Download Further Evidence on the Relation between Analysts` Forecast

Further Evidence on the Relation between
Analysts’ Forecast Dispersion and Stock Returns
Orie E. Barron
Associate Professor
Pennsylvania State University
Smeal College of Business Administration
University Park, PA 16802-1912
814-863-3230
Mary Stanford
Associate Professor, Nobel Faculty Fellow
Texas Christian University
M.J. Neeley School of Business
Fort Worth, TX 76129
Yong Yu
Pennsylvania State University
Smeal College of Business Administration
University Park, PA 16802-1912
September 29, 2005
(This is a preliminary revised draft of a manuscript requiring a major revision for publication. Please
do not quote without permission)
We gratefully acknowledge the contribution of I/B/E/S International Inc. for providing earnings per
share forecast data, available through the Institutional Brokers' Estimate System. These data have been
provided as part of a broad academic program to encourage earnings expectation research.
For their helpful comments we thank Richard Schnieble and workshop participants at the CUNY Baruch
and Penn State University.
ABSTRACT
Previous research finds a negative association between the level of dispersion in analysts’
earnings forecasts and subsequent stock returns. This finding can be consistent with either unsystematic
uncertainty that is priced positively because it increases a firm’s option value (Johnson, 2004) or
overpricing due to a lack` of consensus among investors that limits the short sales of the most
pessimistic traders (Diether et al, 2002). We use the Barron et al. (1998) framework to measure the two
theoretical variables that can both cause dispersion and cause it to be priced. These are (1) uncertainty
or (2) a lack of consensus (i.e., a relatively high level of private information among analysts). A high
level of uncertainty may be priced positively or negatively depending on whether it is systematic or
unsystematic. In contrast, the private information that causes a lack of consensus is likely to be priced
negatively because it reflects information asymmetry and a higher cost of capital (Botosan, Plumlee, and
Xie 2004).
The evidence we report helps distinguish between the different explanations for forecast
dispersion and what drives its relation to stock returns. We find that (1) changes in dispersion capture
primarily changes in consensus (or changes in information asymmetry) whereas the level of dispersion
captures primarily the level of unsystematic uncertainty (and not the level of information asymmetry),
and (2) the uncertainty in forecast dispersion is negatively associated with future stock returns, but the
lack of consensus (or information asymmetry) is positively associated with future stock returns. These
findings support Johnson’s option value explanation but do not support Diether et al.’s overpricing
explanation because lower levels of consensus do not lead to lower future returns.
In addition, our evidence that levels and changes in dispersion reflect fundamentally different
constructs reconciles the evidence on changes in dispersion presented by L’Her and Suret (1996) with
the conclusions of Diether et al.(2002) and Johnson (2004), both of which are inconsistent with L’Her
and Suret’s argument that forecast dispersion represents uncertainty that is priced negatively. We find
that increases in forecast dispersion coincide with more negative stock returns because there is less
consensus (and thus more information asymmetry that adversely affects firms’ cost of capital).
1. Introduction
Prior research posits opposing explanations for the empirically documented
relation between dispersion in analysts’ forecasts and stock returns. Diether et al. (2002)
argue that the negative relation between dispersion levels and future returns is due to
overpricing resulting from investor disagreement and limits on short sales that lead to
optimistic current stock prices and lower future stock returns. Johnson (2004) presents a
model suggesting that this negative relation may also be due to the uncertainty (or risk)
reflected in dispersion which, although unsystematic in nature, increases the option value
of the firm and leads to lower future returns. Further clouding the issue, Deither et al.’s
arguments suggest a positive relation between changes in dispersion and
contemporaneous stock returns. This is contrary to evidence presented by L’Her and
Suret (1996) that increases in forecast dispersion are negatively associated with stock
returns.
Using the Barron, Kim, Lim, and Stevens (1998) (hereafter BKLS) decomposition
of dispersion into uncertainty and lack of consensus we are able to distinguish between
these opposing explanations. Our evidence provides increased empirical support for
Johnson’s conclusion that the level of dispersion analysts’ forecasts reflects unsystematic
risk (uncertainty). In addition, consistent with L’Her and Suret’s (1996) findings, we find
a negative relation between changes in dispersions and stock returns, which we show is
likely caused by increased information asymmetry between informed and uninformed
investors reflected in a decrease in consensus.
Diether et al. (2002) argue that when investors disagree, limitations on trading,
e.g., short sale limitations, result in prices that reflect the views of optimists but not
2
pessimists. This suggests a negative relation between dispersion levels and future stock
returns when the overpricing is corrected and a positive relation between changes in
dispersions and stock returns. In addition, based on tests explaining dispersion with
several measures of risk Diether et al. conclude “…our results strongly reject the
interpretation of dispersion in analysts’ forecasts as a measure of risk.” (p 2115).
By contrast, Johnson (2004) provides a pricing model in which the negative
relation between dispersion levels and stock returns may be due to a form of information
risk (uncertainty) where dispersion reflects nonsystematic risk (idiosyncratic uncertainty)
that increases the option value of the firm and lowers expected future returns. However,
as the author notes, his model is not inconsistent with Diether et al.’s overpricing
argument, i.e., both may explain the relation between dispersion and returns.
We begin by empirically separating dispersion into its theoretical components.
Theoretically, in order for dispersion in analysts’ forecasts to exist there must be both (1)
some uncertainty regarding future performance and (2) some lack of consensus due to the
diversity of private information (Barry and Jennings 1992; Abarbanell, Lanen, and
Verrecchia 1995; Barron, et al. 1998). Thus, it is unclear the degree to which forecast
dispersion reflects uncertainty or a lack of consensus. Finding that dispersion levels
reflect uncertainty rather than consensus would provide some support for Johnson’s
(2004) hypothesis that dispersion levels reflect information risk. Finding that changes in
dispersion reflect changes in consensus would serve to increase understanding of the
findings of L’Her and Suret (1996) and to reconcile these findings with those of Johnson
(2004) and Diether et al. (2002).
3
We provide evidence on whether dispersion in analysts’ forecasts reflects
uncertainty or a lack of consensus using the BKLS empirical proxies for these theoretical
constructs. We examine both the level of dispersion prior to an earnings announcement
and the change in dispersion around earnings announcements.1 We find that the level of
pre-announcement forecast dispersion reflects primarily uncertainty rather than a lack of
consensus. By contrast, changes in forecast dispersion reflect primarily changes in
consensus rather than changes in uncertainty.
Our finding that levels of dispersion reflect uncertainty is consistent with
Johnson’s (2004) conclusion that the negative relation between dispersion levels and
future stock returns is driven by uncertainty. In further analysis, we examine market data
to determine whether the level of forecast dispersion reflects primarily systematic or
unsystematic uncertainty about future performance. We show that higher levels
dispersion are associated with higher idiosyncratic risk and lower future returns. This
combined evidence provides support for Johnson’s argument that the negative relation
between future returns and dispersion is due to investors’ unsystematic uncertainty and
not overpricing.
Although this evidence lends support to Johnson’s theory it does not completely
rule out Deither et al.’s (2002) conclusion that the negative relation results from
overpricing due to investor disagreement. However, Deither et al.’s argument that
dispersion is negatively associated with future returns implies a positive (negative)
relation between consensus (lack of consensus) and future stock returns because
dispersion increases as consensus (lack of consensus) decreases (increases). In contrast
1
Some prior studies measure the change in dispersion from year to year. We do not investigate these types
of changes in forecast dispersion.
