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					Asia-Pacific Journal of Financial Studies (2006) v35 n6 pp141-168




              Self-Selection Bias in Consensus Analysts’
                          Earnings Forecasts*

                                              Bok Baik**
                               Florida State University, Florida, USA

                       Received 04 October 2006; Accepted 31 October 2006


                                               Abstract

   Self-selection arises when analysts choose not to release earnings forecasts if unfavor-
able future prospects are expected. This behavior makes the observed distribution of earn-
ings forecasts appear overoptimistic. By using two firm specific measures of the degree of
self-selection, I provide evidence suggesting that some portion of observed optimism stems
from self-selection, rather than from incentives or analysts’ underreaction. Firms experi-
encing financial distress, low long-term growth, and stock price declines appear more
likely to be subject to self-selection by analysts. Moreover, I find empirical evidence sug-
gesting that investors do not fully recognize self-selection and overprice firms which are
dropped by analysts.

Keywords: Self-Selection; Optimism in analyst forecasts; Analyst forecasts;
            Market mispricing; Analyst underreaction




 * This paper is part of my dissertation completed at UC Berkeley. I thank helpful comments
   by two anonymous reviewers, Anwer Ahmed, Bruce Billings, Jong-Hag Choi, Hemang
   Desai, Bruce Johnson, Roby lehavy, Terry Marsh, Rick Morton, Kathy Petroni, Mort Pincus,
   Tom Rothenberg, and Brett Trueman. Any erros are my own.
** Corresponding Author, Address: Department of Accounting, College of Business, Florida
   State University, Tallahassee, FL 32306; E-mail: bbaik@garnet.acns.fsu.edu;
   Tel: 850-644-9847; Fax: 850-644-8234.

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Self-Selection Bias in Consensus Analysts’ Earnings Forecasts



1. Introduction

  This study scrutinizes the relation between analyst self-selection and optimism in
consensus analysts’ earnings forecasts. One stylized fact emerging from prior re-
search on analyst forecasts is that consensus analyst forecasts are optimistic, on av-
erage.1) In fact, there is an ongoing debate about what causes analyst optimism. One
explanation for optimism is that analyst self-selection results in an overoptimistic ex
post observed distribution of forecasts even though analysts issue ex ante unbiased
forecasts. Self-selection arises when an analyst reports his true expectation of firm
performance, but only if he chooses to report. If poor performance is expected, he or
she may choose not to release a report. Aside from the selection explanation, there
are two alternative explanations for apparent analyst optimism: (1) analysts inten-
tionally add bias to their true beliefs, and (2) analysts unintentionally underreact to
past information about the firm’s performance. Although a rich literature exists ex-
ploring analyst forecasts, prior research has not fully explored interactions between
self-selection and other explanations. Moreover, little research has examined whether
the market incorporates the implications of self-selection in consensus forecasts.
  This paper examines three primary issues. First, I investigate whether self-
selection explains the cross-sectional variation of analyst optimism after controlling
for other explanations associated with analyst optimism. Second, I empirically exam-
ine factors that may affect the relation between self-selection and analyst optimism.
Finally, I examine whether the market fully recognizes the implications of self-
selection in predicting analyst optimism.
  In particular, I show that a positive association between self-selection measures
(TRUNC1 and TRUNC2) and forecast optimism over the period 1983-2003 continues
to exist, even after controlling for other explanations such as incentives and underre-
action. Also, I confirm that firms experiencing financial distress, low long-term
growth, and stock price declines appear more likely to be subject to self-selection by
analysts. Furthermore, I find that investors seem to overprice firms subject to self-
selection, as evidenced by the existence of negative returns to portfolios of firms with
a higher selection measure over the 12 month holding period. By forming portfolios
ranked on the degree of selection, I was able to find a profitable trading strategy. The

1) I use optimism in analysts’ consensus forecasts with analyst optimism interchangeably in this paper.

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Asia-Pacific Journal of Financial Studies (2006) v35 n6



mean one-year buy-and- hold raw return for the lowest self-selection group (formed 4
months after the fiscal period end) is higher than the mean for the highest self-
selection group by 8.1 percent (3.5 percent) using the first self-selection measure (the
second measure), and the difference is statistically significant at below the 1 percent
level. Further, results also indicate that the predictability of future returns using the
degree of self-selection is incremental to the returns expected from risk factors.
  This research contributes to the literature on analyst forecasts in several ways. I
examine the incremental contribution of self-selection relative to incentives, underre-
action and other control variables. As a result, this study provides evidence on the
extent to which the pervasive observed optimism stems from self-selection, rather
than analysts’ inflation of their true beliefs or cognitive reaction to past information.
Prior literature has not identified the portion of analyst optimism attributable to se-
lection. In addition, this work provides additional evidence on market inefficiency
with regard to analyst forecasts (for example, Barber et al., 2001), and in the course
of doing so, it suggests ways to debias forecasts subject to self-selection.
  The remainder of the paper is organized as follows. In section 2, I describe prior lit-
erature. Section 3 discusses the sample while section 4 presents the findings. Section
5 provides some concluding remarks.


2. Literature Review

  Many studies report evidence that analysts’ forecasts are optimistic.2) Numerous
explanations have been advanced in prior literature to explain analyst optimism (See
Kothari, 2001).
  In terms of incentives, an important incentive motivating analysts to inflate fore-
casts is the “facilitation” of investment banking relationships. Consistent with this
explanation, Lin and McNichols (1998) and Dugar and Nathan (1995) present evi-
dence that affiliated analysts tend to issue more optimistic growth forecasts than un-
affiliated analysts. In addition, analysts may inflate forecasts to cultivate information
acquisition as Francis and Philbrick (1993) and Das et al. (1998) suggest. Francis and
Philbrick (1993) argue that earnings forecasts are more optimistic for stocks that


2) A non-exhaustive list includes Fried and Givoly (1982), Brown, Foster, and Noreen (1985), Abarbanell
   (1991), Klein (1990), and Brown (1998).

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Self-Selection Bias in Consensus Analysts’ Earnings Forecasts



