Post on 31-Mar-2020
Implied cost of equity capital estimates as predictors of accounting returns
Stephannie Larocque Mendoza College of Business University of Notre Dame Notre Dame, IN 46556 Phone: (574) 631‐6136 larocque.1@nd.edu
Matt Lyle Kellogg School of Management
Northwestern University Evanston, IL 60208
Phone: (847) 491‐2664 m‐lyle@kellogg.northwestern.edu
August 12, 2013
We thank Jeffrey Callen and Peter Easton for helpful comments and suggestions. Larocque appreciates the support of the Mendoza College of Business and the Ernst and Young Fellowship at the University of Notre Dame. Any errors remain our responsibility.
Abstract
Assuming that managers invest in NPV positive projects, these projects are expected to yield returns at, or better than, the firm’s cost of capital. Given this assumption, one would expect future firm accounting returns to be correlated with cost of equity capital (COEC) estimates. We find that very few of the implied COEC estimates which are commonly employed in academic studies are positively associated with future return on equity (ROE); in fact some implied COEC estimates are significantly negatively correlated with future ROE. These results hold over several time horizons and are robust to various control variables. A subset of COEC estimates based on the residual income model are positively associated with future ROE, as is the earnings‐to‐price ratio; however, all the COEC estimates based on the abnormal earnings growth model of Ohlson and Juettner‐Nauroth (2005) are negatively associated with future ROE.
Keywords: cost of capital; expected returns; return on equity
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1. Introduction
A number of influential articles in the finance and accounting literature describe how to reverse
engineer a market‐based estimate of a firm's cost of capital (or discount rate) from current price and
future cash flows or earnings expectations.1 A key motivation of these studies is that a cost of capital
estimate is important for capital budgeting and investment decisions. This suggests that these estimates
provide useful information when making investment decisions within the firm. If indeed a firm invests in
positive net present value projects, it naturally follows that firms with higher cost of capital should, on
average, generate higher future cash flows (or return on assets). We test this simple relation and find
that for a number of commonly‐used implied cost of equity capital (COEC) estimates, their relation to
future accounting returns is negative.
Cost of equity capital estimates have typically been compared with average ex post realized
stock returns, a common proxy for expected returns. So far, there is limited evidence of a positive
correlation between realized returns and COEC estimates implied from current price and forecasted
earnings (Easton and Monahan 2005; Botosan, Plumlee, and Wen 2011). A common explanation
provided for the lack of association between returns and COEC estimates is that realized returns are
noisy (Elton 1999) and that realized returns deviate from expected returns when expectations about
future cash flows and/or about future discount rates change (see for example Easton and Monahan
2005).
Unlike prior studies which have tried to determine if COEC estimates are associated with future
stock returns, our study examines the link between COEC estimates and future accounting returns. Our
motivation for doing so is straightforward. To the extent that firm managers invest in projects expected
to yield returns at or better than the firm’s cost of capital, one would expect COEC estimates to be
1 See, for example, Botosan (1997), Claus and Thomas (2001), Gebhardt, Lee, and Swaminathan (2001), Easton, Taylor, Shroff, and Sougiannis (2002), Gode and Mohanram (2003), Easton (2004), Nekrasov and Ogneva (2011), and Hou, van Dijk, and Zhang (2011).
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correlated with future accounting returns. As discussed in Modigliani and Miller (1958), the cost of
capital represents both the expected return to the firm’s investors and the expected yield at which
investments are attractive to the firm. Indeed the log‐linearization of Campbell and Shiller (1988) shows
that the link between COEC and future cash flows is tautological. Applying a similar log‐linearization,
Vuolteenaho (2002) provides an equivalent expression to show that COEC and future ROE must be
positively linked. In light of this relation, we investigate the association between the implied COEC
estimates commonly used in the literature and future return on equity (ROE).
Among the implied COEC estimates commonly employed in academic studies, we find that both
the Claus and Thomas (2001) COEC estimate (hereafter rCT) and a simple earnings yield (rEP) are
positively associated with future accounting return on equity (ROE). We find mixed evidence of a
positive correlation between the Gebhardt, Lee, and Swaminathan (2001) (hereafter, rGLS) COEC
estimate and realized ROE. This is perhaps unsurprising. The rCT and rGLS estimates use one‐ and two‐
year ahead expected earnings (proxied by analysts’ earnings forecasts), while rEP is simply expected
earnings scaled by the market value of equity.2 What is troubling is the negative and significant
correlation between future accounting returns and the COEC estimates put forward by Easton (2004)
(rPEG and rMPEG), and Gode and Mohanram (2003) (rGM). Each of these three COEC estimates is
derived from the Ohlson and Juettner‐Nauroth (2005) abnormal earnings growth (AEG) model, and none
of these three abnormal earnings growth‐based COEC measures is positively associated with future ROE.
We investigate this lack of positive association between accounting returns and implied COEC
estimates. First, we follow Larocque (2013) in predicting and removing analysts’ errors from implied
COEC estimates. Using these adjusted implied COEC estimates, we continue to find a positive and
significant relation between future ROE and each of rCT and rEP, and no evidence of a positive
2rCT and rEP are both significantly correlated with expected ROE (derived from analysts’ earnings forecasts) for the upcoming year, with respective Spearman correlations of 0.25 and 0.24. For rGLS, the Spearman correlation with expected ROE for the upcoming year is ‐0.10.
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association between future ROE and each of rPEG, rMPEG, and rGM. Second, to ensure that our results
are not driven by the use of analyst forecast data, we also test COEC estimates derived from the cross‐
sectional earnings forecast model of Hou et al. (2012). Using these cross‐sectional earnings forecasts, we
obtain little evidence of an association of rPEG, rMPEG, and rGM with future accounting returns. Third,
we investigate the association between each of the COEC estimates and future ROE by forming double
sorted portfolios similar to that of Armstrong, Core, Taylor, and Verrecchia (2011) and Fama and French
(1992). We first sort firms by variables including market‐to‐book (MB) ratio, size, earnings quality, and
earnings volatility and then we perform within sorts on COEC estimates. This allows us to evaluate the
relation between COEC and future ROE among firms with similar MB ratios, size, etc. However, even
after these sorts, we fail to find evidence of a positive association between future ROE and the COEC
estimates based on the AEG model (i.e., rGM, rMPEG, and rPEG). On the contrary, there is a remarkably
robust and strong negative association between future ROE and these COEC estimates.
Our study contributes to the literature in several ways. We provide first evidence that very few
of the implied COEC estimates used in the literature are positively correlated with future firm
accounting performance. The lack of an association is problematic, because a valid COEC measure must
be associated with future ROE. To illustrate this, we use the Vuolteenaho (2002) log‐linearization to
show that there is a tautological relation between the COEC, market‐to‐book, and future ROE. Given this
tautological relation, the results we provide suggest that we should question the validity of such implied
COEC estimates.
Second, the accounting‐based return decomposition allows us to formulate our empirical tests
of COEC estimates using accounting returns (ROE) and without relying upon stock returns. ROE is far less
noisy and much more predictable than are stock returns, which alleviates, to some extent, the issues
which arise in tests that use stock returns. We rely upon the fact that that a valid cost of capital estimate
must be tied to MB, and positively related to future ROE. This research design allow us to conduct
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validity tests using observable MB and future accounting data, without relying on future stock returns.
By doing this we shed new light on why there may be mixed results on the reliability of some of the
commonly‐used implied COEC estimates: we believe that this may be caused by the fact that many of
the COEC proxies do not forecast future accounting returns as theory suggests they should.
The next session discusses relation between ROE and the cost of equity capital. Section 3
discusses the sample used in this study and its research design. Section 4 presents the results of
empirical tests. Section 5 concludes. An appendix provides all variable definitions.
2. Implied cost of equity capital estimates and accounting returns
Motivated by the importance of the cost of capital for capital budgeting and investment
decisions, financial economists have developed numerous approaches to estimate the cost of equity
capital. Early work by Gordon and Shapiro (1956) derived the expected rate of profit on a share of stock
using the dividend discount model. A more recent literature that reverse engineers COEC estimates from
current prices and future cash flows or earnings expectations started with Botosan (1997) who tests for
an association between firm disclosure levels and a COEC estimate derived from the residual income
model (RIM). Studies by Claus and Thomas (2001) and Easton et al. (2002) derive implied COEC
estimates from RIM in order to impute the market risk premium. Also grounded in RIM, Gebhardt et al.
(2001) develop an implied COEC estimate that they associate with various firm and industry
characteristics. Ohlson and Juettner‐Nauroth (2005) as well as Gode and Mohanram (2003) and Easton
(2004) develop implied COEC estimates based on an abnormal earnings growth model. More recent
innovations to COEC estimation have been developed from simultaneously‐derived estimates of the
COEC and growth (Nekrasov and Ogneva 2011), earnings estimates derived from cross‐sectional models
(Hou et al. 2012), the rate of return inferred using option prices (Callen and Lyle 2013), individual
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analysts’ earnings and target price forecasts (Fitzgerald, Gray, Hall, and Jeyaraj 2013), and recursive
regression‐based models (Lyle and Wang 2013).
