Download Analysts` Forecast Dispersion, Analysts` Forecast Bias and Stock

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. Empirical evidence also suggest that the covariance between bias and personal opinion
is positive. Chen and Jiang (2006) document that analysts overweight their private information
more when issuing forecasts conveying more favorable information, and overweight less private
information when issuing less favorable forecasts, indicating a positive correlation between the
favorableness of the opinion and the magnitude of the bias.
31
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Mean Forecast Bias in Each Analysts' Forecast Dispersion
Quintile
0.80
0.60
0.40
BiasA
Skewness
BiasM
0.20
0.00
Low Disp
Disp2
Disp3
Disp4
High Disp
-0.20
Figure 1: Mean Forecast Bias and Mean Dispersion in Analysts’ Forecast
This figure illustrates the relation between analysts’ forecast bias and dispersion in analysts’ forecasts. All firms
are sorted into five groups based on dispersion in analyst earnings forecasts using NYSE breakpoints. Mean bias
is computed for each of the dispersion quintile. 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