The Relation between Expected Returns, Realized Returns,
and Firm Risk Characteristics*
CHRISTINE A. BOTOSAN, University of Utah
MARLENE A. PLUMLEE, University of Utah
HE WEN, University of Utah
1. Introduction
Existing literature employs two general approaches to assess the validity of alternative
proxies for firm-specific cost of equity capital or expected return (hereafter Et)1(rt)). The
first approach involves examining the association between the proxy for Et)1(rt) and
future realized returns. The second approach focuses on the association between the
Et)1(rt) proxy and contemporaneous risk characteristics of firms.
The results of these two streams of literature are mixed. Easton and Monahan (2005)
(hereafter EM) and Guay, Kothari, and Shu (2005) (hereafter GKS) focus on the association between alternative proxies for Et)1(rt) and future realized returns and conclude that
none of the proxies they examine provide valid estimates of the construct of interest. In
contrast, Botosan and Plumlee (2005) (hereafter BP) conclude that two common proxies
for Et)1(rt) — rDIV (Botosan and Plumlee 2002) and rPEG (Easton 2004) — are valid,
based on their finding that both are associated with firm-specific risk characteristics in a
theoretically predictable and stable manner. Furthermore, Pastor, Sinha, and Swaminathan (2008) document a positive association between market-level implied cost of capital
and risk as measured by the volatility of market returns, consistent with the estimates capturing time-varying Et)1(rt).
In this paper, our goal is to reconcile the conflict between these two streams of literature and provide additional evidence pertaining to the construct validity of the proxies
employed in extant research. Contrary to the results documented in EM and GKS, we
document a positive association between ten of the twelve Et)1(rt) proxies included in our
study and future realized returns after controlling for new information.1 We reconcile our
findings to those in EM and GKS by demonstrating that the prior results are due to
empirical misspecification. Finally, we show that two of the proxies, rDIV and rPEG, demonstrate not only the expected relation with future realized returns, but also with firm-specific risk.
We also address several other issues regarding the use of implied cost of capital estimates including: (1) analysts’ forecast bias, (2) the efficacy of realized returns for Et)1(rt)
before and after controlling for news, (3) the effectiveness of averaging several Et)1(rt)
proxies, and (4) the substitution of realized values for analysts’ forecasts of cash flows or
earnings. Our evidence suggests that deviations between analysts’ expectations and those
of the market lead to potentially less powerful proxies but do not generate biased or
*
Accepted by Steven Salterio. We gratefully acknowledge the financial support of the David Eccles School of
Business. We also wish to thank Kin Lo, K. Ramesh, Matt Magilke, and the workshop participants at the
London School of Business, Michigan State University, Rotterdam School of Management – Erasmus University, the University of North Carolina, the University of British Columbia, Arizona State University,
Georgetown University, and University of Akron for helpful comments on previous drafts of the paper.
1.
Of the twelve estimates we examine, nine are implied cost of capital proxies, two are popular averages of
subsets of these proxies, and the final estimate is derived from the Fama-French four factor model.
Contemporary Accounting Research Vol. 28 No. 4 (Winter 2011) pp. 1085–1122 CAAA
doi:10.1111/j.1911-3846.2011.01096.x
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inconsistent results. Furthermore, we find that realized returns do not proxy for Et)1(rt)
even after controlling for news, and that averaging several proxies does not yield an
enhanced metric. Finally, substituting realized values for analysts’ forecasts of cash flows
yields systematically biased estimates, which might yield biased and inconsistent results
when such estimates are employed in empirical research.
Given the current state of the literature, the validity of the various cost of capital estimates is unclear and it is not uncommon for similar studies to document dissimilar results
because they employ different cost of capital estimates. For example, Ogneva, Subramanyam, and Raghunandan (2007) (hereafter OSR) conclude that firms with internal control
weaknesses do not bear a higher cost of equity capital, while Ashbaugh-Skaife, Collins,
Kinney, and LaFond (2009) (hereafter ACKL) conclude the opposite. These contradictory
results are wholly attributable to differences in the authors’ choices of Et)1(rt) proxies.2
Thus, additional evidence regarding the validity of alternative Et)1(rt) proxies is needed to
help guide researchers’ proxy selection.
Based on our evidence, we recommend that researchers requiring a valid proxy for
Et)1(rt) employ either rDIV or rPEG. We caution against the use of realized returns or the
other implied cost of capital estimates we examine to proxy for Et)1(rt). Finally, we suggest that researchers introducing new proxies for Et)1(rt) to the literature subject their
proposed measures to both of the construct validity tests employed in the current study,
and provide support for how the measure enhances the existing technology for estimating
Et)1(rt).
Our findings should be of interest to researchers requiring a valid proxy for Et)1(rt).
The need for such a proxy is far-reaching. It extends from accounting research that examines the impact of financial reporting and disclosure on required returns, to finance
research that investigates market anomalies, asset pricing theory, and capital budgeting.
These areas of research produce findings of interest to standard setters, regulators, investors, preparers, and auditors. Accordingly, the validity of the Et)1(rt) proxies employed in
research is an important issue with pervasive implications.
We organize the remainder of our paper as follows. Section 2 reviews the related literature and sets forth the development of our hypotheses. Section 3 presents our empirical
models and proxies. Section 4 delineates our sample selection procedure and provides
descriptive statistics for our sample. We discuss the results of our construct validity assessment in section 5. In section 6 we provide evidence pertaining to several other issues
related to implied cost of capital estimates. Section 7 reconciles the results of our realized
return analysis with those documented in prior literature. Finally, section 8 summarizes
our conclusions.
2. Literature review and hypotheses development
Construct validity is woven into the theoretical fabric of the social sciences, and is thus
central to the measurement of abstract theoretical concepts.. .. Fundamentally, construct
validation is concerned with the extent to which a particular measure relates to other
measures consistent with theoretically derived hypotheses concerning the concepts (or constructs) being measured.
2.
OSR replicate ACKL’s findings using ACKL’s proxy for cost of equity capital, but discount the results,
citing conflicting evidence regarding the relative validity of alternative implied cost of capital measures.
Our results provide little support for the Et)1(rt) proxy employed in OSR, but strong support for the
proxy employed in ACKL.
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The preceding quote describes the classic, well-accepted method routinely employed to examine construct validity.3 Consistent with standard practice, we rely on the preceding quote to
guide our approach to examining construct validity. Specifically, we examine the relationship
among alternative proxies for Et)1(rt) and future realized returns, which are a function of
Et)1(rt). In addition, we examine the relationship among alternative proxies for Et)1(rt) and
contemporaneous risk characteristics finance theory suggests are predictably associated with
Et)1(rt). The following paragraphs detail the theories underlying our examination.
Realized returns
Realized return at time t (rREALt) is modeled as the expected return at time t conditional
on information available at t ) 1 (Et)1(rt)) plus the unexpected (or abnormal) return due
to new information (URt):
rREAL;t ¼ Et1 ðrt Þ þ URt
ð1Þ:
Relying on prior research (e.g., Campbell 1991;Vuolteenaho 2002) further decomposes
the unexpected return to new information (URt) into two components — the unexpected
return due to cash flow news (Ncf,t), and the unexpected return due to expected return
news (Nr,t). This gives rise to equation 2:
rREAL;t ¼ Et1 ðrt Þ þ ðNcf ;t Nr;t Þ
ð2Þ;
where:
rREAL,t = realized return from t)1 to t;
Et)1(rt) = expected return at t, conditional on information at t)1;
Ncf,t
= return due to cash flow news from t)1 to t; and
Nr,t
= return due to expected return news from t)1 to t.
Traditionally, research that employs realized returns to proxy for expected returns
relies on the assumption that URt is mean zero, and that in-sample averaging of realized
returns across firms or time purges URt to produce a valid proxy for Et)1(rt). Some more
recent research goes further by using firm-specific (i.e., not averaged) realized returns to
proxy for Et)1(rt) (e.g., Easley, Hvidkjaer, and O’Hara 2002; McInnis 2010).
Nevertheless, a growing body of research questions the validity of realized returns as a
proxy for Et)1(rt). Elton (1999) argues that averaging does not eliminate URt because
unexpected returns tend to be large and correlated across firms and time. Vuolteenaho
(2002) demonstrates that the unexpected component is the dominant factor driving firmlevel stock returns, and that cash flow news is largely firm-specific, whereas expected return
news is linked to systematic macroeconomic factors. Consistent with the latter finding,
Campbell and Ammer (1993) find that expected return news drives aggregate stock returns.
These findings suggest that firm-level and portfolio-level realized returns could be poor
proxies for Et)1(rt). At the firm level the URt due to firm-specific cash flow news, as well
as the URt due to systematic expected return news, contaminate the realized return proxy.
At the portfolio level sufficient averaging might mitigate the URt due to firm-specific cash
flow news, but it is less likely to mitigate the URt due to systematic, macroeconomic
expected return news. Moreover, if cash flow news is correlated across firms and ⁄ or time,
averaging, even over large numbers of firms or long periods, might not purge either
3.
Carmines and Zellner (CZ) 1979: 23; bolding added. Because theory rarely models abstract theoretical
concepts completely, construct validation does not require the identification of an exhaustive list of the
observable measures believed to be associated with the underlying unobservable construct. On the contrary, a theoretical basis for hypothesizing a directional association between the empirical proxy of interest
and some set of measures associated with the underlying unobservable construct is paramount to credible
construct validation.
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component of the URt. Attempts to mitigate the problem by averaging over increasingly
larger samples or longer periods invoke unpalatable stationarity assumptions (Chan and
Lakonishok 1993).
(2) and the research discussed in the preceding paragraph suggest that an examination
of the association between rREAL,t and Et)1(rt) is vulnerable to omitted variables if Ncf,t
and Nr,t are ignored. If Et)1(rt) is correlated with Ncf,t or Nr,t the resulting correlated
omitted variable bias could result in biased and inconsistent results. Even if Et)1(rt) is not
correlated with Ncf,t or Nr,t, however, omitting the latter two variables reduces the power
of the analysis. In this case, no statistically significant correlation between rREAL,t and
Et)1(rt) might be observed even if one exists.
(2) suggests that if an Et)1(rt) estimate is a valid proxy, we should observe a positive
correlation between the proxy and rREAL,t after controlling for Ncf,t and Nr,t. This gives
rise to our first hypothesis.4
HYPOTHESIS 1. After controlling for Ncf,t and Nr,t, a positive correlation between a proxy
for Et)1(rt) and rREAL,t provides support for the validity of that Et)1(rt) proxy.