4
to the positive relation implied by the overpricing argument, we find a negative (positive)
relation between consensus (lack of consensus) and future returns. This finding also
increases understanding of L’Her and Suret’s (1996) evidence that increases in dispersion
coincide with decreases in stock returns. Specifically, we show that increases in forecast
dispersion coincide with decreases in consensus that reflect information asymmetry
between informed and uninformed investors and that increases in dispersion coincides
with decreases in stock returns. Because low consensus stocks have high information
asymmetry, this is also consistent with the positive relation between information
asymmetry and the cost of equity capital hypothesized in Amihud and Mendelson (1986
and 1989), King et al. (1990), Diamond and Verrecchia (1991), among others, and
documented in previous studies (see Barron et al. 2005 for further discussion).
Uninformed investors demand a return premium to compensate for their risk of trading
with privately informed investors. This risk is not diversifiable since uninformed
investors are always at a disadvantage relative to informed investors (O’Hara 2003) and
demand to be compensated with higher expected future returns.
This evidence is of interest to accounting and finance researchers wishing to
understand the relation between forecasts dispersion and stock returns. For example,
understanding that levels and changes in dispersion reflect different theoretical constructs
can help researchers choose the appropriate proxy. In addition, to the extent that
dispersion is easily measured by investors while the BKLS measures are more complex
and cannot be measured ex-ante our evidence allows investors as well as researchers to
more precisely interpret the meaning of levels versus changes in forecast dispersion.2
2
Determining what forecast dispersion reflects the most is important to for methodological reasons. For
example, over fifty empirical studies published in selected top tier accounting and finance journals use
5
The discussion proceeds as follows. Section 2 describes our empirical proxies
and research design as it relates to the strength of the associations between both levels of
and changes in forecast dispersion, analysts’ uncertainty, and analysts’ lack of consensus
(or diversity of information). Section 3 investigates the relation between the two
components of dispersion levels and future stock returns then provides evidence on the
relation between dispersion levels and both systematic and unsystematic risk. Section 4
reconciles our evidence on changes in dispersion with prior research. Section 5 discusses
robustness checks on the BKLS measures and alternate specifications. Finally, section 6
contains our conclusions.
2. Forecast Dispersion: Earnings Uncertainty or Lack of Consensus
BKLS show how one can measure the theoretical constructs uncertainty and consensus
by exploiting the fact that forecast dispersion and error in analysts’ forecasts reflect these
theoretical constructs differently. The intuition underlying their results stems from the
fact that forecast dispersion and error differentially reflect error in analysts' common and
idiosyncratic information. The BKLS empirical proxies for consensus and uncertainty
are:
DISPERSION = V(1-)
(1)
CONSENSUS = ρ = 1-D/V
(2)
Where:
D=
dispersion in analysts’ forecasts, i.e., the sample variance of the
individual forecasts (FCi ) around the mean forecast ( F C ),
n
measured as
 ( FC
i 1
i
 F C ) 2 (n  1) , where n is the number of
forecasts.
analyst forecast dispersion as an empirical proxy for various firm characteristics. Appendix 1 lists papers
published in The Accounting Review (15 papers), Journal of Accounting Research (11 papers), Journal of
Accounting and Economics (7 papers), Journal of Finance (4 papers) , Journal of Financial Economics (5
papers), Review of Accounting Studies (5 papers), Contemporary Accounting Research (7 papers), and
Journal of Financial and Quantitative Analysis (3 papers) for the period 1990 to 2004.
6
V=
Uncertainty, i.e., the mean of the squared differences between
individual analysts’ forecasts (FCi ) and reported earnings per
n
share (EPS) measured as  ( FCi  EPS ) 2 n .3
i 1
From equation (1), dispersion is the product of uncertainty (V) and lack of consensus (1ρ). Thus, forecast dispersion is simultaneously determined by both uncertainty and lack
of consensus.
To understand the intuition for these measures it is helpful to consider the extreme
examples where CONSENSUS is zero or one and a large number of forecasts (n) exist as
described in Barron, Harris, and Stanford (2005). With a large number of forecast, the
difference between the mean forecast ( F C ) and realized earnings per share (EPS) only
reflects error due to common information because idiosyncratic error is averaged out of
the mean. When the mean forecast equals realized earnings CONSENSUS equals zero
and D/V = 1. When this is true, the BKLS model suggests that forecasts are based
entirely on private information because all forecast error is idiosyncratic. The difference
between individual forecasts (FCi) and the mean forecast ( F C ) reflects error due to
private information. When all individual forecasts are exactly equal to the mean forecast
CONSENSUS equals one and D/V = 0. When this is true, the BKLS model suggests that
forecasts are based entirely on common information because all forecast error is
common. Consistent with V reflecting overall uncertainty, if all forecasts exactly equal
realized earnings then V is equal to zero, consistent with perfectly accurate information,
i.e., no uncertainty.
3
The relations we report between dispersion, consensus, and uncertainty are not merely mechaincal.
Theoretically, which component, V or (1-ρ), has more explainatory power for dispersion is, ex ante, not
clear (Barron et al. 1998). Also see Section 3 for empirical evidence this relation is not merely mechanical.
7
We investigate both the level of dispersion prior to earnings announcements and
the change in dispersion estimated around earnings announcements and nonannouncement dates. Specifically, we estimate the following models and use a Vuong test
to compare the explanatory power of equation (3) and (4) to determine whether the level
of dispersion in analysts’ forecasts is more highly associated with lack of consensus or
uncertainty prior to the earnings announcement. Similarly, comparing the explanatory
power of equations (5) and (6) tests whether the change in dispersion around earnings
announcements is better explained by changes in consensus or changes in uncertainty.
Log(D/P) = b0 +bLog(V/P) + 


Log(D/P) = a0 +aLog(1-CONSENSUS)+ 





Δlog(D/P) d0 +d ΔLog(V/P) + 



Δlog(D/P) c0 +c ΔLog(1-CONSENSUS) + 



where
Log(D/P) = natural log of dispersion D scaled by the stock price P. D is preannouncement dispersion in analysts’ forecasts measured as the variance of analysts’
earnings forecasts issued within 30 days prior to the earnings announcement;
Log(V/P) = natural log of overall uncertainty V scaled by the stock price P. V is preannouncement uncertainty estimated with equation (2) using forecasts issued within 30
days prior to the earnings announcement
Log(1-CONSENSUS) = natural log of one minus pre-announcement consensus (i.e.,
lack of consensus) estimated with equation (1) using forecasts issued within 30
days prior to the earnings announcement
Δlog(V/P) = change in natural log of overall uncertainty V scaled by the stock price
P, estimated with equation (1) using forecasts issued within the 30-day preannouncement window and a 30-day post-announcement window.
Δlog(D/P) = change in the log-transformed dispersion D scaled by the stock price P,
measured as the variance of the annual earnings forecast issued within the 30-day preannouncement window and a 30-day post-announcement window;
8
Δlog(1-CONSENSUS) = change in the log-transformed lack of consensus (1 minus
consensus), where consensus is estimated with equation (1) using forecasts issued within
the 30-day pre-announcement window and a 30-day post-announcement window;
Reported results scale dispersion (D) and uncertainty (V) by the stock price (P) measured
at the end of the prior fiscal quarter. We take the natural log of the variables for two
reasons: first, BKLS demonstrates that dispersion is equal to the product of uncertainty
and lack of consensus (i.e. D=V(1- CONSENSUS)). Thus, it is natural to make this
relation linear by taking the natural log; the second purpose is to mitigate skewness
problems with dispersion and uncertainty. 4
2.1. Sample Selection and Empirical Results
The sample consists of quarterly and annual earnings per share forecasts from
1986 to 2003. Analysts’ earnings forecasts and actual earnings per share data are obtained
from Institutional Brokers Estimate (I/B/E/S).5 Earnings announcement dates and other
financial data are obtained from the quarterly COMPUSTAT Primary, Supplementary, or
Tertiary file. We investigate one-quarter-ahead forecast and two-year-ahead forecasts.
