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Earnings Forecasts: The Case for Combining Analysts’ Estimates
with a Mechanical Model I
Vitor G. Azevedoa, Patrick Bielsteinb, Manuel Gerharta
aDepartment of Financial Management and Capital Markets, TUM School of Management, Technical
University of Munich, Arcisstr. 21, 80333 Munich, Germany
bEDHEC-Risk Institute, Scientific Beta, 10 Fleet Place, London EC4M 7RB, United Kingdom
Abstract
We propose a novel method to forecast corporate earnings, which combines the accu-
racy of analysts’ forecasts with the unbiasedness of a mechanical model. We build on
recent insights from the earnings forecasts literature to select variables that have predic-
tive power with respect to earnings. Our model outperforms the most popular methods
from the literature in terms of forecast accuracy, bias, and earnings response coefficient.
Furthermore, using our estimates in the implied cost of capital calculation leads to a
substantially stronger correlation with realized returns compared to extant mechanical
earnings estimates.
Keywords: Earnings forecasts; analysts’ forecasts; forecast evaluation; implied cost of
capital; expected returns. JEL classifications: G12, G29, M41.
IWorking Paper; this version: September 6, 2018. We thank Tobias Berg, Daniel Bias, J¨urgen
Ernstberger, Robert Heigermoser, Christoph Kaserer, Lisa Knauer, Jake Thomas, and participants at
the Paris Financial Management Conference 2017, European Accounting Association 2018, and TUM
School of Management, Finance Department, summer workshop 2016 for insightful discussions and helpful
comments. Part of this research was undertaken while Patrick was visiting INSEAD. The authors also
thank the National Council for Scientific and Technological Development (CNPq) and the Science without
Borders Program for financial support, which included a research scholarship. Disclosures: Patrick works
for EDHEC-Risk Institute (ERI) Scientific Beta, a smart beta index provider. The views expressed in
this paper are those of the author and do not necessarily reflect or represent those of ERI Scientific Beta.
Contacts: vitor.azevedo@tum.de (Vitor G. Azevedo). Phone: +49 (0)89 289 25179.
1. Introduction
Earnings forecasts are a critical input in many academic studies in finance and ac-
counting as well as in practical applications. They are central to firm valuation, are
widely used in asset allocation decisions, and are the basis for the accounting-based cost
of capital calculations such as the Implied Cost of Capital (ICC). It is, therefore, crucial
to have precise and unbiased estimates.
The most popular source for obtaining earnings forecasts are financial analysts. These
forecasts are aggregated by data providers, such as the Institutional Brokers’ Estimate
System (I/B/E/S), and subsequently made available to academics and practitioners by
these providers. Although analysts’ forecasts are fairly accurate (O’Brien,1988;Hou
et al.,2012), researchers have found a significant optimism bias (Francis and Philbrick,
1993;McNichols and O’Brian,1997;Easton and Sommers,2007).
The alternative to analysts’ earnings forecasts is a mechanical model, which can either
solely be based on past realizations of earnings (time-series models) or on a combination
of past earnings and other financial variables. The literature first developed time-series
models. These models use past realizations of earnings in a linear or an exponential
smoothing framework (Ball and Brown,1968;Brown et al.,1987). The results are un-
derwhelming; these forecasts are neither accurate nor unbiased. In addition, they suffer
from survivorship bias as only firms with a long history of earnings can be included in
the model. Fried and Givoly (1982) conclude that time-series models are worse than ana-
lysts’ forecasts for predicting future earnings. This result was later confirmed by O’Brien
(1988).
Recently, cross-sectional models to forecast earnings proliferated. Fama and French
(2006) create one of the first cross-sectional models that predict future profitability and
show that earnings as an independent variable are highly persistent in forecasting prof-
itability. Hou et al. (2012) develop a cross-sectional model (henceforth HVZ model) based
on assets, earnings, and dividends, which outperforms analysts’ forecasts in terms of cov-
erage, Earnings Response Coefficients (ERC),1and forecast bias2but still trailed analysts’
forecasts with respect to forecast accuracy.3Gerakos and Gramacy (2013) find that a sim-
1The ERC estimates the relationship between earnings surprises and stock returns.
2Bias is defined as the difference between the actual earnings and earnings forecast.
3Accuracy is defined as the absolute value of the forecast error.
2
ple Random Walk (RW) model, in which the previous period’s value is used as a forecast,
performs as well as other, more sophisticated, earnings forecast models. Finally, Li and
Mohanram (2014) implement an Earnings Persistence (EP) and a Residual Income (RI)
model to forecast earnings. They show that these models are superior to the HVZ and
RW models in terms of bias, accuracy, and ERC.
More recently, Ball and Ghysels (2017) develop a model based on mixed data sampling
regression methods (MIDAS), which combines various high-frequency time-series data to
forecast earnings. Their model outperforms raw analysts’ forecasts in some cases and
also can be combined with analysts’ forecasts to improve forecast accuracy. The findings
from Ball and Ghysels (2017) tie in with ours as they show that mechanical models can
be used to improve earnings forecasts. One significant difference to our study is that the
model from Ball and Ghysels (2017) is not suited to estimate the ICC as the focus is on
short-term forecast horizons (next quarter), whereas the ICC also requires medium- and
long-term forecasts (up to five years in the future). We provide empirical evidence on the
advantages of combining analysts forecasts with a regression-based model for longer-term
earnings forecasts.
In summary, existing studies show that analysts’ earnings forecasts are more accurate
than mechanical earnings forecasts but they do less well in terms of bias and ERC. In
addition, analysts’ forecasts have two important shortcomings: sluggishness4and poor
long-term estimates.5
This study proposes a parsimonious cross-sectional regression model consisting of an-
alysts’ earnings forecasts, gross profits, and past stock performance. The inclusion of an-
alysts’ forecasts aims to improve forecast accuracy, in particular of short-term forecasts as
analysts’ have a timing and information advantage over forecasts based solely on account-
ing data (Ball and Ghysels,2017). Including gross profits is motivated by findings from
Novy-Marx (2013), which suggest that gross profits predict future earnings. Furthermore,
Novy-Marx (2013) shows that gross profits explain many earnings-related asset pricing
anomalies, such as return on assets, earnings-to-price, asset turnover, gross margins, and
4Guay et al. (2011) show that analysts, on average, are slower than the stock market in processing
new, earnings-related information. They suggest to use short-term stock returns to mitigate the effect of
sluggish analysts forecasts.
5For instance, Bradshaw (2012) report that even when analysts have timing and information advan-
tages, analysts’ forecasts of future earnings are not consistently more accurate than mechanical models
for longer forecast horizons.
3
standardized unexpected earnings. It is intuitive that stock returns also contain informa-
tion regarding future earnings. Indeed, Richardson et al. (2010) and Ashton and Wang
(2012) find that changes in stock prices predict future earnings and Abarbanell (1991)
shows that stock returns are related to future earnings forecasts revisions. Including past
stock returns in our combined model has a further advantage as this variable mitigates
the effect of sluggish analysts’ forecasts (Guay et al.,2011). We term our method the
combined model (CM), as it combines analysts’ forecasts with a cross-sectional method.
We compare our combined model to the most popular methods in the literature,
namely raw analysts’ forecasts and the RW, EP, RI, and HVZ models. To isolate the
value of analysts forecasts within the CM, we also estimate a cross-sectional analysts’
forecasts (CSAF) model.6We show that the combined model delivers earnings forecasts
that are slightly more accurate than analysts’ forecasts and markedly more accurate than
the mechanical models, while beating all other tested methods in terms of bias and ERC.
Concerning the CSAF model, this model underperforms not only the combined model but
also the raw analysts’ forecasts in terms of bias and accuracy. This suggests that using the
analysts’ forecasts in a mechanical model is not sufficient to improve the accuracy of the
forecasts nor to decrease bias. However, the fact that the combined model outperforms
all of the analyzed models, including the CSAF, shows that the variables gross profits and
past stock performance substantially improve earnings forecasts.
One important application of earnings forecasts is to estimate a firm’s cost of capital, in
particular, the ICC. To further evaluate the earnings forecasts from our tested models, we
use them as inputs in computing the ICC. We find that many of our benchmark models
produce ICC estimates that have a negative and significant relation to gross profits.
This evidence conflicts with Novy-Marx (2013) and Fama and French (2015) who derive
theoretically and show empirically that firms with high gross profitability should have
higher expected returns. In contrast, the ICC based on our combined model shows a
positive and significant relation, in line with the theoretical derivation. In addition, the
ICC based on the combined model displays a stronger association with ex-post realized
returns for both dimensions (cross-sectional and time-series) than the ICC based on the
other benchmark models. A long-short strategy of buying the highest ICC decile and
6This model is based on a cross-sectional regression using only analysts’ earnings forecasts as an
input.
4
short-selling the lowest ICC decile based on the ICC estimated with the combined model
yields a significant average annual returns of up to 6.65%.
This study contributes to the finance and accounting literature in several ways. First,
we document that combining analysts’ earnings forecasts with a regression-based model
leads to more accurate and less biased estimates than each of the components alone. It
takes advantage of each method’s favorable characteristics while mitigating their short-
comings. The CM also outperforms the most popular models from the literature in all
three dimensions analyzed: bias, accuracy, and ERC. Second, we analyze one application
of earnings forecasts, the estimation of the ICC, and show that using earnings forecasts
from the CM leads to an increase in the relation between ICC and future returns cross-
sectionally. Thus, one major criticism of the ICC, namely the weak correlation between
ICC estimates and realized returns7, is attenuated by using more accurate earnings fore-
casts. The improvement in earnings forecast quality is also economically meaningful as
long/short portfolios constructed using the ICC based on earnings forecasts from the CM
have significant excess portfolio returns.
Third, we provide evidence that using analysts’ forecasts in a cross-sectional forecast
model is not sufficient to remove the optimistic bias nor to improve the accuracy of
forecasts. The cross-sectional models use in-sample coefficients to predict earnings out-of-
sample and this approach seems to introduce a large amount of noise in the out-of-sample
estimates, in particular for long-term estimates. The results show that the longer the
time horizon is, the worse the CSAF model’s performance in comparison with the raw
analysts’ forecasts.
The paper is organized as follows. In Section 2, we describe our sample selection,
the cross-sectional models, and provide details on the ICC estimation. In Section 3,
we compare the performance of earnings forecasts proxies in terms of bias, accuracy,
and ERC. In Section 4, we evaluate the performance of ICC estimates calculated using
different methods to forecast earnings. We conclude in Section 6.
7Easton and Monahan (2005) analyze the cross-sectional correlation between returns and different
ICC approaches and find that none of the ICC estimates has a positive association with returns. The
authors conclude that the ICC estimates are unreliable for the entire cross-section of firms.