Risk characteristics
Ross’s 1976 Arbitrage Pricing Theorem (APT) models the expected return for a given period
as a function of the risk free rate (rf) plus the risk premiums arising from K risk factors:
XK
Et1 ðrt Þ ¼ rf ;t1 þ
k ðE ðr Þ rf ;t1 Þ:
ð3Þ
k¼1 k t1 k
Ross’s APT does not identify the risk factors, although existing research suggests several candidates. The capital asset pricing model (CAPM) suggests that Et)1(rt) is increasing in market beta (Lintner 1965; Mossin 1966; Sharpe 1964). Modigliani and Miller
(1958) support a positive association between leverage and Et)1(rt). Berk (1995) argues
that market value of equity is systematically decreasing in priced risk such that Et)1(rt) is
inversely related to the market value of equity and positively related to the book-to-price
ratio. Finally, Beaver, Kettler, and Scholes (1970) assert that abnormal earnings arising
from growth opportunities are inherently more risky, leading to a positive association
between Et)1(rt) and growth. Equation 3 above and this body of research gives rise to our
second hypothesis.5
HYPOTHESIS 2. A positive correlation between a proxy for Et)1(rt) and the risk free rate,
market beta, leverage, book-to-price ratio and growth, and a negative correlation
with market value of equity provides support for the validity of that Et)1(rt) proxy.
Related empirical research
Prior empirical research examines the association between alternative proxies for Et)1(rt),
realized returns, and firm-specific risk characteristics. Nonetheless, as noted earlier, the
4.
5.
Our paper seeks to provide guidance to researchers seeking a valid proxy for Et)1(rt) by examining the
extent to which implied cost of capital estimates proxy for expected returns (i.e., Et)1(rt)). Lee, So, and
Wang (2010) provides guidance to those seeking to predict future returns by investigating the ability of
certain implied cost of capital proxies to predict future realized returns (i.e., rREAL,t). These roles for
implied cost of capital estimates are quite different. In the presence of cash flow news and expected return
news, it is quite possible that a particular proxy might be a poor (good) proxy for Et)1(rt), but a good
(poor) predictor of rREAL,t.
Readers interested in a more in-depth discussion of these risk characteristics are referred to Botosan and
Plumlee 2005.
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findings from this research are mixed. GKS regress realized returns on five alternative
proxies for Et)1(rt).6 The authors do not document the expected positive association
between realized returns and their proxies, but their analysis does not control for Ncf,t or
Nr,t. EM control for Ncf,t and Nr,t in their examination of the association between realized
returns and seven proxies for Et)1(rt). Even so, EM find that none of the proxies are positively associated with realized returns. GKS and EM conclude that their results do not
provide support for the construct validity of the proxies they examine. In contrast, BP
examine the association among five proxies for Et)1(rt) and firm-specific risk characteristics. They conclude that rDIV and rPEG, are valid proxies for Et)1(rt) as both are correlated
with firm risk characteristics in a theoretically predictable manner.
While GKS, EM, and BP examine different sets of Et)1(rt) proxies, rPEG is examined
by all three. Accordingly, the findings of GKS and EM versus those of BP present an
explicit conflict in the evidence regarding this metric’s construct validity. The conflict with
respect to rDIV is implied as opposed to explicit since neither GKS nor EM include rDIV in
their analyses. In addition, since 2005 there has been an explosion in Et)1(rt) proxies
employed in the literature, without a rigorous construct validity assessment of the same.
Accordingly, the primary objectives of the construct validity portion of this study are
threefold: first, to investigate the source of the disparate results noted above; second, to
augment BP’s risk-based construct validity analysis of rDIV with a realized return analysis
and extend their findings over an additional period of time; and third, to use both the realized return and risk-based approaches to examine the construct validity of the more recent
additions to the set of alternative proxies for Et)1(rt).
3. Empirical models and proxies
Empirical method for realized return analysis
Realized return model
Our empirical specification of the return decomposition model (2) is given below.
rREALit ¼ a0 þ b1 ERit1 þ b2 CFN 1it þ b3 CFN TVit þ b4 EWER Nit þ b5 FSER Nit þ eit
ð4Þ;
where:
rREALit
ERit)1
CFN_1it
= 12-month buy and hold return, beginning the month after estimation of ER;
= expected return proxy at t conditional on information at time t)1;
= news about period t to t+1 cash flows received during the 12-month realized
return period;
CFN_TVit = news incorporated in target prices during the 12-month realized return
period;
EWER_Nit= economy-wide expected return news during the 12-month realized return
period; and
FSER_Nit = firm-specific expected return news during the 12-month realized return
period.
Recall that equation 2 models realized returns (rREAL,t) from t)1 to t as a function of
expected returns at t conditional on information at time t)1 (Et)1(rt)), as well as cash flow
news (Ncf,t) and expected return news (Nr,t) received from t)1 to t. In our specification
ERit)1 is one of a number of alternative expected return estimates intended to proxy for
Et)1(rt).7 Hypothesis 1 states that, after controlling for Ncf,t and Nr,t, a positive correlation between a given proxy for Et)1(rt) and rREAL,t (i.e., a positive ß1 coefficient) provides
support for the validity of that Et)1(rt) proxy.
6.
7.
The Appendix summarizes the Et)1(rt) proxies examined in GKS, EM, BP, and the current study.
We enumerate the expected return estimates included in our study in the Appendix and in section 3.
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In theory ß1 should equal 1. Such a test is not only a test of the extent to which the
proxy captures cross-sectional variation in Et)1(rt), but also the extent to which it captures the magnitude of Et)1(rt). Most empirical research employing Et)1(rt) proxies is
concerned with cross-sectional variation in Et)1(rt). Accordingly, an Et)1(rt) proxy that
captures cross-sectional variation in Et)1(rt) (i.e., ß1 > 0) might be valid for use in empirical research even if the magnitude of the proxy is biased (ß1 „ 1). Under such circumstances, a test of ß1 = 1 is an unnecessarily rigorous test of construct validity. For this
reason, in testing our first hypothesis we do not require ß1 to meet the more stringent test
of equivalence to the theoretical value of one, but we report the results of this test.
Our empirical specification includes two proxies for Ncf,t. CFN_1t captures cash flow
news related to near-term cash flows, and is measured as the earnings surprise during the
realized return period. Our second proxy, CFN_TVt, is the revision in analysts’ forecasts
of target prices during the realized return period. We include this variable to capture cash
flow news related to long-horizon cash flows. Since realized returns are increasing in cash
flow news (see (2)), we expect ß2 and ß3 to be significantly positive.
Our model also incorporates two proxies for Nr,t. Since expected returns are a function
of the risk free rate, we include the change in the risk free rate between t)1 and t to proxy
for economy-wide expected return news linked to macroeconomic factors (EWER_Nt).
Since expected returns are also a function of the amount of risk a particular firm’s stock
presents, we include the change in firm-specific market beta between t)1 and t to proxy
for expected return news linked to changes in the amount of risk associated with the firm
(FSER_Nt). As shown in (2), expected return news is negatively associated with realized
returns. Accordingly, we expect both ß4 and ß5 to be significantly negative.
Target prices, which we employ in the computation of CFN_TVt, reflect the present
value of infinite horizon cash flows beyond the forecast horizon. As noted above, our primary objective for including CFN_TVt in our empirical model is to capture long-horizon
cash flow news. Nevertheless, analysts’ revisions of target prices reflect changing beliefs
about discount rates as well as future cash flows.8 Since target prices are increasing in
future cash flows but decreasing in the discount rate, we expect the association between
CFN_TVt and realized returns to be positive regardless of whether CFN_TVt captures cash
flow news, expected return news, or both. As both types of news are important to the
theoretical model, CFN_TVt is a particularly important control variable.
The following paragraphs provide details of the measurement of all variables included
in (4) except for the Et)1(rt) proxies. The Et)1(rt) proxies are outlined following our discussion of the empirical model we employ in our risk analysis.
Realized returns. We calculate realized returns using CRSP data as the buy and hold
realized return computed over the 12 months beginning the month after we estimate
expected returns.
Cash flow news. To calculate our cash flow news proxies we rely on Value Line analysts’ forecasts of annual earnings per share for the current year (Year t) and target prices
at the end of Year t+4. All forecasts are made in the third calendar quarter of the year.
Our proxy for the current year cash flow news (CFN_1) is the difference between the
reported annual earnings per share for year t announced during the 12-month period we
estimate realized returns, less analysts’ forecasts of those annual earnings issued the day
we estimate Et)1(rt). Thus, CFN_1 captures ‘‘earnings surprise’’ similar to that employed
in numerous other studies. We compute CFN_TV as the difference between the midpoint
of the forecasted target price range made 12 months after we estimate our expected return
proxies and the midpoint of the forecasted target price range made at the date we estimate
8.
Consistent with this, Lambert (2009) highlights that target prices are ‘‘free to reflect whatever assumption
regarding future discount rates are deemed appropriate’’ (261, note 1).
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our Et)1(rt) proxies. In our analyses, we scale our cash flow news variables by stock
price on the day we estimate expected returns. We obtain actual earnings per share from
COMPUSTAT and forecast and stock price data, which is stock price as of the publication date or within three days after publication, from Value Line. Panel A of Table 1 provides a description of the cash flow news proxies employed in our analysis.
Expected return news. We compute our proxy for economy-wide expected return news
(EWER_N) as the change in the risk free rate (rf) over the 12-month realized return period. Specifically, EWER_N is the rf during the last month of the realized return estimation
period less rf twelve months earlier.9 We measure rf as the five-year treasury constant
maturity rate obtained from the U.S. Federal Reserve at http: ⁄ ⁄ www.federalreserve.gov.
Our proxy for firm-specific expected return news (FSER_N) is calculated as the change in
market beta (MBETA) over the 12-month realized return period.10 We use CRSP data to
estimate MBETA via the market model with a minimum of 20 out of 60 monthly returns
and a market index return equal to the value weighted NYSE ⁄ AMEX return. Each beta
estimation period ends in June. Panel B of Table 1 provides a description of the expected
return news proxies employed in our analysis.
Empirical method for risk analysis
Expected return model
(5) provides our empirical specification of the expected return model given by equation 3:
ERit1 ¼ v0 þ c1 rft1 þ c2 UBETAit1 þ c3 DMit1 þ c4 LMKVLit1 þ c5 LBPit1
þ c6 EXGRWit1 þ git1
ð5Þ;
where:
ERit)1
= expected return proxy;
rft)1
= risk-free rate of interest;
UBETAit)1 = unlevered CAPM beta;
DMit)1
= leverage;
LMKVLit)1 = log of the market value of common equity;
LBPit)1
= log of book-to-market ratio;
EXGRWit)1 = expected growth in earnings per share.