The one-quarter-ahead sample consists of quarterly forecasts measured within 30 days
before the current quarterly earnings announcement. The two-year-ahead sample consists
of annual earnings forecasts measured within 30 days before the prior annual earnings
announcement.6 To be included in the pre-announcement (levels) sample, two or more
individual analysts must have issued forecasts within a 30-day pre-announcement
window. To be included in the change sample two or more individual analysts must have
4
Our results and inferences are the same when we do not scale by price and when we do not log transform
the variables.
5
IBES forecasts and actual data are adjusted historically for stock splits and rounded to two decimals in the
summary file and four decimals in the detail file. This rounding will introduce measurement errors into our
main variables, e.g., artificially reducing forecast dispersion (see Payne and Thomas 2003 for a detailed
discussion). To avoid this problem, we conduct our analyses on the raw forecast data, unadjusted for stock
splits.
6
All results and inferences are the same for a one-year-ahead sample. We report the two-year sample to
emphasize short-run versus long-run uncertainty and consensus.
9
issued forecasts within a 30-day pre-announcement window and these same analysts must
have revised their forecast within a 30-day post-announcement window.
Table 1 reports descriptive statistics and tests of the determinants of the level
analysts’ forecast dispersion measured for one-quarter- and two-year-ahead forecasts.
From panel A, the quarterly forecast sample consist of relatively large firms with a mean
(median) market value of equity $6,073 ($1,450) million. The annual forecast sample,
although still large, exhibits a slightly wider range of firm size with a mean (median)
market value of equity of $5,667 ($1,288) million (Panel B). With respect to the variables
of interest, both dispersion and uncertainty are less at the median for the quarterly
forecast sample (0.001 and 0.002) than for the annual forecast sample (0.011 and 0.157).
This is consistent with dispersion and uncertainty increasing with the forecast time
horizon. Note that the standard deviation of the log-transformed uncertainty (D/V) is
much smaller than the raw variable, e.g., 2.516 versus 85.535 for the quarterly forecasts.
Thus, in addition to being the correct empirical specification given the multiplicative
relation between dispersion, consensus and uncertainty suggested by BKLS, the log
transformation corrects for the fact that uncertainty is not naturally scaled. Finally,
consensus (), which ranges from zero to one, is lower for the quarterly sample, 0.530
versus 0.912, at the median. This is consistent with analysts’ relying on common, i.e.,
public information for longer range forecasts.
In Table 1, Vuong’s (1989) Z-statistic tests which independent variable exhibits a
greater association with the dependent variable. We use the procedures outlined in
Dechow (1994) to compute the Z-statistic; a positive (negative) Z-statistic indicates that
lack of consensus (uncertainty) has a greater association with the dependent variable.
10
Panel A reports results of estimating equations (3) and (4) for the one-quarter ahead
sample. As expected, the coefficients on pre-announcement consensus (measured as lack
of consensus, 1-) and preannouncement uncertainty are both significantly positive. The
adjusted R2 for the model with preannouncement uncertainty is 55.30% while the
adjusted R2 for the model with prior consensus is 3.99%. The Vuong’s Z-statistic is 68.92 ( = 0.001) indicating that the level of preannouncement uncertainty explains more
of the variation in preannouncement dispersion levels than variation in consensus for
quarterly forecasts. Panel B leads to the same conclusion for the annual forecast sample.
Specifically, the adjusted R2 for the model with preannouncement uncertainty is 38.04%
while the adjusted R2 for the model with prior lack of consensus is 7.20%. The Vuong’s
Z-statistic is -29.13 ( = 0.001) indicating that preannouncement uncertainty levels
explain more of the variation in preannouncement dispersion levels than variation in
consensus for both long- and short-range forecasts.
Table 2 reports descriptive statistics and tests of the determinants of changes in analysts’
forecast dispersion around both quarterly and annual earnings announcements. The
requirement that the same analysts that provided a forecast prior to an earnings
announcement revise that forecast within 30 days after the announcement results in a
much smaller sample of relatively large firms. Panel A describes the sample of quarterly
earnings forecast updates around quarterly earnings announcements (n=10,150).
Dispersion, uncertainty and consensus all decline after quarterly earnings announcements
at both the mean and median. Panels B describe the sample of annual earnings forecast
updates around annual earnings announcements (n=4,493). Consistent with the quarterly
results, dispersion, uncertainty and consensus all decline after annual earnings
announcements at both the mean and median. The decrease in consensus is consistent
with that reported by Barron, Byard, and Kim (2002). They argue that consensus
declines because analysts have incentives to use their own private knowledge to create
private information (or private interpretations) from earnings announcements (see also
Kim and Verrecchia 1994; 1997 and Fischer and Verrecchia 1998).
Panel A of Table 2 also reports the results of estimating equations (5) and (6) for
quarterly earnings announcement. As expected, the coefficients on both changes in
uncertainty and change in lack of consensus are significantly positive. The adjusted R2
for the model with change in uncertainty is 14.21% while the adjusted R2 for the model
with change in lack of consensus is 51.79%. The Vuong Z-statistic is 23.07 ( = 0.001),
11
indicating that changes in analysts’ lack of consensus explain more of the variation in
changes in dispersion in analysts’ forecasts than changes in uncertainty. Panel B reports
the results of estimating equations (5) and (6) for the annual earnings announcement. The
results are consistent with those in Panel A with changes in lack of consensus explaining
approximately 74% of changes in dispersion.
Overall, the evidence indicates that pre-announcement levels of dispersion in
analysts’ forecasts proxy much more for pre-announcement uncertainty levels than for
pre-announcement levels of lack of consensus, which supports the arguments in previous
studies (e.g., Barron and Stuerke 1998; Johnson 2004). In contrast, changes in forecast
dispersion around earnings announcements dates proxy much more for changes in
analysts’ lack consensus than for changes in uncertainty, which supports the conjectures
in Ziebart (1990).
Whether cross-sectional variation in forecast dispersion levels is driven primarily
by cross-sectional variation in uncertainty levels or variation in consensus levels was an
empirical issue that, from an ex-ante perspective, could have gone either way. Ex-post,
the descriptive evidence that cross-sectional variation in uncertainty is relatively high
compared to cross-sectional variation in consensus largely explains why cross-sectional
variation in forecast dispersion levels is mostly attributable to variation in uncertainty
levels. For example, in panel A of table 1 cross sectional variation measured by the
standard deviations of log transformed dispersion (D), uncertainty (V), and lack of
consensus (1-) is 2.214, 2.516, and 1.717, respectively. Cross-sectional variation in
annual forecast sample is similar for dispersion and uncertainty but somewhat higher for
lack of consensus.