have been given sell recommendations in order to maintain good relations with man-
agement. Das et al. (1998) propose that analysts may have stronger incentives to is-
sue optimistic forecasts for firms with higher uncertainty in order to facilitate man-
agement communication.
  Cognitive bias explanations contend that forecast optimism results from analysts’
inefficient processing of past information. De Bondt and Thaler (1990) and La Porta
(1996) provide evidence that analysts overreact to information. They find that ana-
lysts tend to be overly optimistic about firms experiencing good performance. On the
other hand, Klein (1990), Abarbanell (1991), and Abarbanell and Bernard (1992) re-
port that analysts underreact to past information. Easterwood and Nutt (1999) argue
that analysts underreact to bad news and overreact to good news.
  Another explanation for analyst optimism (which is examined here) is that ana-
lysts’ selective issuance of forecasts makes the ex post observed distribution of fore-
casts overly-optimistic, even if analysts issue ex ante unbiased forecasts. McNichols
and O’Brien (1997) find that analysts are more likely to release a report about a firm
for which they have favorable views. Hayes and Levine (2000) undo the effect of self-
selection on optimistic bias in analyst’s earnings forecasts using the maximum likeli-
hood estimation, and find that when they do, the maximum likelihood estimate of
earnings is more accurate than the sample mean or median of forecasts.
  On the other hand, recently Abarbanell and Lehavy (2003) look at the observed opti-
mistic bias in analyst’s forecasts from management’s perspective. They argue that the
optimistic bias is attributable to management’s incentive to engage in income decreasing
earnings management and to analyst’s inability or unwillingness to forecast it.
  Little research has been directed at whether self-selection is subsumed by other
explanations for optimism in consensus analyst’s forecasts. To my best knowledge,
only Francis and Willis (2001) show that subsequent year industry-adjusted return
on equity, as a proxy for selection, helps explain forecast errors after controlling for
other explanations. Hayes (1998) develops a theoretical model of the analyst’s effort
allocation decision to generate brokerage commission, which yields a prediction con-
sistent with self-selection. Previous research does not provide established empirical
findings on the determinants of selection. A separate question is whether the market
can or does undo the bias induced from self-selection. Hayes and Levine (2000) exam-
ine the association between the stock market excess returns and forecast errors over
the period from the forecast to the earnings announcement. However, their method-

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Asia-Pacific Journal of Financial Studies (2006) v35 n6



ology used for the market efficiency test results in inconclusive outcomes.


3. Sample Selection, Variable Measurement, and Descriptive Sta-
   tistics

  My study uses data from the IBES Detail file of analyst annual forecasts for the
forthcoming fiscal year (FY1) over the period of 1983~2003. Table 1 summarizes my
sample selection process.
  To be included in the sample, there must be data on price, actual earnings (in the
IBES actual file) and a CUSIP to match with COMPUSTAT and CRSP. The Detail
file contains records of individual analyst forecasts organized by the date on which
the forecast was issued. For my study, I include all forecasts for the forthcoming fis-
cal year in the IBES Detail database which usually collects analyst’s estimates from
at least one month after the previous fiscal year end to the earnings announcement.3)

                                  Table 1. Sample selection criteria
                                                                           TRUNC1              TRUNC2
                                                                          (1983-2003)         (1984-2003)
 Firm years on IBES                                                         104,615              101,777
 Delete firm years if the information on actual earnings,
                                                                             (25,857 )           (25,320)
 price, and cusip is not available on IBES
 Delete old forecasts if the same analyst issues more than
 one forecast (individual analyst’s forecasts)
 Delete top 1% and bottom 1% of forecasts (individual ana-
 lysts’ forecasts)
 Delete firm years whose forecast errors belong to top 1%
                                                                              (1,576)              (1,530)
 and bottom 1%
                                                                             77,182               74,927
 Delete firm years with less than 10 analysts                                (51,893)            (50,586)
                                                                             25,289               24,341
 Delete firm years for which the percentage of dropped
                                                                                                   (2,146)
 forecasts is greater than 50 percent
 Final sample                                                                25,289               22,195



3) As a robustness check, I also required each firm year to have the earnings announcement information (in
   the IBES earnings announcement file) for both fiscal year t-1 and fiscal year t. Then, I confined individual


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Self-Selection Bias in Consensus Analysts’ Earnings Forecasts



  If the same analyst issues more than one estimate for a given firm year, I take the
most recent estimate.4) Then, I eliminate individual analyst forecasts larger (smaller)
than the 99th (1st) percentile of the IBES detail population to control for the effect of
extreme outliers.5) In addition, I delete firm-years greater (less) than the 99th (1st)
percentile of the distribution of forecast errors.6)
  Following Hayes and Levine (2000), I construct a selection measure labeled as
TRUNC1 using estimates from the maximum likelihood estimation.

                                       ⎡ φ (θ ) ⎤
                            TRUNC1 = σ ⎢           ⎥                                                     (1)
                                       ⎣1 − Φ (θ ) ⎦
              Lit − μ it
where θ =                  and φ (θ ) and Φ (θ ) are the probability density and cumulative
                 σ it

distribution functions of the standard normal. μ it and σ it are the maximum likeli-
                                                          2


hood estimators for mean and dispersion under a truncated normal distribution (i.e.,
mean and standard deviation estimators of a untruncated normal distribution) and
the minimum forecast of any forecasts is an estimate of the threshold Lit .
  The first measure is based on the assumption that analysts’ information follows a
normal distribution and analysts do not report their forecasts if their expectations
are below a particular threshold (a truncated normal distribution). More specifically,
suppose that analyst j’s forecast for firm i at time t can be denoted as xitj = μ it + ε itj .

The error term follows N( 0, σ it 2 ). This means that analysts’ information follows a
normal distribution. Let’s assume that analysts do not report their forecasts if their
expectations are below a particular threshold. In other words, they choose not to fol-
low the firm when their information is xit ≤ Lit .


   analysts’ one-year ahead forecasts to the period between the earnings announcement for fiscal year t-1 and
   the earnings announcement for fiscal year t. Similar results are obtained using this subsample.
4) Although the most recent estimate from individual analysts in the detail file is used, it may not completely
   control for forecast staleness. I also computed the consensus forecast and two self-selection measures us-
   ing the most recent individual forecasts within alternative time horizons (between forecast release dates
   and earnings announcement dates) such as 1 month, 3 months, 6 months and 9 months. Then I repeated the
   analyses. Results hold in every subgroup. This demonstrates that my results are not driven by forecast
   staleness.
5) This procedure deletes extreme individual analyst forecasts at the IBES population level. The inclusion of
   these observations does not change the results.
6) The inclusion of these firm years does not change the results.

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Asia-Pacific Journal of Financial Studies (2006) v35 n6



  Using the properties of the truncated normal distribution, I can represent the ex-
pected value of xit as follows:
                                                     ⎡ φ (θ ) ⎤
                              E[ xit ] = μ it + σ it ⎢          ⎥                        (2)
                                                     ⎣1 − Φ(θ ) ⎦

              Lit − μ it
where θ =                  and φ (θ ) and Φ (θ ) are the probability density and cumulative
                σ it
distribution functions of the standard normal, respectively.
                                                      ⎡ φ (θ ) ⎤
  If one knew the truncation point, one could compute ⎢          ⎥ assuming normality
                                                      ⎣1 − Φ(θ ) ⎦
and multiply this by dispersion to measure self-selection bias.
  Although several methods of estimating the parameters using a truncated sample
can be used, I apply the Newton-Raphson method. For some sets of forecasts, the
MLE is sensitive to the starting values. As a result, I choose the global maximum of
the MLE’s using 930 combinations of the starting values.
  I define the second selection measure, TRUNC2 as follows:
 TRUNC2 = median of observed forecasts – median of the distribution including
dropped forecasts. This measure is based on the notion that when a variable is trun-
cated, its median can be recovered if the median is in the untruncated region. In
other words, the true median can be found as long as the total number of dropped
forecasts is known and the number of dropped observations is less than or equal to 50
percent of the entire distribution. Self-selection implies that the ranking of those
dropped forecasts is below a certain threshold. Without knowing their forecast values,
I am able to find the median of the entire distribution as long as their ranking is be-
low the median of the entire distribution. As an analogy, suppose that out of 50 stu-
dents who took a midterm, the lowest scoring 5 students are dropped. I can find the
median for the entire class (inclusive of those 5 students) without knowing the
dropped scores since the median score shifts predictably. Using brokerage and ana-
lyst codes from the IBES Detail file, I compare the current year analyst codes with
the previous year analyst codes for a given firm. Those analysts who do not appear in
the current year (provided that they existed in the previous year) are considered as
dropped analysts. Using the difference between a median after truncation and a me-
dian before truncation, I can measure the degree self-selection without the normality
assumption.