Hypothesis 2 states that a theoretically predictable relation between a given proxy for
Et)1(rt) and the risk-free rate of interest, market beta, leverage, market value of equity,
book-to-price, and earnings growth provides support for the validity of that proxy. Specifically, we expect ERit)1 to be increasing in the risk-free rate, market beta, leverage, bookto-price, and growth and decreasing in the market value of equity. Accordingly, finding c1,
c2, c3, c5, and c6 greater than zero and c4 less than zero provides support for a given
9.
10.
Monahan and Easton (2010) question the use of this proxy, stating that the risk-free rate has ‘‘nothing to
do with risk’’ and claiming that a change in rf is a cross-sectional constant. From (3), rf is an economywide parameter that bears directly on Et)1(rt). Thus, a change in rf gives rise to a change in Et)1(rt), such
that a change in rf constitutes economy-wide expected return news, our construct of interest. In addition,
rf is not a cross-sectional constant because, as stated in Table 1, we measure the change in rf using the
five-year treasury constant maturity rate as of the month the Et)1(rt) proxy is estimated.
Monahan and Easton (2010) question the use of changes in MBETA to capture firm-specific expected
return news. We employ the change in MBETA to proxy for firm-level changes in the amount of risk. In
so doing, we do not presume that market risk is the only relevant priced risk, but we do assume that
changes in MBETA are correlated with changes in the overall level of risk an investment presents to the
market. The power of this proxy is reduced if this assumption is violated, but the potential detrimental
effect of this is mitigated by the inclusion in our model of the change in expected terminal value, which
also captures firm-specific expected return news.
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TABLE 1
Variable descriptions: cash flow news, expected return news, and firm-specific risk factors
Panel A: Cash flow news proxies
Descriptiona
Variable
CFN_1
CFN_TV
= Current period cash flows news = (A_epsit – eps1it) ⁄ |Priceit|.
Calculated as COMPUSTAT actual earnings per share for
Year t+1 less the related Value Line forecast of Year t+1 earnings,
made in the third quarter of Year t, scaled by the absolute value
of the Value Line reported stock price at the time r is estimated (in Year t).
= Terminal value cash flow news = (TPit+1 – TPit) ⁄ |Priceit|.
Calculated as the Value Line forecast of target price made in
Year t+1 less the Value Line forecast of target price made in Year t,
scaled by the absolute value of the price at the time r is estimated (in Year t).
Panel B: Expected return news proxies
EWER_N
FSER_N
= Economy-wide expected return news = Change in discount
rate = rft+1 – rft. Calculated as the five-year treasury constant maturity
as of the month Et)1(rt) in Year t+1 less the five-year treasury
constant maturity at the time Et)1(rt) is estimated (in Year t). rf is
drawn from the U.S. Federal Reserve at http: ⁄ ⁄ www.federalreserve.gov.
= Firm-specific expected return news = Change in market beta =
mbetat+1 – mbetat.
Panel C: Risk proxies
MBETA
UBETA
DM
MKVL
BP
EXGRW
= CAPM beta estimated via the market model using the value weighted
NYSE ⁄ AMEX market index return. Require a minimum of 20 monthly
returns over the 60 months prior to June of the year Et)1(rt) is estimated.
= unlevered CAPM beta = MBETA ⁄ (1 + Debt ⁄ Equity) where
debt is long-term liabilities (COMPUSTAT items dltt) and equity
is total common stockholders’ equity (COMPUSTAT item ceq)
as of the end of the fiscal year prior to the date Et)1(rt) is estimated.
= long-term liabilities (COMPUSTAT items dltt) at the end of
the fiscal year prior to the date Et)1(rt) is estimated scaled by MKVL.
= market value of equity on December 31st of the Year t)1
(prior to the date Et)1(rt)) is estimated. If the market value of
equity from the Center for Research on Security Prices (CRSP) is not
available use the one from COMPUSTAT as of the end of the fiscal
year prior to the date Et)1(rt) is estimated, stated in millions of dollars.
LMKVL is the natural log of MKVL.
= book value of equity at the end of the most recent quarter prior
to the date Et)1(rt) is estimated scaled by MKVL. LBP is the natural log of BP.
= earnings growth computed by dividing the difference in forecasted earnings
five periods in the future less forecasted earnings four periods in the future
by the absolute value of forecasted earnings four periods in the future.
Notes:
a
Throughout the description of the variables, Year t refers to the year that the expected return
estimates (Et)1(rt)) are made.
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proxy for expected return. In theory c1 should equal 1, although a test of c1 = 1 is a particularly rigorous construct validity test. Nevertheless, we also report the results of a test
of c1 = 1.
We do not infer construct validity from the magnitude of the R2 of the cost of
equity capital models because assumptions regarding the terminal value imposed by the
researcher in the derivation of some implied cost of capital estimates can lead to induced
spurious correlation between the proxy and certain risk characteristics, yielding a high
R2 by construction. For example, if an assumption related to long-range growth in earnings is used to derive the terminal value (as in the PEG model), it is not surprising that
growth, a firm-specific risk factor, explains a significant portion of the variation in that
expected return proxy. Thus, it is particularly important to assess the association
between the expected return estimates and various firm-specific risk factors after controlling for risk factors that are potential candidates for spurious correlation (primarily
growth).
Finally, Berk (1995) argues that book-to-price and market value of equity play similar
roles in an incomplete model of expected returns, in that both variables capture otherwise
unmeasured risk. Accordingly, it is unclear whether both variables should achieve significance in the empirical model. The ‘‘catch-all’’ nature of these variables, however, mitigates
the concern that the model is susceptible to omitted risk factors.
Below is a detailed discussion of our measurement procedures for the risk proxies
employed in our analysis. Panel C of Table 1 summarizes their descriptions.
Unlevered beta. We include unlevered beta (UBETA) to capture the theoretical relation
between Et)1(rt) and CAPM beta. Including the traditional levered beta (MBETA) in the
model captures leverage risk as well as market risk (e.g., Hamada 1972; Chung 1989),
which complicates the interpretation of the coefficients on both leverage and beta.
Employing unlevered beta circumvents this issue. We ‘‘unlever’’ MBETA using the procedure described in standard finance textbooks (e.g., Kester, Fruhan, Piper, and Ruback
1997).11 Briefly,
Debti
MBETAi ¼ UBETAi þ Equity
UBETA;
i
which yields
MBETAi
UBETAi ¼ 1þ½Debt
:
i =Equityi MBETA is estimated as described earlier. We compute debt-to-equity by dividing
long-term debt by stockholders’ equity using COMPUSTAT data measured at the end of
the fiscal year prior to the time we estimate the Et)1(rt) proxies.
Leverage. Modigliani and Miller (1958) suggest that as debt in a firm’s capital structure increases, risk increases. As discussed above, estimating the model with UBETA
allows us to predict unequivocally a positive coefficient on DM (c3). We measure DM as
the ratio of long-term debt (described above) to the market value of common equity measured on December 31 prior to the year we estimate expected return. We collect market
value of common equity from CRSP, or from COMPUSTAT if the data are unavailable
on CRSP.
Market value of equity. Our proxy for the market value of equity is the natural log of
the market value of common equity (LMKVL) and is collected as described above. Consistent with prior research, we log transform the data to mitigate skewness.
Book-to-price. We calculate book-to-price (BP) as the book value per share at the
quarter end closest to a date on or before June 30th of the Value Line publication year
11.
The formula we employ to unlever beta assumes no certainty, and consequently no benefit arising from
the tax deduction of interest payments. The Hamada 1972 formula is an alternative approach that incorporates the value of the tax shield on interest by including an adjustment for tax (1)t) in the denominator.
In the context of our analysis, there is no reason to expect the tax adjustment to play a role. Accordingly,
we follow the approach typically used by investment banks and practitioners, and ignore the tax shield.
CAR Vol. 28 No. 4 (Winter 2011)
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Contemporary Accounting Research
scaled by price per share. Price per share is the stock price on the Value Line publication
date or closest date thereafter within three days of publication. We log transform these
data to mitigate skewness (LBP).
Expected growth. We estimate expected earnings growth (EXGRW) using the forecasted growth in earnings five years hence. We calculate EXGRW for each firm-year as the
forecasted earnings for Year t+5 less forecasted earnings for Year t+4, scaled by the
absolute value of the Year t+4 forecast.
Before moving on to the measurement of the Et)1(rt) proxies, we emphasize the
importance of timing in our analyses. As noted in (2), realized returns (rREAL) are a function of Et)1(rt) determined prior to the period over which realized returns and news are
measured. Thus, in our test of Hypothesis 1 we measure realized returns, cash flow news,
and expected return news contemporaneously, but our estimates of Et)1(rt) are measured
at the end of the prior year. As noted in (3), however, firm-specific risks existing at t)1
are part of the t)1 information set investors use to determine Et)1(rt). Thus, in our test of
Hypothesis 2, we employ risk proxies estimated contemporaneously with our Et)1(rt)
proxies.
Expected return proxies
We analyze twelve proxies for Et)1(rt); all drawn from extant research. Nine are implied
cost of capital proxies included in at least one of the three studies (GKS; EM; BP) that
contribute to the debate regarding the validity of expected return estimates: rCT, rDIV,
rGLS, rGOR, rOJN, rMPEG, rPEGST, rGM and rPEG (see the Appendix). Due to the popularity
of this measure, we also include estimates derived from the Fama-French four-factor
model (rFF), as well as two popular ‘‘composite’’ proxies not examined in any of the three
earlier studies (rHL and rDKL).
The implied cost of capital proxies are derived from the short-horizon form of
the classic dividend discount model, which equates current stock price to a finite series
of expected future cash flows and a terminal value, discounted to the present at the cost
of equity capital. Alternative estimates arise from models that deal with the terminal value
in different ways. Table 2 summarizes the assumptions that underlie the nine unique
implied cost of capital proxies and the Value Line forecasts needed to estimate each
proxy.12
We follow the estimation procedures employed in prior literature. Specifically, we follow the procedures outlined in: (1) BP to compute rDIV, rGLS, rGOR, rOJN, and rPEG; (2)
GKS to compute rCT; (3) EM to compute rMPEG and rPEGST; (4) Gode and Mohanram
2003 to compute rGM; (5) Barth, Konchitchki, and Landsman 2010 to compute rFF; (6)
Hail and Leuz 2006, 2009 to compute rHL; and (7) Dhaliwahl, Krull, and Li 2007 to compute rDKL. We provide a brief description of each of the proxies below, with an emphasis
on key similarities and differences. Table 3 provides details that are not repeated in the
text below.
rDIV
The target price method relies strictly on current stock price and analysts’ forecasts of dividends and target prices. It employs a short-horizon form of the dividend discount model
in which a forecasted terminal value truncates the infinite series of future cash flows at the
end of Year 5. The only empirical assumption underlying this method is that analysts’
forecasts of dividends during the forecast horizon and target price at the end of the forecast horizon capture the market’s expectation of those values. Beliefs about the evolution
12.
