled by the absolute value of the mean forecast. Skewness is defined as the difference between mean and the median forecast scaled by the absolute value of the mean forecast. BiasM is defined as the difference between the consensus forecast and the expected forecast defined in Table I, scaled by the absolute value of the mean forecast. MktCap is shares outstanding times price from the CRSP monthly returns file. Market-to-Book is defined as market value of equity divided by book equity plus deferred taxes. Illiquidity is the average ratio of absolute return to dollar volume. The ratio is computed daily and averaged within each firm-year-month. StockPrice is from CRSP monthly file. AnalystFollowing is the number of outstanding forecasts from I/B/E/S file. Stocks with price less than $5 are excluded on the data of portfolio formation. For expositional convenience, Skewness is multiplied by 100 and MktCap is reported in millions. Dispersion BiasA Skewness BiasM Mktcap Market-to-book Illiquidity StockPrice AnalystFollowing Low Disagree Disagree2 Disagree3 Disagree4 High Disagree High-Low 0.057 0.052 0.573 0.521 0.149 0.117 0.776 0.694 4,066 3,671 3.102 2.943 0.244 0.176 48.074 29.713 8.908 8.600 0.027 0.024 0.061 0.050 0.058 0.052 0.133 0.132 5,732 4,923 3.133 3.081 0.127 0.096 50.275 33.802 10.768 10.415 0.039 0.034 0.038 0.027 0.046 0.035 0.058 0.055 4,475 3,952 3.024 2.868 0.147 0.099 64.659 31.745 10.284 9.801 0.067 0.060 0.033 0.021 0.079 0.043 0.013 -0.002 3,600 3,637 2.916 2.819 0.169 0.129 66.240 28.522 9.660 9.218 0.398 0.369 0.292 0.218 0.452 0.312 0.204 0.128 2,147 2,027 3.481 3.004 0.277 0.212 39.296 21.753 8.575 8.392 0.341 (44.2) -0.280 (-34.97) 0.304 (6.06) -0.573 (-15.05) -1,919 (-17.77) 0.380 (4.40) 0.033 (2.86) -8.777 (-1.78) -0.333 (-6.60) 44 Table VI: Portfolio Returns Sorted on Dispersion in Analysts’ Forecasts and Analyst Disagreement This table reports two-way sorts on dispersion and analyst disagreement. Panel A reports average returns of portfolios and Panel B reports average dispersion in analysts’ forecasts. Dispersion is measured as the standard deviation of all outstanding earnings-per-share forecasts for the current fiscal year scaled by the absolute value of the mean forecast (with zero-mean-forecast observations excluded from the sample). Analyst disagreement is the regression residual reported in Table III. Each month, stocks are sorted in five groups based on the level of dispersion in analysts’ forecast of the previous month. Stocks in each dispersion group are then sorted into five additional groups based on analyst disagreement for the previous month. The sample period is from January 1986 to December 2012. Stocks with price less than five dollars are excluded on the portfolio formation date. Panel A: Mean Returns Dispersion Quintiles Disagreement Quintiles Low Disp Disp2 Disp3 Disp4 High Disp Low Disagree Disagree2 Disagree3 Disagree4 High Disagree 0.278 0.877 1.181 1.517 2.227 -0.300 0.525 1.112 1.633 2.347 -0.472 0.529 1.228 1.532 2.703 -0.805 0.604 1.258 1.633 2.810 -1.193 0.522 1.382 1.833 1.657 High Disagree-Low Disagree t-statistic 1.949 14.77 2.648 18.01 3.175 18.84 3.615 20.99 2.850 18.11 Panel B: Mean Dispersion in Analysts’ Forecasts Dispersion Quintiles Disagreement Quintiles Low Disagree Disagree2 Disagree3 Disagree4 High Disagree Low Disp Disp2 Disp3 Disp4 High Disp 0.028 0.015 0.015 0.017 0.021 0.035 0.027 0.026 0.026 0.031 0.054 0.042 0.041 0.042 0.048 0.099 0.073 0.073 0.078 0.089 0.317 0.189 0.215 0.320 0.966 45 Table VII: Portfolio Returns Sorted on Size