From an ex-ante perspective it was reasonable to expect that the evidence might
differ for dispersion changes versus levels. This is due to the nature of the information
analysts’ acquire over time. As a forecasted event approaches, analysts acquire
12
information that is either common (public) or private in nature (perhaps because it is
complementary to publicly conveyed information). Although both types of information
reduce uncertainty, private information decreases consensus while common information
increases consensus. This suggests that uncertainty levels trend steadily downward over
time as the forecast event approaches due to the arrival of both types of information. By
contrast, consensus levels can increase for some firms and decrease for others depending
on the nature of the information analysts acquire during a particular time period. As a
result, cross-sectional variation in changes in uncertainty may be quite small compared to
cross-sectional variation in changes in consensus. Descriptive statistics presented in table
2 are consistent with this. In panel A of table 2, the cross-sectional variation in changes in
uncertainty (standard deviation) is 1.391which is lower than the cross sectional variation
in changes in lack of consensus, 1.855. To underscore these statistics we conducted
supplementary analyses of the correlation between the relative position of individual
firms’ uncertainty within the distribution of all firms’ uncertainty before and after
earnings announcements. This correlation is 0.93, which suggests that around earnings
announcements changes in the relative positions of firms’ uncertainty is minimal. In
contrast this same correlation for lack of consensus is 0.37, suggesting there is a lot of
jumbling in firms’ consensus around earnings announcements. Thus, the cross sectional
variation in both changes in analysts’ lack of consensus and changes in dispersion are
greater around earnings announcements than the variation in changes in uncertainty. This
suggests why changes in consensus explain most of the cross-sectional variation in
changes in dispersion.
13
3. Evidence on Forecast Dispersion Levels: Revisiting Johnson (2004) and
Diether et al. (2002)
Evidence in the previous section shows that the level of dispersion in analysts’
forecasts primarily reflects uncertainty. In this section we present three sets of analyses.
First, in order to differentiate the two competing explanations in Diether et al. (2002) and
Johnson (2004) we examine whether the negative relation between dispersion levels and
stock returns is due to uncertainty or lack of consensus. We do this by separately
examining the relation between returns and uncertainty and returns and consensus. Next
we examine the relation between returns and each component of dispersion after
controlling for the other. Finally, we investigate whether the uncertainty reflected in
dispersion levels is systematic (non-diversifiable) or unsystematic (diversifiable).
3.1 Are stock returns associated with uncertainty or consensus?
In this section we replicate the analysis in Diether et al. (2002) after replacing
dispersion with it components, uncertainty and lack of consensus. Diether et al. argue that
investor disagreement and costly arbitrage lead to overpricing because current stock
prices are optimistic and that when this is corrected prices fall resulting in a negative
association between dispersions and future returns. In contrast, Johnson (2004) poses an
alternate explanation for the negative relation between forecasts dispersion and returns.
He suggests that dispersion reflects information uncertainty (also referred to as parameter
risk) that is idiosyncratic in nature and that this risk is priced because it increases the
option value of the firm. Our evidence that the level of dispersion primarily reflects
uncertainty is consistent with Johnson’s arguments. However, we cannot, ex ante, rule
14
out the possibility that the much smaller explanatory power of the consensus component
drives the negative relation between dispersion and stock returns.
In order to replicate Diether et al. (2002)’s we follow their sample selection and
portfolio analyses.7 We obtain stock returns from CRSP monthly stock file, and analysts’
annual forecasts from the unadjusted IBES database. Each month we assign stocks to 5
quintiles based on dispersion in the previous month. Dispersion is defined as the standard
deviation of earnings forecast scaled by the absolute value of the mean earnings forecast.
If the mean earnings forecast is zero, then the stock is assigned to the highest dispersion
category. We calculate the monthly portfolio return for each quintile as the equalweighted average of the returns of all the stocks in the portfolio. In untabulated analyses,
the monthly return on the low minus high dispersion strategy is 0.74 percent (t=2.94),
which is very similar to the 0.79 percent (t=2.88) reported in Diether et al. (2002). We
also find results very similar to Diether et al. (2002) when we assign stocks based on size
and then dispersion.
To investigate whether uncertainty or consensus drives these results we repeat
Diether et al.’s (2002) portfolio analyses replacing dispersion first with uncertainty (V)
and then with CONSENSUS. We scale uncertainty by the square of the mean forecast. 8
Table 3 reports the results of replicating Deither et al.’s analysis substituting uncertainty
for forecast dispersion. Consistent with Diether et al., we find a strong negative relation
between uncertainty and future stock return. The monthly return on the low minus high
7
Following Diether et al. (2002) the sample period is from January 1983 until December 2000.
We choose this scalar to be consistent with BKLS model: D=V(1-ρ). Note that BKLS dispersion D is the
variance of analysts’ forecasts. The dispersion defined in the portfolio tests is the standard deviation of
analysts’ forecasts scaled by the absolute value of the mean forecast to be consistenet with Diether et al.
(2002). This defintion is equavalent to the BKLS dispersion D scaled by the square of the mean forecast
(which gives the same portfolio ranks). Therefore, we scale uncertainty V also by the square of the mean
forecast. The results are similar if uncertain V is scaled by the absolute value of the mean forecast.
8
15
uncertainty strategy is 1.87 percent per month. Also consistent with finding in Deither et
al., this strategy is more profitable among smaller stocks with a return of 3.65 percent.
Table 4 reports the results of replicating Deither et al.’s analysis substituting
CONSENSUS for forecast dispersion. Note that the analyses reported in Tables 1 and 2
explained dispersion with uncertainty and lack of consensus (1-) because dispersion
increases as lack of consensus increases. In Table 4 we use consensus ( because the
negative relation between dispersion levels and future returns implies a positive
(negative) relation between consensus (lack of consensus) and future stock returns
because dispersion increases as consensus (lack of consensus) decreases (increases). In
contrast to the positive relation implied by the overpricing argument in Diether et al., we
find a negative (positive) relation between consensus (lack of consensus) and future
returns. On average the stocks in the lowest consensus quintile outperform those in the
highest consensus quintile by 1.33 percent per month.9
3.2 Further evidence on Dispersion Levels and Uncertainty
It is possible that negative (positive) relation between consensus (lack of
consensus) and future returns documented in Table 4 might be driven by the positive
correlation between consensus and uncertainty. To investigate this, in Panel A of Table 5,
each month we assign stocks to one of five quintiles based on uncertainty in the previous
month. Then we rank stocks in each uncertainty quintile into five further quintiles based
on consensus in the previous month. After controlling uncertainty, there is a negative
relation between consensus and future returns. In Panel B, each month we assign stocks
to one of five quintiles based on consensus in the previous month. Then we rank stocks in
9
We repeat our analyses in Table3 and 4 by controlling for market-to-book ratios and obtain identical
results.
16
each consensus quintile into five further quintiles based on uncertainty in the previous
month. The negative relation between uncertainty and future stock returns still holds after
controlling for consensus.
To provide further evidence in addition to the portfolio tests in Table 5, we
estimate Fama-MacBeth regressions to test the relation between one dispersion
component and future stock return after controlling for the other:
Re tt 1   0  1 * Rank _ Vt   2 * Rank _(1  t )   3 * Rank _ Sizet
In each month, all the stocks are assigned a quintile rank (1-5) based on uncertainty (V),
lack of consensus (1-ρ) and size independently. The cross section of monthly stock
returns ( Re t t 1 ) is regressed on the quintile ranks of uncertainty ( Rank _ Vt ) and
consensus ( Rank _(1  t ) ) and size ( Rank _ Size t ) which are measured as of the
previous month. Fama and Macbeth (1973) cross-sectional regressions are run every
month for totally 216 continuous months from January 1983 till December 2000. Tstatistics in parentheses are calculated using the coefficients from monthly regressions
and also adjusted for autocorrelation using Newey-West standard errors. Table 6 reports
the results with and without controlling for size. The coefficient on lack of consensus
(disagreement) is significantly positive after controlling for uncertainty, which is
consistent with the portfolio results in Table 4 where returns decrease as consensus
increases.