Since Botosan (1997), numerous studies have investigated the relation between the COEC and
such variables as restatements (Hribar and Jenkins 2004), tax rates (Dhaliwal, Krull, and Li 2007), internal
control deficiencies (Ogneva, Subramanyam, and Raghunanda 2007; Ashbaugh‐Skaife, Collins, Kinney,
and LaFond 2009), cross‐listing (Hail and Leuz 2009), and earnings attributes (Francis, Nanda, and Olsson
2008; Francis, LaFond, Schipper, and Olsson 2004; McInnis 2010), among others. Yet evidence on the
validity of these implied COEC estimates remains mixed, as Easton (2006) points out.
Attempts to validate these implied COEC estimates typically involve a comparison with ex post
realized returns, a common proxy for expected returns.3 Perhaps because of the noise in realized
returns (Elton 1999), there exists limited evidence of a positive association between realized returns and
implied COEC estimates. Guay, Kothari, and Shu (2011) fail to find evidence of a positive association
between realized returns and five implied COEC estimates; nor do Easton and Monahan (2005), even
after controlling for correlated omitted variables. In a study of seven COEC estimates, Botosan et al.
(2011) find that only rPEG and Botosan and Plumlee’s (2002) rDIV, derived from Value Line target prices,
are positively correlated with realized returns. A recent study by Lee, So, and Wang (2011) investigates
the relation between COEC and realized returns both in time‐series and cross‐sectionally.
In light of the limited evidence of an association between implied COEC estimates and realized
returns, it might prove fruitful to revisit the work of early financial economists including Dean (1951) and
Lutz and Lutz (1951) who tie the firm’s cost of capital to its expected return on investments. Building on
this, Modigliani and Miller (1958) state that the cost of capital represents both the expected return to
the firm’s investors and the expected yield at which investments are attractive to the firm. To the extent
3 A related strand of research compares implied COEC with risk factor proxies including beta, size, book‐to‐market ratio, and leverage (Gode and Mohanram 2003; Botosan and Plumlee 2005).
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that firm managers invest in projects expected to yield returns at or better than the firm’s cost of
capital, we can expect cost of capital estimates to be correlated with future, realized accounting returns.
Regardless of the model, or method, used all COEC models are derived from the basic present
value equation relating price to expected discounted dividends:
1
,
(1)
where is the stock price and represents dividends. The implied cost of equity capital is the value
that equates price with the right hand side of the equation. Similar to the Campbell and Shiller (1988)
log‐linearization of the dividend‐to‐price ratio, Vuolteenaho (2002) provides a log‐linear approximation
of the book‐to‐market ratio (see the appendix of Lyle and Wang 2013 for a detailed derivation):
tbm E r E roe , (2)
where is the log book‐to‐market ratio, r is the log stock return, and roe is the log return on
equity. Rearranging this equation shows that future expected return on equity and future returns must
be linked:
E roe E r , (3)
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where is the log market‐to‐book ratio. Thus future ROE and expected returns, tautologically, have a
positive relation after controlling for market‐to‐book. To connect this identity to the implied cost of
equity capital we, like Pástor, Sinha, and Swaminathan (2008) and Li, Ng, and Swamanathan (2013),
define as the (constant) cost of equity capital which allows us to write:
E roe 1
1. (4)
Equation 4 offers a simple and empirically testable implication: future ROE must be a positive function
of each of the market‐to‐book ratio and the cost of equity capital. Moreover, Equation 4 shows that
realized stock returns are not needed to evaluate COEC proxies; instead empirical tests can rely on the
market‐to‐book ratio and future return on equity.
3. Research design
3.1 Sample selection
Our research design follows directly from Equation 4, which says that a valid proxy for expected
returns must be correlated with future ROE, after controlling for the market‐to‐book ratio. To estimate
implied COEC, our proxy for expected returns, we require earnings forecasts, stock prices, and book
value of equity. Earnings forecasts come from I/B/E/S, accounting information such as book value and
ROE from Compustat, and price and returns information from CRSP. From the I/B/E/S unadjusted
summary reports for all U.S. firms we extract median analyst earnings forecasts for the next two years.
Specifically, we collect earnings forecasts for each firm from I/B/E/S immediately following the public
release of the firm’s annual earnings report. For example if a December fiscal year end firm announces
its 2008 annual earnings on February 12, 2009 we collect I/B/E/S consensus annual earnings forecasts
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for fiscal years 2009, , and 2010, , as soon as they become available following the earnings
announcement.
After restricting the sample to firm‐years with non‐missing I/B/E/S, CRSP, and Compustat data,
the six COEC estimates are estimated annually. The data requirements for each COEC estimate, outlined
below in section 3.2, yield a sample of 26,373 firm‐year observations for the period 1994‐2010. Panel A
of Table 1 outlines the sample selection procedure, and Panel B of Table 1 presents descriptive statistics
for the firms in the sample.
3.2 Cost of equity capital estimates
This study makes use of implied COEC estimates commonly used in the literature and derived
from I/B/E/S analysts’ forecasted earnings, specifically, rCT, rEP, rGLS, rGM, rMPEG, and rPEG. Each of
these estimation techniques is briefly outlined below, and the models used to calculate the implied
COEC estimates are listed in Table 2.
Both rCT and rGLS stem from the residual income model:4
1
, (5)
where is the book value of equity, represents abnormal earnings in year t+1 with
being earnings.
Claus and Thomas (2001) use the residual income model in order to estimate cost of capital, rCT.
Claus and Thomas assume that expected abnormal earnings can be estimated from analyst forecasts
over the next 5 years, assuming that clean surplus accounting holds. After five years, Claus and Thomas
4 See, for example, Ohlson (1995) for derivation of the residual income model.
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assume that abnormal earnings grow in perpetuity at the risk‐free rate less 3%. To estimate rCT, we
require non‐negative analysts’ forecasts for year t+1 (AFt+1) and k, the dividend payout ratio from year t‐
1. Analysts’ forecasts beyond year t+1 are set at the prior year’s forecast multiplied by one plus LTG, the
median analysts’ long‐term growth forecast according to I/B/E/S.
To estimate rGLS, Gebhardt et al. (2001) reverse‐engineer the residual income model and
assume that firm‐level return on equity reverts to the industry level over the horizon. Industry‐level ROE
is estimated on a rolling basis, using the median of the positive‐earning firms in the same Fama‐French
(1997) industry for the previous five years. Beyond year t+1, ROE is linearly interpolated to the industry
median by year t+11. Future book value is estimated recursively using the clean surplus relation and
estimates of expected ROE.
The rPEG, rMPEG, and rGM estimates build on the abnormal earnings growth model formed in
Ohlson and Juettner‐Nauroth (2005):
1
, (6)
where 1 .
Gode and Mohanram (2003) build on Ohlson and Juettner‐Nauroth (2005) to derive rGM using
earnings estimates, dividends per share, a long‐term growth rate (γ – 1), and current price. Easton
(2004) derives rMPEG from the abnormal earnings growth model using only earnings estimates,
expected dividends (divt+1), and current price. In a variation of rMPEG, Easton (2004) estimates rPEG
after assuming zero dividends. Both rMPEG and rPEG assume no change in abnormal earnings growth
beyond year t+1. Estimation of both rMPEG and rPEG requires non‐negative and increasing analysts’
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forecasts for year t+1. As in other COEC studies, these data requirements likely bias the sample towards
more stable and less risky firms.
The final COEC estimate used in this study, rEP, is simply estimated using the predicted earnings
yield ratio (AFt+1 divided by Pt).5
A summary of these six implied COEC estimates for 1994 to 2010 is presented in Panel A of
Table 3. For rCT, the mean estimate is 9.4% and for rEP it is 6.8%. For rGLS, the mean estimate is 10.8%.
For rGM, the mean estimate is 13.7%. The respective means for rMPEG and rPEG are 13.2% and 12.0%.
These averages compare with mean realized annual returns (calculated by compounding daily cum
dividend returns), RETt,t+1, of 13.4% in the year following the measurement of the COEC estimate and
mean realized return on equity (ROEt,t+1) of 13.8% during the fiscal year in which the COEC is estimated.
ROEt,t+1 calculated as income before extraordinary items (Compustat data item IB) in year t divided by
beginning common equity (Compustat data item CEQ).6 Inferences throughout this study are unchanged
when we winsorize each of the COEC estimates, ROE measures, and MB at the top and bottom 1% level.
Panel B of Table 3 reports average annual correlations among the firm‐level COEC estimates,
RETt,t+1, and ROEt,t+1. As in previous studies, the COEC measures are quite highly correlated, with the
cross‐correlations ranging from 0.13 to 0.83. This is not surprising as the models rely on many of the
same inputs, albeit with different growth and terminal value assumptions.
3.4 Tests associating cost of equity capital estimates with future return on equity
We evaluate the implied COEC estimates by testing their association with future ROE. First,
following Gode and Mohanram (2003), we form quintiles according to the annual level of each COEC
5 For each of the six COEC estimates, price is discounted back to the beginning of the fiscal year in order to be aligned with the measurement of book value, as in Easton and Sommers (2007). 6 Inferences are unchanged when ROE is calculated as net income (Compustat data item NI) divided by beginning common equity.
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estimate with quintile 1 (5) representing the quintile portfolio with the lowest (highest) COEC estimate.
We then report the average future realized ROE for each quintile portfolio.
We next conduct cross‐sectional regression analyses. Based on Equation 4, we estimate the
following specification in order to assess the extent to which firm‐level COEC estimates are associated
with future ROE. Specifically we estimate the following equation:
, , (7)
where represents the log COEC estimate and , represents the log of year return on
equity.