5
2. Data and methodology
2.1. Sample selection
We select firms at the intersection of the Center for Research in Security Prices
(CRSP), Compustat fundamentals annual, and I/B/E/S summary files. We filter for
firms listed on NYSE, AMEX, and NASDAQ with share codes 10 and 11. Our sample
starts in June 1977, as this is the first year for which I/B/E/S provides analysts’ forecasts,
and ends in June 2015. We require at least five years of data for the 10-year pooled re-
gressions of the cross-sectional forecast models. To evaluate the earnings forecasts, we use
data from the year after the forecast was made. Therefore, our forecasts cover the period
from 1982 to 2014. We require non-missing one- and two-year-ahead earnings forecasts,
price, and shares outstanding from I/B/E/S and book values, earnings, and dividends
from Compustat to include a firm-year in the sample. Our proxy for the risk-free rate is
the yield on the U.S. 10-year government bond, which we obtain from Thomson Reuters
Datastream. We use the following variables from Compustat: income before extraor-
dinary items (Compustat IB), gross profits (Compustat items: (REVT −COGS)), total
assets (Compustat AT ), dividends (Compustat DVC ), book value (Compustat CEQ),
book value of debt (Compustat items: (DLC +DLTT )), and capital expenditures (Com-
pustat CAPX).
2.2. Earnings Forecasts
We develop a model that combines analysts’ earnings forecasts with a cross-sectional
regression model to forecast earnings. We benchmark this approach to popular methods
from the literature, namely using only analysts’ forecasts, the RW model,8and four cross-
sectional models: the CSAF, Hou et al. (2012) (HVZ),9EP, and RI models.10 Although
one of the benefits of the cross-sectional models is the wider coverage as accounting vari-
ables are usually more widely available than analysts’ forecasts, Li and Mohanram (2014)
show that cross-sectional earnings forecasts in the sample without I/B/E/S coverage are
8We include the RW based on evidence that at a one-year horizon, the RW model performs as well
as more sophisticated estimation methods (Gerakos and Gramacy,2013).
9According to Hou et al. (2012), their cross-sectional model is superior to analysts’ forecasts in terms
of forecast bias and ERC.
10We include the Earnings Persistence and Residual Income Models as a benchmark due to evidence
of Li and Mohanram (2014) that these models outperform the HVZ model in terms of forecast bias,
accuracy, earnings response coefficient, and correlation of ICCs with future earnings and risk factors.
6
substantially more inaccurate and biased than the sample with I/B/E/S coverage. This
is intuitive as firms without analyst coverage tend to be smaller firms with a lower infor-
mation environment (Hou et al.,2012), which makes it more difficult to forecast earnings
mechanically. In addition, the sample covered by I/B/E/S “represents 90 percent or more
of the total market capitalization”11 of all firms on NYSE, AMEX, and Nasdaq.
We obtain analysts’ forecasts and share prices from I/B/E/S as of June for each year
in the sample period. To compare analysts’ forecasts to the above-mentioned models, we
transform analysts’ estimates from a per share level to a dollar level by multiplying the
per share figures by the number of shares outstanding provided by I/B/E/S. For the RW
model, following Gerakos and Gramacy (2013), we use income before extraordinary items
from year (t) as earnings forecasts for year (t+τwith τ= 1 to 3).
We follow the approach of Hou et al. (2012) when estimating the cross-sectional re-
gressions. First, we run a rolling window pooled regression (in-sample) using the previous
ten years of data (see Equation 1). We regress the dependent variable earnings (E(i,t))
for firm (i) in year (t) on the independent variables (x1, x2,· · · , xn) for firm (i) in the
relevant year (t−τwith τ= 1 to 3). ((i,t)) is the error term for period (t). We perform
the regression at the dollar level with unscaled data.12
E(i,t)=α0+α1x1(i,t−τ)+α2x2(i,t−τ)+· · · +αnxn(i,t−τ)+(i,t).(1)
Second, we forecast earnings (E(i,t+τ)) (out-of-sample) for year (t+τ) (see Equation 2).
We obtain the forecast by multiplying the independent variables for each firm (i) of year
(t) with the coefficients (α0, α1, α2,· · · , αn) from the pooled regression from Equation 1.
The advantage of this approach is that there are no strict survivorship requirements as
we require firms only to have sufficient accounting data for year (t) to forecast earnings.
˜
E(i,t+τ)=α0+α1x1(i,t)+α2x2(i,t)+· · · +αnxn(i,t).(2)
Consider the following example. Assume that 2010 is year (t) and we want to forecast the
11Claus and Thomas (2001, pp. 1638).
12We estimate our results based on a dollar level instead of per share level because we apply the
earnings forecasts to estimate ICC approaches that rely on clean surplus relation, and this assumptions
is even more critical at the per share level. “Per share clean surplus relation does not hold if a firm
issues/buys shares insofar the transaction changes bvps [book value per share]”(Ohlson,2005, p. 327).
7
earnings for 2011 (t+τwith τ= 1). First, we run a pooled regression with the dependent
variable data for the period 2001–2010 (from year t−9 to year t) on the independent
variables for the period 2000–2009 (from year (t−9−τ) to year (t−τwith τ= 1) and
store the regression coefficients. Then, we multiply these coefficients (α0, α1, α2,· · · , αn)
by the independent variables (x1, x2, ..., xn) from year 2010 (year = t) to estimate the
earnings for 2011 (year t+τwith τ= 1).
We forecast earnings in June of each year (t). We take care to avoid the use of data
that was not publicly available at the estimation dates. To this end, we collect accounting
data only for companies with fiscal year end between April of year (t−1) to March of year
(t). To mitigate the influence of outliers, we winsorize earnings and other level variables
each year at the first and last percentile as in Hou et al. (2012) and Li and Mohanram
(2014).
Note that when evaluating forecast bias, accuracy, and ERC the researcher has to en-
sure that the definition of earnings forecasts and realized earnings are in line. More specif-
ically, analysts typically forecast street earnings, which differ from earnings according to
the Generally Accepted Accounting Principles (GAAP) in significant points (Bradshaw
and Sloan,2002). To account for this difference, we compare analysts’ forecasts and the
combined model forecasts to realized street earnings. For the other models (HVZ, RI,
EP, RW), we make the comparison based on realized income before extraordinary items,
which is based on GAAP. This distinction is also made in other papers (e.g., Hou et al.
(2012)).Furthermore, in order to report a fair comparison among the models, the sam-
ple of earnings forecast models is restricted to firm-year observations for which analysts’
forecasts are available.
2.2.1. Combined model
The combined model aims to take advantage of the high accuracy of analysts’ fore-
casts, while incorporating the low bias of the cross-sectional models. To include analysts’
forecasts, we use the last available forecast from I/B/E/S. Our cross-sectional model is a
parsimonious approach that includes gross profits and two variables related to past stock
returns. Our use of gross profits is motivated by findings from Novy-Marx (2013), who
shows that this variable explains most earnings related anomalies and a wide range of
seemingly unrelated profitable trading strategies. We include two variables related to
past stock returns because Ashton and Wang (2012) and Richardson et al. (2010) show
8
that price changes drive earnings. The model is presented in Equation 3:
E(i,t)=α0+α1eIBES1(i,t−τ)+α2GP(i,t−τ)+α3r10(i,t−τ)+α4r122(i,t−τ)+(i,t),(3)
(E(i,t)) represents the street earnings of firm (i) in year (t), (eIBES1(i,t−τ)with τ= 1 to 3)
is the I/B/E/S one-year-ahead earnings forecast, (GP(i,t−τ)) is gross profits, (r10(i,t−τ))13
is the change of market capitalization over the preceding month. (r122(i,t−τ))14 is the
change in market capitalization from t−12 to t−2 months. As the regression is carried
out at the dollar level, the I/B/E/S one-year-ahead earnings per share forecast, as well
as the realized street earnings per share, are multiplied by the number of shares provided
by I/B/E/S.
2.2.2. Cross-Sectional Analysts’ Forecasts
To show that the combined model benefits from the combination of analysts’ forecast
with a mechanical model (and that neither of its components drives the strong forecast
performance), we include a model that uses analysts’ forecast in a cross-sectional regres-
sion. We estimate the cross-sectional analysts’ forecasts (CSAF) model with Equation 4:
E(i,t)=α0+α1eIBES1(i,t−τ)+(i,t),(4)
where (E(i,t)) represents the street earnings of firm (i) in year (t) and (eIBES1(i,t−τ)with
τ= 1 to 3) are the I/B/E/S one-year-ahead earnings forecasts. This regression is carried
out at the dollar level.15
2.2.3. The HVZ Model
We estimate the Hou et al. (2012) model with Equation 5:
E(i,t)=α0+α1eA(i,t−τ)+α2D(i,t−τ)+α3DD(i,t−τ)+α4E(i,t−τ)+α5N egE(i,t−τ)+
α6Ac(i,t−τ)+(i,t),(5)
13We estimate (r10(i,t−τ)) by multiplying market equity of month (t−1−τ) with the total return
(including dividends) from month (t−1−τ) to (t−τ).
14We estimate (r122(i,t−τ)) by multiplying market equity of month (t−12 −τ) with the total return
(including dividends) from month (t−12 −τ) to (t−2−τ).
15In unreported tests we confirmed that the main results still hold if we perform the regression at the
per share level.
9
where (E(i,t)) represents income before extraordinary items of firm (i) in year (t), (A(i,t−τ))
represents total assets in year (t−τwith τ= 1 to 3), (D(i,t−τ)) denotes paid dividends of
firm (i) in year (t−τwith τ= 1 to 3), (DD(i,t−τ)) is a dummy variable that equals 1 if firm
(i) paid a dividend in year (t−τ) and 0 otherwise, (NegE(i,t−τ)) is a dummy variable, which
is set to 1 if company (i) reported negative earnings and 0 otherwise, and (Ac(i,t−τ)) is ac-
cruals for firm (i) in year (t−τwith τ= 1 to 3). Accruals are estimated until 1987 as the
change in non-cash current assets less the change in the current liabilities, excluding the
change in short-term debt and the change in taxes payable minus depreciation and amorti-
zation expenses (Compustat items: (ACT −CHE)−(LCT−DLC −TXP)−DP). Starting
in 1988, we estimate accruals as the difference between earnings and cash flows from
operations (Compustat items: IB−(OANCF−XIDOC )).
2.2.4. The Earnings Persistence Model
The Earnings Persistence (EP) model according to Li and Mohanram (2014) is speci-
fied as:
E(i,t)=α0+α1eNegE(i,t−τ)+α2E(i,t−τ)+α3N egE ∗E(i,t−τ)+(i,t),(6)
where (E(i,t)) represents income before extraordinary items for firm (i) in year (t),16
(NegE(i,t−τ)) is a dummy variable, which is set to 1 if company (i) reported negative
earnings and 0 otherwise, and (NegE ∗E(i,t−τ)) is the interaction term of the latter two
variables.