In summary, interpretation of the evidence of a negative relation between
dispersions levels and stock returns is clouded by the fact that dispersion reflects both
uncertainty and a lack of consensus. We show that this negative relation is driven by
uncertainty rather than lack of consensus. This is an important finding because it allows
17
us to begin to differentiate between the two explanations for this relation suggested in the
finance literature. Evidence in Table 3 supports Johnson’s argument that the negative
relation between dispersion and future returns is due to investors’ uncertainty. Evidence
in Table 4 of a positive relation between lack of consensus and stock returns is
inconsistent with Diether etl al.’s overpricing explanation for the negative relation
between dispersion and returns. Evidence in Tables 5 and 6 strengthens our conclusion
that the level of dispersion mainly reflects the level of uncertainty and that this
uncertainty drives the relation between dispersion and returns.
3.3 Does forecast dispersion reflect systematic or unsystematic uncertainty/risk?
To provide further evidence on the relation between analysts’ forecast dispersion
and firm risk, we explore how firms’ systematic risk and idiosyncratic risk explains the
variation in dispersion. We use market beta as a proxy for systematic risk and mean
squared errors (MSE) - from the estimation of the market model as a proxy for
idiosyncratic risk. Dispersion is measured as before, defined as the ratio of the standard
deviation of analysts’ forecasts to the absolute value of the mean forecast for each firm
month. We estimate the market model to obtain beta and mean squared errors using a
minimum of 36 month and a maximum of 60 months of return data prior to each firm
month when we measure forecast dispersion. To mitigate the high skewness problem in
dispersion and mean squared errors, we log transform these two variables in our
regression. Our sample covers all the firm months with valid earnings forecasts from
IBES and monthly return data from CRSP and consists of 382,789 firm-month
observations.
18
In Table 7, Panel A reports descriptive statistics for the variables used in the
regression and Panel B reports correlations between these variables. The variables,
Dispersion and MSE, are highly skewed and the log transformation avoids this problem.
Dispersion is positively correlated with both beta and MSE (p-values < 0.001),
suggesting that both systematic and idiosyncratic firm risks may be determinants of
dispersion. In Panel B, we regress log-transformed dispersion on beta and logtransformed MSE separately (Model 1 and 2) and then on both variables together (Model
3). We find that beta, MSE and both variables explain 2.5%, 5.8% and 5.9% of the
variation in dispersion respectively. The small change in adjusted R2, from 5.8% to
5.9%, when MSE is added to the model with beta indicates that systematic risk has very
little incremental explanatory power for the variation in dispersion.10
Finally, we perform a robustness check using a rank regression framework. Each
month, we rank all the firms into deciles based on dispersion, beta and MSE
independently. We regress decile ranks of dispersion on decile ranks of beta and MSE.
The results are reported in Panel C. Again, we find that beta provides almost no
incremental explanatory power for dispersion over MSE.
In summary, the evidence in Tables 3 through 6 suggests that the negative relation
between dispersion levels and stock returns documented in prior studies reflects a relation
between uncertainty levels and returns rather than a lack of consensus. The evidence in
Table 7 suggests that this uncertainty is idiosyncratic firm risk rather than systematic risk.
Both results support the conclusions in Johnson (2004).
10
To further gauge the economic significance of the relation between dispersions and MSE, we determined
that one standard deviation increase in MSE from the median MSE is associated with the increase in
dispersion by 27%.
19
4. Reconciling evidence on Changes versus Levels of Dispersion
This section reconciles our evidence on changes in dispersion with prior research.
In addition, because we find that changes in dispersion reflect analysts’ lack of consensus
rather than uncertainty we discuss the link between consensus and stock prices.
L’Her and Suret (1996) document a negative relation between changes in
dispersion and contemporaneous stock returns (as dispersion increases stock returns
decrease). L’Her and Suret interpret this as evidence that increases in dispersion reflects
increased uncertainty which is priced negatively. We replicated their finding in a
supplementary analysis. Recall that our primary results show that changes in dispersion
mainly reflect changes in analysts’ lack of consensus. Thus, it is not surprising that our
supplementary results reveal that increased lack of consensus is (significantly) negatively
associated with contemporaneous stock returns.
To the extent that increases in lack of consensus reflect increases in information
asymmetry risk that is not diversifiable, uninformed investors demand a return premium
for their risk of trading with privately informed investors (O’Hara 2003). In other words,
increases in dispersion coincide with negative stock returns because increased dispersion
reflects increased information asymmetry that adversely affects firm cost of capital. This
is consistent with other evidence on the relation between consensus, trading volume and
cost of capital. Barron, Harris, Stanford (2005) document a negative relation between
changes in consensus and trading volume; as consensus decreases, and lack of consensus
increases, trading volume increases. Because consensus declines when private
information increases, this trading volume suggests that some investors develop private
20
information that increases information asymmetry (See Holthausen and Verrecchia’s
1990).
Finally, our evidence in Panel A Table 4 indicates that low levels of consensus are
associated with higher returns, i.e., lack of consensus is paid a premium. This is
consistent with evidence in Botosan, Plumlee, and Xie (2004). They show that the level
of analysts’ consensus is negatively related to firms’ cost of equity capital. Both results
are consistent with relatively high levels of private information among analysts (low
consensus levels) leading to greater information asymmetry between informed and
uninformed investors that results in a higher cost of capital. Botosan et al. document a
relation between analysts’ consensus and expected cost of capital. We find a similar
relation between analysts’ consensus and realized cost of capital.
In summary, our evidence helps interpret the negative association between
changes in dispersion and stock returns documented in L’Her and Suret (1996). We find
that changes (increases) in dispersion reflect changes (increases) in analysts’ lack of
consensus and that it is these changes in consensus that explain L-Her and Suret’s (1996)
results. To the extent that increases in analysts’ lack of consensus reflect increases in
information asymmetry a negative relation with stock returns is expected, i.e. a higher
cost of capital.
5. Robustness
The BKLS measures assume that analysts issue forecasts simultaneously without
any time dispersion (variation). Ivkovic and Jegadeesh (2004) argue that differences in
analysts’ forecasting dates may affect the validity of the uncertainty and consensus
proxies. We investigate this issue using the variance of analysts’ forecasting dates as a
proxy for differences in analysts’ forecasting dates. When we estimate equations (3)
21
through (6) with this variable in all our samples, we find that it adds very little
explanatory power of to any of the models and does not change any of the inferences. We
also investigate the explanatory power of the variance of forecasts dates with respect to
cross-sectional variation in forecast dispersion, uncertainty and consensus in univariate
regressions. The adjusted R2 for each of these regressions is less than 0.05%, suggesting
that differences in analysts forecast dates has almost no explanatory power for analysts’
dispersion, consensus or uncertainty. Overall, contrary to concerns raised by Ivkovic and
Jegadeesh (2004), we find that time variation in analysts’ forecasts does not affect any of
our results and explains almost none of the cross-sectional variation in forecast dispersion
levels, dispersion changes, analyst uncertainty, or analyst consensus. This finding
suggests that the validity of BKLS measures is not affected by the assumption that
analysts issue forecasts simultaneously.
To generalize our results, we replicated our analyses of both the changes and levels for
samples of two-quarter- and two-year-ahead forecasts, all results and inferences remain
the same. In addition, we investigate the changes in analysts’ forecast dispersions around
non-earnings announcement dates. Particularly, we select the midpoint of two
consecutive earnings announcements as a non-announcement date. To be included there
must be no earnings announcements during this 60 day window. Untabulated results of
estimating equations (5) and (6) for a non-announcement dates at the mid-point of two
consecutive quarterly or annual earnings announcements are consistent with those
reported in Table 2, indicating that changes in consensus explain more of the variation in
changes in dispersion.