To the extent that the cost of equity capital represents the expected yield at which investments
are attractive to the firm, and investments with varying horizons are made by the firm, we expect that
COEC estimates are correlated with not only next period ROE, but also with future year’s accounting
returns. As a result, Equation 7 is estimated using each of one year ahead ROE, , , two year ahead
ROE, , , and three year ahead ROE, , . If COEC estimates predict accounting returns, we
should obtain a positive coefficient on in Equation 7. We also expect a positive coefficient on .
3.5 Tests associating cost of equity capital estimates from which predictable analysts’ errors have been removed with realized return on equity
Implied expected rates of return may not equal ex ante expected returns if analysts’ earnings
forecasts are not the market’s earnings expectations (see, for example, Easton 2006). The findings of
Larocque (2013) and Mohanram and Gode (2013) suggest that removing bias from analysts’ forecasts
could generate a more reliable COEC proxy. We thus form implied cost of equity capital estimates using
analysts’ forecasts from which predictable errors are removed. Following Larocque, we predict analysts’
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forecast errors using lagged forecast errors, returns, and firm size. We then test the extent to which
these adjusted COEC estimates are associated with ROE, as in Equation 7.
3.6 Tests associating cost of equity capital estimates formed using cross‐sectional earnings estimates with realized return on equity
In a recent study, Hou et al. (2012) use earnings forecasts from a cross‐sectional model to
estimate the implied COEC for a large sample of firms. The authors find that their COEC estimates
formed from cross‐sectional earnings estimates more reliably proxy for expected returns than do COEC
estimates derived from analysts’ forecasts. In our study, we form cross‐sectional earnings estimates
using lagged earnings, assets, dividend payment, and accruals as predictive variables as in Hou et al. We
then test the extent to which COEC estimates formed from these cross‐sectional earnings estimates are
associated with ROE, as in Equation 7.
3.7 Double sorted portfolios
Equation 4 says that expected returns should forecast future ROE, over and above the
information contained in the market‐to‐book ratio. In our cross‐sectional regression equations we
control for the average market‐to‐book effect. Alternatively, by sorting first on market‐to‐book and then
on COEC within each of the market‐to‐book portfolios we can isolate the ability of COEC to forecast ROE
for firms with similar market‐to‐book ratios. We also use this analysis to determine if other
characteristics such as size, earnings quality, and earnings volatility affect the relation between COEC
and future ROE.
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4. Empirical results
4.1 Tests associating cost of equity capital estimates with future accounting returns
We examine the relation between COEC estimates and future ROE in two ways. First, following
Gode and Mohanram (2003), quintiles are formed according to the annual level of each COEC estimate
with quintile 1 (5) representing the quintile portfolio with the lowest (highest) COEC estimate. As shown
in Table 4, across quintiles of rCT, realized ROE for the upcoming year ( , ) and the following year
( , ) increase, although not monotonically. For , , the difference between quintile 1 and
quintile 5 is positive and statistically significant for rCT. Similarly, across quintiles of rEP, ROE for each of
the three upcoming years increases although not quite monotonically. For each of , , , and
, , the difference between quintile 1 and quintile 5 is positive and statistically significant for rEP.
For the rGLS quintiles, , , , and , decrease monotonically. For each of , ,
, and , , the difference between quintile 1 and quintile 5 is negative and statistically
significant for rGLS. For the rGM and rMPEG quintiles, , decreases monotonically, while for the
rPEG quintiles, , decreases nearly monotonically, with a negative and statistically significant
difference between quintile 1 and quintile 5 for each of rGM, rMPEG, and rPEG. Across the rGM, rMPEG
and rPEG quintiles, the decrease in each of , and , across quintiles is monotonic or nearly
monotonic. This analysis provides preliminary evidence of a positive relation between each of rCT and
rEP, and realized ROE, and of a negative relation between realized return on equity and each of rGLS,
rGM, rMPEG, and rPEG.
Results of estimating Equation 7 are presented in Table 5, with , tests in Panel A, ,
tests in Panel B, and , tests in Panel C. Mean coefficients across the 13 sample years, the t‐
statistic testing whether the mean coefficient is different from zero, and the mean adjusted R2 from the
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annual regressions are reported, following Fama and MacBeth (1973).7 Throughout Table 5, the
coefficient on mb is positive and significant, as predicted by Equation 7. In Panel A, each of the rEP, rCT,
and rGLS COEC estimates is positively and significantly associated with , . For rCT in Column 1, the
coefficient is 1.141 (t‐statistic = 7.90); for rEP in Column 2, the coefficient is 2.043 (t‐statistic = 16.15);
and, for rGLS in Column 3, the coefficient is 0.747 (t‐statistic = 5.77). Surprisingly, each of the three
abnormal earnings growth‐based COEC estimates, rGM, rMPEG, and rPEG, has a significantly negative
relation with , . For rGM in Column 4, the coefficient is ‐0.495 (t‐statistic = ‐7.02); for rMPEG in
Column 5, the coefficient is ‐0.450 (t‐statistic = ‐6.35), and for rPEG in Column 6, the coefficient is ‐0.696
(t‐statistic = ‐7.77).
In Panel B, only the rCT and rEP COEC estimates are positively and significantly associated with
, . For rCT, the coefficient is 0.729 (t‐statistic = 6.46) while for rEP the coefficient is 1.441 (t‐
statistic = 10.24). The rGLS estimate is negatively, but not significantly, associated with , . Each of
the three abnormal earnings growth‐based COEC estimates, rGM, rMPEG, and rPEG, has a significant,
negative association with , . For rGM, the coefficient is ‐0.413 (t‐statistic = ‐4.86); for rMPEG, the
coefficient is ‐0.386 (t‐statistic = ‐4.55), and for rPEG, the coefficient is ‐0.658 (t‐statistic = ‐5.57).
We next test the relation between COEC estimates and longer‐horizon future ROE. To the extent
that the true underlying COEC represents the expected yield at which investments are attractive to the
firm (Dean 1951; Lutz and Lutz 1951), and those investments are made with varying horizons, we might
see a stronger association between the implied COEC estimates and future ROE over longer‐horizons. At
the same time, the results for longer horizons are naturally subject to possible survivorship bias.
In Panel C of Table 5, only the rCT and rEP COEC estimates are positively and significantly
associated with , . For rCT, the coefficient is 0.693 (t‐statistic = 6.86) while for rEP the coefficient
is 1.285 (t‐statistic = 14.20). rGLS is negatively, but not significantly, associated with , . Each of the
7 In untabulated analysis, we find that inferences are unchanged when we instead cluster by firm and time.
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AEG‐based COEC estimates, rGM, rMPEG and rPEG, has a significant negative correlation with , .
For rGM, the coefficient is ‐0.348 (t‐statistic = ‐5.09), for rMPEG, the coefficient is ‐0.324 (t‐statistic = ‐
4.79), and for rPEG, the coefficient is ‐0.552 (t‐statistic is ‐6.31).
To summarize, in both portfolio tests and regression analyses, we find consistent evidence that
rCT and rEP are associated with realized accounting returns, some evidence of an association between
rGLS and realized ROE, and consistent evidence of a negative, significant relation between future ROE
and each of the abnormal earnings growth‐based COEC estimates (rGM, rMPEG, and rPEG).
4.2 Tests associating cost of equity capital estimates from which predictable analysts’ errors have been removed with future return on equity
Table 6 presents the results of tests that regress realized ROE of varying horizons on adjusted
COEC estimates, i.e., COEC estimates based on analysts’ forecasts from which predictable errors have
been removed. Sample sizes are smaller for these tests, based on the variables used to predict and
remove analysts’ forecast errors in Larocque (2013)—in particular, lagged forecast errors, as well as size
and returns. As in Table 5, we find consistent evidence that rCT and rEP are significantly, positively
associated with realized accounting returns of varying horizons. For example, in Panel A, the coefficient
on rCT is 1.160 (t‐statistic = 6.81) and the coefficient on rEP is 1.433 (t‐statistic = 7.12). For rGLS, the
evidence is mixed, as in Table 5: for , , the coefficient on rGLS is positive and significant (0.911; t‐
statistic = 6.23) in Panel A while for , , the coefficient on rGLS is negative and significant (‐0.352; t‐
statistic = ‐1.87) in Panel C. We also continue to find evidence of a negative relation between future ROE
and each of the abnormal earnings growth‐based COEC estimates (rGM, rMPEG, and rPEG), although in
several cases those associations are not statistically significant.
In summary, after removing the impact of predictable analysts’ errors from COEC estimates, we
find consistent evidence that rCT and rEP are associated with realized accounting returns, mixed
evidence of an association between rGLS and realized ROE, and no evidence of a positive, significant
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relation between future ROE and each of the abnormal earnings growth‐based COEC estimates (rGM,
rMPEG, and rPEG).