As noted in the text, two of the proxies are based on an average of a subset of these, whereas rFF is not
an implied cost of capital estimate.
CAR Vol. 28 No. 4 (Winter 2011)
• Earnings per share; two year ahead.
• Beyond the forecast horizon zero growth
in ‘‘abnormal earnings’’.
• Beyond the forecast horizon zero growth
in ‘‘abnormal earnings’’.
rPEGST
(The table is continued on the next page.)
• Earnings per share; one and two
year ahead.
• Dividends per share; current year.
• Beyond the forecast horizon zero growth
in ‘‘abnormal earnings’’.
• Analysts’ earnings forecasts in Years
1 and 2 equal the market’s expectation.
• Zero dividends in Year 1.
• Year 1 earnings and Year 2
‘‘abnormal earnings’’ (specification 2b)
are positive.
• Analysts’ earnings forecasts in Years
1 and 2 equal the market’s expectation.
• Year 1 earnings and Year 2
‘‘abnormal earnings’’ (specification 2b)
are positive.
• Analysts’ earnings forecasts in Years
1 and 2 equal the market’s expectation.
• Zero dividends in Year 1.
• Year 1 earnings and Year 2
‘‘abnormal earnings’’ (specification 2b)
are positive.
rPEG
rMPEG
• Dividends per share; current year,
one year ahead, and long range.
• Long range minimum and maximum
target price.
• Earnings per share; one and two year
ahead and long range.
• Beyond the forecast horizon analysts’
forecasts of stock price equal the market’s
expectation.
• During the forecast horizon, analysts’
dividend forecasts equal the market’s
expectation.
rDIV
Value Line forecasts
Terminal value
Short-horizon
TABLE 2
Summary of forecast assumptions and data requirements for implied cost of capital expected return proxiesa
Expected Returns, Realized Returns, and Firm Risk Characteristics
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CAR Vol. 28 No. 4 (Winter 2011)
b
a
• Beyond Year 5, ‘‘abnormal earnings’’
grow at a constant rate, which is
assumed to be the inflation rate.
• Book value per share; current year,
one year ahead and long range.
• Earnings per share; one year ahead
and long range.
• Dividends per share; current year, one
year ahead and long range.
• Earnings per share; long range.
• Earnings per share; current year, one
year ahead, and long range.
• Dividends per share; one year ahead
and long range.
• Book value per share; current year,
one year ahead, and long range.
• Dividends per share; current year.
• Earnings per share; one year ahead
and long range
• Growth in ‘‘abnormal earnings’’ is a
constant rate for all t.
• Estimated abnormal earning growth
rate equals the market’s expectation.
• Growth rate is less than the cost
of equity and exceeds zero.
• Beyond the forecast horizon,
each firm’s ROE equals its cost of
equity capital.
• Beyond the forecast horizon, firms
earn their industry ROE in perpetuity.
• Beyond the forecast horizon, firms
have a 100% dividend payout ratio.
• Analysts’ earnings forecasts in Years
1 and 2 and of dividends in Year
1 equal the market’s expectation.
• Year 1 earnings and Year 2
‘‘abnormal earnings’’ (specification 1b)
are positive.
• During the forecast horizon, analysts’
dividend forecasts equal the market’s
expectation.
• During the analysts’ forecast horizon,
analysts’ forecasts of earnings and
book value equal the market’s
expectation.
• During the forecast horizon without
forecasts, firm ROE fades linearly to
industry ROE.
• Analysts’ earnings forecasts from
Years 1 to 5 equal the market’s
expectations.
• Analysts’ book value forecasts from
Years 1 to 4 equal the market’s
expectation.
Two definitions of abnormal earnings are used in the various models. Specification 1 is defined as r)1(eps2 + rdps1 ) Reps1). Specification 2 is
defined as r)1(eps2 ) Reps1).
The assumptions above are stated in general terms and underlie the theoretical form of each model. For empirical purposes, additional assumptions
are imposed regarding the length of the forecast horizon.
Notes:
rCT
rGLS
rGOR
rOJN
and rGM
Value Line forecasts
Terminal value
Short-horizon
TABLE 2 (Continued)
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Contemporary Accounting Research
Fama-French and momentum
four-factor model (Barth et al. 2010).
Mean implied cost of capital (Hail and
Leuz 2006).
Mean, adjusted implied cost of capital
(Dhaliwal et al. 2007).
rFF
rDKL
rHL
Economy-wide (Claus and Thomas 2001).
Industry method (Gebhart et al. 2001).
Economy-wide growth (Ohlson and JuettnerNauroth 2003).
Modified economy-wide growth
(Gode and Mohanram 2003).
Finite horizon (Gordon and Gordon 1997).
rCT
rGLS
a
c
rGOR
rGM
rOJN
rPEGST
4
P
t¼1
The average of rCT, rGLS, and rGM after limiting each implied estimate to 0.5
The average of rCT, rGLS, rMPEG, and rOJN
rFF ¼ Rft þ bRMRFði;tÞ ðRM Rf ÞðtÞ þ bSMBði;tÞ SMBt þ bHMLði;tÞ HMLt þ bMOMði;tÞ MOMt
P0 ¼
1
ð1 þ rGOR Þt ðdpst Þ þ rGOR ð1 þ rGOR Þ4 ðeps5 Þ
t¼1
11
P
P0 ¼ b0 þ ð1 þ rGLS Þt ððroet rGLS Þbt1 Þ þ ðrGLS ð1 þ rGLS Þ11 Þ1 ððroe12 rGLS Þb11 Þ
t¼1
5
P
P0 ¼ b0 þ ð1 þ rCT Þt ðroet rCT Þbt1 þ ðrCT gÞ1 ð1 þ rCT Þ5 ðroe5 rCT Þb4 ð1 þ gÞ
A ¼ ððc 1Þ þ dps1 =P0 Þ=2
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
rGM ¼ A þ A2 þ ðeps1 =P0 Þ ½ðeps2 eps1 Þ=eps1 ðc 1Þ; A ¼ ððc 1Þ þ dps1 =P0 Þ=2
rOJN
rPEGST ¼
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðeps2 eps1 Þ=P0
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
¼ A þ A2 þ ðeps1 =P0 Þ f½ðeps3 eps2 Þ=eps2 þ ðeps5 eps4 Þ=eps4 =2 ðc 1Þg;
rPEG ¼ ðepsp
eps4 Þ=P0
5
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ffi
rMPEG ¼ A þ A2 þ ðeps2 eps1 Þ=P0 ; A ¼ dps1 =ð2P0 Þ
b
Price-earnings-growth ratio (Easton 2004).
Modified price-earnings-growth
(Easton 2004).
Price-earnings-growth ratio (Easton 2004).
þ ð1 þ rDIV Þ5 ðP5 Þ
rPEG
rMPEG
ð1 þ rDIV Þt ðdpst Þ
t¼1
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Formula
P0 ¼
5
P
Target price (Botosan and Plumlee 2002).
Common name for method and original
source
rDIV
Variable
TABLE 3
Formulas for expected return proxies
Expected Returns, Realized Returns, and Firm Risk Characteristics
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Contemporary Accounting Research
of cash flows beyond the forecast horizon are permitted to vary across firms as a function
of analysts’ beliefs embedded in target prices.
rPEG, rMPEG, and rPEGST
The primary assumption underlying the models used to estimate these proxies is that the
market expects zero growth in abnormal earnings beyond the forecast horizon. This
assumption simplifies the dividend discount model sufficiently that it can be solved for
expected return directly. The rPEG model also assumes that the market expects dividends
in Year t+1 to be zero, whereas rMPEG relaxes this assumption. Following BP we employ
long-range earnings forecasts (Year t+5 and Year t+4) in lieu of the short-range earnings
forecasts (Year t+2 and Year t+1) to estimate rPEG. Doing so increases our sample size
and, we believe, is more in keeping with the assumption regarding future cash flows. In
contrast, consistent with many studies (including EM), we employ near-term earnings forecasts (Year t+2 and Year t+1) to estimate rPEGST. Finally, as in EM, estimating rMPEG
includes a modification for forecasted dividends.
rOJN and rGM
Ohlson and Juettner-Nauroth (2005) derive an accounting-based valuation model that
imposes a series of assumptions regarding the market’s expectations of near term earnings,
abnormal earnings, and the rates of short- and long-term growth in abnormal earnings.
We employ analysts’ forecasts to calculate short-term earnings growth rates and, consistent with prior research, set the infinite growth in abnormal earnings equal to rf less 3 percent. The sole difference between rOJN and rGM lies in the empirical procedures employed
in estimating the model: rGM is estimated with short-term growth in earnings, whereas
rOJN is estimated with short- and long-term growth in earnings.
rGOR
This estimate is derived from a finite specification of the Gordon and Gordon 1997 model,
which assumes that beyond the forecast horizon the market expects each firm’s ROE to
revert to its expected return.
rCT and rGLS.
Claus and Thomas (2001) (hereafter CT) and Gebhardt, Lee, and Swaminathan (2001)
(hereafter GLS) employ the residual income model derived from the dividend discount
model (Ohlson 1995) to specify prices in terms of forecasted ‘‘return on equity’’ and
expected return. The two approaches deal with the terminal value issue in a different manner, however. CT assume that the market expects abnormal earnings beyond the forecast
horizon to grow at a constant rate, which they set equal to the inflation rate. GLS assume
that the market anticipates ROE will linearly fade to an industry-based ROE 12 years
hence, which GLS estimate based on historical industry ROE.
rFF
Barth et al. (2010) among others (e.g., Kothari, Li, and Short 2009) employ expected
return estimates based on the Fama-French four-factor model. The four factors included
in the model are a market factor, size factor, book-to-market-factor, and price momentum
factor. These factors explain some of the variation in realized returns, but use of this
model to estimate Et)1(rt) assumes the factors they employ explain variation in Et)1(rt)
and offer a complete representation of the sources of risk for which investors demand
compensation. This is a distinct difference vis-à-vis implied cost of capital approaches,
which do not presuppose the set of priced risks. We estimate the expected annual factor
returns (bRMRF(i,t), bSMB(i,t), bHML(i,t), and bMOM(i,t)) by first calculating each factor’s
CAR Vol. 28 No. 4 (Winter 2011)
Expected Returns, Realized Returns, and Firm Risk Characteristics
1099
average monthly return over the 60 months prior to month m, and then compounding the
resulting average monthly returns over the twelve months prior to the beginning of firm i’s
fiscal year. rFF is calculated as an annualized predicted return computed using compounded monthly returns, consistent with Barth et al. 2010.
rHL and rDKL
The final two proxies we examine are averages of certain other proxies. Specifically, Hail
and Leuz (2006, 2009) calculate rHL as the mean of rCT, rGLS, rMPEG, and rOJN, whereas
Dhaliwal et al. 2007 calculate rDKL as the mean of rCT, rGLS, and rGM, after ‘‘winsorizing’’
each of these values to a maximum value of 0.5.