We also replicate our analyses using analysts’ sales forecasts and cash flow
forecasts and obtain similar results (untabulated) with only one exception: for the
dispersion change test using quarterly sales forecast updates around the midpoint of two
consecutive quarterly earnings announcements. The adjusted R2 is 36% for model (5),
and 26% for model (6), suggesting that the change in consensus explains less the change
in dispersion than the change in uncertainty. However, this difference is not statistically
22
significant (Vuong’s Z= - 0.76) and the sample size is only 221. One possible reason for
this different result is large measurement errors and the lack of power for the test. On the
other hand, this inconsistent result also shows that out test is not merely capturing a
mechanical relation between dispersion, lack of consensus, and uncertainty.
Overall, these alternate specifications lead to the same conclusions as the
tabulated analyses and provide support for the validity of the BKLS measures.
6. Conclusion
Using the empirical proxies developed by BKLS we provide evidence that
changes in consensus better explain changes in dispersion whereas the level of
uncertainty is better explains the level of dispersion. We also show empirically that the
negative association between the level of dispersion in analysts’ forecasts and future
stock returns documented in prior research is most likely due to the fact that forecast
dispersion reflects unsystematic uncertainty (or risk) that is part of the option value of
stocks. This finding provides strong support for Johnson (2004) and lends little support
for Deither et al.’s (2002) argument that dispersion reflects stock overpricing due to
differences of opinion. In addition, our finding that changes (increases) in dispersion
reflect changes (increases) in analysts’ lack of consensus helps reconcile L-Her and
Suret’s (1996) findings that changes in forecast dispersion are negatively associated with
contemporaneous stock returns with other research. To the extent that increases in
analysts’ lack of consensus reflect increases in information asymmetry a negative relation
with stock returns is expected, i.e. a higher cost of capital.
Finally, our evidence may be useful to investors who want to know how to interpret
forecast dispersion. That is to say, the evidence suggests that levels of forecast dispersion
23
reflects option value due to unsystematic uncertainty (or risk) and not overpricing and
changes (increases) in forecast dispersion reflect changes (decreases) in analyst
consensus and changes in information asymmetry,
24
Appendix 1:
Papers published in the Accounting Review, Journal of Accounting Research, Journal of
Accounting and Economics, Journal of Finance, Journal of Financial Economics,
Contemporary Accounting Research, Review of Accounting Studies, Journal of Financial
and Quantitative Analysis between 1990 and 2004 using dispersion of analysts’ earnings
forecasts as an empirical proxy.
1. The Accounting Review (14 papers)
Authors
Heflin, F., K R Subramanyam and Y. Zhang
Bowen, R., A. Davis and D. Matsumoto
Bamber, L., O. Barron and T. Stober
Ho, L., C. Liu and R. Ramanan
Lang, M. and R. Lundholm
Bamber, L. and Y. Cheon
Barron, O.
Baginski, S., E. Conrad and J. Hassell
Brown, L. and J. Han
Imhoff, E. and G. Lobo
Morse, D., J. Stephan and E. Stice
Ajinkya, B., R. Atiase and M. Gift
Swaminathan, S.
Ziebart, D.
Elliott, J. and D. Philbrick
Year
2003
2002
1997
1997
1996
1995
1995
1993
1992
1992
1991
1991
1991
1990
1990
2. Journal of Accounting Research (11 papers)
Authors
Bens, D. and S. Monahan
Clement, M., R. Frankel and J. Miller
Leuz, C.
Lang, M., K. Lins and D. Miller
Kinney, W., D. Burgstahler and R. Martin
Affleck-Graves, J., C. Callahan and N. Chipalkatti
Barron, O., D. Byard, C. Kile and E. Riedl
Gebhardt, W., C. Lee and B. Swaminathan
Botosan, C. and M. Harris
Aboody, D. and B. Lev
Wiedman, C.
Year
2004
2003
2003
2003
2002
2002
2002
2001
2000
1998
1996
25
3. Journal of Accounting and Economics (7 papers)
Authors
Brown, S., S. Hillegeist and K. Lo
Palmrose, Z., V. Richardson and S. Scholz
Farrell, K. and D. Whidbee
Gu, Z. and J. Wu
Francis, J., D. Hanna and D. Philbrick
Atiase, R. and L. Bamber
Kross, W., G. Ha and F. Heflin
Year
2004
2004
2003
2003
1997
1994
1994
4. Journal of Finance (4 papers)
Authors
Johnson, T.
Bailey, W., H. Li, C. Mao and R. Zhong
Diether, K., C. Malloy and A. Scherbina
Loderer, C., J. Cooney and L. Drunen
Year
2004
2003
2002
1991
5. Journal of Financial Economics (5 papers)
Authors
Flannery, M., S. Kwan and M. Nimalendran
Lowry, M.
D’Avolio, G.
Thomas, S.
Krishnaswami, S. and V. Subramaniam
Year
2004
2003
2002
2002
1999
6. Review of Accounting Studies (5 papers)
Authors
Copeland, T., A. Dolgoff, and A. Moel
Liang, L.
Gode, D. and P. Mohanram
Chambers, D., R. Jennings, and R. Thompson
Soffer, L., T. Ramn, and B. Walther
Year
2004
2003
2003
2002
2000
26
7. Contemporary Accounting Research (7 papers)
Authors
Hope, O.
Roulstone, D.
Barron, O., C. Kile and T. O’Keefe
Healy, P., A. Hutton and K. Palepu
Marquardt, C., and C. Wieldman
L’Her, J., and J. Suret
Elliot, J., D. Philbrick and C. Wieldman
Year
2003
2003
1999
1999
1998
1996
1995
8. Journal of Financial and Quantitative Analysis (3 papers)
Authors
Kim, D. and M. Kim
Denielsen, B. and S. Sorescu
Chung, K. and H. Jo
Year
2003
2001
1996
27
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32
TABLE 1
Test of the Determinants of
Pre-Announcement Dispersion in Analysts’ Earnings Forecasts a
Panel A: Descriptive statistics and tests for quarterly earnings forecasts measured within 30-days
before the current quarterly earnings announcement (N=47,782)a
Variable b
Mean
Median
Standard Deviation
D (log(D/P))
0.056 (-10.614)
0.001 (-10.763)
6.065 (2.214)
V (log(V/P))
1.197 (-9.318)
0.002 (-9.500)
85.535 (2.516)
ρ (log(1-ρ))
0.416 (-1.296)
0.530 (-0.765)
0.508 (1.717)
Size ($ millions)
6,073
1,450
18,499
Dependent
Variable
Log(D/P)
Log(D/P)
Intercept
Log(V/P)
-4.517
(<0.001)
-10.280
(<0.001)
0.654
(<0.001)
Log(1-ρ)
0.258
(<0.001)
Adjusted R2
Vuong’s Z b
55.30%
-68.92
(<0.001)
3.99%
Panel B: Descriptive statistics and tests for annual earnings forecasts measured within 30-days
before the prior annual earnings announcement (N=11,711)
Variable b
Mean
Median
Standard Deviation
D (log(D/P))
0.167 (-7.658)
0.011 (-7.659)
3.577 (2.192)
V (log(V/P))
7.893 (-5.037)
0.157 (-5.007)
271.873 (2.621)
ρ (log(1-ρ))
0.682 (-2.621)
0.912 (-2.433)
0.455 (2.142)
Size ($ millions)
5,667
1,288
18,232
Dependent
Variable
Log(D/P)
Intercept
Log(V/P)
-5.060
(<0.001)
0.516
(<0.001)
Log(D/P)
-6.938
(<0.001)
Log(1-ρ)
0.275
(<0.001)
Adjusted R2
Vuong’s Z b
38.04%
-29.13
(<0.001)
7.20%
a
This table reports results for two different samples of unadjusted IBES data where at least two analysts
issued a forecast during the period 1986 to 2003.
b
Vuong’s (1989) Z-statistic compares the explanatory power of the two models to determine which
independent variable has a greater association with the dependent variable, positive (negative) values
indicate that lack of consensus (uncertainty) has a greater association.
c
D = forecast dispersion, measured as the variance of analysts’ earnings forecasts.