2.2.5. The Residual Income Model
The Residual Income (RI) model was introduced by Edwards and Bell (1961) and
Feltham and Ohlson (1996). The model was subsequently adjusted by Li and Mohanram
(2014) to forecast earnings. We estimate the model according to Equation 7:
E(i,t)=α0+α1eNegE(i,t−τ)+α2E(i,t−τ)+α3N egE ∗E(i,t−τ)+α4B(i,t−τ)+
α5T AC C(i,t−τ)+(i,t),(7)
16Like Hou et al. (2012), we use income before extraordinary items as a proxy for earnings forecasts. We
use the same proxy for the benchmark models in order to make the comparison consistent. The results
are robust to using income before special and extraordinary items as proposed by Li and Mohanram
(2014).
10
where (E(i,t)) represents income before extraordinary items for firm (i) in year (t), (NegE(i,t−τ))
is a dummy variable, which is set to 1 if company (i) reported negative earnings and 0
otherwise, (NegE ∗E(i,t−τ)) is the interaction term between the negative earnings dummy
variable and earnings, (B(i,t−τ)) denotes book value for firm (i) in year (t−τwith τ= 1 to
3), and (T AC C(i,t−τ)) is total accruals for firm (i) in year (t−τwith τ= 1 to 3). Total ac-
cruals are based on Richardson et al. (2005), calculated as the sum of change in net working
capital (Compustat items: (ACT −C H E)−(LCT −DLC)), the change in net non-current
operating assets (Compustat items: (AT −ACT −IV AO)−(LT −LC T −DLT T )), and
the change in net financial assets (Compustat items: (I V ST +I V AO)−(DLT T +DLC +
P ST K )).
2.3. Estimating the ICC
The ICC is defined as the discount rate that equates a stock’s current price to the
present value of its expected future free cash flows to equity. The cash flows are estimated
using earnings forecasts and expected growth in earnings. There are many different ap-
proaches to estimate the ICC in the literature, so for the purpose of our tests, we choose
four common methods. We implement two methods that are based on a residual income
model, namely Gebhardt et al. (2001) (GLS) and Claus and Thomas (2001) (CT).17 In
addition, we employ two methods that are based on an abnormal earnings growth model,
namely Ohlson and Juettner-Nauroth (2005) (OJ) and Easton (2004) (modified price-
earnings growth or MPEG). Last, we estimate a composite ICC, which is the average of
the four above-mentioned approaches. To maximize the coverage of the composite ICC,
we only require a firm to have at least one non-missing individual ICC estimate (as in
Hou et al. (2012))
For the ICC calculation, we require each firm to have a one-year-ahead, a two-year-
ahead, and a three-year-ahead earnings forecast. If the three-year-ahead forecast is not
available, we estimate it by multiplying the two-year-ahead mean earnings forecast by
one plus the consensus long-term growth rate. If neither the three-year-ahead earnings
forecast nor the long-term growth rate is available, we compute the growth rate between
the one-year and two-year-ahead earning forecasts and use this to estimate the three-year-
17Although the CT and GLS approaches are both based on a residual income valuation model, the
methods have an important difference. While the CT model is designed to compute the market-level cost
of capital, the GLS model is made to compute the firm-level cost of capital.
11
ahead earnings forecast. Following Hou et al. (2012), we assume that the annual report
becomes publicly available at the latest 90 days after the fiscal year-end. Like Gebhardt
et al. (2001), we create a synthetic book value when this information is not yet public.
Specifically, we estimate the synthetic book value using book value data for year (t−1) plus
earnings minus dividends (Bt=Bt−1+EP St−Dt). Regarding the payout ratio, we use
the current payout ratio for firms with positive earnings. Like Gebhardt et al. (2001),for
firms with negative earnings, we compute the payout ratio as the ratio between dividends
and 6% of total assets. For the residual income models, we estimate the book value in
year18 t+τusing the clean surplus relation B(t+τ)=B(t+τ−1) +EP S(t+τ)∗(1 −P ayoutR).
We set the Payout Ratio to zero when the EP S(t+τ)is negative to avoid economically
questionable negative dividends. Furthermore, we exclude all observations with negative
book value per share. Following P´astor et al. (2008), we winsorize growth rates below 2%
and above 100%. See Appendix A for a detailed description of the ICC methodologies.
3. Empirical results of earnings forecasts methods
3.1. Coefficient estimates of cross-sectional regressions
In this section, we present the first step of our procedure to forecast earnings, i.e.,
the pooled (in-sample) regression using lagged ten years of data. We report the average
coefficients, the respective t-statistics with Newey and West (1987) adjustment and the
Adjusted R-squared. The earnings are estimated yearly from 1983 to 2015 for one-year-
ahead forecasts, from 1985 to 2015 for two-year-ahead forecasts, and from 1987 to 2015
for three-year-ahead forecasts. We regress earnings at time (t) on lagged independent
variables. (τ= 1), (τ= 2), and (τ= 3) indicate that the independent variables are
lagged by one, two and three years, respectively.
Panel A of Table 1reports the results for the combined model. First, we can see
that lagged analysts’ earnings forecasts (eIBES1i,t−τwith τ= 1 to 3) are highly signif-
icant in explaining earnings even when controlling for other variables from the earnings
forecasts literature. Various studies have documented the accuracy of analysts’ earnings
forecasts (e.g., Fried and Givoly (1982); O’Brien (1988); Hou et al. (2012)) and this find-
ing corroborates our choice of including analysts’ forecasts in our combined model. In
18The CT (GLS) ICC approach requires the calculation of book value from the year tto year t+τ
with τ= 4 (τ= 11).
12
terms of magnitude, the average coefficient for analysts’ earnings forecasts is less than 1
(0.957 for one-year-lagged regression, 0.872 in two-year-lagged regression, and 0.774 in the
three-year-lagged regression), which confirms the result from the literature that analysts’
forecasts tend to be too optimistic.
Table 1: Coefficient estimates from the pooled (in-sample) regressions
Panel A: Combined Model
Intercept eIBE S1(t−τ)GP(t−τ)r10(t−τ)r122(t−τ)Adj. R-squared
τ= 1 -1.550 0.957 -0.006 0.057 0.013 0.94
[4.33]** [33.31]** [2.62]* [4.74]** [2.02]
τ= 2 0.914 0.872 0.026 0.086 0.014 0.86
[0.53] [21.37]** [7.32]** [4.24]** [2.25]*
τ= 3 3.947 0.774 0.057 0.054 0.037 0.81
[1.08] [13.08]** [12.53]** [3.13]** [1.18]
Panel B: Cross-Sectional Analysts’ Forecasts (CSAF)
Intercept eIBE S1(t−τ)Adj. R-squared
τ= 1 -1.675 0.953 0.94
[3.85]** [35.87]**
τ= 2 5.941 0.971 0.85
[1.74] [22.08]**
τ= 3 15.343 0.992 0.78
[2.6]* [20.38]**
Panel C: Hou et al. (2012) Mo del
Intercept E(t−τ)A(t−τ)D(t−τ)Acc(t−τ)DD(t−τ)Neg E(t−τ)Adj. R-squared
τ= 1 -2.202 0.733 0.002 0.339 -0.086 5.572 4.258 0.77
[1.85] [42.69]** [3.80]** [9.49]** [-0.86] [8.56]** [1.15]
τ= 2 -1.675 0.641 0.004 0.460 -0.135 7.848 6.972 0.69
[-1.09] [27.86]** [3.4]** [8.01]** [-0.49] [6.63]** [1.40]
τ= 3 1.249 0.668 0.004 0.411 -0.168 6.905 16.315 0.66
[1.16] [10.85]** [5.05]** [8.04]** [2.03] [6.63]** [2.37]*
Panel D: Earnings Persistence
Intercept E(t−τ)NegE ∗E(t−τ)N egE(t−τ)Adj. R-squared
τ= 1 2.380 0.968 -0.980 -9.728 0.77
[6.05]** [77.46]** [6.41]** [3.26]**
τ= 2 6.046 0.993 -1.394 -11.644 0.68
[4.64]** [34.54]** [7.57]** [2.46]*
τ= 3 10.411 1.038 -1.990 -19.516 0.63
[2.63]* [23.05]** [7.37]** [3.47]**
Panel E: Residual Income
Intercept E(t−τ)NegE ∗E(t−τ)B(t−τ)T AC C(t−τ)N egE(t−τ)Adj. R-squared
τ= 1 -0.362 0.767 -0.502 0.035 -0.049 -8.476 0.78
[-0.30] [18.80]** [6.17]** [8.81]** [-1.14] [2.70]*
τ= 2 1.346 0.688 -0.661 0.053 -0.072 -10.737 0.70
[0.91] [25.59]** [5.62]** [9.68]** [-1.35] [2.23]*
τ= 3 3.128 0.679 -1.108 0.062 -0.055 -15.394 0.66
[1.42] [12.72]** [7.21]** [7.40]** [1.81] [2.23]*
This table shows the average coefficients, the respective t-statistics with Newey and West (1987) ad-
justment (in brackets) and the Adjusted R-squared from pooled regressions using 10 years of data. We
regress Earnings from year t on lagged independent variables from year (t−τwith τ= 1 to 3 years).
The regressions are performed from 1982 to 2014 for τ= 1, from 1983 to 2013 for τ= 2, and from
1984 to 2012 for τ= 3.** and * denote significance at 0.01 and 0.05 level, respectively. Panel A re-
ports the coefficients from the Combined Model, Panel B from the Cross-sectional Analysts’ Forecasts,
Panel C from HVZ model, Panel D from Earnings Persistence, and Panel E from Residual Income. The
columns display the variables used in the regression (see section 2.2 for details on the construction of
these variables).
Although the one-year-lagged gross profits variable (GPi,t−1) is negative and weakly
significant in explaining earnings, the two-, and three-year-lagged coefficients of gross
profits are positive and significant with a t-statistic of 7.32 and 12.53 and coefficients of
0.026 and 0.057, respectively. The low significance and the negative coefficients in the
13
one-year-lagged (τ= 1) regression are likely due to the large explanatory power of ana-
lysts’ one-year-ahead earnings forecasts, leaving one-year-lagged gross profits redundant.
The positive and significant coefficients of gross profits in the two and three-year-lagged
regressions confirm the results of Novy-Marx (2013) that this variable is a good proxy for
future earnings.