Comparison of terminal value assumptions
The rDIV approach assumes analysts’ beliefs about infinite horizon cash flows accord with
market participants’ beliefs imbedded in stock price. All of the other implied cost of capital approaches assume market participants’ expectations regarding infinite horizon cash
flows are consistent with the assumptions imposed by the researcher. Because rDIV does
not constrain the behavior of infinite growth in expected cash flows to be the same across
firms, we expect rDIV to display the greatest cross-sectional variation. Whether this reflects
variation in the underlying Et)1(rt) however, depends on whether analysts’ forecasts adequately proxy for the market’s expectations. Moreover, as discussed previously, researcher
imposed assumptions about the behavior of infinite horizon growth in cash flows can create a spurious correlation between the Et)1(rt) estimates produced and growth. Nevertheless, if the researcher-imposed assumptions mirror those of market participants, such
correlations need not be spurious. Finally, rFF limits the set of priced risk factors to a predetermined set resulting in an association between rFF and the predetermined set of risk
factors by construction.
4. Sample construction, descriptive statistics, and correlations
Sample construction
For each firm-year, we require: (1) CRSP data to calculate realized returns, (2) Value Line
forecasts required to estimate expected return and cash flow news proxies, (3) current
stock price, and (4) COMPUSTAT data to calculate our firm-specific risk factor variables.
The primary sample for our analysis of the association among the expected returns proxies
and firm-specific risk factors consists of 17,904 firm-years drawn from 1984–2004. The primary sample for our analysis of the association among realized returns and the expected
return proxies includes 14,521 firm-years from the same period. Fewer observations appear
in our realized return analysis because our cash flow news and expected return news variables are change variables, such that a firm must have sufficient data in adjacent years to
be included in the sample employed in this analysis.
Descriptive statistics
Expected and realized return estimates
Panel A of Table 4 provides pooled descriptive statistics pertaining to the twelve
Et)1(rt) proxies and realized returns (rREAL). Mean (median) estimates of expected
return range from 7.36 (7.27) percent for rGLS to 15.60 (14.50) percent for rFF. The high
volatility of realized returns (39.91) compared to the low volatility of expected returns
(8.73 at most for rFF) is consistent with variability in the unexpected component of the
return swamping variation in the expected return component. This underscores the
severity of the power issue that could arise if cash flow and expected return news are
ignored.
CAR Vol. 28 No. 4 (Winter 2011)
CAR Vol. 28 No. 4 (Winter 2011)
)67.39
)8.19
33.19
143.65
39.91
17,904
15.27%
11.72
2.52
10.49
19.01
36.89
7.02
17,904
15.26%
14.35
rDIV
4.94
9.20
13.41
23.48
3.76
17,904
11.63%
11.09
rPEG
5.92
9.53
13.96
28.61
4.61
17,904
12.36%
11.31
rMPEG
4.34
8.48
12.80
27.54
4.63
17,904
11.23
10.22
rPEGST
Mean
Median
Percentiles
1%
25%
75%
99%
STD
N
)16.11
)2.36
1.25
11.18
4.50
14,521
)0.76%**
)0.16**
CFN_1
)133.33
)23.26
25.02
134.02
49.64
14,521
0.69%*
0.00
CFN_TV
Cash flow news (scaled by price)
Panel B: Cash flow newsb and expected return news proxiesc
Mean
Median
Perc.
1%
25%
75%
99%
STD
N
rREAL
Panel A: Expected return proxiesa
TABLE 4
Descriptive statistics
5.89
10.11
14.98
30.54
4.99
17,904
13.20%
12.11
rGM
3.92
7.48
10.79
17.59
2.98
17,904
9.23%
8.93
rGOR
0.98
5.27
9.17
15.39
3.57
17,904
7.36%
7.27
rGLS
)268.00
)36.67
20.38
321.54
1.20
14,521
)0.99%*
)2.44
CFN_1A
)57.89
)13.33
16.13
84.21
26.94
14,521
2.43%*
0.00
CFN_TVA
Cash flow news (scaled by forecast)
5.42
9.49
13.11
21.20
3.67
17,904
11.55%
11.14
rOJN
5.48
8.62
11.90
19.11
2.92
17,904
10.48%
10.13
rHL
5.12
8.39
11.91
19.83
3.06
17,904
10.39%
9.99
rDKL
)3.01
)0.98
0.50
2.06
1.20
14,521
)0.32**
)0.42**
EWER_N
)0.72
)0.14
0.09
0.63
0.24
14,521
)0.03**
)0.02**
FSER_N
Expected return news
0.91
9.45
20.48
41.25
8.73
15,608
15.60%
14.50
rFF
(The table is continued on the next page.)
4.98
8.82
12.11
18.66
3.17
17,904
10.65%
10.37
rCT
1100
Contemporary Accounting Research
d
c
b
a
1.02
0.98
0.73
0.64
UBETA
0.42
0.22
DM
4106.62
909.14
MKVL
0.55
0.50
BP
Number of observations for these variables is 17,904. **, * denotes significance at the 0.01 and 0.05 or better levels, respectively (2-tailed t-test).
Cash flow news, firm-specific risk proxies variables are defined in Table 1.
CFN_1A and CFN_TVA are analogous to CFN_1 and CFN_TV except for the scaling. The original values are scaled by recent stock price, but the
variables labeled ‘A’ are scaled by the absolute value of the original forecast.
13.54
12.50
EXGRW
rREAL is the buy and hold realized return computed over the 12 months beginning after the month expected return proxies are estimated. See
detailed descriptions and calculations for each proxy in Tables 2 and 3.
Notes:
Mean
Median
MBETA
Panel C: Firm-specific risk proxiesd
TABLE 4 (Continued)
Expected Returns, Realized Returns, and Firm Risk Characteristics
1101
CAR Vol. 28 No. 4 (Winter 2011)
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Contemporary Accounting Research
Explanatory variables
Panel B of Table 4 provides descriptive statistics for our cash flow and expected return
news proxies.13 CFN_1 captures current year cash flow news via an ‘‘earnings surprise’’
variable. CFN_1 has a mean (median) value of )0.76 ()0.16) percent of recent stock price.
Both the mean and median values are statistically negative, consistent with analyst optimism. CFN_1A measures the earnings surprise as a percentage of beginning earnings forecast. The mean (median) value indicates an earnings surprise of approximately )1.0 ()2.4)
percent of the initial earnings forecast. CFN_TV captures the change in analysts’ expectations of target price over the 12-month realized return period. The mean change in the target price is significantly positive (0.69 percent of stock price), while the median value is
0.0. This is consistent with ‘‘good’’ news on average with respect to infinite horizon discounted expected cash flows.
The mean (median) value of our economy-wide expected return news proxy is
significantly negative at )0.32 ()0.42) indicating an annual decline in the risk free rate of
one-third to almost one-half of one percent. Similarly, the mean (median) value of our
firm-specific expected return news proxy is significantly negative at )0.03 ()0.02).
Finally, panel C of Table 4 reports pooled mean and median statistics for our firmspecific risk factors including MBETA, UBETA, DM, MKVL, BP, and EXGRW. These
statistics describe a sample similar in average market risk to that of the market portfolio
with a mean debt-to-market ratio of 42 percent and a market value of equity that is heavily skewed to larger firms. The average book-to-price ratio of 55 percent is consistent with
the relatively healthy rate of 13.54 percent average growth in expected earnings.
Correlations
Table 5 presents Spearman correlations among sets of variables employed in our regression analyses. We present the mean value of the year-by-year correlations along with the
number of years (out of 21) that the annual correlation is significantly (positive ⁄ negative).
The first row of panel A, Table 5 presents univariate correlations among realized
returns and the twelve proxies for Et)1(rt). The correlations are quite small, ranging from
0.00 (rPEGST and rFF) to 0.09 (rGOR). Four of our Et)1(rt) proxies (rOJN, rGOR, rGLS, and
rCT) correlate positively with rREAL in ten or more years but, in four cases (rDIV, rPEG,
rPEGST, and rGLS), the proxies correlate negatively with rREAL in five or more years. Nonetheless, this analysis fails to consider critical controls for cash flow and expected return
news as modeled in (2).
Except for the correlation between rDIV and rGLS, where the correlation is statistically
positive in ‘‘only’’ 19 years, the pair-wise correlations among the implied cost of capital
proxies are statistically positive in all 21 years. rHL and rDKL are highly correlated
(q = 0.96) despite being the product of an average of somewhat different subsets of alternative measures, and there is a strong positive correlation among rMPEG, rPEGST, and rGM
(q > 0.90). This indicates that these groups of estimates capture essentially the same
underlying construct. In contrast, the correlation between rFF and the implied cost of capital estimates is almost as likely to be negative as positive. This suggests that rFF and the
implied cost of capital estimates do not capture the same underlying construct.
Panel B of Table 5 presents the correlations among the variables we employ in testing
Hypothesis 1. Consistent with cash flow news playing an important role in explaining
realized returns, the correlation between rREAL and the cash flow news proxies is large
13.
We provide cash flow news statistics after scaling each component of cash flows news by recent stock
price, the variable included in our empirical analyses. We also provide cash flow news statistics after scaling each component by the absolute value of the relevant forecast at the beginning of the period. We provide these data to convey the economic magnitude of the revisions in cash flows.