4.3 Tests associating cost of equity capital estimates formed using cross‐sectional earnings estimates with future return on equity
Table 7 presents the results of tests that regress realized return on equity of varying horizons on
COEC estimates formed from a cross‐sectional earnings forecast model. Sample sizes are smaller for
these tests, based on the variables used to forecast earnings in Hou et al. (2012)—in particular, lagged
values of assets, earnings, dividend payments, and accruals. As in Table 5, we find consistent evidence
that rCT and rEP are significantly, positively associated with realized accounting returns of varying
horizons. For example, in Panel A, the coefficient on rCT is 0.963 (t‐statistic = 10.34) and the coefficient
on rEP is 1.218 (t‐statistic = 9.56). We again find mixed evidence of a positive association between
realized ROE and rGLS. For rGLS, the evidence is mixed, as in Table 5: for , , the coefficient on
rGLS is positive and significant (1.183; t‐statistic = 9.68) in Panel A while for , , the coefficient on
rGLS is negative and significant (‐0.368; t‐statistic = ‐1.94) in Panel C. Further, we find little evidence of a
positive, significant relation between realized ROE and each of the abnormal earnings growth‐based
COEC estimates (rGM, rMPEG, and rPEG), with one exception—for rMPEG and , where the
coefficient on rMPEG is 0.126 (t‐statistic = 2.10)
To summarize, using COEC estimates formed using cross‐sectional earnings estimates that do
not rely upon analysts’ forecasts, we find consistent evidence that rCT and rEP are associated with
realized accounting returns, mixed evidence of an association between rGLS and realized ROE, and
limited evidence of a positive relation between future ROE and each of the abnormal earnings growth‐
based COEC estimates (rGM, rMPEG, and rPEG).
17
4.4 Tests associating cost of equity capital estimates formed using double sorted portfolios Our cross‐sectional tests allow us to estimate the average relation between future ROE, market‐
to‐book, and implied COEC estimates. However, if the relation between future ROE and COEC is itself a
function of market‐to‐book then our cross‐sectional regressions may “hide” important patterns in the
data. As a test for this, we use double sorts as in Armstrong et al. (2011), where portfolios are formed
annually by sorting first on the market‐to‐book ratio and then on the COEC estimate within each of the
market‐to‐book portfolios. This allows us to compare the predicative ability of COEC estimates among
firms with similar market‐to‐book ratios. Table 8 presents the results of these tests, using each of rCT,
rEP, rGLS, rGM, rMPEG, and rPEG.
The double sorts provide fresh insight into the relation between COEC and future ROE. The
results for rCT and rEP confirm our cross‐sectional results: these two measures robustly forecast higher
future ROE. What is striking is that across all the panels, each of the COEC metrics performs much better
conditional on market‐to‐book being high. That is, firms with high COEC estimates and high MB generate
high future ROE compared to firms with high COEC and low MB. For example, rGLS forecasts low future
ROE in the low MB quintile, but rGLS forecasts high future ROE in the high MB quintile. This general
improvement in forecasting ability is also true for each of the AEG‐based COEC estimates, however,
even within the high MB quintile, all of the AEG models forecast low future ROE.
Collectively, our double‐sorted portfolio tests show the following. First, only two of the six COEC
estimates appear to consistently have a significant positive association with future accounting returns:
rCT and rEP. Second, each of COEC estimates is most highly correlated with future ROE for high market‐
to‐book firms. For all of the COEC models, their ability to forecast positive future ROE is lower for low
MB firms. Third, AEG based models never provide positive forecasts of future ROE, and for low MB firms
their performance is exceptionally poor. For example, for firms with low MB and high rPEG have close to
18
14% lower future ROE than do low rPEG firms; similar numbers are obtained when rGM (a high minus
low difference of around 11%) and rMPEG (a high minus low difference also around 11%) are used.
4.5 Additional Empirical Tests
In addition to our main empirical results we also conduct addition tests to determine if our
results are robust, or if there are situations under which the results we document change or are no
longer significant.
4.5.1 Tests that control for correlated omitted variables and alternative accounting return measures
In additional analyses, we attempt to control for correlated omitted variables. First, since ROE
may also be subject to the same issues that drive stock returns (i.e. they move because of changes in
expectations about discount rates and future expected ROE) we attempt to control for correlated
omitted variables as in Easton and Monahan (2005) and Botosan et al. (2011). In untabulated analysis,
after controlling for returns and earnings news, we find that the relation between future ROE and each
of rCT and rEP continues to be positive and significant while the relation between future ROE and each
of rGLS, rGM, rMPEG, and rPEG is negative and significant.
Second, in a Dupont‐style analysis, we break ROE into ROA, operating leverage, and balance
sheet leverage. In untabulated analysis, when we regress ROA on each of the implied COEC estimates as
well as operating leverage and balance sheet leverage, we obtain similar inferences.
4.5.2 Tests associating cost of equity capital estimates with future stock returns
In addition to our main tests which use accounting returns, we also explore the relation
between COEC estimates and future stock returns to ensure that the relation between future stock
returns and COEC estimates hold in our sample. First, following Gode and Mohanram (2003), quintiles
19
are formed according to the annual level of each COEC estimate with quintile 1 (5) representing the
quintile portfolio with the lowest (highest) COEC estimate. As shown in Panel A of Table 9, realized
returns (RETt+1) increase monotonically across the rCT, rGLS, rMPEG, and rPEG quintiles and they
increase nearly monotonically (with the exception of one quintile portfolio) across the rEP and rGM
quintiles.
Second, we regress future returns on each implied COEC estimate, as in Equation 8:
RETt,t+1 = (8)
Panel B of Table 9 presents the results of estimating Equation 8 for each of the six COEC
estimates. Mean coefficients across the 13 sample years, the t‐statistic testing whether the mean
coefficient is different from zero, and the mean adjusted R2 from the annual regressions are reported,
following Fama and MacBeth (1973). Results of the regression of realized stock returns on COEC
estimates are difficult to interpret given low levels of statistical significance. Indeed, only the rGLS COEC
estimate is positively and significantly associated with realized returns (coefficient = 0.882; t‐statistic =
1.81). Each of the other five COEC estimates is positively, but not significantly, associated with realized
returns.
These low levels of statistical significance echo the findings from prior literature. In a study of
five implied COEC estimates from 1983 to 2004, Guay et al. (2011) find that none of them has a positive
association with ex post returns; Easton and Monahan (2005) provide similar evidence even after
controlling for correlated omitted variables
20
4.5.3 Additional analysis controlling for additional variables
Our main tests control for the market‐to‐book ratio, both in cross‐sectional tests and in our
portfolio analysis. However, other factors may also affect our results. For example, Dichev and Tang
(2009) find that earnings volatility, not surprisingly, affects both earnings persistence and predictability.
They also find that earnings volatility affects analyst forecasts errors. Similarly, firms with low market
values (i.e., small firms) may systematically affect the predictability of future accounting returns. Finally,
the ability to estimate and forecast future ROE may be compromised for firms with poor earnings quality
since low quality earnings potentially provide less information about future cash flows.
As a supplement to the cross‐sectional regressions we also provide portfolio sorts of future ROE
based on earnings volatility, firm size, and earnings quality; the results are presented in panels A
through C of Table 10. In each panel, we sort firms into quintiles based on the firm characteristic
(earnings volatility, firm size, and earnings quality), and then within each of these quintiles we sort
based on COEC estimates. Across all panels of Table 10, the only two COEC measures that show a
positive association with future accounting returns are rCT and rEP. The other four measures, including
rGLS and the AEG‐based estimates, are decreasing in future accounting returns.
5. Conclusion
To the extent that managers invest in NPV positive projects, one would expect future firm
accounting returns to be correlated with the cost of equity capital. Extension of Vuolteenaho (2002)
shows that return on equity is tautologically related to both expected returns and the market‐to‐book
ratio. In our empirical tests, we find that very few of the implied COEC estimates commonly employed in
academic studies are positively associated with future return on equity (ROE); in fact, some implied
COEC estimates are significantly negatively correlated with future ROE. Our results hold over several
time horizons and are robust to various control variables.
21
Many accounting and increasingly finance studies employ implied cost of equity capital
estimates as a firm’s “true” cost of capital in cross‐sectional tests of the relation between the COEC and
variables of interest. While there is no disputing that the ideas put forward by Gebhardt et. al. (2001),
Easton (2004), Gode and Mohanram (2003) to imply discount rates from current stock prices and
valuation models are both novel and creative; the empirical evidence suggests that some of these
models offer, at best, noisy proxies for cost of capital. Our results echo those of Easton and Monahan
(2005) who show that a simple earnings‐to‐price outperforms most of the commonly employed implied
cost of capital measures.
Our findings suggest that researchers should exercise caution in relying on some of the
commonly used COEC estimates—in particular the estimates derived from the abnormal earnings
growth model. Moreover, there appears to be room for researchers to continue to develop and validate
COEC estimates based on accounting data and market values.