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Self-Selection Bias in Consensus Analysts’ Earnings Forecasts


                 Table 2. Descriptive statistics for self-selection measures
                    N             Mean           Std. Dev       Median       Quartile3         Quartile1
  TRUNC1         25,289          0.0916           0.2428        0.0157         0.0864            0.0013
  TRUNC2         22,195          0.0463           0.1349        0.0100         0.0400            0.0000

                                TRUNC1                                        TRUNC2

                    N       Mean (Median)        Std. Dev         N       Mean (Median)         Std. Dev

 1983~1987       5,062          0.14(0.03)         0.318        3,831        0.08(0.03)           0.202

 1988~1993       6,419          0.09(0.02)         0.202        5,953        0.05(0.02)           0.143

 1994~1999       7,862          0.06(0.01)         0.141        7,283        0.03(0.01)           0.084

 2000~2003       5,946          0.08(0.01)         0.301        5,128        0.03(0.01)           0.112

                                                       ⎡ φ (θ ) ⎤
Notes) TRUNC1 is self-selection measure defined as σ ⎢              ⎥ obtained from the maximum likelihood
                                                       ⎣ 1 − Φ (θ ) ⎦
       estimation. TRUNC2 is self-selection measure defined as the median of observed forecasts less the
       median of the whole forecasts including dropped forecasts.


  To calculate the first self-selection measure, TRUNC1, I need enough forecasts to
run the maximum likelihood estimation for each firm year. I drop firm years with the
number of analysts less than 107) To maintain consistency with TRUNC1, I delete
firm years with a number of analysts less than 10 for my second self-selection meas-
ure, TRUNC2. To measure TRUNC2, I compare the current year analyst codes with
the previous year analyst codes for a given firm. Those analysts who do not appear in
the current year (provided that they existed in the previous year) are considered as
dropped analysts and then replace the dropped forecasts with the minimum forecast
available and find medians.8) For TRUNC2, I also require the percentage of dropped
forecasts to be less than or equal to 50 percent. My final sample consists of 25,289
observations, specifically, 25,289 firm years from 1983 to 2003 for TRUNC1 and
22,195 firm years from 1984 to 2003 for TRUNC2.9)
  Descriptive data related to self-selection measures (TRUNC1 and TRUNC2) are


7) I performed the same analyses using different cut off points. My results are not sensitive to this cut off
   point.
8) This procedure may bias the degree of self-selection if an analyst has moved from one broker to another
   and continues to follow the same firm.
9) TRUNC2 needs a base year to compare the next year in order to compute dropped forecasts. So it starts
   from 1984.

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Asia-Pacific Journal of Financial Studies (2006) v35 n6



reported in Table 2. The mean of TRUNC1 (TRUNC2) is 9.2 cents (4.6 cents),
whereas the median is 1.6 cent (1.0 cent). This suggests that self-selection raises the
consensus forecast by 9.2 cents (4.6 cents) based on TRUNC1 (TRUNC2) on average.
The standard deviations of TRUNC1 and TRUNC2 are 24.3 cents and 13.5 cents, re-
spectively, indicating large variation in self-selection measures. In particular,
TRUNC2 has 5,835 firm years with zero values. The number of firms included in my
investigation has marginally decreased in the period of 2000~2003. Relatedly, self-
selection appears to increase in that period based on TRUNC1, although TRUNC2
remains the same. One interpretation is that selection increased since the U.S. stock
market experienced a turbulent period from 1998 to 2001. Also, untabulated analysis
indicates that the Spearman (Pearson) correlation coefficient between TRUNC1 and
TRUNC 2 is a significant 0.357(0.331) at the 1% level. It is suggestive that the second
measure is a good complement to the first measure.


4. Results

4.1 Self-Selection and Optimism in Consensus Analysts’ Forecasts


  First, to determine the impact of self-selection on analyst optimism, I perform a
univariate analysis. Decile portfolios are formed by the degree of self-selection la-
beled as TRUNC1 and TRUNC2, and I check forecast errors across decile portfolios.
Self-selection suggests that the ex post forecasted numbers are larger than actual
unbiased forecasts because pessimistic forecasts are dropped by self-selection. This
suggests that selection is associated with optimism in analyst forecasts.
  My measure of analyst forecast errors is defined as follows:

                                         ERRit = ( Ait − F1it ) / price              (3)

where Ait = Actual EPS for fiscal year t, F1it = the average of the most recent indi-
vidual analysts’ forecasts on IBES data for fiscal year t , and Price is price (reported
in IBES) during the month of the fiscal year end. Then, I multiply forecast errors by
100 to report results in %.




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Self-Selection Bias in Consensus Analysts’ Earnings Forecasts


      Table 3. Forecast errors on portfolios formed on the degree of self-selection
This table reports the relation between self-selection measures and forecast errors. The fore-
cast error is defined as actual earnings less the mean forecast divided by price and then multi-
plied by 100. For TRUNC2, zeros are reported in a separate row. 1-10 is the difference in fore-
cast errors between the highest decile of self-selection and the lowest decile of self-selection. t-
test of differences in means. Wilcoxon ranksum-test of differences in medians. * denotes signifi-
cance at the 5% level. ** denotes significance at the 1% level.

  Trunc1           N         Mean         Median        Trunc2      N        Mean        Median
 Degree of Self-Selection
      Zero                                                        5,835     -0.249       0.004
  1 Low          2,519      -0.020        0.064                   1,567     -0.205       0.019
       2         2,530      0.007         0.076                   1,731     -0.303       0.003
       3         2,531      -0.031        0.078                   1,319     -0.310       0.000
       4         2,533      -0.137        0.060                   2,047     -0.373       -0.008
       5         2,526      -0.205        0.019                   1,494     -0.474       -0.028
       6         2,535      -0.393        -0.023                  1,698     -0.642       -0.002
       7         2,533      -0.549        -0.121                  1,604     -0.642       -0.064
       8         2,531      -0.753        -0.233                  1,632     -0.900       -0.052
       9         2,530      -1.450        -0.545                  1,636     -1.370       -0.126
  10 High        2,521      -3.577        -1.491                  1,632     -2.849       -0.163
       All      25,289      -0.710        -0.016                 22,195     -0.661      -0.465
   1 – 10                            **            **                        2.644**     0.182
                                                                                               **
                            3.557         1.555
  Zero-10                                                                    2.600**     0.167**
Pearson Correlation -0.372 (p-value = 0.0001) -0.274(p-value = 0.0001)
Spearman Correlation -0.460 (p-value = 0.0001) -0.105(p-value = 0.0001)


  Table 3 reports statistics about the forecast errors across portfolios. Consistent
with the self-selection conjecture, Columns 3 and 4 of Table 3 show that optimism
increases from low deciles to high deciles of TRUNC1 in general. Similar patterns
emerge when TRUNC2 is used. The difference in the mean forecast errors between
the lowest decile and the highest decile is statistically significant at 3.56 using
TRUNC1 (a significant 2.64 using TRUNC2). Table 3 also provides Pearson and
Spearman correlation coefficients and related p-values between TRUNC1 (TRUNC2)
and the forecast error, ERR. As expected, the analyst forecast error is negatively cor-
related with self-selection, TRUNC1 and TRUNC2 (p-values <0.0001). The results
are consistent with the idea that selection contributes to the optimistic ex post distri-
bution of forecasts.