CAR Vol. 28 No. 4 (Winter 2011)
rHL
rFF
rCT
rGLS
rGOR
rGM
rOJN
rPEGST
rMPEG
rPEG
rDIV
rREAL
rPEG
0.01
(8 ⁄ 5)
0.61
(21 ⁄ 0)
—
rDIV
0.04
(6 ⁄ 6)
—
0.02
(6 ⁄ 4)
0.46
(21 ⁄ 0)
0.51
(21 ⁄ 0)
—
rMPEG
0.00
(5 ⁄ 5)
0.46
(21 ⁄ 0)
0.62
(21 ⁄ 0)
0.91
(21 ⁄ 0)
—
rPEGST
Panel A: Correlations among expected return proxies
TABLE 5
Correlations
0.05
(10 ⁄ 3)
0.56
(21 ⁄ 0)
0.73
(21 ⁄ 0)
0.40
(21 ⁄ 0)
0.29
(21 ⁄ 0)
—
rOJN
0.01
(5 ⁄ 4)
0.44
(21 ⁄ 0)
0.51
(21 ⁄ 0)
0.98
(21 ⁄ 0)
0.91
(21 ⁄ 0)
0.38
(21 ⁄ 0)
—
rGM
0.09
(12 ⁄ 2)
0.57
(21 ⁄ 0)
0.60
(21 ⁄ 0)
0.62
(21 ⁄ 0)
0.50
(21 ⁄ 0)
0.68
(21 ⁄ 0)
0.53
(21 ⁄ 0)
—
rGOR
0.08
(12 ⁄ 5)
0.22
(19 ⁄ 0)
0.22
(21 ⁄ 0)
0.39
(21 ⁄ 0)
0.25
(21 ⁄ 0)
0.36
(21 ⁄ 0)
0.30
(21 ⁄ 0)
0.70
(21 ⁄ 0)
—
rGLS
0.00
(4 ⁄ 4)
)0.04
(2 ⁄ 7)
0.00
(21 ⁄ 6)
0.00
(5 ⁄ 7)
0.00
(7 ⁄ 6)
)0.01
(3 ⁄ 3)
)0.01
(5 ⁄ 7)
0.04
(8 ⁄ 3)
0.07
(9 ⁄ 2)
0.04
(9 ⁄ 3)
—
rFF
0.06
(9 ⁄ 2)
0.56
(21 ⁄ 0)
0.64
(21 ⁄ 0)
0.79
(21 ⁄ 0)
0.66
(21 ⁄ 0)
0.70
(21 ⁄ 0)
0.73
(21 ⁄ 0)
0.90
(21 ⁄ 0)
0.72
(21 ⁄ 0)
0.80
(21 ⁄ 0)
0.03
(7 ⁄ 3)
—
rHL
0.05
(9 ⁄ 3)
0.49
(21 ⁄ 0)
0.54
(21 ⁄ 0)
0.86
(21 ⁄ 0)
0.74
(21 ⁄ 0)
0.52
(21 ⁄ 0)
0.80
(21 ⁄ 0)
0.84
(21 ⁄ 0)
0.72
(21 ⁄ 0)
0.74
(21 ⁄ 0)
0.03
(8 ⁄ 3)
0.96
(21 ⁄ 0)
rDKL
(The table is continued on the next page.)
0.08
(13 ⁄ 3)
0.55
(21 ⁄ 0)
0.56
(21 ⁄ 0)
0.51
(21 ⁄ 0)
0.43
(21 ⁄ 0)
0.63
(21 ⁄ 0)
0.43
(21 ⁄ 0)
0.87
(21 ⁄ 0)
0.54
(21 ⁄ 0)
—
rCT
Expected Returns, Realized Returns, and Firm Risk Characteristics
1103
CAR Vol. 28 No. 4 (Winter 2011)
0.35 (21 ⁄ 0)
0.46 (21 ⁄ 0)
—
0.33 (21 ⁄ 0)
—
CAR Vol. 28 No. 4 (Winter 2011)
FSER_N
EWER_N
CFN_TV
CFN_1
rPEG
0.00
(2 ⁄ 3)
)0.14
(0 ⁄ 18)
)0.04
(2 ⁄ 4)
)0.01
(5 ⁄ 6)
rDIV
)0.06
(0 ⁄ 8)
)0.25
(0 ⁄ 21)
)0.02
(4 ⁄ 7)
)0.01
(6 ⁄ 9)
0.04
(6 ⁄ 1)
)0.06
(0 ⁄ 8)
)0.01
(0 ⁄ 3)
0.01
(4 ⁄ 4)
rMPEG
0.05
(8 ⁄ 1)
)0.06
(0 ⁄ 5)
)0.03
(1 ⁄ 6)
0.00
(5 ⁄ 6)
rPEGST
)0.04
(0 ⁄ 6)
)0.16
(0 ⁄ 19)
)0.03
(0 ⁄ 5)
0.01
(4 ⁄ 5)
rOJN
0.06
(7 ⁄ 1)
)0.06
(0 ⁄ 7)
)0.03
(0 ⁄ 6)
0.01
(3 ⁄ 3)
rGM
)0.07
(0 ⁄ 6)
)0.13
(0 ⁄ 15)
0.00
(4 ⁄ 3)
0.00
(7 ⁄ 6)
rGOR
Panel C: Correlations among expected return and cash flow news and expected return new proxies.
rREAL
CFN_1
CFN_TV
EWER_N
CFN_TV
CFN_1
Panel B: Correlations among realized returns, cash flow news, and expected return news proxies.
TABLE 5 (Continued)
)0.04
(0 ⁄ 7)
)0.05
(3 ⁄ 10)
0.01
(5 ⁄ 3)
0.01
(7 ⁄ 5)
rGLS
0.01
(2 ⁄ 2)
0.00
(2 ⁄ 3)
)0.01
(3 ⁄ 3)
)0.13
(3 ⁄ 14)
rFF
)0.01
(2 ⁄ 4)
)0.12
(0 ⁄ 13)
)0.02
(3 ⁄ 3)
0.01
(6 ⁄ 5)
rHL
0.01
0.00
)0.01
)0.01
0.01
(4 ⁄ 4)
)0.09
(0 ⁄ 11)
)0.02
(4 ⁄ 4)
0.01
(6 ⁄ 6)
rDKL
(10 ⁄ 4)
(4 ⁄ 5)
(2 ⁄ 3)
(2 ⁄ 4)
FSER_N
(The table is continued on the next page.)
)0.08
(0 ⁄ 6)
)0.14
(0 ⁄ 19)
)0.03
(1 ⁄ 4)
0.01
(6 ⁄ 4)
rCT
)0.01 (7 ⁄ 8)
)0.01 (0 ⁄ 1)
)0.01 (0 ⁄ 1)
—
EWER_N
1104
Contemporary Accounting Research
0.18
(17 ⁄ 0)
0.11
(15 ⁄ 0)
0.05
(7 ⁄ 1)
)0.16
(1 ⁄ 17)
0.24
(20 ⁄ 0)
0.36
(20 ⁄ 0)
)0.05
(8 ⁄ 9)
)0.04
(8 ⁄ 10)
0.03
(10 ⁄ 8)
0.02
(7 ⁄ 5)
0.07
(8 ⁄ 3)
)0.05
(4 ⁄ 10)
0.31
(21 ⁄ 0)
0.19
(19 ⁄ 0)
0.09
(12 ⁄ 0)
)0.29
(0 ⁄ 21)
0.30
(21 ⁄ 0)
0.78
(21 ⁄ 0)
rPEG
0.08
(11 ⁄ 0)
)0.05
(1 ⁄ 7)
0.30
(21 ⁄ 0)
)0.25
(0 ⁄ 21)
0.46
(21 ⁄ 0)
0.20
(20 ⁄ 0)
rMPEG
0.27
(21 ⁄ 0)
0.14
(18 ⁄ 0)
0.16
(19 ⁄ 0)
)0.29
(0 ⁄ 21)
0.33
(21 ⁄ 0)
0.36
(21 ⁄ 0)
rPEGST
)0.02
(2 ⁄ 4)
)0.09
(0 ⁄ 15)
0.20
(21 ⁄ 0)
)0.16
(0 ⁄ 18)
0.37
(21 ⁄ 0)
0.45
(21 ⁄ 0)
rOJN
0.10
(12 ⁄ 0)
)0.02
(2 ⁄ 6)
0.26
(21 ⁄ 0)
)0.24
(0 ⁄ 21)
0.40
(21 ⁄ 0)
0.27
(20 ⁄ 0)
rGM
)0.02
(3 ⁄ 7)
)0.15
(0 ⁄ 18)
0.39
(21 ⁄ 0)
)0.24
(0 ⁄ 20)
0.63
(21 ⁄ 0)
0.06
(9 ⁄ 3)
rGOR
)0.16
(0 ⁄ 20)
)0.25
(0 ⁄ 21)
0.43
(21 ⁄ 0)
)0.17
(0 ⁄ 18)
0.69
(21 ⁄ 0)
)0.23
(0 ⁄ 21)
rGLS
0.03
(6 ⁄ 4)
)0.09
(1 ⁄ 13)
0.23
(21 ⁄ 0)
)0.12
(1 ⁄ 13)
0.35
(21 ⁄ 0)
0.08
(11 ⁄ 1)
rCT
0.19
(14 ⁄ 2)
0.10
(10 ⁄ 4)
0.07
(10 ⁄ 1)
0.06
(10 ⁄ 5)
0.01
(7 ⁄ 5)
)0.03
(6 ⁄ 9)
rFF
Table values are the mean of year-by-year correlations. Figures in parentheses are the number of years the correlation is significantly
(positive ⁄ negative) at 5% level in year-by-year correlations. All variables are defined in Tables 1 or 3.
Notes:
EXGRW
LBP
LMKVL
DM
UBETA
MBETA
rDIV
rREAL
Panel D: Correlations among expected return and risk proxies.
TABLE 5 (Continued)
)0.01
(3 ⁄ 4)
)0.14
(0 ⁄ 18)
0.39
(21 ⁄ 0)
)0.25
(0 ⁄ 20)
0.62
(21 ⁄ 0)
0.18
(17 ⁄ 1)
rHL
0.00
(4 ⁄ 4)
)0.14
(0 ⁄ 17)
0.39
(21 ⁄ 0)
)0.24
(0 ⁄ 20)
0.61
(21 ⁄ 0)
0.09
(13 ⁄ 1)
rDKL
Expected Returns, Realized Returns, and Firm Risk Characteristics
1105
CAR Vol. 28 No. 4 (Winter 2011)
1106
Contemporary Accounting Research
(greater than 0.30) and significantly positive in all 21 years. We also document a strong
positive correlation between our cash flow news proxies (0.46), suggesting that ‘‘good’’ current period cash flow news tends to be associated with ‘‘good’’ long-horizon cash flow
news. There is little relationship between our macroeconomic expected return news proxy
(EWER_N) and our firm-specific expected return news proxy (FSER_N), and the fact that
neither is strongly correlated with rREAL supports the conclusion in prior research that
cash flow news is the primary driver of realized returns. Finally, the expected return news
proxies are not highly correlated with the cash flow news proxies, suggesting that cash flow
news is distinct from expected return news.
Panel C of Table 5 presents correlations between the Et)1(rt) proxies, and our proxies
for cash flow and expected return news. There is a fairly strong negative correlation
between CFN_TV and several of the Et)1(rt) proxies (rDIV, rPEG,, rOJN, rGOR, rCT, and
rHL), which suggests that terminal values tend to decline when cost of equity capital is
high at the beginning of the realized return period. The low correlation among most of the
Et)1(rt) proxies and our two proxies for expected return news is reasonable since there is
no obvious basis for expected return news to be correlated with the initial level of expected
returns.