22
APPENDIX: Variable Definitions
Variable Definition
AFt+1 = Median EPS forecast for year t+1 according to the first I/B/E/S unadjustedsummary report following the release of year t earnings
AFt+2 = Median EPS forecast for year t+1 according to the first I/B/E/S unadjustedsummary report following the release of year t earnings
bm = The natural logarithm of the book to market ratio
B = Book value per share
Dt+1 = Expected dividends in year t, calculated as k, the dividend payout ratio from yeart‐1, multiplied by AFt+1
EQ = Dechow‐Dichev (2002) earnings quality, measured following Francis et al. (2004)
E(•) = Expectations operator
Evol = Earnings volatility, measured as the five year rolling standard deviation ofearnings deflated by average assets.
k = Dividend payout ratio from year t‐1
LTG = Median long‐term growth forecast according to the first I/B/E/S unadjustedsummary report following the release of year t earnings
MB = Market value of equity measured following the release of year t‐1 earnings (MV), from CRSP, divided by beginning of year t book value (Compustat data item CEQ)
mb = The natural logarithm of the market to book ratio
MV = Market value of equity measured following the release of year t‐1 earnings, from CRSP
Pt = Earliest price available from CRSP in the five trading days following release of the firstl I/B/E/S summary report following the release of year t earnings
= The natural logarithm of one plus the cost of equity capital
rCT = Implied COEC estimated according to Claus and Thomas (2001)
rEP = Implied COEC estimated as expected year t+1 earnings scaled by current price
rGLS = Implied COEC estimated according to Gebhardt, Lee, and Swaminathan (2001)
rGM = Implied COEC estimated according to Gode and Mohanram (2003)
rMPEG = Implied COEC estimated according to Easton’s (2004) “PEG” model
rPEG = Implied COEC estimated according to Easton’s (2004) modified “PEG” model
ret = The natural logarithm of one plus net stock returns
roe = The natural logarithm of one plus return on equity RETt,t+1 = Compounded annual returns beginning on the day following estimation of the
COEC estimate ROEt‐1,t = Income before extraordinary items (Compustat data item IB) for year t‐1 divided
by lagged book value (Compustat data item CEQ), reported during year t
23
ROEt,t+1 = Income before extraordinary items (Compustat data item IB) for year t divided by
lagged book value (Compustat data item CEQ), reported during year t+1 ROEt,t+2 = Income before extraordinary items (Compustat data item IB) for year t+1 divided
by lagged book value (Compustat data item CEQ), reported during year t+2 ROEt,t+3 = Income before extraordinary items (Compustat data item IB) for year t+2 divided
by lagged book value (Compustat data item CEQ), reported during year t+3 = Earnings in year t+1 = Abnormal earnings in year t+1, or
24
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TABLE 1 Sample selection and descriptive statistics
This table summarizes the procedure used to select the sample used in this study (Panel A) and provides descriptive statistics for the sample (Panel B). Variable definitions are in the Appendix.
Panel A: Sample selection procedure
Criteria
Firm‐years
Remaining firm‐years
Firm‐years with I/B/E/S consensus analyst earnings forecasts for years t+1 and t+2 available in year t+1, following the release of year t earnings, from 1994 to 2010
60,325 60,325
Less: Firms with missing CRSP price or returns (6,605) 53,720
Less: Firms without Compustat data available to compute ROEt,t+1 (9,884) 43,826
Firms for which rCT, rEP, rGLS, rGM, rMPEG, and rPEG can be estimated 26,373
Panel B: Descriptive statistics
No. of Obs.
Mean
P25
Median
P75
Std. Dev.
AFt 26,373 1.729 0.740 1.400 2.300 1.398
AFt+1 26,373 2.069 1.000 1.700 2.660 1.532
LTGt 26,373 16.472 10.000 15.000 20.000 10.230
BtoM 26,373 0.501 0.280 0.447 0.648 0.323
pricet 26,373 27.791 13.770 23.125 36.440 20.272
RETt,t+1 26,373 0.126 ‐0.215 0.083 0.362 0.605
ROEt,t+1 26,373 0.138 0.060 0.132 0.203 0.345
rCT 26,373 0.093 0.071 0.087 0.107 0.039
rEP 26,373 0.067 0.043 0.062 0.083 0.041
rGLS 26,373 0.107 0.088 0.106 0.126 0.036
rGM 26,373 0.136 0.100 0.120 0.153 0.063
rMPEG 26,373 0.131 0.096 0.115 0.148 0.062
rPEG 26,373 0.119 0.087 0.106 0.137 0.055
28
TABLE 2 Implied cost of equity capital estimates
This table summarizes the implied cost of equity capital models used in this study. Variable definitions are in the Appendix.
Variable Equation
rCT
∗1
∗1
rEP
rGLS ∗
1∗
1
rGM
1
where ))1((2
1 1
t
t
P
DA and
1
122
)(
t
tt
AF
AFAFg
rMPEG
t
ttt
P
AFDAFrMPEG
)( 112
rPEG
t
tt
P
AFAFrPEG
)( 12
29
TABLE 3 Implied COEC Estimates, Returns, and Return on Equity
This table provides implied COEC estimates as well as one‐year ahead returns and return on equity for 1994 to 2010. In Panels A and B, Column (1) estimates the COEC following Claus and Thomas (2001). Column (2) estimates the COEC using the earnings to price ratio. Columns (3) and (4) respectively estimate the COEC following Gebhardt, Lee, and Swaminathan (2001) and Gode and Mohanram (2003). Columns (5) and (6) estimate the COEC following Easton (2004). Column (7) presents year t+1 realized returns (RETt,t+1), and Column (8) presents year t realized return on equity (ROEt,t+1). In Panel B, Column (9) presents year t‐1 realized return on equity (ROEt‐1,t). In Panel B, Pearson correlations are presented, using the average of the annual correlations for 1994 to 2010, with t‐statistics provided in parentheses. Variable definitions are in the Appendix.
Panel A: Mean implied COEC estimates, returns, and return on equity
No. rCT (1)
rEP (2)
rGLS (3)
rGM (4)
rMPEG (5)
rPEG (6)
RETt,t+1 (7)
ROEt,t+1(8)
1994 1,211 0.102 0.070 0.106 0.145 0.136 0.125 0.022 0.169 1995 1,284 0.115 0.081 0.113 0.151 0.141 0.129 0.281 0.164 1996 1,465 0.101 0.070 0.107 0.138 0.131 0.121 0.191 0.150 1997 1,679 0.100 0.064 0.106 0.142 0.132 0.123 0.283 0.131 1998 1,700 0.091 0.060 0.101 0.132 0.125 0.116 ‐0.105 0.118 1999 1,591 0.099 0.073 0.111 0.141 0.136 0.125 0.254 0.152 2000 1,454 0.108 0.079 0.112 0.145 0.136 0.124 0.116 0.130 2001 1,313 0.097 0.069 0.109 0.141 0.136 0.123 0.061 0.076 2002 1,418 0.086 0.060 0.104 0.137 0.132 0.122 ‐0.117 0.122 2003 1,604 0.096 0.075 0.117 0.144 0.142 0.128 0.599 0.141 2004 1,738 0.074 0.054 0.097 0.119 0.116 0.106 0.122 0.165 2005 1,745 0.077 0.057 0.100 0.119 0.116 0.106 0.182 0.162 2006 1,746 0.079 0.057 0.098 0.117 0.113 0.104 0.133 0.175 2007 1,783 0.080 0.058 0.098 0.120 0.116 0.105 ‐0.154 0.142 2008 1,754 0.091 0.070 0.109 0.137 0.135 0.117 ‐0.536 0.053 2009 1,394 0.112 0.095 0.133 0.162 0.163 0.144 0.681 0.126 2010 1,494 0.086 0.066 0.109 0.139 0.138 0.123 0.270 0.168 1994‐2010 0.094 0.068 0.108 0.137 0.132 0.120 0.134 0.138
30
TABLE 3 (continued)
Panel B: Correlation between implied COEC estimates, returns, and return on equity
rCT
(1) rEP (2)
rGLS (3)
rGM (4)
rMPEG (5)
rPEG (6)
RETt,t+1 (7)
ROEt,t+1 (8)
ROEt‐1,t (9)
rCT 0.769
(55.44)
0.527 (21.13)
0.624 (32.93)
0.656 (36.14)
0.448 (22.09)
0.048 (1.39)
0.012 (0.78)
0.051 (4.88)
rEP 0.512 (18.32)
0.129 (4.84)
0.173 (6.19)
0.099 (3.08)
0.064 (1.68)
0.041 (2.43)
0.060 (5.97)
rGLS 0.325 (12.06)
0.355 (12.40)
0.470 (22.89)
0.062 (1.97)
‐0.001 (‐0.06)
‐0.031 (‐0.031)
rGM 0.998 (217.82)
0.826 (44.91)
0.017 (0.64)
‐0.147 (‐11.16)
‐0.069 (‐5.36)
rMPEG 0.829 (44.60)
0.021 (0.79)
‐0.146 (‐11.19)
‐0.067 (‐5.23)
rPEG 0.028 (0.86)
‐0.164 (‐11.17)
‐0.080 (‐5.57)
RETt,t+1 0.191 (9.79)
‐0.012 (‐0.89)
ROEt,t+1 0.155 (6.01)
ROEt‐1,t
31
TABLE 4 Implied COEC Estimates and Realized Return on Equity in Quintile Portfolios
This table provides mean realized accounting return on equity for the upcoming three years ( , ,
, , and , ) across quintiles of firms formed annually for each COEC estimate. Row (1) estimates
the COEC following Claus and Thomas (2001). Row (2) estimates the COEC using the earnings to price ratio. Rows (3) and (4) respectively estimate the COEC following Gebhardt, Lee, and Swaminathan (2001) and Gode and Mohanram (2003). Rows (5) and (6) estimate the COEC following Easton (2004). Variable definitions are in the Appendix.