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Asia-Pacific Journal of Financial Studies (2006) v35 n6



  To assess whether the negative relation between self-selection and the forecast er-
ror is concentrated in a particular decile portfolio of forecast errors, I partition the
sample by the forecast error and examine how my self-selection measures behave.
The unreported evidence indicates that the magnitude of self-selection generally in-
creases as analyst forecasts become more optimistic relative to actual earnings, and it
suggests that the negative relation between selection and the forecast error is not
concentrated in a particular decile group of forecast errors.
  However, the relation between self-selection and optimism could be driven by other
factors that contribute to analyst optimism. The observed bias ex post would be due
to analyst incentives to inflate forecasts, analyst underreaction, or other factors
shown to influence forecast errors. To distinguish among these possible reasons, I
examine whether self-selection is subsumed by other explanations.
  I consider several control variables that affect forecast errors. Prior studies (Klein,
1990; Abarbanell, 1991; Ali et al., 1992) have documented a positive association between
analyst forecast errors and past stock returns. Abarbanell (1991) claims that this is con-
sistent with analyst underreaction to past information. To control for analyst underreac-
tion, I use the firm’s prior 12 month market adjusted return (MRET).10) I also consider
firm size and analyst following. Das et al. (1998) show that the size is positively related to
forecast errors. Analyst following is also likely to be related to forecast errors. Han,
Manry and Shaw (1996) find that analyst following is negatively associated with the
forecast error, whereas Adair (1996) finds that it is positively related to the forecast error.
Firm size (LSIZE) is measured as log of market cap, and analyst following (LNUM) is log
of the number of analysts for the forthcoming fiscal year.
  Brown (1997) and Hwang et al. (1996) find that forecasts for firms with losses are
more optimistic than for firms with profits. They explain that managers have differ-
ent incentives to manage losses from profits. To control for optimism driven by losses,
I use a dummy variable for loss labeled LOSS. Gu and Wu (2003) find that skewness
in actual earnings is related to analyst optimism. I include skewness in the distribu-
tion of actual earnings, MNMD (the difference between the mean and the median of
the price deflated actual earnings distribution) in the control variables.
  Moreover, additive bias could generate the same observed distributions of optimis-
tic forecasts as does self-selection. Analysts may prefer to issue inflated reports about

10) Results remain intact if I replace prior returns with the price deflated earnings surprises as a measure of
    prior performance.

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Self-Selection Bias in Consensus Analysts’ Earnings Forecasts


  Table 4. Descriptive statistics for dependent, self-selection, and control variables
This table presents summary statistics for the sample from 1983 to 2003. MRET: market-
adjusted return compounded over the past 12 month period ending the month prior to the fis-
cal period t-1. LSIZE: log of market cap at the fiscal period end of year t. LNUM: log of the
number of analysts following at the fiscal period t. LOSS: indicator variable equal to 1 if firm
reports a loss in fiscal year t, otherwise zero. MNMD: skewness of actual earnings distribution
defined as the mean less the median of price deflated EPS from 4 quarters before the fiscal
period t based on Gu and Wu (2003). IPO: indicator variable equal to 1 if the firm issued an
IPO/SEO in years t-2, t-1, or t, otherwise 0.

                              N          Mean         Std. Dev   Median    Quartile3   Quartile1

                                          Dependent variable

ERR                        25,289        -0.7102       3.400     -0.0164    0.1672      -0.4871

                                  Self-selection and Control variables

 TRUNC1                    25,289        0.0916        0.2428    0.0157     0.0864      0.0013

 TRUNC2                    22,195        0.0463        0.1349     0.010     0.0400      0.0000

 MRET                      22,154        0.1852        0.7593    0.1017     0.3926      -0.1778

 LSIZE                     21,909        7.3077        1.5110    7.2283     8.2645      6.2750

 LNUM                      25,289        2.9090        0.4425    2.8332     3.2188      2.5649

 LOSS                      22,097        0.1492        0.3563       0         0           0

 MNMD                      22,322        -0.0006       0.0112    0.0000     0.0009      -0.0006

 IPO                       25,289        0.2724        0.4452       0         1           0


  a firm which is issuing new equity because underwriting is highly lucrative for the
brokerage firms (Lin and McNichols, 1993; Michaely and Womack, 1999; Dechow et
al., 2000). I consider a dummy variable, IPO with regard to whether firms issued an
IPO or SEO within the past two years in order to control for the additive bias expla-
nation. For analysis that requires information about initial public offerings (IPOs)
and secondary equity offerings (SEOs), I use domestic US public offerings drawn from
Securities Data Corporation’s New Issues. I match the sample firms with the data
over the period of 1983~2003.
Table 4 reports descriptive statistics of the forecast error (ERR) and these control
variables. The mean of forecast errors in the sample is negative (and significantly
different from zero), reflecting overoptimism in analysts’ forecasts. Recall that I limited
limited the sample to firm-year observations where analyst following is at least 10.

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Reflective of high analyst coverage, LSIZE and LNUM are relatively large.11) About
15 percent of the sample experienced losses. MNMD has a mean (median) of –0.0006
(0.000). Note that MNMD covers the period from 1985, due to the data requirement
to compute MNMD. Twenty seven percent of the firm year observations are associ-
ated with IPOs or SEOs over the past 2 years (inclusive of the current year). Varia-
tion in all these variables could potentially affect the forecast error. Furthermore, in
my unreported results, the six variables (past return, firm size, analyst following,
loss, actual earnings skewness, and IPO) to control for analyst optimism are corre-
lated with TRUNC1 and TRUNC2 as measures of self-selection at the 1 percent level
or better except IPO (an indicator with regard to IPOs and SEOs) using the Spear-
man correlation coefficient and all but LNUM (log of analyst following), and IPO are
also significant using the Pearson correlation coefficient. I can infer from the correla-
tions that selection potentially interacts with other explanations associated with ana-
lyst optimism.
  My main test examines the extent to which the pervasive observed optimism stems
from self-selection, rather than analysts’ inflation of their true beliefs, cognitive reac-
tion to past information, or other factors related to the forecast error. To examine the
incremental contribution of self-selection to ex post analyst optimism, I estimate the
following regression model:

      ERRit = β 0 + β1TRUNCit + β 2 MRETit −1 + β 3 LISZEit + β 4 LNUM it + β 5 LOSS it
                                                                                           (4)
               + β 6 MNMDit + β 7 IPOit


where ERRit is actual earnings less mean forecast deflated by price, TRUNCit is a
measure of self-selection, MRETit −1 is prior year’ s market adjusted return, LSIZEit
is the log of size, LNUM it is the log of the number of analysts, LOSS it is a dummy
variable taking the value of 1 for loss, otherwise 0 and MNMDit is the mean minus
the median of price deflated EPS from 4 quarters before the end of the fiscal period of
interest based on Gu and Wu (2003), IPOit is an indicator variable equal to 1 if the
firm issued an IPO/SEO in years t-2, t-1 or t, otherwise 0.
  I estimate the above equation for each of the 21 years (20 years for TRUNC2) in the


11) The mean (median) market value of equity in the sample is $5.5 ($1.3) billion.