Panel D of Table 5 presents the correlation coefficients among rREAL, our Et)1(rt)
proxies, and the firm-specific risk factors. Although we use UBETA in our regression
model, we include MBETA in this table for discussion purposes. Six of the proxies
(rDIV, rPEG, rPEGST, rMPEG, rGM, and rFF) correlate positively with MBETA in at least
11 years, while one (rGLS) correlates negatively with MBETA in 20 years.14 In contrast,
only three of the Et)1(rt) proxies are positively related to UBETA in at least 11 years
(rDIV, rPEG, and rPEGST), while six of the proxies (rOJN, rGOR, rGLS, rCT, rHL, and rDKL) are
negatively related to UBETA in 11 or more years. All Et)1(rt) proxies other than rDIV
and rFF are significantly positively related to leverage in at least 11 years. This finding,
combined with the fact that several of the Et)1(rt) proxies are positively correlated
with MBETA but not UBETA, highlights the importance of separating leverage risk and
market risk.
Except for an unexpected negative association between rGLS and EXGRW ()0.23) and
an unexpected positive association between rFF and LMKVL, the remaining correlations
among the Et)1(rt) proxies and the risk factors accord with expectations. Despite the
counterintuitive nature of the negative association between rGLS and EXGRW, this finding
is consistent with prior research (e.g., BP 2005; Gebhardt et al. 2001). The particularly
strong correlation between EXGRW and rPEG (q = 0.78) is explained in part by the algebraic relationship between rPEG and growth, and serves to underscore the importance of
controlling for growth in our firm-specific risk analysis. Nevertheless, EXGRW is also
highly correlated with rDIV (q = 0.36), which does not have an algebraic relationship with
growth, which is consistent with growth being an important risk factor in its own right.
Finally, the correlation between rREAL and the risk proxies are frequently contrary to
expectations if rREAL is viewed as a proxy for expected returns.
Taken in their entirety, the results presented in panel D suggest that only rDIV, rPEG,
and rPEGST are associated with all of the firm-specific risk factors in a theoretically predictable manner. With respect to rDIV and rPEG this finding is consistent with BP, who
study a more limited set of proxies over an earlier time period (1983–1993). Nonetheless,
in light of the association among the risk proxies, it is important to examine the association between the expected return and firm-specific risk proxies in a multivariate setting.
14.
Because MBETA captures both market and leverage risk, documented correlations with MBETA might be
due to associations with either risk characteristic.
CAR Vol. 28 No. 4 (Winter 2011)
Expected Returns, Realized Returns, and Firm Risk Characteristics
1107
5. Empirical results
Test of Hypothesis 1
Baseline model
Panel A of Table 6 provides the results of estimating a baseline realized return model that
includes our cash flow and expected return news proxies, but excludes the Et)1(rt) proxy.
We estimate this model to assess the incremental explanatory power attributable to the
Et)1(rt) proxies. We report the time-series averages of the coefficients from annual crosssectional regressions and t-statistics based on the standard error of the coefficient (Fama
and MacBeth 1973).
The average R2 of the baseline model is 25.9 percent, indicating that our proxies for
cash flow and expected return news capture one-quarter of the variation in rREAL. We document a strong positive relation between realized returns and the cash flow news variables
(CFN_1 and CFN_TV), consistent with expectations, as well as results in Voulteenaho
2002. We document a significant negative relation between rREAL and economy-wide
expected return news (EWER_N), but the coefficient on firm-specific expected return news
(FSER_N) is insignificant. These findings are consistent with prior research, which concludes that expected return news is driven by macroeconomic, not firm-specific factors
(Vuolteenaho 2002; Campbell and Ammer 1993). Alternatively, CFN_TV might capture
firm-specific expected return news, leaving no role for FSER_N.
Full regression model
Panel B of Table 6 presents the results of estimating twelve specifications of the realized
return model with the various Et)1(rt) proxies. In all specifications the coefficients on
CFN_1 and CFN_TV are significantly positive, the coefficient on EWER_N is significantly
negative, and the coefficient on FSER_N is not statistically different from zero. Thus, adding Et)1(rt) proxies to the model has no effect on the associations between realized returns
and cash flow and expected return news.
Below the coefficient on the Et)1(rt) proxy, we present t-statistics related to
whether the mean proxy coefficient is significantly positive and whether the mean proxy
coefficient is equal to 1. We also present the number of years the proxy coefficient is (1)
significantly positive and not different from one, (2) significantly positive, and (3)
significantly negative.
Except for the coefficients on rPEGST and rFF, the mean coefficients on the Et)1(rt)
proxies are significantly positive, with average values ranging from 0.30 (rGM) to 2.14
(rGOR). The sign of the coefficient is most stable across years for rDIV (significantly positive
in 19 of 21 years). Moreover, in all but one specification (rFF) adding Et)1(rt) to the baseline models improves explanatory power. The models employing rDIV and rGOR show the
greatest increase in R2— an increase of 15 percent to almost 30 percent in both cases.
For several of the proxies (rDIV, rPEG, rOJN, rGLS, rCT, rDKL, and rDKL) the average
coefficient is statistically indistinguishable from the theoretical value of one. rDIV and rOJN
perform best in this respect with coefficients not different from one in nine years. Also, if
the empirical model is well-specified, the intercept should be zero, which is the case in all
but one of the specifications (rGOR), providing further support for the appropriateness of
our models and proxies.
While most of the expected return proxies correlate positively with realized returns,
rDIV seems to rise to the forefront in terms of strength of results. The average coefficient
on rDIV is significantly positive, but statistically indistinguishable from 1. It is significantly
positive in the greatest number of years (19) and indistinguishable from one in close to
half the years (9). The model estimated with rDIV is also tied for the greatest increase in
R2 (15 percent increase).
CAR Vol. 28 No. 4 (Winter 2011)
1108
Contemporary Accounting Research
TABLE 6
Regressions of realized returns on cash flow news and expected return news proxies.
Panel A: Model 1: rREALit ¼ a0 þ b1 CFN 1it þ b2 CFN TVit þ b3 EWER Nit þ b4 FSER Nit þ eit
Intercept
)0.018 ()0.18)
CFN_1 (+)
CFN_TV (+)
EWER_N ())
0.014 (14.22**) 0.002 (15.31 **) )0.144 ()1.85*)
FSER_N ()) Avg. Adj. R2
0.008 (0.15)
25.9
Panel B: Model 2:
rREALit ¼ a0 þ b1 ERit1 þ b2 CFN 1it þ b3 CFN STit þ b4 CFN TVit þ b5 EWER Nit þ b6 FSER Nit þ eit
rDIV
>0
=1
=1 ⁄ + ⁄ )
rPEG
>0
=1
=1 ⁄ + ⁄ )
rMPEG
>0
=1
=1 ⁄ + ⁄ )
rPEGST
>0
=1
=1 ⁄ + ⁄ )
rOJN
>0
=1
=1 ⁄ + ⁄ )
rGM
>0
=1
=1 ⁄ + ⁄ )
rGOR
>0
=1
=1 ⁄ + ⁄ )
rGLS
>0
=1
=1 ⁄ + ⁄ )
rCT
>0
=1
=1 ⁄ + ⁄ )
Intercept
ER (+)
)0.131
()1.13)
0.883
(6.67**)
(0.40)
{9 ⁄ 19 ⁄ 0}
0.893
(3.50**)
(0.69)
{7 ⁄ 13 ⁄ 3}
0.434
(2.44**)
()2.77**)
{5 ⁄ 10 ⁄ 2}
0.322
(1.54)
()3.05**)
{7 ⁄ 10 ⁄ 2}
1.157
(4.46**)
(0.60)
{9 ⁄ 14 ⁄ 0}
0.304
(1.83*)
()2.68**)
{4 ⁄ 9 ⁄ 2}
2.141
(6.99**)
(3.33**)
{5 ⁄ 17 ⁄ 0}
0.964
(3.23*)
(0.92)
{4 ⁄ 12 ⁄ 0}
1.581
(5.07**)
(1.52)
{8 ⁄ 16 ⁄ 0}
)0.104
()1.34)
)0.056
()0.53)
)0.044
()0.43)
)0.124
()1.44)
)0.045
()0.42)
)0.177
()2.14**)
)0.056
()0.67)
)0.161
()1.57)
CFN_1
(+)
CFN_TV
(+)
EWER_N
())
FSER_N
())
Avg.
Adj. R2
0.014
(17.99**)
0.002
(16.22**)
)0.126
()1.91*)
0.018
(0.44)
29.7
0.014
(15.51**)
0.002
(15.09**)
)0.131
()1.95*)
0.008
(0.17)
27.6
0.014
(16.67**)
0.002
(15.66**)
)0.133
()1.88*)
0.008
(0.17)
26.7
0.014
(16.29**)
0.002
(15.69**)
)0.137
()1.95*)
0.002
(0.05)
26.9
0.014
(16.47**)
0.002
(15.42**)
)0.125
()1.94*)
0.014
(0.29)
27.3
0.014
(16.33**)
0.002
(15.48**)
)0.136
()1.87*)
0.008
(0.15)
26.6
0.015
(18.16**)
0.002
(16.14**)
)0.114
()2.06*)
0.007
(0.17)
29.8
0.015
(17.63**)
0.002
(14.90**)
)0.118
()1.94*)
0.017
(0.37)
28.0
0.015
(17.68**)
0.002
(16.13**)
)0.122
()1.90*)
0.016
(0.36)
28.2
(The table is continued on the next page.)
CAR Vol. 28 No. 4 (Winter 2011)
Expected Returns, Realized Returns, and Firm Risk Characteristics
1109
TABLE 6 (Continued)
Intercept
rFF
>0
=1
=1 ⁄ + ⁄ )
rHL
>0
=1
=1 ⁄ + ⁄ )
rDKL
>0
=1
=1 ⁄ + ⁄ )
0.032
(0.45)
)0.131
()1.36)
)0.107
()1.08)
ER (+)
)0.051
()0.56)
()6.04**)
{1 ⁄ 5 ⁄ 7}
1.430
(4.33**)
(0.30)
{5 ⁄ 13 ⁄ 0}
1.177
(3.74**)
(0.65)
{8 ⁄ 12 ⁄ 0}
CFN_1
(+)
CFN_TV
(+)
EWER_N
())
FSER_N
())
Avg.