and Analyst Disagreement This table reports two-way sorts on size and analyst disagreement. Panel A reports average returns of portfolios. Panel B reports average analyst disagreement. Size is shares outstanding times price from the CRSP monthly returns file. Analyst disagreement is the regression residual reported in Table III. Each month, stocks are sorted in five groups based on the level of size of the previous month. Stocks in each size group are then sorted into five additional groups based on analyst disagreement for the previous month. The sample period is from January 1986 to December 2012. Stocks with price less than five dollars are excluded on the portfolio formation date. Panel A: Mean Returns Size Quintiles Disagreement Quintiles Small Size2 Size3 Size4 Large Low Disagree Disagree2 Disagree3 Disagree4 High Disagree -1.076 1.042 1.623 1.810 1.869 -0.423 0.848 1.552 1.614 2.031 -0.049 0.897 1.156 1.560 1.724 0.214 0.765 1.128 1.305 1.546 0.446 0.781 0.953 1.104 1.361 High Disagree-Low Disagree t-statistic 2.944 18.04 2.453 11.63 1.774 9.02 1.332 6.95 0.916 5.41 Panel B: Mean Analyst Disagreement Size Quintiles Disagreement Quintiles Low Disagree Disagree2 Disagree3 Disagree4 High Disagree High Disagree-Low Disagree Small Size2 Size3 Size4 Large -0.137 -0.071 -0.046 0.007 0.339 0.476 -0.112 -0.076 -0.057 -0.023 0.229 0.341 -0.108 -0.079 -0.063 -0.036 0.174 0.283 -0.108 -0.079 -0.067 -0.043 0.142 0.250 -0.108 -0.083 -0.072 -0.051 0.064 0.173 46 Table VIII: Portfolio Returns Sorted on Size and Forecast Bias This table reports average portfolio returns (Panel A) and forecast bias (Panel B). Column 2 to 6 reports two-way sorts on size and analyst forecast bias and Column 7 reports a one-way sort on forecast bias. Size is shares outstanding times price from the CRSP monthly returns file. Analyst forecast bias is the difference between dispersion and analyst disagreement. Dispersion is measured as the standard deviation of all outstanding earnings-per-share forecasts for the current fiscal year scaled by the absolute value of the mean forecast (with zero-mean-forecast observations excluded from the sample). Analyst disagreement is regression residual reported in Table III. Each month, stocks are sorted in five groups based on the level of size of the previous month. Stocks in each size group are then sorted into five additional groups based on forecast bias for the previous month. The sample period is from January 1986 to December 2012. Stocks with price less than five dollars are excluded on the portfolio formation date. Panel A: Mean Returns Size Quintiles Bias Quintiles Small Size2 Size3 Size4 Large All Stocks Low Bias Bias2 Bias3 Bias4 High Bias 3.185 1.941 0.962 0.000 -1.264 2.680 1.716 1.054 0.340 -0.461 2.430 1.537 0.932 0.418 -0.211 2.110 1.454 0.832 0.385 0.121 1.827 1.228 0.859 0.425 0.254 2.692 1.679 1.029 0.452 -0.534 High Bias-Low Bias t-statistic -4.450 -25.99 -3.141 -17.74 -2.641 -15.94 -1.988 -11.02 -1.573 -9.32 -3.225 -24.25 Panel B: Mean Forecast Bias Size Quintiles Bias Quintiles Low Bias Bias2 Bias3 Bias4 High Bias Small Size2 Size3 Size4 Large All Stocks 0.063 0.099 0.116 0.151 0.436 0.063 0.094 0.106 0.123 0.274 0.064 0.094 0.103 0.117 0.225 0.066 0.094 0.101 0.114 0.211 0.070 0.094 0.100 0.110 0.174 0.065 0.095 0.104 0.121 0.282 47 48 -0.932 -3.55 HighDisp-LowDisp t-statistic -0.500 -1.45 -0.466 -1.41 -0.380 -1.17 Mean Returns Size Quintiles Size2 Size3 Size4 1.306 1.191 1.162 1.104 0.946 1.041 1.047 0.884 1.107 0.888 1.077 1.008 0.806 0.725 0.782 -0.489 -1.49 Large 1.301 1.020 