Realized ROE across COEC quintiles
(1) (2) (3) (4) (5) (5) – (1) t‐statistic
rCT (1) , 0.085 0.123 0.126 0.128 0.101 0.016 0.96
, 0.063 0.103 0.116 0.111 0.085 0.022 1.24
, 0.055 0.105 0.105 0.105 0.085 0.029 1.54
rEP (2) , 0.060 0.128 0.131 0.130 0.113 0.053 2.85
, 0.040 0.108 0.121 0.113 0.094 0.054 2.77
, 0.041 0.107 0.111 0.107 0.088 0.047 2.51
rGLS (3) , 0.138 0.131 0.118 0.100 0.075 ‐0.063 ‐4.02
, 0.121 0.117 0.098 0.078 0.062 ‐0.059 ‐3.30
, 0.108 0.106 0.096 0.088 0.057 ‐0.051 ‐2.81
rGM (4) , 0.156 0.154 0.128 0.096 0.027 ‐0.129 ‐8.36
, 0.119 0.127 0.107 0.086 0.037 ‐0.082 ‐4.42
, 0.110 0.116 0.097 0.081 0.051 ‐0.059 ‐3.27
rMPEG (5) , 0.157 0.152 0.131 0.095 0.029 ‐0.128 ‐8.05
, 0.116 0.125 0.110 0.089 0.036 ‐0.080 ‐4.35
, 0.108 0.114 0.099 0.081 0.052 ‐0.055 ‐2.99
rPEG (6) , 0.152 0.155 0.135 0.097 0.022 ‐0.131 ‐7.84
, 0.127 0.125 0.111 0.083 0.029 ‐0.098 ‐5.39
, 0.114 0.119 0.100 0.077 0.044 ‐0.070 ‐3.83
32
TABLE 5 Implied COEC Estimates and Realized Return on Equity
This table tests the relation between realized accounting return on equity, implied COEC estimates, and market‐to‐book for the period 1994 to 2010, using the following specification:
,
In Panel A (B), the dependent variable is , ( , ). In Panel C, the dependent variable uses , . In each panel, Column (1) estimates the
COEC following Claus and Thomas (2001). Column (2) estimates the COEC using the earnings to price ratio. Columns (3) and (4) respectively estimate the COEC following Gebhardt, Lee, and Swaminathan (2001) and Gode and Mohanram (2003). Columns (5) and (6) estimate the COEC following Easton (2004). T‐statistics are in parentheses and are based on Fama‐MacBeth regressions. Significance levels are based on one‐tailed tests where there is a prediction for the sign of the coefficient and based on two‐tailed tests otherwise. ***, ** and * denote significance at the 1%, 5% and 10% levels, respectively. Variable definitions are in the Appendix.
Panel A: Regression of , on COEC estimates
rCT
rEP
rGLS
rGM
rMPEG
rPEG
Predicted sign (1) (2) (3) (4) (5) (6)
Intercept ‐0.113*** (‐7.75)
‐0.165*** (‐12.17)
‐0.088*** (‐6.08)
0.065*** (4.42)
0.057*** (4.04)
0.081*** (7.33)
+ 1.141*** (7.90)
2.043*** (16.15)
0.747*** (5.77)
‐0.495*** (‐7.02)
‐0.450*** (‐6.35)
‐0.696*** (‐7.77)
+ 0.148*** (16.03)
0.171*** (21.51)
0.144*** (15.23)
0.128*** (12.88)
0.128*** (12.91)
0.126*** (12.74)
N 26,060 26,060 26,060 26,060 26,060 26,060
Adj. R2 0.216 0.256 0.206 0.203 0.201 0.208
33
TABLE 5 (continued)
Panel B: Regression of , on COEC estimates
rCT
rEP
rGLS
rGM
rMPEG
rPEG
Predicted sign (1) (2) (3) (4) (5) (6)
Intercept ‐0.045* (‐1.96)
‐0.089*** (‐3.94)
0.033 (1.24)
0.080*** (3.78)
0.075*** (3.57)
0.101*** (5.45)
+ 0.729*** (6.46)
1.441*** (10.24)
‐0.090 (‐0.58)
‐0.413*** (‐4.86)
‐0.386*** (‐4.55)
‐0.658*** (‐5.57)
+ 0.088*** (6.09)
0.105*** (7.73)
0.078*** (5.35)
0.074*** (5.03)
0.074*** (5.00)
0.072*** (4.87)
N 22,098 22,098 22,098 22,098 22,098 22,098
Adj. R2 0.078 0.097 0.072 0.076 0.075 0.081
Panel C: Regression of , on COEC estimates
rCT
rEP
rGLS
rGM
rMPEG
rPEG
Predicted sign (1) (2) (3) (4) (5) (6)
Intercept ‐0.029 (‐1.39)
‐0.064*** (‐3.13)
0.061** (2.53)
0,085*** (4.06)
0.080*** (3.92)
0.102*** (5.12)
+ 0.693*** (6.86)
1.285*** (14.20)
‐0.220 (‐1.58)
‐0.348*** (‐5.09)
‐0.324*** (‐4.79)
‐0.552*** (‐6.31)
+ 0.064*** (5.21)
0.079*** (6.56)
0.053*** (4.18)
0.052*** (3.90)
0.052*** (3.87)
0.050*** (3.75)
N 18,838 18,838 18,838 18,838 18,838 18,838
Adj. R2 0.040 0.051 0.035 0.037 0.036 0.041
34
TABLE 6 Implied COEC Estimates formed using Adjusted Earnings Estimates and Realized Return on Equity
This table tests the relation between implied COEC estimates formed using earnings estimates that are adjusted for predictable analysts’ errors following Larocque (2013) and realized accounting return on equity for the period 1994 to 2010, using the following specification:
,
In Panel A (B), the dependent variable is , ( , ). In Panel C, the dependent variable uses , . In each panel, Column (1) estimates the
COEC following Claus and Thomas (2001). Column (2) estimates the COEC using the earnings to price ratio. Columns (3) and (4) respectively estimate the COEC following Gebhardt, Lee, and Swaminathan (2001) and Gode and Mohanram (2003). Columns (5) and (6) estimate the COEC following Easton (2004). T‐statistics are in parentheses and are based on Fama‐MacBeth regressions. Significance levels are based on one‐tailed tests where there is a prediction for the sign of the coefficient and based on two‐tailed tests otherwise. ***, ** and * denote significance at the 1%, 5% and 10% levels, respectively. Variable definitions are in the Appendix.
Panel A: Regression of , on COEC estimates
rCT
rEP
rGLS
rGM
rMPEG
rPEG
Predicted sign (1) (2) (3) (4) (5) (6)
Intercept ‐0.108*** (‐4.12)
‐0.107*** (‐3.78)
‐0.118*** (‐4.67)
‐0.005 (‐0.22)
‐0.011 (‐0.51)
0.004 (0.21)
+ 1.160*** (6.81)
1.433*** (7.12)
0.911*** (6.23)
‐0.124 (‐1.41)
‐0.078 (‐0.89)
‐0.211** (‐2.38)
+ 0.156*** (11.42)
0.163*** (12.33)
0.163*** (11.28)
0.145*** (10.00)
0.146*** (10.11)
0.143*** (9.94)
N 6,311 6,311 6,311 6,311 6,311 6,311
Adj. R2 0.274 0.294 0.255 0.243 0.242 0.243
35
TABLE 6 (continued)
Panel B: Regression of , on COEC estimates
rCT
rEP
rGLS
rGM
rMPEG
rPEG
Predicted sign (1) (2) (3) (4) (5) (6)
Intercept ‐0.076** (‐2.28)
‐0.075** (‐2.12)
‐0.045 (‐1.30)
‐0.010 (‐0.54)
‐0.014 (‐0.73)
0.001 (0.03)
+ 0.745*** (2.36)
0.898** (2.53)
0.274 (0.94)
‐0.048 (‐0.40)
‐0.019 (‐0.16)
‐0.160 (‐1.21)
+ 0.135*** (10.99)
0.139*** (10.65)
0.132*** (8.56)
0.128*** (10.28)
0.129*** (10.34)
0.126 (9.85)
N 5,608 5,608 5,608 5,608 5,608 5,608
Adj. R2 0.132 0.136 0.122 0.120 0.120 0.120
Panel C: Regression of , on COEC estimates
rCT
rEP
rGLS
rGM
rMPEG
rPEG
Predicted sign (1) (2) (3) (4) (5) (6)
Intercept ‐0.053 (‐1.63)
‐0.051* (‐1.86)
0.039 (1.31)
‐0.007 (‐0.27)
‐0.008 (‐0.33)
0.007 (0.32)
+ 0.735*** (2.74)
0.854*** (4.49)
‐0.352* (‐1.87)
0.070 (0.59)
0.088 (0.67)
‐0.042 (‐0.32)
+ 0.102*** (11.80)
0.106*** (11.38)
0.088*** (7.93)
0.097*** (10.89)
0.097*** (10.61)
0.094*** (10.19)
N 4,824 4,824 4,824 4,824 4,824 4,824
Adj. R2 0.096 0.094 0.081 0.084 0.085 0.084
36
TABLE 7 Implied COEC Estimates formed using Cross‐Sectional Earnings Forecasts and Realized Return on Equity
This table tests the relation between implied COEC estimates formed using Hou et al. (2012) earnings forecasts and realized accounting return on equity for the period 1994 to 2010, using the following specification:
,
In Panel A (B), the dependent variable is , ( , ). In Panel C, the dependent variable uses , . In each panel, Column (1) estimates the
COEC following Claus and Thomas (2001). Column (2) estimates the COEC using the earnings to price ratio. Columns (3) and (4) respectively estimate the COEC following Gebhardt, Lee, and Swaminathan (2001) and Gode and Mohanram (2003). Columns (5) and (6) estimate the COEC following Easton (2004). T‐statistics are in parentheses and are based on Fama‐MacBeth regressions. Significance levels are based on one‐tailed tests where there is a prediction for the sign of the coefficient and based on two‐tailed tests otherwise. ***, ** and * denote significance at the 1%, 5% and 10% levels, respectively. Variable definitions are in the Appendix.