Log(D/P) = natural log of D scaled by the stock price at the prior fiscal quarter end.


V = BKLS overall uncertainty, measured as 1 
1
 D  SE , where D is forecast dispersion, SE is the
N
squared error in the mean forecast, and N is the number of forecasts.
Log(V/P) = natural log of V scaled by the stock price at the prior fiscal quarter end.
ρ = BKLS consensus, measured as 1 
D
, where D is forecast dispersion and V is BKLS uncertainty.
V
log(1-ρ) = natural log of one minus ρ (lack of consensus).
Size = Market capitalization (share price time number of shares outstanding) at the end of the fiscal
period.
33
TABLE 2
Tests of the Determinants of
Changes in Dispersion in Analysts’ Earnings Forecasts Around Earnings Announcements
Panel A: Descriptive statistics and tests of quarterly earnings forecasts measured within 30-days
before and after the prior quarterly earnings announcements (N=10,150) a
Variable
Mean
Median
Standard Deviation
ΔD (Δlog(D/P)) b
-0.017 (-0.501)
-0.000 (-0.409)
1.251 (1.859)
ΔV (Δlog(V/P))
-0.060 (-0.764)
-0.003 (-0.615)
1.399 (1.391)
Δρ (Δlog(1-ρ))
-0.067 (0.262)
-0.008 (0.182)
0.563 (1.855)
Size ($ millions)
9,839
2,193
27,673
Dependent
Variable
Δlog(D/P)b
Δlog(D/P)
Intercept
Δlog(V/P)
-0.116
(<0.001)
-0.690
(<0.001)
0.504
(<0.001)
Δlog(1-ρ)
0.721
(<0.001)
Adjusted R2
Vuong’s Z c
14.21%
23.07
(<0.001)
51.79%
Panel B: Descriptive statistics and test of annual earnings forecasts measured 30-days before and
after the prior annual earnings announcements (N=4,493)
Variable
Mean
Median
Standard Deviation
ΔD (Δlog(D/P))
-0.050 (-0.336)
-0.001 (-0.288)
1.879 (1.958)
ΔV (Δlog(V/P))
-0.522 (-0.366)
-0.032 (-0.267)
5.785 (1.053)
Δρ (Δlog(1-ρ))
-0.011 (0.031)
-0.000 (0.028)
0.456 (1.989)
Size ($ millions)
8,371
2,022
24,358
Dependent
Variable
Δlog(D/P)
Intercept
Δlog(V/P)
-0.173
(<0.001)
0.445
(<0.001)
Δlog(D/P)
-0.361
(<0.001)
Δlog(1-ρ)
0.844
(<0.001)
Adjusted R2
Vuong’s Z c
5.70%
26.83
(<0.001)
73.57%
This table reports results for two different samples of unadjusted IBES data requiring at least 2 analysts’
earnings forecasts to be updated within 30 days before the announcement, with the same 2 analysts
updating within 30 days after the announcement.
b
Vuong’s (1989) Z-statistic, which compares the two models to determine which independent variable
has a greater association with the dependent variable, positive (negative) values indicate that the change
in consensus (change in uncertainty) has a greater association.
c
ΔD = change in forecast dispersion, measured as Dafter  Dbefore , where Dafter is the variance of
a
analysts’ earnings forecasts issued within 30 days after the announcement, and Dbefore is the variance of
analysts’ earnings forecasts issued within 30 days before the announcement.
Δlog(D/P) = change in natural log of forecast dispersion scaled by the stock price at the prior quarter end,
measured as log( Dafter / P)  log( Dbefore / P) .
ΔV = change in overall uncertainty, measured as Vafter  Vbefore , where Vafter is overall uncertainty
calculated with analysts’ earnings forecasts issued within 30 days after the announcement, and Vbefore is
34
overall uncertainty calculated with analysts’ earnings forecasts issued within 30 days before the
announcement. Please see Table 1 footnote for the definition of V.
Δlog(V/P) = change in natural log of overall uncertainty scaled by the stock price at the prior quarter end,
measured as log( Vafter / P)  log( Vbefore / P) .
Δρ = change in analysts’ consensus, measured as  after   before , where  after is analysts’ consensus
calculated with analysts’ earnings forecasts issued within 30 days after the announcement, and  before is
overall uncertainty calculated with analysts’ earnings forecasts issued within 30 days before the
announcement. Please see Table 1 footnote for the definition of ρ.
Δlog(1-ρ) = change in natural log of 1 minus ρ, measured as log( 1   after )  log( 1   before ) .
Size = Market capitalization (share price time number of shares outstanding) at the end of the
fiscal period.
35
TABLE 3
Relation between Returns and Uncertainty Controlling for Size
Replication of Diether et al. (2002) Table2 Substituting BKLS Uncertainty for Forecast
Dispersion
Average Monthly Returns to Portfolios Based on Firm Size And Uncertainty
(t-statistics in parentheses)a
Panel A: Average monthly returns to portfolios based on firm size and uncertainty.
Mean returns
Size Quintiles
Uncertainty Small
Quintiles
S1
1(low)
2.11
2
1.92
3
1.43
4
0.29
5(high)
-1.55
1-5
3.65
t-statistic
13.85
S2
1.86
1.77
1.47
0.88
-0.58
2.44
8.19
S3
1.57
1.59
1.43
1.22
-0.12
1.69
5.20
S4
1.44
1.38
1.29
1.03
0.62
0.82
2.44
Large
S5
1.35
1.41
1.12
1.26
1.20
0.15
0.41
All
Stock
1.60
1.57
1.45
1.12
-0.26
1.87
5.99
Panel B: Uncertainty levels for size quintiles.
Mean (median) Uncertainty
Size Quintiles
Uncertainty Small
Quintiles
S1
1(low)
0.003
(0.002)
2
0.024
(0.014)
3
0.108
(0.059)
4
0.589
(0.302)
5(high)
631,202.2
(194.1)
S2
0.002
(0.001)
0.017
(0.010)
0.073
(0.047)
0.352
(0.180)
20,392.3
(141.1)
S3
0.002
(0.001)
0.012
(0.007)
0.056
(0.032)
0.279
(0.136)
942.3
(60.1)
S4
0.001
(0.001)
0.010
(0.005)
0.044
(0.025)
0.181
(0.115)
594.7
(41.6)
Large
S5
0.001
(0.001)
0.005
(0.004)
0.027
(0.017)
0.118
(0.097)
2,336.3
(33.3)
All
Stock
0.002
(0.001)
0.012
(0.007)
0.055
(0.034)
0.244
(0.146)
130,586.4
(290.0)
Each month stocks are assigned to one of five size quintiles based on their market capitalization at the end
of the previous month. Within each size quintile stocks are assigned to five further quintiles based on
BKLS uncertainty scaled by the square of the mean forecast, measured in the previous month.
Uncertainty, V, is defined in equation (2). Portfolio returns are equal-weighted returns for one month. The
sample consists of 521,091 monthly stock return observations for 216 months from January 1983 to
December 2000.
a
t-statistics are adjusted for autocorrelation using Newey-West standard errors.
36
TABLE 4
Relation between Returns and Consensus Controlling for Size
Replication of Diether et al. (2002) Table2 Substituting BKLS Consensus for Forecast
Dispersion
Average Monthly Returns to Portfolios Based on Firm Size and Consensus
(t-statistics in parenthases)a
Panel A: Average monthly returns to portfolios based on firm size and consensus.