The coefficients of the one-month past stock return (r10(t−τ)) are all positive (0.057,
0.086, and 0.054, for τ= 1 to 3, respectively) and significant at the 1% level in all analyzed
periods. Finally, past stock return from −12 to −2 months (r122(t−τ)) is significant at the
5% significance level for the two-year-lagged period (t-statistics of 2.25) having a positive
coefficient (0.014 for τ= 2). These results confirm the findings from Ashton and Wang
(2012) and Richardson et al. (2010) that stock price changes have a positive correlation
with forward earnings and they tie in with the evidence from Abarbanell (1991) that
analysts’ forecasts do not fully reflect the information in prior stock price changes. Our
results are also in line with Guay et al. (2011) who find that analysts tend to react slowly
to information contained in recent stock price changes.
In Panel B of Table 1, we see the results regarding the CSAF model. In particular, the
coefficients of analysts’ earnings forecasts in the one-year-lagged regressions are quite close
to the CM (coefficient of 0.953 with t-statistics of 35.87 for the CSAF compared to the
coefficient of 0.957 and t-statistics of 33.31 for the CM). However, the two- and three-year-
lagged regressions show a different picture. While the coefficients of analysts’ earnings
forecasts on the CSAF regression are closer to one (0.971 in the two-year-lagged regression
and 0.992 in the three-year-lagged regression), the coefficients of the CM are lower (0.872
in the two-year-lagged regression and 0.774 in the three-year-lagged regression). This
indicates that the additional variables gross profits and lagged returns in the CM become
more important in the two- and three-year ahead earnings forecasts compared to the one-
year ahead ones. These results are in line with Bradshaw et al. (2012) who show that
analysts’ forecasts are accurate for one-year-ahead horizons, but the two- and three-year-
ahead forecasts can underperform even a random walk model.
In Panel C of Table 1, we see the results regarding the HVZ model. The model pro-
posed by Hou et al. (2012) shows a positive and significant relation between earnings
(E(t)) and one-, two-, and three-year-lagged (τ= 1 to 3) earnings (E(t−τ)), lagged div-
idends (D(t−τ)), lagged assets (A(t−τ)) and the dummy of lagged dividends (DD(t−τ)).
14
The coefficient of the dummy variable indicating lagged negative earnings (NegE(t−τ))
is positive and statistically significant in three-year-lagged regression and the accruals
(Ac(t−τ)) variable is significant in none of the regressions. The magnitude and the sign
of the coefficients are similar to Hou et al. (2012) and Li and Mohanram (2014), even
though the sample period is different.19
For the EP model (see Panel D of Table 1), the lagged dummy variable of negative
earnings (NegE(t−τ)) is negative and significant, lagged earnings (E(t−τ)) is positive and
significant, and the interaction term (Neg E * E(t−τ)) is negative and significant in all
analyzed regressions (τ= 1 to 3).
For the RI model (see Panel E of Table 1), the lagged dummy of negative earnings
(NegE(t−τ)) is negative and significant, lagged earnings (E(t−τ)) is positive and significant,
the interaction term (Neg E * E(t−τ)) is negative, and lagged book value (B(t−τ)) is
positive and significant. All these results are similar to Li and Mohanram (2014) with the
only difference being that (T AC C(t−τ)) is negative but not significant in our regression.
This difference is probably due to the different estimation period and a possibly different
calculation method of standard errors for the t-statistics.
When we compare the adjusted R-squared figures of the tested models, we see that the
combined model and the CSAF present the highest values for all analyzed periods. For
the one-year-lagged regression, the adjusted R-squared of the combined model is 0.94,
compared to 0.94 (CSAF), 0.77 (HVZ model), 0.77 (EP model), and 0.78 (RI model).
For the two-year-lagged regression, the combined model has an adjusted R-squared of
0.86, which is higher than the CSAF(0.85) HVZ (0.69), EP (0.68), and RI (0.70) models.
For the three-year-lagged regression, the adjusted R-squared values are 0.81 (combined
model), 0.78 (CSAF), 0.66 (HVZ model), 0.63 (EP model), and 0.66 (RI model). Our
adjusted R-squared values for the EP and RI models are higher than in Li and Mohanram
(2014) as we estimate these models at the dollar level so that the heteroskedasticity of the
dollar level data inflates the adjusted R-squared. Although a high in-sample R-squared
value is not a sufficient condition for high out-of-sample performance, it is a necessary
one (Welch and Goyal,2008). These in-sample results bode well for the combined model.
We will analyze the forecast bias in the next section.
19Hou et al. (2012) perform the regression yearly from 1968 to 2008 using ten years of lagged data,
while Li and Mohanram (2014) use the period from 1968 to 2012.
15
3.2. Bias comparison
There is ample evidence that analysts’ forecasts tend to be too optimistic (e.g., Lin
and McNichols (1998); Hong and Kubik (2003); Merkley et al. (2017)) with one of the
reasons being that they face a conflict of interest. In a survey of 365 analysts, Brown
et al. (2015) find that 44% of respondents say their success in generating underwriting
business or trading commissions is very important for their compensation. There is also
empirical evidence for the conflict of interest hypothesis. Hong and Kubik (2003) find
that controlling for accuracy, analysts who are optimistic compared to the consensus
are more likely to have favorable job separations. In particular, for analysts who cover
stocks underwritten by their houses, optimism becomes more relevant than accuracy for
favorable job separations. This optimism bias carries over into many applications that use
these forecasts as an input. Easton and Sommers (2007) estimate that overly-optimistic
analysts’ earnings forecasts lead to an upward bias in the ICC of 2.84%. Given the
importance of bias, we now compare the mean and median biases of all tested earnings
forecast models. We define bias as the difference between actual earnings and earnings
forecasts, scaled by the firm’s end-of-June market equity. We estimate bias out-of-sample
for one-, two-, and three-year-ahead forecasts (τ= 1 to 3).
Bias(i,t+τ)=(Actual Earnings(i,t+τ)−Earnings F or ecast(i,t+τ))
Market Equity(i,t)
(8)
As we can see in Equation 8, a negative (positive) bias means overly-optimistic (pes-
simistic) earnings forecasts. A bias of zero means unbiased forecasts. We estimate bias
at the end of June of each year20 for each firm. Then, we estimate the yearly mean and
median forecast biases. In Panel A of Table 2, we report the average of the yearly mean
and median biases and the respective t-statistics with the Newey-West adjustment for all
tested models.
In Panel A of Table 2, we see that the combined model is the only model that has no
statistically significant bias at the 0.05 significance level. We emphasize that this result
also holds when analyzing the mean and median biases and when testing one-, two- or
20We estimate one, two, three-year-ahead forecast bias for the periods 1985–2015, 1987–2015, and
1989-2015, respectively.
16
three-year-ahead forecasts. Our results confirm the positive bias of analysts’ forecasts,
as the mean and median biases are negative and statistically significant for one-, two,
and three-year-ahead forecasts. The one-year-ahead median bias is small in magnitude
(−0.002), i.e., it overestimates earnings by an amount of 0.2% of market equity. However,
the median bias increases in two and three-year ahead forecasts to −0.009 and −0.013,
respectively. Our results are different from those in Abarbanell and Lehavy (2003), who
show that the median bias is zero for analysts’ forecasts. This is possibly due to the
different sample period (Abarbanell and Lehavy (2003) analyze the period from 1985 to
1998) and the different forecast periodicity (the authors use quarterly forecasts while we
use yearly forecasts).
Moving to the benchmark models, the HVZ and RI models present an optimistic
mean bias in the one-, two-, and three-year-ahead forecasts. The EP model displays an
optimistic bias in the mean one-year-ahead forecasts as well as in the median two- and
three-year-ahead regressions. The forecasts based on the RW model show a positive bias
which means that they are overly pessimistic. This is intuitive as this model does not
take growth in earnings into account. Finally, the CSAF model performs well in that it
only has a significant bias at the two-year ahead forecast horizon. However, it does show
a greater bias in terms of magnitude for the three-year ahead forecasts compared to the
raw analysts’ forecasts. This indicates that simply incorporating analysts’ forecasts into
a cross-sectional regression does not remove the overly-optimistic bias.
17
Table 2: Earnings Forecasts Bias
Panel A: Bias of earnings forecasts
Bias Et+1 Bias Et+2 Bias Et+3
Mean Median Mean Median Mean Median
CM -0.006 0.005 -0.009 0.000 -0.005 -0.001
[-1.08] [1.99] [-1.06] [0.09] [-0.38] [-0.33]
AF -0.033 -0.002 -0.036 -0.009 -0.028 -0.013
[2.79]** [2.62]* [4.77]** [5.29]** [3.23]** [3.84]**
CSAF -0.008 0.005 -0.035 -0.010 -0.047 -0.018
[-1.21] [2.03] [3.10]** [2.58]* [1.88] [2.04]
HVZ -0.038 0.002 -0.040 -0.004 -0.053 -0.008
[3.49]** [0.92] [2.23]* [-0.84] [2.29]* [-1.15]
EP -0.048 -0.003 -0.073 -0.013 -0.078 -0.016
[3.44]** [-1.16] [4.69]** [3.08]** [7.41]** [2.42]*
RI -0.026 0.003 -0.040 -0.005 -0.051 -0.010
[2.06]* [1.10] [2.61]* [-1.46] [3.41]** [1.72]
RW 0.004 0.006 0.029 0.010 0.036 0.014
[0.49] [5.32]** [1.65] [3.13]** [1.53] [2.73]*
Panel B : Difference of bias of earnings forecasts
Bias Et+1 Bias Et+2 Bias Et+3
Mean Median Mean Median Mean Median
CM-AF 0.027 0.007 0.027 0.009 0.023 0.012
[2.50]* [2.31]* [3.33]** [2.83]** [6.60]** [5.13]**
CM-CSAF 0.003 0.000 0.026 0.011 0.042 0.016
[1.00] [0.48] [4.73]** [3.96]** [2.99]** [2.67]*
CM-HVZ 0.032 0.003 0.032 0.004 0.049 0.006
[2.42]* [0.86] [1.51] [0.80] [2.19]* [1.05]
CM-EP 0.042 0.008 0.065 0.013 0.074 0.015
[2.80]** [2.24]* [4.10]** [3.16]** [4.48]** [3.44]**
CM-RI 0.02 0.00 0.03 0.01 0.05 0.01
[1.44] [0.78] [1.88] [1.51] [2.55]* [2.06]*
CM-RW -0.010 -0.001 -0.037 -0.009 -0.041 -0.015
[0.96] [0.45] [2.34]* [3.26]** [1.91] [7.50]**
This table summarizes the mean and median bias for the US market. Bias is defined as the
difference between earnings forecasts and actual earnings, scaled by the firm’s end-of-June
market equity. The rows in Panel A show the different models: Combined Model (CM),
raw analysts’ forecasts (AF), Cross-Sectional Analysts’ Forecasts (CSAF), Hou, van Dijk
and Zhang (HVZ, 2012), Residual Income (RI), Earnings Persistence (EP), and Random
Walk (RW). Panel B displays the difference in bias between the CM and each of the other
forecast methods. The Newey-West t-statistics are presented in brackets. Results are shown
for one-, two-, and three-year ahead earnings forecasts. We estimate one, two, three-year
ahead forecast bias for the periods 1985–2015, 1987–2015, and 1989–2015, respectively. **
and * denote significance at 0.01 and 0.05 levels, respectively.