Panel A: Regression of , on COEC estimates
rCT
rEP
rGLS
rGM
rMPEG
rPEG
Predicted sign (1) (2) (3) (4) (5) (6)
Intercept ‐0.089*** (‐5.46)
‐0.095*** (‐5.61)
‐0.139*** (‐8.34)
‐0.013 (‐0.81)
‐0.021 (‐1.31)
‐0.009 (‐0.59)
+ 0.963*** (10.34)
1.218*** (9.56)
1.183*** (9.68)
0.051 (0.91)
0.126** (2.10)
0.021 (0.21)
+ 0.160*** (15.24)
0.170*** (16.52)
0.174*** (17.16)
0.147*** (13.46)
0.149*** (13.82)
0.147*** (13.59)
N 8,591 8,591 8,591 8,591 8,591 8,591
Adj. R2 0.259 0.275 0.259 0.239 0.239 0.241
37
TABLE 7 (continued)
Panel B: Regression of , on COEC estimates
rCT
rEP
rGLS
rGM
rMPEG
rPEG
Predicted sign (1) (2) (3) (4) (5) (6)
Intercept ‐0.047* (‐2.09)
‐0.053** (‐2.31)
‐0.012 (‐0.46)
0.013 (0.66)
0.006 (0.31)
0.024 (1.10)
+ 0.719*** (6.60)
0.924*** (8.25)
0.223** (1.92)
0.011 (0.09)
0.073 (0.56)
‐0.102 (‐0.51)
+ 0.113*** (7.98)
0.122*** (8.82)
0.108*** (7.29)
0.103*** (7.32)
0.104*** (7.44)
0.101*** (7.23)
N 7,088 7,088 7,088 7,088 7,088 7,088
Adj. R2 0.099 0.104 0.091 0.094 0.094 0.096
Panel C: Regression of , on COEC estimates
rCT
rEP
rGLS
rGM
rMPEG
rPEG
Predicted sign (1) (2) (3) (4) (5) (6)
Intercept 0.0003 (0.02)
‐0.006 (‐0.30)
0.072** (2.75)
0.048** (2.13)
0.043* (1.88)
0.063** (2.55)
+ 0.408*** (3.04)
0.559*** (3.89)
‐0.368* (‐1.94)
‐0.126 (‐1.11)
‐0.090 (‐0.73)
‐0.318 (‐1.65)
+ 0.075*** (6.52)
0.081*** (7.02)
0.061*** (4.90)
0.066*** (5.46)
0.067*** (5.45)
0.063*** (5.13)
N 6,000 6,000 6,000 6,000 6,000 6,000
Adj. R2 0.037 0.039 0.037 0.037 0.037 0.041
38
TABLE 8 ROE Portfolios Double‐Sorted on Market‐to‐Book and COEC
This table provides mean future accounting return on equity (roet,t+1) across portfolios of firms formed annually. Portfolios are formed by sorting first on market‐to‐book (MB) and then on the COEC estimate. Row 1 (5) represents the lowest (highest) MB portfolio while column 1 (5) represents the lowest (highest) COEC portfolio. COEC estimates include rCT, the Claus and Thomas (2001) estimate; rEP, the earnings‐to‐price ratio; rGLS, the Gebhardt, Lee, and Swaminathan (2001) estimate; rGM, the Gode and Mohanram (2003) estimate; and rMPEG and rPEG from Easton (2004). Variable definitions are in the Appendix.
39
TABLE 8 (continued)
Low (1) (2) (3) (4) High (5) (5) – (1) t‐statistic
Sort on MB then on rCT (1) Low ‐0.050 0.011 0.028 0.034 0.007 0.057 4.372
(2) 0.027 0.075 0.090 0.094 0.092 0.065 5.601
(3) 0.052 0.101 0.112 0.120 0.119 0.066 5.355
(4) 0.056 0.124 0.138 0.165 0.176 0.120 9.446
(5) High 0.149 0.200 0.255 0.300 0.354 0.205 7.279
Sort on MB then on rEP (1) Low ‐0.080 ‐0.010 0.039 0.041 0.040 0.119 8.855
(2) 0.000 0.058 0.093 0.102 0.126 0.126 11.796
(3) 0.021 0.089 0.118 0.133 0.142 0.121 11.443
(4) 0.024 0.113 0.147 0.171 0.204 0.180 13.196
(5) High 0.111 0.209 0.246 0.301 0.388 0.278 10.866
Sort on MB then on rGLS (1) Low 0.039 0.032 0.017 ‐0.012 ‐0.046 ‐0.085 ‐5.336
(2) 0.076 0.086 0.084 0.080 0.054 ‐0.022 ‐1.964
(3) 0.099 0.114 0.099 0.112 0.079 ‐0.020 ‐1.116
(4) 0.116 0.130 0.136 0.132 0.145 0.029 2.661
(5) High 0.198 0.191 0.211 0.254 0.408 0.210 8.324
Sort on MB then on rGM (1) Low 0.050 0.046 0.010 ‐0.012 ‐0.064 ‐0.114 ‐9.350
(2) 0.105 0.095 0.089 0.071 0.019 ‐0.086 ‐12.851
(3) 0.120 0.130 0.103 0.100 0.050 ‐0.070 ‐6.553
(4) 0.149 0.154 0.147 0.118 0.090 ‐0.059 ‐4.914
(5) High 0.262 0.259 0.272 0.257 0.206 ‐0.056 ‐1.739
Sort on MB then on rMPEG (1) Low 0.047 0.045 0.011 ‐0.012 ‐0.062 ‐0.109 ‐8.657
(2) 0.104 0.096 0.087 0.070 0.022 ‐0.082 ‐11.938
(3) 0.116 0.124 0.116 0.096 0.052 ‐0.064 ‐5.778
(4) 0.140 0.155 0.148 0.121 0.094 ‐0.047 ‐4.206
(5) High 0.253 0.259 0.272 0.249 0.223 ‐0.030 ‐0.907
Sort on MB then on rPEG (1) Low 0.060 0.049 0.017 ‐0.018 ‐0.079 ‐0.138 ‐9.213
(2) 0.103 0.106 0.090 0.065 0.015 ‐0.088 ‐12.251
(3) 0.121 0.127 0.115 0.092 0.048 ‐0.073 ‐6.249
(4) 0.154 0.151 0.140 0.120 0.094 ‐0.060 ‐5.594
(5) High 0.280 0.250 0.270 0.254 0.202 ‐0.078 ‐2.343
40
TABLE 9 Implied COEC Estimates and Realized Returns
This table tests the relation between implied COEC estimates and realized returns for the period 1994 to 2010. Panel A provides mean realized returns (RETt,t+1) across quintiles of firms formed annually for each COEC estimate. Panel B uses the following specification:
RETt,t+1 = a0 + a1 Et(COEC) + et rCT estimates the COEC following Claus and Thomas (2001). rEP estimates the COEC using the earnings to price ratio. rGLS and rGM respectively estimate the COEC following Gebhardt, Lee, and Swaminathan (2001) and Gode and Mohanram (2003). rMPEG and rPEG estimate the COEC following Easton (2004). T‐statistics are in parentheses and are based on Fama‐MacBeth regressions. Significance levels are based on one‐tailed tests where there is a prediction for the sign of the coefficient and based on two‐tailed tests otherwise. ***, ** and * denote significance at the 1%, 5% and 10% levels, respectively. Variable definitions are in the Appendix.
Panel A: Realized stock returns ( , ) across quintiles
(1) (2) (3) (4) (5) (5) – (1) t‐statistic
Quintiles formed according to: rCT(1) 0.101 0.106 0.131 0.147 0.187 0.087 0.69
rEP (2) 0.118 0.099 0.127 0.137 0.191 0.073 0.56
rGLS (3) 0.084 0.099 0.125 0.164 0.200 0.116 1.03
rGM (4) 0.105 0.131 0.128 0.153 0.154 0.050 0.46
rMPEG (5) 0.100 0.129 0.132 0.153 0.157 0.057 0.52
rPEG (6) 0.102 0.123 0.132 0.149 0.165 0.063 0.59
41
TABLE 9 (continued)
Panel B: Regression of , on COEC estimates
rCT
rEP
rGLS
rGM
rMPEG
rPEG
Predicted sign (1) (2) (3) (4) (5) (6)
Intercept 0.083
(1.24) 0.092 (1.32)
0.028 (0.47)
0.102* (2.06)
0.098* (1.98)
0.087* (1.98)
COEC + 0.500 (1.00)
0.546 (0.99)
0.882** (1.81)
0.200 (0.85)
0.224 (0.95)
0.336 (1.04)
N 26,373 26,373 26,373 26,373 26,373 26,373
Adj. R2 0.021 0.027 0.020 0.011 0.012 0.017
42
TABLE 10 ROE Portfolios Double‐Sorted on Firm Characteristics and COEC
This table provides mean future accounting return on equity (roet,t+1) across portfolios of firms formed annually. Portfolios are formed by sorting first on a variable of interest (either market value or earnings quality or earnings volatility) and then on the COEC estimate. Row 1 (5) represents the lowest (highest) MV or EQ or Evol portfolio while column 1 (5) represents the lowest (highest) COEC portfolio. COEC estimates include rCT, the Claus and Thomas (2001) estimate; rEP, the earnings‐to‐price ratio; rGLS, the Gebhardt, Lee, and Swaminathan (2001) estimate; rGM, the Gode and Mohanram (2003) estimate; and rMPEG and rPEG from Easton (2004). Variable definitions are in the Appendix.