                                                                                          153
Self-Selection Bias in Consensus Analysts’ Earnings Forecasts


Table 5. Mean coefficient estimates for regression of forecast errors on self-selection
           and other firms characteristics
This table reports the mean coefficients for regressions of a set of explanatory variables on ana-
lyst optimism. MRET: market-adjusted return compounded over the past 12 month period end-
ing the month prior to the fiscal period t-1. LSIZE: log of market cap at the fiscal period end of
year t. LNUM: log of the number of analysts following at the fiscal period t. LOSS: indicator
variable equal to 1 if firm reports loss in fiscal year t, otherwise zero. MNMD: skewness of ac-
tual earnings distribution defined as the mean less the median of price deflated EPS from 4
quarters before the fiscal period t based on Gu and Wu (2003). MNMD covers the period of
1985-2003 due to the data availability of the IBES Detail file. Coefficients are the mean of an-
nual regression estimates during the sample period (for regressions with MNMD, the testing
period starts from 1985.).IPO: indicator variable equal to 1 if the firm issued an IPO/SEO in
years t-2, t-1, or t, otherwise 0. t-statistic is computed as the ratio of the mean of the annual
coefficients to the standard error from the coefficients distribution.
              ERRit = β 0 + β1TRUNCit + β 2 MRETit −1 + β 3 LISZEit   + β 4 LNUM it   + β 5 LOSS it
                      + β 6 MNMDit + β 7 IPOit

                              TRUNC1:independent var                        TRUNC2: independent var
  Variable                    Coefficient            t-stat                  Coefficient              t-stat
  Intercept                       -1.02              -3.85                        -1.73               -4.48
  TRUNC                           -4.03              -8.91                        -3.01               -4.25
  MRET                             0.07              1.22                         0.09                1.72
  LSIZE                            0.23              6.35                         0.28                6.48
  LNUM                            -0.21              -3.91                        -0.31               -4.66
  LOSS                            -2.47              -3.43                        -2.61               -3.88
  MNMD                             37.0              3.08                        46.37                3.33
  IPO                              0.03              0.93                         0.05                1.22
  Mean R2                                   0.31                                              0.32


sample. Tests of statistical significance of β1 are based on the standard error calcu-
lated from the distribution of the annual coefficients, following Fama and Macbeth
(1973).12) The average coefficients are reported in Table 5.
  Table 5 shows that the self-selection variable adds significantly in explaining fore-
cast errors, even after controlling for other explanatory factors. Apparently, the mean
coefficient on the selection variable is significant and negative at the 1 percent level
regardless of which selection measure is used. Further, in my untabulated results,
the self-selection variable adds the most in explaining ex post analyst optimism. The

12) This test overcomes bias due to cross-sectional correlation in error terms but assumes independence in
    error terms across time. To correct for autocorrelation, I performed the analysis using the pooled time-
    series cross-section regression. MRET becomes insignificant after controlling for autocorrelation. Other
    than MRET, results are similar.


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Asia-Pacific Journal of Financial Studies (2006) v35 n6



value of R2 increases from 18 percent to 31 percent, on average, over the years when
TRUNC1 is included in the regression.
  The fit of other variables in Table 5 is similar to that reported in prior research.
MRET is insignificant using TRUNC1 (marginally significant using TRUNC2) when
all the independent variables are included in the regression. This evidence suggests
that the observed pattern of underreaction could be magnified by selection. Consis-
tent with prior studies, LSIZE is significantly positive at the 1 percent level. Consis-
tent with Han et al. (1999), LNUM is significantly negative. The smaller the firm size,
the more optimistic the forecast. LOSS is significantly negative at the 1 percent level,
consistent with Hwang et al. (1996). Consistent with Gu and Wu (2003), MNMD is
positive and significant at the 1 percent level. Finally, with regard to underwriting
incentives, the mean coefficient on IPO is not significantly different from zero. It sug-
gests that underwriting incentives (measured by a dummy variable of IPOs/SEOs)
might not explain analyst optimism.13) Lin and McNichols (1998) report that earnings
forecasts issued by affiliated analysts are not more optimistic than those issued by
unaffiliated analysts, a result that is consistent with the insignificance of the IPO
variable here. Overall, I find that selection contributes to ex post analyst optimism
even after controlling for incentives, cognitive reactions, and other control variables.
In addition, I find that other factors (firm size, analyst following, the existence of loss,
and actual earnings skewness) are significant in explaining the forecast error. The
evidence in the regression results is consistent with self-selection.


4.2 Determinants of Self-Selection


  Turning to the second issue, I seek to explain what factors affect selection. This
analysis provides some insights into why some sets of forecasts are missing for a
given firm and furthers understanding the relation between selection and analyst
optimism.
  Analysts weigh the ramifications of reporting bad news against not reporting bad


13) In robustness checks of my results, I varied the time period used to define underwriting incentives with
    little effect on the regression results. In addition to the IPO variable, I performed the analysis using a
    dummy variable which equals to 1 if the firm’s statement of cash flows indicates a positive sale of com-
    mon and preferred stocks (#108) greater than 20% of the market value of equity in year t, t-1, or t-2. Simi-
    lar results are obtained.

                                                                                                           155
Self-Selection Bias in Consensus Analysts’ Earnings Forecasts


news. One of the disincentives to reporting bad news is trading commissions. Hired
by full-service brokerage houses, analysts in the IBES database provide research re-
ports and forecasts to the brokerage firm sales force and their clients. By issuing a
research report about a particular firm, they can generate trading in the security and
increase the expected commission revenue from trading and potential consulting
revenue from the covered firm.14) The opportunity cost of the analyst dropping cover-
age is the lost brokerage revenue that could have been generated by issuing the fore-
cast. Other things being equal, the higher the degree of selection gets, the lower the
opportunity cost of non-reporting. Hayes (1998) models analysts’ incentives to gener-
ate trading commissions and develops conditions under which self-selection is likely
to occur.
  First, expected future performance is related to trading commissions. Under short
sale constraints, buy recommendations generate greater trading commissions than
sell recommendations. Sell recommendations can motivate trading commissions, but
trading commissions on a stock with bad prospects may be limited to the investor’s
initial holdings of the stock. For this reason, self-selection may be more pronounced
when the firm’s future prospects are unfavorable. I expect that the degree of selection
is expected to increase with unfavorable future prospects. I consider two measures as
proxies for expected future performance. First, I use financial distress as a proxy for
expected future performance. Analysts may face a lower opportunity cost for firms
that they expect to be financially distressed. Lost brokerage revenue from dropped
coverage would be minimal for those firms. Common methods for detecting company
operating and financial difficulties are the financial ratios measuring profitability,
liquidity, and leverage, which prove to be significant indicators of financial distresses
(Altman, 2000; Zmijewski, 1984). I use an index of financial distress to combine these
three ratios based on Zmijewski (1984). The financial distress measure is defined
as Φ ( B * ) , where B * is a standard normal variable:


                         NetIncome             TotalDebt            CurrentAssets
B * = −4.803 − 3.599 ×               + 5.406 ×             − 0.1 ×                                      (5)
                         TotalAssets           TotalAssets         CurrentLiabilities

 and Φ (•) is the cumulative distribution function of the standard normal.