18
Figure 1: One-year-ahead Mean Bias Figure 2: One-year-ahead Median Bias
Figure 3: Two-year-ahead Mean Bias Figure 4: Two-year-ahead Median Bias
Figure 5: Three-year-ahead Mean Bias Figure 6: Three-year-ahead Median Bias
Panel B of Table 2shows whether the bias of the combined model is statistically
different in comparison to other models. The first row presents the difference between the
combined model and analysts’ forecasts, and we see that in all periods, for the mean and
the median, the biases are statistically different. Thus, we document that the combined
model is not as overly-optimistic as raw analysts’ forecasts. In the second row, we can
compare the CM to the CSAF, and we can see that the bias is statistically different
for two- and three-year-ahead mean and median forecasts. These results show that the
additional variables of the CM (compared to the CSAF) are important to obtain unbiased
19
forecasts, in particular for long-term earnings. When we compare the combined model to
the RI model, we see differences only for the three-year-ahead forecast. Furthermore, the
CM is statistically less optimistic than the HVZ for one- and three-year-ahead forecasts
and less pessimistic than the RW for two- and three-year-ahead forecasts. Last, we show
that the combined model is not as overly-optimistic as the EP model at a statistically
significant margin for all analyzed periods. In short, the combined model displays the
lowest bias of all tested models for all forecast horizons.
In order to analyze forecast bias over time, Figures 1 to 6 show the mean and median
forecast bias for one-, two-, and three-year-ahead earnings forecasts. For the sake of clarity,
we only include the raw analysts’ forecasts, the combined model, and the benchmark
model with forecast bias closest to zero in the figure. The optimism bias of the raw
analysts’ forecasts is immediately apparent. The corresponding graph is almost always
below zero for different forecast horizons and aggregation methods (mean and median).
We also see spikes in the bias for the RW model that correspond to economic shocks. For
example, the burst of the Internet bubble in 2001 results in an overly-optimistic estimate
as the previous (high) level of earnings is used as a forecast.
3.3. Accuracy comparison
There is substantial evidence that analysts’ forecasts are more accurate than mechani-
cal models (e.g., Fried and Givoly (1982); O’Brien (1988); Hou et al. (2012)). Researchers
argue that the higher accuracy of analysts’ forecasts is due to their “innate ability and
task-specific experience”21 (e.g., Clement et al. (2007)), industry related experience ob-
tained before becoming an analyst (e.g., Bradley et al. (2017)), and the number of analysts
covering each industry (e.g., Merkley et al. (2017)).
In this section, we compare the forecast accuracy of all tested models. We use absolute
error as a proxy for accuracy. Following Bradley et al. (2017), we estimate the absolute
error as the absolute difference between actual earnings and earnings forecasts, scaled by
the firm’s end-of-June market equity. The lower the value of the absolute error, the more
21According to Clement et al. (2007), task-specific experience is defined as the analyst’s experience in
forecasting around a particular type of situation or event, such as forecasting earnings when restructurings
occur or forecasting earnings around an acquisition.
20
accurate the forecast.
Absolute error(i,t+τ)=abs "(F orecast E arnings(i,t+τ)−Actual Earnings(i,t+τ))
Market Equity(i,t)#(9)
We estimate the out-of-sample absolute error at the end of June of each year,22 based
on Equation 9, for one-, two-, and three-year-ahead time horizons (τ= 1 to 3) for each
firm. In Panel A of Table 3, we report the yearly average of the mean and median absolute
errors (accuracy) and the respective t-statistics with the Newey-West adjustment for all
tested models.
As we see in Panel A of Table 3, the combined model is slightly superior to the raw
analysts’ forecasts and the CSAF model and markedly superior to the benchmark models
in terms of mean accuracy. If we compare the three most accurate models, the CM has
the best accuracy (0.046), followed by CSAF (0.050) and AF (0.057). The mean absolute
error of the benchmark models is roughly twice as high (inaccurate) as the CSAF model,
raw analysts’ forecasts or the combined model for the one-year-ahead forecast. For two-
and three-year ahead mean absolute error, the combined model again is more accurate
than the other models but we note that the difference to analysts’ forecasts is smaller
(the combined model has a mean absolute error of 0.063 and 0.070 for two- and three-
year-ahead forecasts, in comparison, the mean absolute error of analysts’ forecasts is
0.070 and 0.076). Regarding the CSAF model, the difference in terms of accuracy to the
CM becomes higher for long-term forecasts since the absolute error for the CSAF model
is 0.076 for two-year-ahead and 0.099 for three-year-ahead forecasts. The CSAF model
outperforms the raw analysts’ forecasts for the one-year-ahead horizon (mean error), but
it is less accurate for two- and three-year-ahead forecasts. Finally, the mean absolute
error of the other benchmark models is on average five percentage points higher than the
combined model.
22We estimate one-, two-, and three-year-ahead forecast accuracy for the periods 1985–2015, 1987–
2015, and 1989–2015, respectively.
21
Table 3: Earnings Forecasts Accuracy
Panel A: Accuracy of earnings forecasts
Accuracy Et+1 Accuracy Et+2 Accuracy Et+3
Mean Median Mean Median Mean Median
CM 0.046 0.015 0.063 0.026 0.070 0.033
AF 0.057 0.011 0.070 0.024 0.076 0.033
CSAF 0.050 0.016 0.076 0.030 0.099 0.042
HVZ 0.109 0.033 0.119 0.045 0.128 0.048
EP 0.112 0.029 0.135 0.045 0.135 0.050
RI 0.104 0.028 0.117 0.041 0.120 0.046
RW 0.114 0.025 0.124 0.037 0.127 0.044
Panel B : Difference of accuracy of earnings forecasts
Accuracy Et+1 Accuracy Et+2 Accuracy Et+3
Mean Median Mean Median Mean Median
CM-AF -0.010 0.005 -0.007 0.002 -0.006 -0.001
[1.48] [3.68]** [2.07]* [1.67] [3.61]** [0.84]
CM-CSAF -0.004 -0.001 -0.013 -0.004 -0.029 -0.009
[3.50]** [1.10] [2.46]* [1.89] [2.38]* [3.22]**
CM-HVZ -0.062 -0.018 -0.056 -0.019 -0.058 -0.015
[5.41]** [8.30]** [6.94]** [16.60]** [6.71]** [13.65]**
CM-EP -0.065 -0.013 -0.072 -0.019 -0.064 -0.017
[5.90]** [4.29]** [7.85]** [13.00]** [7.64]** [12.76]**
CM-RI -0.058 -0.013 -0.054 -0.014 -0.050 -0.014
[4.49]** [3.05]** [8.19]** [11.54]** [10.06]** [16.02]**
CM-RW -0.067 -0.010 -0.061 -0.011 -0.056 -0.011
[4.02]** [2.73]* [4.21]** [6.97]** [4.52]** [6.40]**
This table summarizes the mean and median forecast accuracy for the US market. We define
accuracy as the absolute difference between actual earnings and earnings forecasts, scaled by the
firm’s end-of-June market equity. The rows of Panel A show the different models: Combined
Model (CM), raw analysts’ forecasts (AF), Cross-Sectional Analysts’ Forecasts (CSAF), Hou,
van Dijk and Zhang (HVZ, 2012), Residual Income (RI), Earnings Persistence (EP), and Random
Walk (RW). Panel B displays the difference in forecast accuracy between the CM and each of the
other forecast methods. We show Newey-West t-statistics in brackets. We estimate one-, two-,
and three-year ahead forecast accuracy for the periods 1985–2015, 1987–2015, and 1989–2015,
respectively. ** and * denote significance at 0.01 and 0.05 levels, respectively.
With regard to median absolute error, the results of analysts’ forecasts are slightly
superior to the combined model for one- and two-year-ahead horizons (0.011 and 0.024
for raw analysts’ forecasts and 0.015 and 0.026 for the combined model for one-year and
two-year forecasts, respectively). For three-year-ahead forecasts, the median absolute
error is 0.033 for both models. The third best model in terms of median accuracy is
the CSAF, with absolute errors of 0.016, 0.030, and 0.042 for one-, two-, and three-year-
22
ahead forecasts. Concerning the other benchmark models, the median absolute error is
substantially higher (more inaccurate) compared to the raw analysts’ forecasts, the CSAF
and the CM. We also highlight that the analysts’ forecasts are more accurate than the
ones estimated with the CSAF model in one-, two-, and three-year-ahead forecasts. This
is evidence that only including the analysts’ forecasts in a cross-sectional model is not
sufficient to improve the forecasts.
In Panel B of Table 3, we test whether the differences are statistically significant. The
CM shows superior accuracy compared to all cross-sectional models and the RW model.
Like Gerakos and Gramacy (2013), we find that the RW model is as accurate as the cross-
sectional models. Comparing the combined model to analysts’ forecasts, the combined
model outperforms the analysts in the medium and long-term (two- and three-year-ahead)
forecasts. However, the results for one-year-ahead are mixed since the analysts’ forecasts
have a better median accuracy, while the mean accuracy is not statistically different
between both models.
In Figures 7 to 12, we plot the forecast accuracy over time for the tested methods.
The raw analysts’ forecasts are superior to the combined model in terms of one-year-
ahead median accuracy, in particular for the first years of the sample period. When we
split the analyzed period into two equal-length sub-periods, we see that the difference
in median accuracy during the period 1985–2000 is 0.0073, while in the period 2001–
2015 it decreases to 0.0022. We observe the same pattern for two-year-ahead median
accuracy; here the difference falls from 0.0032 (earlier period) to 0.0000 (later period),
which indicates that the combined model has improved the accuracy compared to the
raw analysts’ forecasts over the years. Last, note that the raw analysts’ forecasts and the
combined model outperform the benchmark models in all periods.