43
TABLE 10 (continued)
Panel A: Sorts on Market Values Low (1) (2) (3) (4) High (5) (5) – (1) t‐statistic
Sort on MV then on rCT (1) Low MV 0.009 0.061 0.070 0.072 0.037 0.028 1.546
(2) 0.037 0.082 0.093 0.114 0.085 0.048 2.739
(3) 0.073 0.120 0.121 0.132 0.129 0.056 3.929
(4) 0.091 0.141 0.142 0.146 0.140 0.050 3.336
(5) High MV 0.141 0.183 0.183 0.165 0.148 0.007 0.566
Sort on MV then on rEP (1) Low ‐0.026 0.052 0.067 0.079 0.075 0.101 4.962
(2) 0.017 0.084 0.093 0.111 0.106 0.089 7.015
(3) 0.058 0.122 0.135 0.129 0.131 0.072 4.492
(4) 0.092 0.132 0.146 0.152 0.138 0.047 3.040
(5) High 0.137 0.196 0.183 0.161 0.141 0.004 0.301
Sort on MV then on rGLS (1) Low 0.093 0.080 0.059 0.023 ‐0.005 ‐0.098 ‐5.246
(2) 0.097 0.104 0.098 0.077 0.034 ‐0.063 ‐4.588
(3) 0.118 0.129 0.122 0.112 0.094 ‐0.023 ‐1.455
(4) 0.137 0.140 0.126 0.127 0.131 ‐0.006 ‐0.576
(5) High 0.173 0.178 0.162 0.154 0.152 ‐0.020 ‐1.524
Sort on MV then on rGM (1) Low 0.088 0.115 0.068 0.025 ‐0.049 ‐0.137 ‐7.554
(2) 0.124 0.122 0.091 0.059 0.015 ‐0.110 ‐8.319
(3) 0.143 0.143 0.126 0.102 0.060 ‐0.083 ‐6.344
(4) 0.146 0.167 0.144 0.136 0.065 ‐0.081 ‐6.412
(5) High 0.189 0.205 0.170 0.144 0.110 ‐0.078 ‐7.294
Sort on MV then on rMPEG (1) Low 0.087 0.113 0.071 0.023 ‐0.048 ‐0.135 ‐7.633
(2) 0.123 0.118 0.093 0.060 0.016 ‐0.107 ‐7.992
(3) 0.143 0.143 0.122 0.103 0.065 ‐0.078 ‐5.785
(4) 0.145 0.164 0.150 0.130 0.070 ‐0.075 ‐5.388
(5) High 0.193 0.199 0.173 0.142 0.113 ‐0.080 ‐6.594
Sort on MV then on rPEG (1) Low 0.095 0.111 0.073 0.023 ‐0.056 ‐0.151 ‐8.255
(2) 0.123 0.120 0.098 0.065 0.004 ‐0.118 ‐8.560
(3) 0.138 0.145 0.131 0.105 0.055 ‐0.082 ‐4.813
(4) 0.137 0.157 0.166 0.134 0.066 ‐0.071 ‐5.719
(5) High 0.188 0.197 0.176 0.150 0.108 ‐0.080 ‐5.216
44
TABLE 10 (continued)
Panel B: Sorts on Earnings Volatility Low (1) (2) (3) (4) High (5) (5) – (1) t‐statistic
Sort on Evol then on rCT (1) Low Evol 0.121 0.148 0.132 0.124 0.114 ‐0.008 ‐0.568
(2) 0.105 0.138 0.131 0.130 0.088 ‐0.016 ‐0.722
(3) 0.093 0.129 0.130 0.138 0.104 0.011 0.484
(4) 0.064 0.109 0.123 0.131 0.098 0.034 1.956
(5) High Evol 0.001 0.069 0.082 0.100 0.068 0.067 2.432
Sort on Evol then on rEP (1) Low 0.128 0.147 0.136 0.121 0.106 ‐0.023 ‐1.961
(2) 0.094 0.135 0.142 0.124 0.096 0.002 0.150
(3) 0.074 0.129 0.130 0.150 0.110 0.037 1.705
(4) 0.040 0.117 0.112 0.139 0.118 0.078 3.922
(5) High ‐0.044 0.049 0.102 0.102 0.110 0.153 6.018
Sort on Evol then on rGLS (1) Low 0.153 0.153 0.134 0.115 0.084 ‐0.069 ‐5.644
(2) 0.162 0.141 0.137 0.094 0.059 ‐0.103 ‐5.982
(3) 0.155 0.142 0.121 0.106 0.071 ‐0.084 ‐6.457
(4) 0.140 0.116 0.118 0.090 0.062 ‐0.078 ‐5.332
(5) High 0.061 0.093 0.069 0.057 0.041 ‐0.019 ‐0.711
Sort on Evol then on rGM (1) Low 0.143 0.159 0.139 0.129 0.069 ‐0.073 ‐8.319
(2) 0.162 0.161 0.122 0.097 0.050 ‐0.113 ‐6.406
(3) 0.168 0.167 0.118 0.099 0.042 ‐0.126 ‐7.387
(4) 0.172 0.154 0.108 0.065 0.027 ‐0.146 ‐8.229
(5) High 0.133 0.137 0.098 0.004 ‐0.053 ‐0.186 ‐7.571
Sort on Evol then on rMPEG (1) Low 0.145 0.157 0.138 0.126 0.072 ‐0.073 ‐8.136
(2) 0.165 0.156 0.133 0.087 0.051 ‐0.114 ‐6.410
(3) 0.172 0.161 0.118 0.099 0.044 ‐0.129 ‐7.778
(4) 0.168 0.155 0.106 0.072 0.024 ‐0.144 ‐7.864
(5) High 0.128 0.130 0.106 0.008 ‐0.053 ‐0.181 ‐7.014
Sort on Evol then on rPEG (1) Low 0.129 0.161 0.149 0.125 0.076 ‐0.053 ‐5.139
(2) 0.169 0.156 0.126 0.099 0.042 ‐0.127 ‐6.455
(3) 0.173 0.164 0.127 0.088 0.042 ‐0.131 ‐7.842
(4) 0.182 0.152 0.114 0.067 0.009 ‐0.173 ‐8.160
(5) High 0.137 0.129 0.109 0.002 ‐0.060 ‐0.196 ‐8.297
45
TABLE 10 (continued)
Panel C: Sorts on Earnings Quality Low (1) (2) (3) (4) High (5) (5) – (1) t‐statistic
Sort on EQ then on rCT (1) Low EQ 0.096 0.138 0.125 0.122 0.117 0.021 1.393
(2) 0.090 0.138 0.150 0.134 0.108 0.019 1.305
(3) 0.079 0.116 0.132 0.136 0.092 0.013 0.542
(4) 0.086 0.116 0.126 0.126 0.096 0.011 0.389
(5) High EQ 0.055 0.112 0.107 0.118 0.074 0.019 0.832
Sort on EQ then on rEP (1) Low 0.095 0.132 0.125 0.121 0.125 0.029 2.364
(2) 0.079 0.137 0.154 0.139 0.111 0.032 2.199
(3) 0.033 0.131 0.132 0.149 0.109 0.076 3.368
(4) 0.049 0.127 0.135 0.135 0.103 0.054 2.109
(5) High 0.018 0.108 0.124 0.120 0.094 0.076 2.840
Sort on EQ then on rGLS (1) Low 0.149 0.134 0.124 0.111 0.083 ‐0.066 ‐5.572
(2) 0.155 0.152 0.137 0.105 0.078 ‐0.077 ‐5.751
(3) 0.140 0.148 0.130 0.098 0.045 ‐0.095 ‐4.369
(4) 0.144 0.132 0.125 0.089 0.073 ‐0.070 ‐2.983
(5) High 0.132 0.086 0.121 0.089 0.043 ‐0.089 ‐4.092
Sort on EQ then on rGM (1) Low 0.143 0.150 0.123 0.109 0.073 ‐0.071 ‐5.757
(2) 0.165 0.163 0.140 0.111 0.042 ‐0.123 ‐9.351
(3) 0.168 0.166 0.124 0.093 0.004 ‐0.164 ‐6.096
(4) 0.163 0.165 0.113 0.092 0.016 ‐0.147 ‐10.117
(5) High 0.157 0.156 0.105 0.047 ‐0.001 ‐0.159 ‐10.415
Sort on EQ then on rMPEG (1) Low 0.147 0.144 0.125 0.109 0.073 ‐0.074 ‐5.454
(2) 0.168 0.161 0.141 0.105 0.044 ‐0.124 ‐9.416
(3) 0.166 0.170 0.122 0.092 0.007 ‐0.159 ‐6.271
(4) 0.167 0.157 0.116 0.091 0.018 ‐0.149 ‐9.975
(5) High 0.160 0.150 0.107 0.049 ‐0.001 ‐0.161 ‐10.461
Sort on EQ then on rPEG (1) Low 0.131 0.149 0.140 0.108 0.070 ‐0.061 ‐3.914
(2) 0.166 0.163 0.134 0.119 0.037 ‐0.128 ‐7.040
(3) 0.171 0.162 0.136 0.089 ‐0.003 ‐0.174 ‐6.743
(4) 0.166 0.155 0.123 0.092 0.013 ‐0.153 ‐10.406
(5) High 0.165 0.151 0.103 0.052 ‐0.007 ‐0.172 ‐10.560
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