Mean returns
Size Quintiles
Consensus Small
Quintiles
S1
1(low)
2.06
2
1.37
3
1.04
4
0.10
5(high)
-0.36
1-5
2.42
t-statistic
16.13
S2
1.70
1.70
1.42
0.42
0.16
1.54
7.72
S3
1.53
1.59
1.21
0.93
0.44
1.09
5.77
S4
1.48
1.42
1.23
0.91
0.73
0.74
5.08
Large
S5
1.48
1.35
1.29
1.07
1.15
0.33
2.05
All
Stock
1.66
1.47
1.26
0.76
0.33
1.33
10.43
Panel B: Consensus levels for size quintiles.
Mean (median) Consensus
Size Quintiles
Consensus Small
Quintiles
S1
1(low)
-0.257
(-0.261)
2
0.481
(0.501)
3
0.845
(0.858)
4
0.970
(0.974)
5 (high)
0.998
(0.999)
S2
-0.183
(-0.202)
0.465
(0.469)
0.819
(0.841)
0.961
(0.968)
0.997
(0.998)
S3
-0.132
(-0.143)
0.438
(0.463)
0.793
(0.818)
0.948
(0.959)
0.995
(0.996)
S4
-0.085
(-0.086)
0.408
(0.422)
0.750
(0.769)
0.926
(0.942)
0.991
(0.994)
Large
S5
-0.042
(-0.034)
0.363
(0.380)
0.699
(0.722)
0.895
(0.920)
0.985
(0.991)
All
Stock
-0.142
(-0.149)
0.428
(0.451)
0.783
(0.814)
0.945
(0.956)
0.995
(0.997)
Each month stocks are assigned to one of five size quintiles based on their market capitalization at the end
of the previous month. Within each size quintile stocks are assigned to five further quintiles based on
BKLS consensus measured in the previous month. Consensus, , is defined in equation (1). Portfolio
returns are equal-weighted returns for one month. The sample consists of 521,091 monthly stock return
observations for 216 months from January 1983 to December 2000.
a
t-statistics are adjusted for autocorrelation using Newey-West standard errors.
37
TABLE 5
Relation between Returns and Uncertainty Controlling for Consensus
And Returns and Consensus Controlling for Uncertainty
Average Monthly Returns to Portfolios Based on Uncertainty, V, and Consensus, 
(t-statistics in parenthases)a
Panel A: Average monthly returns to portfolios based on uncertainty (V) and consensus ()
Uncertainty Quintiles
Consensus Small
Quintiles
V1
1.45
1 (low)
1.63
2
1.56
3
1.68
4
1.70
 5 (high)
-0.25
1   5
t-statistic
-2.17
V2
1.67
1.63
1.49
1.57
1.51
0.16
1.19
V3
1.72
1.59
1.52
1.34
1.08
0.64
3.77
V4
1.62
1.19
0.97
0.77
1.06
0.56
2.65
Large
V5
0.78
0.11
-0.61
-0.64
-0.95
1.73
5.31
Panel B: Average monthly returns to portfolios based on consensus () and uncertainty (V)
Consensus Quintiles
Uncertainty Small
Quintiles
1
V1(low)
1.48
V2
1.62
V3
1.57
V4
1.90
V5(high)
1.74
V1-V5
-0.26
t-statistic
-0.88
2
1.56
1.64
1.65
1.48
1.01
0.55
1.65
3
1.64
1.42
1.49
1.37
0.36
1.28
4.00
4
1.50
1.30
1.18
0.52
-0.67
2.17
6.52
Large
5
1.66
1.01
0.99
0.19
-2.19
3.85
10.45
In Panel A, stocks are assigned to five quintiles first based on the level of BKLS uncertainty, V, in the
previous month then based on BKLS consensus, ρ, for the previous month. In Panel B, stocks are
assigned to five quintiles first based on the level of BKLS consensus, ρ, in the previous month then based
on BKLS uncertainty, V, for the previous month.
a
t-statistics are adjusted for autocorrelation using Newey-West standard errors.
38
TABLE 6
Further Evidence of the Relation between Returns, Uncertainty and Lack of Consensus
Fama-McBeth Regressions of Returns on Ranked Uncertainty V and Lack of Consensus (1-
(t-statistics in parentheses)
Re tt 1   0  1 * Rank _ Vt   2 * Rank _(1  t )   3 * Rank _ Sizet
Model 1
0.0145
(4.24)
Model 2
0.0140
(3.33)
Uncertainty
-0.0035
(-4.61)
-0.0035
(-4.66)
Lack of Consensus
0.0017
(6.02)
0.0018
(6.06)
Intercept
Size
0.0002
(0.320)
In each month, all the stocks are assigned a quintile rank (1-5) based on uncertainty (V),
consensus (ρ) and size independently. The cross section of monthly stock returns ( Re t t 1 ) is
regressed on the quintile ranks of uncertainty ( Rank _ Vt ) and lack of consensus ( Rank _(1  t ) )
and size ( Rank _ Size t ) which are measured as of the previous month. Fama and Macbeth (1973)
cross-sectional regressions are run every month for totally 216 continuous months from January
1983 till December 2000. T-statistics in parentheses are calculated using the coefficients from
monthly regressions and also adjusted for autocorrelation using Newey-West standard errors.
39
TABLE 7
Tests of the Explanatory Power of Firm Risk for Analysts Forecast Dispersion
Panel A: Descriptive Statistics
Variables
Mean
DISP
0.278
Log(DISP)
-2.784
BETA
1.127
MSE
0.012
Log(MSE)
-4.800
Median
0.054
-2.926
1.068
0.008
-4.837
S.D.
3.349
1.377
0.560
0.018
0.865
Skewness
102.335
0.647
0.932
27.993
0.274
Panel B: Regression results with raw values of dispersion, beta, and mean squared error
Intercept
BETA
Model 1
-3.218
(<0.001)
0.386
(<0.001)
Log(MSE)
N
R-squared
382,789
0.025
Model 2
-0.952
(<0.001)
0.382
(<0.001)
382,789
0.058
Model 3
-1.263
(<0.001)
0.115
(<0.001)
0.344
(<0.001)
382,789
0.059
Panel C: Regression results with decile ranks of dispersion, beta and mean squared errors
Intercept
Rank_BETA
Model 1
4.656
(<0.001)
0.154
(<0.001)
Rank_MSE
N
R-squared
382,789
0.024
Model 2
3.837
(<0.001)
0.303
(<0.001)
382,789
0.092
Model 3
3.846
(<0.001)
-0.004
(0.046)
0.304
(<0.001)
382,789
0.092
The sample contains all the firm-months with valid earnings forecasts from IBES and monthly return data
from CRSP from 1983 till 2000 and consists of 382,789 firm month observations. Dispersion is measured
as standard deviations of earnings forecasts divided by the absolute value of the mean forecasts. BETA is
the market beta and estimated using 36-60 monthly returns prior to the firm month of measuring
dispersions. MSE is the mean squared errors from the estimation of the above market model. Log(beta)
and log(MSE) are the log transformation of beta and MSE. Panel A reports descriptive statistics. Panel B
reports Pearson (upper half) and Spearman (lower half) correlations and p-values (two tailed) are in
parentheses. Panel C reports the results of regressing log-transformed dispersion on beta and logtransformed MSE. Panel D reports the results of regressing the decile ranks for dispersion on decile ranks
for beta and MSE. Decile ranks are obtained by ranking all firms in each month into deciles based on
dispersion, beta and MSE independently.
40