23
Figure 7: One-year-ahead Mean Accuracy Figure 8: One-year-ahead Median Accuracy
Figure 9: Two-year-ahead Mean Accuracy Figure 10: Two-year-ahead Median Accuracy
Figure 11: Three-year-ahead Mean Accuracy Figure 12: Three-year-ahead Median Accuracy
3.4. Earnings Response Coefficient
The ERC is the coefficient that measures the response of stock prices to surprises (new
information) in accounting earnings announcements (Easton and Zmijewski (1989)). Li
and Mohanram (2014) explain that a higher ERC suggests that the market reacts more
strongly to the unexpected earnings from a model that represents a better approximation
of market expectations. According to Brown (1993), assuming an informationally efficient
market, the accuracy and market association could be considered “two sides of the same
24
coin.”23 However, it is important to clarify that while bias and accuracy are ex-post
assessments of forecasts, the ERC examines the extent to which earnings forecasts provide
the best ex-ante estimates of market expectations. This analysis also helps to rule out
the possibility that our results are only driven by different definitions of earnings (street
versus GAAP).
We estimate the ERC using the sum of the quarterly earnings announcement returns
(market-adjusted, from day −1 to day +1) on one-, two-, and three-year-ahead firm-
specific unexpected earnings (i.e., the forecast bias) measured over the same horizon. The
unexpected earnings, as well as the returns, are standardized to make the ERC comparable
among all models. Panel A of Table 4shows the time-series average of the ERCs, the
respective t-statistics, and the time-series average of adjusted R-squared for all tested
models. Panel B of Table 4shows the pairwise comparison between the combined model
and the other models.
As we see in Panel B of Table 4, for one-year-ahead forecasts, the combined model out-
performs raw analysts’ forecasts regarding ERC coefficient and adjusted R-squared. The
difference in the ERC coefficient is also highly statistically significant (t-statistic of 3.76).
For the same forecast horizon, the combined model does not significantly outperform the
other benchmark models. When analyzing two-year-ahead forecasts, we note that the
combined model shows a higher ERC coefficient than the CSAF, HVZ, EP, RI, models
and a higher adjusted R-squared than the CSAF, HVZ and RI models at a statistically
significant margin. Finally, for three-year-ahead forecasts, the results are statistically
different when comparing the combined model to the RW or the CSAF models.
In summary, we find that the combined model is not just the less biased and more
accurate one but also represents market expectations most consistently among all tested
models.
23Brown (1993, pp. 296).
25
Table 4: Earnings Response Coefficient
Panel A: Earnings Response Coefficient (ERC)
Et+1 Et+2 Et+3
ERC Adj. R-squared ERC Adj. R-squared ERC Adj. R-squared
CM 0.132 0.016 0.130 0.017 0.098 0.009
[13.12]** [5.72]** [6.75]**
AF 0.104 0.011 0.097 0.011 0.087 0.008
[9.25]** [5.15]** [6.60]**
CSAF 0.129 0.016 0.109 0.013 0.061 0.005
[12.66]** [4.96]** [4.09]**
HVZ 0.120 0.015 0.081 0.010 0.057 0.006
[10.75]** [5.30]** [3.25]**
EP 0.114 0.015 0.069 0.007 0.068 0.006
[9.03]** [4.53]** [5.85]**
RI 0.124 0.017 0.082 0.008 0.072 0.006
[11.03]** [7.83]** [5.94]**
RW 0.120 0.015 0.088 0.009 0.061 0.005
[7.37]** [6.80]** [4.38]**
Panel B: Comparison of the difference
Et+1 Et+2 Et+3
ERC Adj. R-squared ERC Adj. R-squared ERC Adj. R-squared
CM-AF 0.028 0.005 0.033 0.007 0.011 0.002
[3.76]** [4.27]** [1.21] [1.47] [1.32] [1.51]
CM-CSAF 0.003 0.000 0.021 0.004 0.037 0.004
[0.59] [0.23] [3.16]** [3.08]** [2.45]* [2.88]**
CM-HVZ 0.011 0.000 0.049 0.007 0.041 0.003
[0.95] [0.15] [2.12]* [2.12]* [1.98] [1.64]
CM-EP 0.018 0.000 0.060 0.010 0.030 0.003
[1.72] [0.14] [2.42]* [2.02] [1.51] [1.83]
CM-RI 0.007 -0.001 0.047 0.010 0.027 0.003
[0.70] [0.35] [2.63]* [2.21]* [1.34] [1.82]
CM-RW 0.012 0.001 0.042 0.008 0.037 0.004
[0.68] [0.26] [1.88] [2.02] [3.69]** [2.53]*
This table reports the time-series averages of the earnings response coefficients (ERC) for forecasts from the
Combined Model (CM), raw analysts’ forecasts (AF), Cross-Sectional Analysts’ Forecasts (CSAF), Hou,
van Dijk and Zhang (HVZ, 2012), Residual Income (RI), Earnings Persistence (EP), and Random Walk
(RW) models, as well as their pairwise comparisons. The Newey-West t-statistics are reported in brackets.
The ERC is estimated by regressing the sum of the quarterly earnings announcement returns (market-
adjusted, from day −1 to day +1) over the next one-, two-, and three-years on firm-specific unexpected
earnings (i.e., the forecast bias) measured over the same horizon. We standardize the unexpected earnings
and the returns to make the ERC comparable among all models. ** and * denote significance at 0.01, and
0.05 levels, respectively.
4. Implied Cost of Capital
The ICC is a popular proxy for expected returns (see e.g., P´astor et al. (2008); Frank
and Shen (2016)) as its estimates contain less noise than estimates based on realized
returns (e.g., Lee et al. (2009)). Better earnings estimates should improve the correlation
between the ICC and subsequent realized earnings leading to better ICC estimates. In this
26
section, we analyze the performance of ICC estimates using proxies for earnings forecasts
based on the combined model, analysts’ forecasts, and the benchmark models. First, we
compute the ICC on an aggregate level and evaluate its ability to predict realized returns
over time. Then, we analyze the cross-sectional correlation between ICC and ex-post
forward returns.
4.1. Relation between ICC and returns on an aggregate level
There is evidence that the ICC at an aggregate level is a good proxy for time-varying
expected returns (e.g., P´astor et al. (2008); Li et al. (2013)). Due to the fact that one of
the main inputs for the ICC estimation are earnings forecasts, we believe that this input
can strongly influence the ICC’s performance as a proxy for expected returns. In this
section, we test whether the slopes of ICC calculated using different proxies for earnings
forecasts at predicting future market returns are greater than zero.24 We regress ex-post,
one-year-forward value-weighted (VW) excess market returns on VW ICC equity premia.
For each earnings forecast method, we estimate five different ICC models (GLS, CT, OJ,
MPEG, and a Composite, which is the average of the four previous models). We employ
the following proxies for earnings forecasts: the combined model, analysts’ forecasts, the
HVZ model, the EP model, and the RI model.25 To compute the ICC premia and excess
returns, we use the yield on the U.S. 10-year government bond. Panel A of Table 5
presents the results.
For the one-year-forward return predictive regressions, we document that the ICC
estimated with earnings from the combined model offers the largest number of significant
regression slopes. For three ICC methods (CT, OJ, and MPEG) the coefficients are
significant at the 0.05 level. In contrast, the HVZ and CSAF models, as well as raw
analysts’ forecasts, only produce two significant coefficients. By comparing the t-statistics,
the ICC estimated with the combined model reports the highest t-statistics in three out
of the five ICC approaches.
24Following Li et al. (2013), we use a one-sided test of the null hypothesis to test whether the slopes are
greater than zero. We use one-sided test to analyze the correlation between ICC and returns over-time
as well as cross-sectionally.
25We do not include the RW model because this method does not allow for earnings growth and is,
therefore, not suitable for estimating the ICC.
27
Table 5: Regressions of ICC and ex-post realized returns
Panel A: Forecasting at the aggregate level
Model CM AF CSAF HVZ EF RI
Intercept Coefficient Intercept Coefficient Intercept Coefficient Intercept Coefficient Intercept Coefficient Intercept Coefficient
GLS 3.381 1.553 1.571 1.470 3.244 1.615 4.414 1.376 4.261 1.252 4.358 1.240
[0.795] [1.156] [0.279] [1.132] [0.741] [1.152] [1.170] [0.900] [1.086] [0.816] [1.122] [0.800]
CT -1.087 4.056 -6.656 3.257 -2.095 4.506 3.549 2.942 3.674 1.945 3.217 2.158
[-0.209] [1.833]* [-0.832] [1.913]* [-0.367] [1.841]* [0.857] [1.263] [0.753] [0.622] [0.625] [0.779]
OJ -1.994 2.713 -10.315 2.899 -2.145 2.697 -2.016 4.066 5.234 -0.020 0.535 3.274
[-0.352] [1.988]* [-0.893] [1.626] [-0.345] [1.712]* [-0.419] [2.707]** [1.133] [-0.007] [0.100] [1.426]
MPEG 1.889 1.668 -6.416 2.294 3.011 1.025 4.062 2.189 5.319 0.626 4.705 1.798
[0.468] [2.697]** [-0.705] [1.712]* [0.773] [1.429] [1.158] [1.892]* [1.717]* [0.323] [1.388] [1.139]
Composite 1.181 2.473 -4.899 2.483 0.908 2.516 3.947 2.323 4.741 1.126 4.073 1.745
[0.249] [1.679] [-0.578] [1.595] [0.180] [1.570] [1.007] [1.276] [1.301] [0.476] [0.996] [0.846]
Panel B: Fama-Macbeth regression
Model CM AF CSAF HVZ EF RI
Intercept Coefficient Intercept Coefficient Intercept Coefficient Intercept Coefficient Intercept Coefficient Intercept Coefficient
GLS 3.796 0.827 3.440 0.576 4.342 0.653 4.151 0.473 4.118 0.417 4.219 0.474
[1.623] [2.354]* [1.303] [1.380] [1.859]* [1.885]* [1.722]* [1.866]* [1.675] [2.132]* [1.736]* [2.097]*
CT 4.086 0.681 4.742 0.300 4.307 0.615 5.233 0.172 4.948 0.158 4.751 0.193
[1.719]* [2.976]** [1.817]* [1.188] [1.846]* [2.778]** [2.155]* [1.529] [2.066]* [1.666] [1.992]* [1.475]
OJ 4.350 0.411 4.852 0.167 5.267 0.262 5.482 0.092 5.478 0.097 4.775 0.215
[2.095]* [1.785]* [1.750]* [0.679] [2.516]** [1.415] [2.411]* [0.882] [2.417]* [0.830] [2.057]* [1.380]
MPEG 5.603 0.223 5.018 0.123 6.150 0.138 5.364 0.091 5.624 0.091 5.004 0.200
[2.484]** [1.368] [1.842]* [0.677] [2.657]** [1.014] [2.423]* [0.965] [2.459]* [0.832] [2.134]* [1.332]
Composite 4.108 0.659 4.344 0.311 4.616 0.553 4.881 0.256 4.867 0.218 4.637 0.289
[1.840]* [2.439]* [1.558] [0.999] [2.055]* [2.218]* [2.017]* [1.688] [2.006]* [1.789]* [1.945]* [1.993]*
Panel A presents univariate OLS regressions of ex-post excess realized returns on ICC premium based on five proxies of earnings forecasts: Combined Model
(CM), Analysts’ Forecasts (AF), Cross-Sectional Analysts’ Forecasts (CSAF), Hou et al. (2012) (HVZ), Earnings Persistence (EP), and Residual Income
(RI). We show the results based on the following ICC approaches: GLS, CT, OJ, MPEG and the composite of the before-mentioned ICC approaches. The
dependent variables are the value-weighted market risk premium. Panel B presents the average coefficients of Fama-Macbeth regressions of realized returns on
ICC premium. To compute the ICC premiums and excess returns, we use the yield on the U.S. 10-year government bond. The Newey-West t-statistics with
three-lag periods are presented in brackets. ** and * denote significance based on one-tailed tests at 0.01 and 0.05 levels, respectively. Our sample is from June
1986 to June 2012.