14) Analysts may also benefit indirectly from trading commissions (i.e., promotion, reputation) and/or com-
    pensation, which may be based on commissions.

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Asia-Pacific Journal of Financial Studies (2006) v35 n6



  Secondly, I include long-term earnings growth forecasts as a proxy for future pros-
pects since they have been used as a measure of market expectations for future per-
formance (La Porta, 1996; Bradshaw, 2004; Dechow et al., 2000).
  In addition, I include other firm characteristics that affect potential trading com-
missions. Brokerage commissions may be positively associated with trading volume.
O’Brien and Bhushan (1990) find evidence suggesting that analysts cover firms with
high trading volume to maximize trading commissions. Thus, I expect that analyst
self-censoring is negatively related to trading volume. Additionally, expected broker-
age commissions would be lower for firms which have experienced a large drop in
stock price. I expect that selection increases with poor stock performance.
  Another group of variables includes firm size and analyst following. These vari-
ables may capture the information environment and the activities of other analysts
who follow the stocks. However, the relationship of these variables with self-selection
is not clear a priori. Analyst benefits (commissions) from following small firms (or low
analyst coverage firms) could be greater than from following large firms (or heavy
analyst coverage firms) due to little competition from other analysts. Alternatively,
these firms may be costly to research due to less transparent information.
  I include additional variables that may influence the potential for self-selection
(Rajan and Servaes, 1997; Francis and Willis, 2001). Analyst coverage may be bi-
ased toward those firms in high growth industries for increased trade and investment
banking business. Although analysts may have incentives to follow firms listed in a
major exchange for trading commissions, they also face severe competition. Thus, I do
not predict a direction for the relation between an exchange dummy and selection. In
addition, I include the number of firms at the industry level as a proxy for the extent
of competition. This variable could potentially increase self-selection.
  The above discussion results in the following regression:

 TRUNCit = β 0 + β1 BANKRUPTit + β 2 LTGTit + β 3VOLit −1 + β 4 MRETit −1 +
                                                                                        (6)
             β 5 LSIZEit + β 6 LNUM it + β 7 MDUMMYi + β 8 NFIRM it + β 9 IGRWOTH it

where TRUNCit is a measure of self-selection , BANKRUPTit is the probability of fi-
nancial distress, LTGTit is analysts’ long-term earnings growth forecast, VOLit − 1 is
the average trading volume over the past 12 months, MRETit −1 is market adjusted
returns over the past 12 months, LSIZE it is the log of size, LNUM it is the log of the


                                                                                       157
Self-Selection Bias in Consensus Analysts’ Earnings Forecasts



number of analysts, MDUMMYi is an indicator variable equal to 1 if equity is not
traded on a major exchange (NYSE, AMEX, and NASDAQ), otherwise 0, NFIRM it is
the number of firms in 2-digit SIC industry, IGRWOTH it is a median sales growth for
the 2-digit SIC industry level.
  Using TRUNC1 and TRUNC2 as proxies for selection, I run the regressions in each
year and average out the coefficients during the sample period. Also, in my untabu-
lated analysis, similar results are obtained using the pooled time-series cross-section
regression. Table 6 presents the regression results.
  As reported in Table 6, the coefficient on financial distress is positive and signifi-
cant. The degree of self-selection appears to increase with financial distress. In other
words, analyst optimism from truncation of low forecasts is likely to increase with
financial distress. In addition, the degree of selection is negatively associated with
long-term growth outlook, as expected from the discussion (p-values <0.01). The sig-
nificance and sign of these two variables in the TRUNC1 regressions (reported in Ta-
ble 6, Columns 2 and 3) are similar to those found in the TRUNC2 regressions (re-
ported in Table 6, Columns 4 and 5).
  My conjecture that self-selection is more likely to occur for low volume stocks, is re-
jected by the positive coefficient on the VOL variable (p-value <0.01) in TRUNC1 and
TRUNC2.15) I measure trading volume on a firm level. Because stock volume cannot
be disaggregated on a brokerage-firm level, the relation between analyst self-selec
tion and volume could be uncertain.16)
  By contrast, the negative relation between firm size and TRUNC1 (TRUNC2) indi-
cates that selection is more intense in small firms. LNUM has a significantly positive
relation to TRUNC1, while the relation between LNUM and TRUNC2 is insignificant.
Selection would be increasing in the extent to which analyst following captures de-
creased trading commissions from competition among analysts following the firm.
As predicted, past stock performance affects self-selection. The mean coefficient on
MRET is negative and statistically significant regardless of selection measures. Self-
selection seems more severe for firms with stock price decreases in the previous year.


15) In contrast, I conjecture that for high trading volume stocks, self-selection is not likely to occur and thus
    the consensus may not be subject to any bias.
16) In addition, my results could be confounded by the nature of volatility in trading volume (Lee and Swa-
    minathan, 2000). Relatedly, I performed the same estimation using different proxies for trading volume
    such as the average turnover (trading volume/no. shares outstanding) and float (no. of shares outstanding*
    price). I find that the relation between selection and trading volume is sensitive to how to measure trading
    volume.

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Asia-Pacific Journal of Financial Studies (2006) v35 n6



                             Table 6. Determinants of self-selection
This table reports the mean coefficients for regressions of a set of explanatory variables on ana-
lyst self-selection measures. BANKRUPT: probability of financial distress based on Zmijewski
(1984). LTGT: analysts’ long-term earnings growth forecasts. VOL: average trading volume
over the past 12 months. LSIZE: log of market cap at the fiscal period end of year t. LNUM: log
of the number of analysts following at the fiscal period t. MRET: market-adjusted return com-
pounded over the past 12 month period ending the month prior to the fiscal period t-1.
MDUMMY: indicator variable equal to 1 if equity is not traded on a major exchange, zero if
traded on a major exchange (NYSE, AMEX, and NASDAQ). NFIRM: number of firms in 2-digit
SIC industry. IGROWTH: median sales growth in 2-digit SIC industry. t-statistic is computed
as the ratio of the mean of the annual coefficients to the standard error from the coefficients
distribution.
           TRUNCit = β 0 + β 1 BANKRUPTit + β 2 LTGTit + β 3VOLit −1 + β 4 MRETit −1 +
                       β 5 LSIZEit + β 6 LNUM it + β 7 MDUMMYi + β 8 NFIRM it + β 9 IGRWOTH it