0.933 1.043 0.812 -0.723 -2.59 All Stocks 1.322 1.062 1.072 0.918 0.599 0.255 Small 0.116 0.119 0.133 0.171 0.370 0.157 0.104 0.079 Mean Bias Size Quintiles Size2 Size3 Size4 0.102 0.104 0.100 0.105 0.101 0.101 0.109 0.104 0.101 0.124 0.112 0.108 0.259 0.208 0.179 Small 1.036 1.068 1.059 0.774 0.691 -0.345 -1.37 Low Disp Disp2 Disp3 Disp4 High Disp HighDisp-LowDisp t-statistic Dispersion Quintiles 0.259 0.75 0.261 0.82 0.168 0.52 0.089 0.25 Mean Returns Size Quintiles Size2 Size3 Size4 Large 0.818 1.002 0.807 0.757 1.121 1.059 0.881 0.687 0.961 0.886 0.880 0.813 0.946 1.009 1.059 0.786 1.077 1.263 0.975 0.846 -0.048 -0.17 All Stocks 0.904 0.948 0.956 0.992 0.857 0.149 Small 0.114 0.115 0.121 0.137 0.263 0.073 0.037 0.046 Mean Bias Size Quintiles Size2 Size3 Size4 0.106 0.105 0.105 0.106 0.105 0.105 0.108 0.107 0.107 0.114 0.106 0.109 0.179 0.143 0.151 Panel B: Portfolio Returns Sorted on Size and Dispersion after the Global Settlements Small 1.348 1.133 0.955 0.656 0.416 Low Disp Disp2 Disp3 Disp4 High Disp Dispersion Quintiles Panel A: Portfolio Returns Sorted on Size and Dispersion before the Global Settlement 0.017 Large 0.105 0.104 0.104 0.106 0.122 0.051 Large 0.099 0.099 0.101 0.103 0.150 0.080 All Stocks 0.108 0.107 0.110 0.117 0.188 0.150 All Stocks 0.106 0.105 0.110 0.124 0.256 This table reports portfolio returns sorted on size and dispersion in analysts’ forecasts before (Panel A) and after (Panel B) the Global Settlement. The column ‘All Stocks’ reports the results for one way sort on dispersion. Size is shares outstanding times price from the CRSP monthly returns file. Dispersion is measured as the standard deviation of all outstanding earnings-per-share forecasts for the current fiscal year scaled by the absolute value of the mean forecast (with zero-mean-forecast observations excluded from the sample). For the two-way sorts, each month, stocks are sorted in five groups based on the level of size of the previous month. Stocks in each size group are then sorted into five additional groups based on dispersion in analysts’ forecasts for the previous month. The sample period for Panel A is from January 1986 to December 2002 and the sample period for Panel B is from January 2003 to December 2012. Stocks with price less than five dollars are excluded on the portfolio formation date. Table IX: Portfolio Returns Sorted on Size and Dispersion before and after the Global Settlement 49 3.288 14.94 High Disagree-Low Disagree t-statistic 2.477 8.70 1.776 6.53 1.347 5.28 Mean Returns Size Quintiles Size2 Size3 Size4 -0.432 -0.131 0.260 0.925 0.917 0.807 1.718 1.268 1.203 1.743 1.597 1.323 2.045 1.646 1.606 0.829 3.81 Large 0.590 0.838 1.062 1.239 1.419 2.302 12.68 All Stocks -0.437 0.957 1.435 1.731 1.864 0.493 Small -0.146 -0.069 -0.042 0.013 0.347 0.359 0.310 0.264 Small -0.770 0.911 1.442 1.571 1.590 2.361 10.53 Low Disagree Disagree2 Disagree3 Disagree4 High Disagree High Disagree-Low Disagree t-statistic Disagreement Quintiles 2.413 8.00 Size Size2 -0.406 0.718 1.270 1.395 2.006 1.770 6.75 1.307 4.62 1.062 3.96 Mean Returns Quintiles Size3 Size4 Large 0.089 0.137 0.202 0.862 0.694 0.683 0.964 0.999 0.769 1.497 1.274 0.873 1.858 1.444 1.264 1.963 9.57 All Stocks -0.311 0.727 1.136 1.406 1.652 0.448 Small -0.123 -0.075 -0.051 -0.004 0.325 0.309 0.236 0.225 0.145 Mean Disagreement Size Quintiles Size2 Size3 Size4 Large -0.109 -0.105 -0.109 -0.104 -0.083 -0.086 -0.086 -0.091 -0.066 -0.072 -0.078 -0.082 -0.034 -0.054 -0.057 -0.064 0.201 0.131 0.116 0.041 0.189 Mean Disagreement Size Quintiles Size2 Size3 