28
4.2. Relation between ICC and returns cross-sectionally
In the previous section, we compared the predictive power of the ICC over time.
Now, we analyze whether the ICC has a positive correlation to the cross-section of stock
returns. To this end, we perform univariate Fama and Macbeth (1973) (FM) cross-
sectional regressions of ex-post-forward return premium on four individual ICC premium
estimates (we use the GLS, CT, OJ, and MPEG approaches) and on the Composite ICC
premium at the firm level. To estimate earnings’ forecasts for the ICC computation, we
use the following proxies: the combined model, analysts’ forecasts, the CSAF model, the
HVZ model, the EP model, and the RI model. The results are reported in Panel B of
Table 5.
When we regress cross-sectional monthly returns on the ICC, we can see that the ICC
estimated with the combined model has the strongest correlation with the cross-section
of returns since the coefficients are statistically significant in four (GLS, CT, OJ, and
Composite) out of five ICC approaches. The ICC estimated with the combined model
has the highest t-statistics in all analyzed ICC approaches. Interestingly, the second model
with the highest number of significant coefficients is the ICC estimated with the CSAF
model. This result shows that although the CSAF model is less accurate and more biased
than the raw analysts’ forecasts, the resulting ICC estimates have a higher correlation
with the cross-section of expected returns.
4.3. Portfolio strategies
As shown in Table 5, the ICC exhibits weak explanatory power in FM regressions.
However, this finding might be driven by small and micro-cap stocks as the FM regressions
weight the observations equally (Novy-Marx,2013). An additional shortcoming of FM
regressions is that they are sensitive to outliers. To address these potential issues, we
analyze the performance of value-weighted portfolios sorted on their ICC.
Table 6presents annual excess of returns (in excess of the risk-free return). The stocks
are sorted into quintiles and deciles based on their respective ICC at the end of June each
year from 1986 to 2012. We report the performance of the long-short strategies 5–1 (fifth
quintile minus the first quintile) and 10–1 (tenth decile minus first decile). We estimate
ICCs based on earnings from the following models: the CM, AF, CSAF, HVZ, RI, EP,
and RW. We sort portfolios based on the following ICC approaches: CT, GLS, OJ, and
29
MPEG. In addition, we include a Composite ICC, which is the average of the above-
mentioned approaches. To compute the excess returns, we use the one-month Treasury
bill rate.
The results of the long-short strategies show that only the ICC estimated with the
combined model and the CSAF Model reported significant excess returns. The ICC
estimated with the combined model has significant excess returns with the GLS approach
for the 5–1 (4.45%) and 10–1 (4.98%) long-short strategies and with the CT approach
for the 10–1 strategy, with annualized excess returns of 6.65%. The ICC estimated with
the CSAF model has significant excess returns for the strategy 10–1 with the CT and
Composite ICC. Some of our results here may differ from the corresponding results in
the original papers for the HVZ, EP, and RI models. This may be due to a different
return frequency used to compute t-statistics, different sample periods, and different stock
universes.
In summary, the ICC estimated with the combined model reports stronger correlation
with returns compared to the other models. The results hold in both dimensions, over-time
and cross-sectionally. The ICC estimated with the CSAF model has similar predictive
power compared to the raw analysts’ forecasts but a stronger correlation with returns
cross-sectionally.
5. Firm characteristics and expected returns
We evaluate whether a set of firm characteristics that have been used to explain the
cross-sectional variation of expected returns proxied by average realized returns also have
the same relation when the ICC as a proxy for expected returns is used. We perform
Fama and Macbeth (1973) (FM) cross-sectional regressions with ex-post excess realized
returns from July (year t) to June (year t+ 1) and excess ICC estimated with different
proxies for earnings forecasts as dependent variables. The independent variables are firm
characteristics available prior to the end of June of the year (t). We estimate the ICC26
based on different proxies of earnings forecasts at the end of June of each year.
We use the following firm characteristics. We estimate market βat the end of June
for each stock and for each year using the stock’s previous 60 monthly excess returns
26For the sake of brevity, following Hou et al. (2012), we provide the results based only on the Com-
posite ICC, which is the average of the CT, GLS, OJ, and MPEG approaches.
30
Table 6: Returns of portfolios formed on ICC
Combined Model Analysts’ Forecasts
GLS CT OJ MPEG Composite GLS CT OJ MPEG Composite
5-1 4.45 2.34 2.38 1.97 2.33 2.52 0.18 -0.79 0.17 0.50
[1.969]* [0.863] [0.978] [0.861] [0.862] [1.064] [0.065] [-0.279] [0.060] [0.177]
10-1 4.98 6.65 3.44 3.22 3.66 4.42 0.46 1.09 -0.24 -0.42
[1.656]* [2.064]* [1.129] [1.145] [1.156] [1.313] [0.117] [0.298] [-0.066] [-0.104]
CSAF Model HVZ Model
GLS CT OJ MPEG Composite GLS CT OJ MPEG Composite
5-1 3.72 2.39 0.64 1.61 2.89 2.28 1.34 2.04 2.02 0.64
[1.555] [0.916] [0.254] [0.673] [1.087] [0.840] [0.417] [0.790] [0.749] [0.217]
10-1 4.22 6.22 2.84 1.94 5.68 1.02 1.84 0.72 1.42 1.13
[1.326] [1.832]* [0.945] [0.656] [1.694]* [0.290] [0.519] [0.225] [0.421] [0.304]
EP Model RI Model
GLS CT OJ MPEG Composite GLS CT OJ MPEG Composite
5-1 2.86 1.60 -0.80 -1.74 0.07 2.21 -1.04 3.48 2.59 0.83
[0.951] [0.471] [-0.313] [-0.644] [0.020] [0.909] [-0.385] [1.556] [1.156] [0.312]
10-1 0.18 2.18 0.48 -1.18 1.42 1.26 1.39 4.26 3.01 1.92
[0.048] [0.557] [0.154] [-0.364] [0.352] [0.369] [0.378] [1.457] [1.023] [0.534]
This table reports the value-weighted excess of returns of portfolios sorted on ICC. We sort stocks at the end of June each
year from 1985 to 2012 into quintiles and deciles based on ICC. We report the results for long-short strategies of 5–1 (fifth
quintile minus first quintile) and 10-1 (tenth decile minus first decile). We sort the portfolios on ICC estimated with earnings
estimated by the Combined Model (CM), raw analysts’ forecasts (AF), Cross-Sectional Analysts’ Forecasts (CSAF), Hou,
van Dijk and Zhang (HVZ, 2012), Residual Income (RI), Earnings Persistence (EP), and Random Walk (RW) models. We
estimate ICC based on Claus and Thomas (2001) (CT), Easton (2004) (MPEG), Gebhardt et al. (2001) (GLS), and Ohlson and
Juettner-Nauroth (2005) (OJ). In addition, we include a Composite ICC, which is the average of all of the above-mentioned
approaches. To compute the excess of returns, we use the one-month Treasury bill rate. The one-month Treasury bill rate
was downloaded at the Kenneth French’s library. OLS t-statistics are presented in brackets. ** and * denote significance
based on one-tailed tests at 0.01 and 0.05 levels, respectively. The excess returns are annualized by multiplying by 12 and
are expressed in percentages. Our sample covers the period from July 1986 to June 2013.
31
(we require a minimum of 24 months, and excess returns are in excess of the one-month
Treasury bill rate taken from Kenneth French’s data library). Idiosyncratic volatility is
the standard deviation of the residuals from regressing the stock’s returns in excess of the
one-month Treasury bill rate on the three Fama and French (1993) factors27 estimated
yearly at the end of June using the previous 60 monthly returns (we require a minimum of
24 months) (e.g., Ang et al. (2006); Hou et al. (2015)). Asset growth is the change in total
assets from the fiscal year ending in year (t−1) to the fiscal year ending in (t), divided
by (t−1) total assets (e.g., Fama and French (2015)). Size is the natural logarithm of
market equity at the end of June in year (t). Gross profitability is the ratio of gross profits
to total assets (e.g., Novy-Marx (2013)). Leverage is book value of debt divided by book
equity. CapEx is capital expenditures divided by total assets from year (t−1). ln(beme)
is the natural logarithm of the ratio of book equity to market equity at the previous fiscal
year-end. In Table 7, we provide the average of the FM regression coefficients estimated
yearly for the period from June 1986 to June 2012 and the respective t-statistics with
Newey-West adjustment.
For market βthe results are mixed. While we see negative and significant coefficients
for the ICC with earnings forecasts from the combined model, as well as from the cross-
sectional (CSAF, HVZ, EP, and RI) models, the ICC using analysts’ earnings forecasts
has a positive relation with market β. The relation between market βand forward returns
is not statistically significant. These results are similar to Hou et al. (2012), as their ICC
model has a negative and significant relation to market βand the relation to realized
returns are not statistically significant. The ICC based on the combined model, analysts’
forecasts, EP, and HVZ earnings forecasts has a positive and significant relation with
leverage, but forward returns and ICC with CSAF and RI earnings forecasts have no
significant coefficients for leverage.
All proxies of expected returns have positive coefficients for idiosyncratic volatility.
However, the coefficients are statistically significant only for the ICC with earnings fore-
casts derived from the combined model (t-statistic of 2.514), analysts’ forecasts (t-statistic
of 4.446), the CSAF model (t-statistics of 2.518), and the EP model (t-statistic of 3.218).
The results for asset growth are interesting since we are able to confirm the negative
cross-sectional relation of asset growth and returns, also shown in Aharoni et al. (2013).
27We download the three Fama-French factor returns from Kenneth French’s website.