                           TRUNC1 : dependent var                       TRUNC2 : dependent var
     Variable               Coefficient  t-stat                          Coefficient   t-stat
  Intercept                      0.113               6.42                    0.049               5.08
  BANKRUPT                       0.275               4.24                    0.175               3.00
  LTGT                          -0.002              -4.44                   -0.001               -4.41
  VOL                            0.013               5.68                    0.005               4.49
  LSIZE                         -0.027              -7.10                   -0.003               -1.68
  LNUM                           0.019               2.41                   -0.011               -1.59
  MRET                          -0.062              -4.57                   -0.013               -1.77
  MDUMMY                         0.026               2.65                    0.012               2.42
  NFIRM                          0.000               0.37                   -0.000               -0.56
  IGROWTH                       -0.110              -1.84                    0.040               1.08
  Mean   R2                              0.12                                            0.08


  An indicator variable with regard to whether firms are listed in a major exchange is
positive and significant, suggesting that selection is more evident for firms in a major
exchange. This is consistent with the negative relation between selection measures and
LNUM. The number of firms in the same industry is not important. A significantly nega-
tive relation between TRUNC1 and industry growth supports that analysts self-select
into growth industries. However, I find that TRUNC2 is insignificant.
  In sum, I find evidence suggesting that expected future performance proxied by fi-
nancial distress and future long-term growth are negatively associated with self-
selection. Furthermore, self-selection appears to decrease with firm size and past
stock performance.


                                                                                                         159
Self-Selection Bias in Consensus Analysts’ Earnings Forecasts



4.3 Self-Selection and Stock Returns


  If the level of self-selection is high, the analysts who have pessimistic views are
underrepresented. As a result, the consensus forecast will be more likely upward bi-
ased. Additionally, prior research suggests that investors use analyst forecasts as
proxies for earnings expectations (Givoly and Lakonishok, 1979; O’Brien, 1988).
  In an efficient market, this upward bias from self-selection will be impounded in
current stock prices. Investors using earnings forecasts for valuation purposes should
be able to infer the true mean of the distribution by estimating the upward bias from
analyst self-selection. Thus, there should be no relation between the level of self-
selection and subsequent excess returns.
  Alternatively, the upward bias in stock valuations will become higher as the level
of self-selection increases if investors do not fully incorporate the implications of ana-
lyst self-selection. The result will be a significantly negative relation between self-
censoring and excess returns in the future.
  I construct a hedge portfolio to examine whether the market can unravel the up-
ward bias from self-selection. Deciles are sorted every year according to the self-
selection measures, TRUNC1 and TRUNC2, before the accumulation period, and
then subsequent performance of the decile portfolios is tracked using raw returns and
size-adjusted returns over the next year. The difference in subsequent returns be-
tween the two extreme decile portfolios is then tested against the null hypothesis of
zero difference in returns. Size-adjusted return represents the difference between the
firm’s buy-and-hold raw return and the buy-and-hold return on a value-weighted
portfolio of firms in the sample size decile:

                               12               12
                    SAR =     ∏ (1 + RETi ) −   ∏ (1 + SRETi )                         (7)
                              i =1              i =1


 SAR : 12-month compounded size-adjusted returns;
 RETi : firm raw return in month I;
 SRETi : return on the size portfolio corresponding to the firm in month i, where the
          size portfolio is supplied by CRSP.

  I compute compounded 12-month size-adjusted returns beginning 4 months after
the current fiscal year end. The four-month lag is to ensure that the market has already

160
Asia-Pacific Journal of Financial Studies (2006) v35 n6



Table 7. Mean returns to portfolios formed on the degree of self-selection(12
              months holding periods)
This table reports the mean raw returns and size-adjusted returns ranked on TRUNC1 over
the period 1983~2003 and TRUNC2 over the period of 1984~2003. For TRUNC2, zeros are re-
ported in a separate row. Size-adjusted returns are computed by subtracting the return on a
size-matched, value-weighted portfolio formed from size decile groupings provided by CRSP. 1
– 10 is the difference in raw return (size-adjusted return) between the lowest and highest dec-
ile. t-test of differences in means. * significant at the 5% level. ** significant at the 1% level.

                             Mean of Mean of Size-                              Mean of Mean of Size-
     Trunc1         N        Raw Re- Adjusted Re- Trunc2                 N      Raw Re- Adjusted Re-
                              turns     turns                                    turns     turns

                                         Degree of     Self-Selection

 Zero                                                                   5,377    0.1752         0.0481
 1 Low            2,354       0.2215        0.0863                      1,439    0.2931         0.1551
 2                2,329       0.1753        0.0380                      1,554    0.1726         0.0428
 3                2,278       0.1813        0.0478                      1,340    0.1809         0.0355
 4                2,243       0.1625        0.0329                      1,708    0.1283         0.0016
 5                2,194       0.1651        0.0346                      1,383    0.1654         0.0291
 6                2,221       0.1575        0.0316                      1,469    0.1301         0.0040
 7                2,186       0.1519        0.0203                      1,429    0.1860         0.0395
 8                2,216       0.1632        0.0348                      1,389    0.1525         0.0142
 9                2,183       0.1449        0.0150                      1,366    0.1408         0.0081
 10 High          2,116       0.1403        0.0092                      1,263    0.1398         0.0048
                                                                                        **
 1 – 10                             **                                          0.1533         0.1503**
                             0.0812         0.0771**                                  **             **
 Zero – 10                                                                      0.0354         0.0433


learned accounting information contained in firms’ annual financial reports.17)
     Table 7 gives raw returns and size-adjusted returns to the investment position over
12 month holding periods. In general, the mean returns are negatively related to the
degree of self-selection. The mean one-year raw return for stocks in the lowest
TRUNC1 portfolio is on average 8.1 percent higher than the mean return for stocks
in the highest TRUNC1 portfolio. The difference is statistically significant (p-value
<0.001). The difference between the mean returns for the lowest TRUNC2 (excluding
zeros) and highest TRUNC2 portfolios is significant, which is 15.3 percent. The difference

17) I also started to accumulate returns from the month after earnings announcement. Similar results are ob-
    tained for a reduced sample with earnings announcement dates.

                                                                                                       161
Self-Selection Bias in Consensus Analysts’ Earnings Forecasts


         Figure 1a. Returns by calendar year to a hedge portfolio using TRUNC1
This figure presents mean returns to a hedge portfolio taking a long position in the stock of
firms in the lowest decile of TRUNC1 and a short position in the stock of firms in the highest
decile of TRUNC1.

                                              returns by calendar year to a hedge portfolio

                                         0.3
                                        0.25
                                         0.2
                                        0.15
                   percentage return




                                         0.1
                                        0.05
                                              0
                                       -0.05
                                            83

                                                    85

                                                           87

                                                                  89

                                                                          91

                                                                                 93

                                                                                         95

                                                                                                97

                                                                                                       99

                                                                                                              01

                                                                                                                     03
                                          19

                                                  19

                                                         19

                                                                19

                                                                        19

                                                                               19

                                                                                       19

                                                                                              19

                                                                                                     19

                                                                                                            20

                                                                                                                   20
                                         -0.1
                                       -0.15
                                         -0.2
                                                                                  year



         Figure 1b. Returns by calendar year to a hedge portfolio using TRUNC2
This figure presents mean returns to a hedge portfolio taking a long position in the stock of
firms with zeros (TRUNC2) and a short position in the stock of firms in the highest decile of
TRUNC2.