Size4 Large -0.114 -0.111 -0.107 -0.111 -0.072 -0.074 -0.075 -0.078 -0.052 -0.057 -0.061 -0.066 -0.016 -0.025 -0.035 -0.044 0.245 0.200 0.157 0.078 Panel B: Portfolio Returns Sorted on Size and Analyst Disagreement after the Global Settlements Small -1.255 1.118 1.730 1.952 2.032 Low Disagree Disagree2 Disagree3 Disagree4 High Disagree Disagreement Quintiles Panel A: Portfolio Returns Sorted on Size and Analyst Disagreement before the Global Settlement 0.296 All Stocks -0.112 -0.084 -0.071 -0.042 0.185 0.339 All Stocks -0.122 -0.073 -0.057 -0.024 0.217 This table reports portfolio returns sorted on size and analyst disagreement before (Panel A) and after (Panel B) the Global Settlement. The column ‘All Stocks’ reports the results for one way sort on analyst disagreement. Size is shares outstanding times price from the CRSP monthly returns file. Analyst disagreement is the regression residual reported in Table III. For the two-way sorts, each month, stocks are sorted in five groups based on the level of size of the previous month. Stocks in each size group are then sorted into five additional groups based on analyst disagreement for the previous month. The sample period for Panel A is from January 1986 to December 2002 and the sample period for Panel B is from January 2003 to December 2012. Stocks with price less than five dollars are excluded on the portfolio formation date. Table X: Portfolio Returns Sorted on Size and Analyst Disagreement before and after the Global Settlement Table XI: Fama and MacBeth (1973) Regression of Dispersion in Analysts’ Forecasts on Forecast Bias before and after the Global Settlement This table reports the relation between forecast bias and forecast dispersion before and after the Global Settlement. The sample period before the Global Settlement is from January 1986 to December 2002 and the sample period after the Global Settlement is from January 2003 to December 2012. The average coefficients of Fama and MacBeth (1973) cross-sectional regressions of dispersion in analysts’ forecasts on three bias measures are reported. Dispersionitm = β̂0 + β̂1 BiasAitm + β̂2 Skewnessitm + β̂3 BiasMitm + εitm (18) For each year each month, regression coefficients are obtained from the cross-sectional regression. The regression coefficients are then averaged across months. Average R2 of the cross-sectional regressions are reported. Dispersion is defined as the standard deviation of analysts’ current-fiscal-year annual earnings per share forecasts scaled by the absolute value of the mean earnings forecast (with zero-mean-forecast observations excluded from the sample). BiasA is defined as the difference between the consensus forecast and the actual annual earnings, scaled by the absolute value of the mean forecast. Skewness is defined as the difference between mean and the median forecast scaled by the absolute value of the mean forecast. BiasM is defined as the difference between the consensus forecast and the expected forecast defined in Table I, scaled by the absolute value of the mean forecast. The t-statistics use the Newey and West (1986) correction for heteroskedasticity and autocorrelation and the column “Wilcoxon” reports one-tail p-values of the Wilcoxon Rank-sum tests. Intercept BiasA Skewness BiasM R-squared Before the Global Settlement After the Glonal Settlement Difference Coefficients 0.088 0.151 0.241 0.027 0.375 Coefficients 0.103 0.104 0.117 0.029 0.250 Wilcoxon 0.152 0.000 0.033 0.167 0.000 t-statistic 31.48 29.97 2.64 8.51 40.57 50 t-statistic 11.39 14.86 1.29 6.99 24.05