32
Although, the ICC estimated with most proxies of earnings forecasts shows a negative
and significant relation with asset growth (the ICC with the combined model earnings
forecasts has a coefficient of −0.497 and t-statistic of 5.386, the ICC with HVZ model has
a coefficient of −1.637 and t-statistic of 5.687, the ICC with the EP model has a coeffi-
cient of −0.417 and t-statistics of 3.521, and the ICC with the RI model has a coefficient
of −0.769 and a t-statistic of 4.986), the ICC with analysts’ forecasts has a positive and
significant relation with a coefficient of 0.181 and a t-statistic of 3.076. These findings
caution against using ICC based on analysts’ forecasts earnings as a proxy for expected
returns.
Table 7: Implied Cost of Capital and Risk Factors
Realized Returns CM AF CSAF HVZ EP RI
Market β0.180 -0.467 0.503 -0.703 -1.428 -0.455 -0.495
[0.106] [-2.669]* [2.170]* [-2.119]* [-3.605]** [-2.306]* [-1.888]
Idiosyncratic Volatility -0.126 0.161 0.184 0.636 0.262 0.533 0.417
[-0.792] [2.514]* [4.446]** [2.518]* [1.496] [3.218]** [1.793]
Asset Growth -4.871 -0.497 0.181 0.143 -1.637 -0.417 -0.769
[-5.563]** [-5.386]** [3.076]** [0.906] [-5.687]** [-3.521]** [-4.986]**
Ln(Size) 0.057 -1.331 -0.781 -3.736 -2.411 -3.236 -2.465
[0.084] [-5.863]** [-10.407]** [-5.168]** [-4.326]** [-6.518]** [-3.515]**
Gross Profitability 5.627 3.013 -0.461 1.439 -5.151 -0.209 -3.012
[3.181]** [8.492]** [-1.518] [1.881] [-6.657]** [-0.315] [-3.280]**
Leverage -0.065 0.107 0.064 0.032 0.132 0.059 0.057
[-0.507] [4.738]** [5.936]** [1.136] [4.599]** [2.078]* [1.472]
CapEX -5.660 -3.527 0.105 -2.412 -4.845 -2.680 -3.659
[-0.731] [-5.016]** [0.151] [-1.799] [-4.032]** [-2.384]* [-3.458]**
Ln(BEME) 2.086 1.951 1.212 2.585 4.263 3.262 3.961
[1.925] [16.141]** [10.602]** [11.665]** [10.974]** [13.213]** [37.946]**
This table presents the time-series average of slope coefficients from cross-sectional FM regressions of annual
Composite ICC premium and ex-post realized returns premium on the following risk factors: market β, id-
iosyncratic volatility, asset growth, size, gross profitability, leverage, CapEx and ln(beme) (book-to-market).
We estimate market βat the end of June for each stock and for each year using the stock’s previous 60
monthly excess returns (we require a minimum of 24 months, and excess returns are in excess of the one-
month Treasury bill rate taken from Kenneth French’s data library). Idiosyncratic volatility is the standard
deviation of the residuals from regressing the stock’s returns in excess of the one-month Treasury bill rate
on the three Fama and French (1993) factors estimated yearly at the end of June using the previous 60
monthly returns (we require a minimum of 24 months). Asset Growth is the change in total assets from the
fiscal year ending in year (t−1) for the fiscal year ending in (t), divided by (t−1) total assets. Size is the
natural logarithm of market equity at the end of June in year (t). Gross profitability is the ratio of gross
profits to total assets. Leverage is book value of debt divided by book equity. CapEx is capital expenditures
divided by total assets from year (t−1). ln(beme) is the natural logarithm of the ratio of book equity to
market equity at the previous fiscal year-end. We estimate ICC with earnings forecasts from the Combined
Model (CM), raw analysts’ forecasts (AF), Cross-Sectional Analysts’ Forecasts (CSAF), Hou, van Dijk and
Zhang (HVZ, 2012), Residual Income (RI), Earnings Persistence (EP), and Random Walk (RW) models.
To compute the ICC premiums and the excess returns, we use the yield on the U.S. 10-year government
bond. The Newey-West t-statistics are presented in parentheses. ** and * denote significance at 0.01 and
0.05 level, respectively. Our sample covers the period from June 1986 to June 2012.
The size effect is stronger when we use the ICC as a proxy for expected returns than
when realized returns are used. The ICCs based on any of the tested earnings forecasts
methods show significant coefficients at the 0.01 level. When we analyze the relation of
33
size and forward realized returns, the coefficient is not statistically significant. Concerning
the value effect, the coefficients of ln(BEME) are positive and statistically significant for
all proxies of expected returns, but the t-statistics are higher when the ICC is used as
a proxy for expected returns than when the ex-post realized returns are used. This is
not surprising as the ICC is a more sophisticated value measure and is therefore highly
correlated with the value factor (e.g., Li et al. (2013)).
According to Novy-Marx (2013), gross profitability has a positive and significant re-
lation to returns. In our study, we confirm these results as the t-statistic of returns is
3.181 and the coefficient is 5.627. The results for the ICC based on the combined model
(a positive coefficient of 3.013 and a t-statistic of 8.492) are also similar to the one from
returns. However, when we analyze the ICCs with earnings forecasts from the HVZ model
and the RI model, the results show a negative and significant relation, with a t-statistic
of 6.657, and 3.280, respectively. Finally, CapEx has a negative and significant relation
with the ICC based on the combined model, HVZ, EP, and RI models and insignificant
with the other proxies of expected returns analyzed in this study.
6. Conclusion
In this study, we develop a new method to forecast corporate earnings. We build upon
analysts’ earnings forecasts, which are known to be accurate, yet upwardly biased. To
improve these analysts’ forecasts we combine them with variables that have proven to be
good predictors of earnings. First, we include gross profits, as Novy-Marx (2013) finds a
strong association with earnings. Second, we follow Ashton and Wang (2012), who show
that stock price changes drive earnings, by including recent stock market performance.
We compare our new approach to several methods from the literature, namely raw
analyst forecasts, the model by Hou et al. (2012), the earnings persistent model (Li
and Mohanram,2014), and the residual income model (Li and Mohanram,2014). In
addition, we add an alternative benchmark, the CSAF model, which is based on a cross-
sectional regression including only analysts’ earnings forecasts as an input. We find that
our combined model has the lowest bias and highest accuracy among all the tested models.
Regarding market expectations, we show that the combined model also performs better
than the other benchmark models. Furthermore, we compute the ICC based on the
different earnings forecast models and find that the combined model leads to ICC estimates
34
that have the strongest association with subsequent realized earnings.
This new method makes a strong case for combining two different approaches to fore-
cast earnings, that is, human forecasts made by financial analysts and mechanical forecasts
based purely on financial data. These two approaches have distinct advantages and dis-
advantages, analysts’ forecasts are known to be accurate, yet upwardly biased. On the
other hand, mechanical forecasts are unbiased, but not as accurate. Combining them into
one model mitigates both disadvantages while conserving the advantages.
Our findings are relevant for practitioners working with earnings forecasts, as well as
academics employing earnings forecasts as inputs for valuation models, such as the ICC.
We recommend the use of our combined model to improve the accuracy and unbiasedness
of earnings forecasts, which benefits methods that build on these forecasts and applications
thereof.
35
Appendix A
Model Formulas and Implementation Details Source
GLS
Mt=Bt+
11
X
τ=1
Et[ROEt+τ−ICC ×Bt+τ−1]
(1 + ICC)k+Et[(ROEt+12 −I CC)×Bt+11]
ICC ×(1 + I CC)11 (.1)
where Mtis the market equity in year t. I CC is the Implied Cost of Capital. Btis
the book equity. Et[] represents market expectations based on information available
in year t, and (ROEt+τ−ICC )×Bt+τ−1, denotes the residual income in year
(t+τ), i.e., the difference between the return on book equity and the ICC multiplied
by the book equity in the previous year. We compute the ROE from years t+1 to
t+3 as F EP St/Bt−1, where the F E P Stis the consensus mean I/B/E/S analysts‘
earnings per share of period t. After year t+3, we linearly fade for the next nine
years to a target industry median. We calculate this proxy as a rolling industry
median over 5 years, considering only firms that have a positive ROE. Our industry
definition is based on Fama and French (1997). Finally, after the period t+12, the
terminal value is a simply perpertuity of the residual incomes. We estimate the
book value based on clean surplus accounting and a constant payout ratio P O, i.e.,
Bt=Bt−1+F EP St+ (1 −P O ).
Gebhardt
et al.
(2001)
CT
Mt=Bt+
5
X
τ=1
Et[ROEt+τ−ICC ×Bt+τ−1]
(1 + ICC)k+Et[(ROEt+5 −I CC)×Bt+4](1 + g)
(ICC −g)×(1 + I CC)5(.2)
where Mtis the market equips in year t. I CC is the Implied Cost of Capital. Btis
the book equity. Et[] represents market expectations based on information available
in year t, and (ROEt+τ−ICC)×Bt+τ−1), denotes the residual income in year
t+τ, i.e., the difference between the return on book equity and tee ICC multiplied
by the book equity in the previous year. We compute the ROE from years t+1 to
t+5 as F EP St/Bt−1, where the F E P Stis the consensus mean I/B/E/S analysts‘
earnings per share of period t. we estimate the forecasts in the years t+4 and
t+5 using a long-term growth forecast, g, and the three-year ahead forecast. We
estimate gas 10-year government bond minus an assumed real risk-free rate of three
percent. Finally, after the period t+5, the terminal value is a simply perpetuity of
the residual incomes. We estimate the book value based on clean surplus accounting
and a constant payout ratio P O , i.e., Bt=Bt−1+F EP St+ (1 −P O).
Claus
and
Thomas
(2001)
MPEG
Mt=Et[Et+2] + I CC ×Et[Dt+1]−Et[Et+1 ]
ICC2(.3)
where Mtis the market equity in year t. IC C is the Implied Cost of Capital. Et[]
represents market expectations based on information available in year t, Et+1 and
Et+2 are, the earnings forecast in years t+1 and t+2, respectively. Dt+1 is the
dividend in year t+1.
Easton
(2004)
OJ
ICC =A+sA2+Et[Et+1 ]
Mt
+ (g−(γ−1)) (.4)
where: A= 0.5((γ−1) + Et[Dt+1]
Mt), Mtis the market equity in year t. IC C is the
Implied Cost of Capital. Et[] represents market expectations based on information
available in year t, Et+1 is the earnings forecast in years t+1. Dt+1 is the dividend
in year t+1. gis the short-term growth, computed as the rate between EPSt+1 and
EPSt+2. γis the perpetual growth rate in abnormal earnings beyond the forecast
horizon, calculated as 10-year government bond minus an assumed real risk-free rate
of three percent.
Ohlson
and
Juettner-
Nauroth
(2005)
36
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