                                                  returns by calendar year to a hedge portfolio

                                       0.4

                                       0.3
             percentage return




                                       0.2

                                       0.1

                                         0
                                          84


                                                    86


                                                           88


                                                                   90


                                                                            92


                                                                                   94


                                                                                               96


                                                                                                       98


                                                                                                              00


                                                                                                                     02




                                       -0.1
                                        19


                                                  19


                                                         19


                                                                 19


                                                                          19


                                                                                 19


                                                                                             19


                                                                                                     19


                                                                                                            20


                                                                                                                   20




                                       -0.2

                                       -0.3
                                                                                      year




162
Asia-Pacific Journal of Financial Studies (2006) v35 n6



between firms with zero TRUNC2 and firms in the highest TRUNC2 decile is 3.5 per-
cent (p-value <0.01). This pattern holds even after size adjustments. The results sug-
gest a profitable trading strategy. A zero-net-investment strategy, long and short po-
sitions in the lowest and highest deciles respectively, would earn positive abnormal
returns. If an investor uses an investment strategy in which he buys the lowest decile
stocks with the money from the short sales of the highest decile stocks, then the in-
vestor is expected to earn about 7.7 percent excess returns using TRUNC1. Likewise,
he would earn 4.3 percent excess returns using TRUNC2, going long the lowest decile
stocks and short the highest decile stocks.
Furthermore, I examine whether this hedge portfolio strategy generates a positive
abnormal return across years. The returns used to produce the plot are size-adjusted
returns. The negative relation between selection measures and abnormal returns pre-
vails in most of the sample period.
  More specifically, Figure 1 indicates that a positive return would have been earned
from this strategy in 16 years out of the 21 years with TRUNC1 (in 15 years out of
the 20 years with TRUNC2). The years generating a negative return are 1985 (-4.2
percent), 1987 (-5.5 percent), 2000 (-6.6 percent), 2002 (-16.3 percent), and 2003 (-1.7
percent), using TRUNC1. By contrast, the hedge portfolio using TRUNC2 generates a
negative return for the following years: 1986 (-1.2 percent), 1987 (–23.8 percent),
1992 (-6.9 percent), 2002 (-11.1 percent), and 2003(-2.0 percent). This indicates that
the market does not completely capture the implications of self-selection.
  These predictable abnormal returns may result from risk factors such as market
risk, size and book-to-market, rather than censored analyst coverage per se. In order
to check this possibility, I examine whether selection forecasts in excess of those pre-
dicted by common risk factors. To examine empirically the incremental effect of selec-
tion to the predictability of abnormal returns, I employ the following Fama and Mac-
Beth-type cross-sectional regressions to control for risk factors:

 RETit +1 = β 0 + β 1TRUNCit + β 2 BETAit + β 3 LSIZEit + β 4 BPit + β 5 MRETit + β 6VOLit
                                                                                              (8)
         + β 7 EPit + β 8 ACCit


where RETit +1 is one-year buy-and-hold raw returns , TRUNC it is a measure of self-
selection, BETAit is the CAPM beta, measured by estimating the market model on
the prior 60 monthly stock returns, LSIZE it is the log of size, BPit is book-to-market


                                                                                             163
Self-Selection Bias in Consensus Analysts’ Earnings Forecasts


Table 8. Mean coefficient estimates for regression of raw returns on self-selection
           and other firm characteristics
This table reports the mean coefficients for regressions of a set of explanatory variables on fu-
ture returns. BETA: CAPM beta, measured by estimating the market model on the prior 60
monthly stock returns. LSIZE: log of size. BP: book-to-market ratio. MRET: market adjusted
returns over the past 12 months. VOL: average trading volume over the past 12 months. EP:
earnings-to-price ratio. ACC: accruals. t-statistic is computed as the ratio of the mean of the
annual coefficients to the standard error from the coefficients distribution.
           RETit +1 = β 0 + β 1TRUNCit + β 2 BETAit + β 3 LSIZEit + β 4 BPit + β 5 MRETit + β 6VOLit
                     + β 7 EPit + β 8 ACCit

                               TRUNC1:independent var                         TRUNC2: independent var
      Variable                  Coefficient            t-stat                  Coefficient             t-stat
      Intercept                     0.156             2.03                         0.125               1.68
      TRUNC                         -0.130            -2.59                       -0.187               -2.83
       BETA                         -0.018            -0.95                       -0.027               -1.15
       LSIZE                        -0.038            -2.72                       -0.039               -2.90
         BP                         0.035             1.12                         0.038               1.19
       MRET                         0.020             1.44                         0.017               0.99
        VOL                         0.027             1.95                         0.032               2.70
         EP                         -0.001            -0.01                        0.048               0.90
        ACC                         -0.154            -3.60                       -0.219               -4.68
      Mean R2                                 0.07                                        0.06


ratio, MRETit is market adjusted returns over the past 12 months, VOLit is the av-
erage trading volume over the past 12 months, and EPit is earnings-to-price ratio,
and ACCit is accruals.
Results from the regressions reported in Table 8 confirm the findings in Table 7.
There is a negative relation between TRUNC1 (coefficient = -0.13) and future returns
that is statistically significant (p<0.01) even after controlling for factors such as firm
size, book-to-market ratio and other firm characteristics. The negative sign on the
coefficient on TRUNC1 is consistent with the notion that the market under-weights
the contribution of self-selection to optimism in analyst’s forecasts. Columns 4 and 5
of Table 8 also suggest that inferences drawn from TRUNC2 are qualitatively similar.
The coefficient on TRUNC2 is a significant –0.19 (p<0.01) when risk factors are con-
trolled. This indicates that the degree of selection predicts returns in excess of the

164
Asia-Pacific Journal of Financial Studies (2006) v35 n6



returns expected from risk factors. Taken together, the market appears to misprice
the implications of self-selection in consensus forecasts



5. Conclusions

  In this paper, I investigate the implications of the conjecture that analysts selec-
tively report, based on whether their expectations are positive or negative. I conduct
three primary analyses regarding the relation between self-selection and optimism in
consensus earnings forecasts. The first tests whether the selection is associated with
forecast optimism and if the association is subsumed by alternative explanations pre-
sented in prior literature. The second examines the determinants of self-selection in
the context of trading commissions. The third investigates whether the market fully
recognizes optimism in analyst forecasts driven by self-selection.
  From a large sample of forecasts from the IBES Detail file from 1983 to 2003, I find
evidence suggesting that self-selection is associated with optimism in consensus ana-
lysts’ forecasts after controlling for other explanations associated with optimism. The
second analysis reveals that firms with financial distress, low long-term growth, and
stock price declines appear more likely to have a higher degree of self-selection. With
respect to the tests of whether the market understands self-selection, I find evidence
consistent with investors not fully adjusting the selection bias over the 12 month
holding period. The abnormal return of 7.7 percent (4.3 percent) to a trading strategy
based on TRUNC1 (TRUNC2) is both statistically and economically significant.




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Self-Selection Bias in Consensus Analysts’ Earnings Forecasts



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