Adj. R2
0.014
(15.56**)
0.002
(16.83**)
)0.111
()1.89*)
0.009
(0.45)
25.2
0.014
(18.17**)
0.002
(16.04**)
)0.117
()1.95*)
0.014
(0.33)
28.0
0.014
(17.64**)
0.002
(15.92**)
)0.120
()1.93*)
0.013
(0.29)
27.7
Notes:
This table includes the time-series averages of the coefficients of the 21 annual cross-sectional regressions (1984–2004) and t-statistics for whether that mean coefficient is statistically positive ⁄ negative (>0) using the standard error of the coefficient estimates across the 21 years (Fama and
MacBeth 1973). In addition, for the ER coefficients, we include the t-statistic for whether the
mean coefficient is equal to one (=1) and the number of times the coefficient in the year-byyear regressions is (significantly positive and equal to one ⁄ significantly positive ⁄ significantly
negative) (based on a 0.05 p-value) (=1 ⁄ + ⁄ )) in {}. **,* denotes significance at the 0.01, 0.05
level or better (1-tailed t-test). Figures in bold are significant at the 0.01 level or better. All
variables are defined in Tables 1 or 3. Sample size is 14,521.
Our results provide support for the construct validity of all the proxies we examine
except rPEGST and rFF. This conclusion is inconsistent with GKS and EM, who document
insignificant, and in some cases significantly negative relationships between the implied
cost of capital estimates they examine and realized returns. We investigate the source of
the difference in our results in section 7.
Although the results in Table 6 provide support for the construct validity of 10 of the
Et)1(rt) proxies, rREAL is only one of the ‘‘other measures’’ that can be used to assess the
construct validity of alternative Et)1(rt) proxies. A second set of ‘‘other measures’’ also
useful for this purpose is the set of firm-specific risk factors that theory predicts should be
associated with Et)1(rt). The next section presents the results of this analysis.
Test of Hypothesis 2
Table 7 presents the results of estimating regression equation 5. The model includes the
risk-free rate along with five risk proxies (UBETA, DM, LMKVL, LBP, and EXGRW).
We find that only rDIV, rPEG, and rPEGST are related as expected to the risk proxies
included in the model. rPEG and rPEGST are related to all of the proxies consistent with theory. rDIV is related to all but LMKVL, but this is expected if LMKVL and LBP both serve
to capture unmeasured risk (Berk 1995). No other expected return proxy performs as well
as rDIV, rPEG or rPEGST with respect to the association with firm-specific risk. In addition,
if the empirical model is well-specified the intercept should be zero, which it is in these
three specifications, and the coefficient on the risk-free rate should be indistinguishable
from 1, which it is in the models estimated with rDIV and rPEGST. rREAL is not correlated
CAR Vol. 28 No. 4 (Winter 2011)
1110
Contemporary Accounting Research
TABLE 7
Regression of expected return specifications on firm-specific risk factors.
Intercept (?)
rREAL
>0
=1
=1 ⁄ + ⁄ )
rDIV
>0
=1
=1 ⁄ + ⁄ )
rPEG
>0
=1
=1 ⁄ + ⁄ )
rMPEG
>0
=1
=1 ⁄ + ⁄ )
rPEGST
>0
=1
=1 ⁄ + ⁄ )
rOJN
>0
=1
=1 ⁄ + ⁄ )
rGM
>0
=1
=1 ⁄ + ⁄ )
rGOR
>0
=1
=1 ⁄ + ⁄ )
rGLS
>0
=1
=1 ⁄ + ⁄ )
rCT
>0
=1
=1 ⁄ + ⁄ )
rFF
>0
=1
=1 ⁄ + ⁄ )
)111.08
()1.52)
)2.34
()0.19)
4.92
(1.65)
7.38
(3.35**)
4.30
(1.19)
6.40
(4.77*)
5.59
(2.35**)
7.73
(3.15**)
9.81
(4.21**)
6.52
(3.17**)
16.34
(4.07**)
rf
(+)
UBETA
(+)
DM
(+)
14.45
(1.61)
(2.57**)
{7 ⁄ 6 ⁄ 0}
1.59
(0.98)
(0.49)
{6 ⁄ 7 ⁄ 1}
0.29
(0.81)
()3.07**)
{6 ⁄ 6 ⁄ 5}
0.61
(2.16**)
()1.85**)
{3 ⁄ 2 ⁄ 2}
0.63
(1.55)
()1.40)
{4 ⁄ 2 ⁄ 2}
0.45
(2.55**)
()4.16**)
{5 ⁄ 0 ⁄ 3}
0.90
(3.28**)
()0.49)
{3 ⁄ 0 ⁄ 1}
0.31
(0.97)
()4.18**)
{4 ⁄ 6 ⁄ 2}
)0.07
()0.18)
()2.78**)
{4 ⁄ 5 ⁄ 2}
0.57
(2.11**)
()2.16*)
{7 ⁄ 0 ⁄ 6}
)0.74
)1.59
()2.63**)
{4 ⁄ 6 ⁄ 2}
1.12
(0.34)
1.36
(1.43)
LBP
(+)
EXGRW
(+)
Avg.
Adj. R2
)0.14
()0.28)
2.40
(2.17**)
)0.07
()0.60)
8.3
1.59
(5.42**)
0.33
)0.16
(2.25**) ()0.87)
2.51
(8.36**)
0.27
(7.03**)
22.3
0.45
(3.30**)
0.37
)0.16
(8.71**) ()4.82**)
1.60
(9.12**)
0.37
(7.56**)
67.3
0.17
(1.19)
0.86
)0.18
(7.97**) ()3.98**)
2.43
(8.07**)
0.16
(11.99**)
28.5
1.07
(4.01**)
0.96
)0.31
(7.96**) ()9.12**)
1.85
(8.21**)
0.21
(13.85**)
30.5
1.51
(9.75**)
0.22
(9.62**)
41.2
2.27
(8.51**)
0.21
(12.38**)
28.0
2.13
(8.27**)
0.02
(2.46**)
39.3
)0.91
()9.71#)
0.08
(0.48)
)0.07
()0.70)
)0.06
()1.06)
LMKVL
())
0.10
(1.81#)
0.81
)0.18
(7.30**) ()4.01**)
0.48
)0.06
(15.36**) ()1.24)
)0.21
()1.06)
0.56
(7.22**)
)0.03
()0.26)
0.37
)0.00
(7.02**) ()0.09)
4.07
(2.36**)
2.34
(2.80**)
0.00
(0.07)
0.15
(0.23)
2.54
)0.07
(6.94**) ()10.78#)
40.8
1.11
(12.19**)
0.02
(1.43)
15.6
0.30
(1.04)
)0.06
()2.72#)
17.9
(The table is continued on the next page.)
CAR Vol. 28 No. 4 (Winter 2011)
Expected Returns, Realized Returns, and Firm Risk Characteristics
1111
TABLE 7 (Continued)
Intercept (?)
rHL
>0
=1
=1 ⁄ + ⁄ )
rDKL
>0
=1
=1 ⁄ + ⁄ )
7.41
(4.50**)
7.20
(4.08**)
rf
(+)
UBETA
(+)
DM
(+)
LMKVL
())
LBP
(+)
EXGRW
(+)
Avg.
Adj. R2
0.39
(1.70)
()3.55**)
{5 ⁄ 1 ⁄ 4}
0.47
(1.89**)
()2.57**)
{6 ⁄ 2 ⁄ 5}
)0.17
()1.87#)
0.55
(3.90**)
)0.02
()0.37)
1.93
(9.99**)
0.08
(7.71**)
39.9
)0.04
()0.32)
0.61
(7.02**)
)0.06
()1.53)
1.98
(10.77**)
0.05
(7.38**)
34.5
Notes:
This table includes the time-series averages of the coefficients of the 21 annual cross-sectional
regressions (1984–2004) and t-statistics for whether that mean coefficient is statistically
positive ⁄ negative (>0) using the standard error of the coefficient estimates across the 21 years
(Fama and MacBeth 1973). In addition, for the rf coefficient, we include the t-statistic for
whether the mean coefficient is equal to one (=1) and the number of years the coefficient in
the year-by-year regressions is (significantly positive and equal to one ⁄ significantly positive ⁄
significantly negative) (based on a 0.05 p-value) (=1 ⁄ + ⁄ )) in {}. **, * denotes significance at
the 0.01, 0.05 level or better (1-tailed t-test). # denotes significant in the wrong direction.
Figures in bold are significant at the 0.01 level or better. All variables are defined in Tables 1
or 3. Sample size is 14,521.
in a reasonable manner with any of the risk factors except for LBP, further supporting the
conclusion that firm-level realized returns are not a valid construct for Et)1(rt).
In summary, the results of this analysis provide support for the validity of rDIV, rPEG
and rPEGST, while the results of the realized return analysis provide support for the construct validity of all of the Et)1(rt) proxies except rPEGST and rFF. Taken together, the two
sets of analyses provide support for the validity of rDIV and rPEG alone, since these are the
only proxies associated with future realized returns and firm-specific risk in the manner
predicted by theory.
Amalgamated proxies
rHL and rDKL attempt to control for noise in the Et)1(rt) proxy by averaging several proxies, but our analysis suggests that neither is superior to their inputs. Nonetheless, we are
sympathetic to concerns regarding noise and the argument that averaging several valid
estimates, each individually measured with error, could yield a superior proxy. To address
this issue, we focus on rDIV and rPEG because we find the greatest support for their construct validity. To combine these measures into one proxy we use factor analysis (to isolate
the covariance between the two original proxies) and a simple average. Based on results
(not tabled) from realized return and risk-based analyses we find that neither measure
yields a proxy that dominates rDIV or rPEG alone.
6. Other issues
In this section, we consider three other empirical issues that arise frequently in the literature regarding Et)1(rt) proxies: (1) the impact of analyst forecast bias, (2) the efficacy of
realized returns for expected returns after controlling for cash flow news, and (3) substituting realizations for analysts’ forecasts.
CAR Vol. 28 No. 4 (Winter 2011)
1112
Contemporary Accounting Research
Impact of analysts’ forecast bias
Most Et)1(rt) estimates employ analysts’ forecasts to proxy for the market’s expectations
of future cash flows, which gives rise to the concern that deviations between the market’s
expectations embedded in stock price and analysts’ forecasts lead to measurement error in
the Et)1(rt) proxies. GKS and Hou, van Dijk, and Zhang (2009) express the concern that
stale forecasts and ⁄ or bias in analysts’ forecasts could lead to measurement error in the
Et)1(rt) proxies.
It is important to note that error or bias in analysts’ forecasts relative to reported
earnings is not the issue. The issue is whether analysts’ beliefs are consistent with those of
the market at the time expected returns are estimated. In addition, even though systematic
bias in analyst forecasts (e.g., optimism relative to the market’s beliefs) might lead to
biased (e.g., overstated) Et)1(rt) estimates, it need not induce spurious correlations when
employing the resulting Et)1(rt) proxy in empirical analyses. For this to occur, measurement error in the Et)1(rt) proxy would need to be systematic and correlated with other
variable(s) of interest. Even so, unsystematic deviations between analysts’ and the market’s
expectations could create noise and reduce the proxy’s power.
Our earlier analysis provides support for the construct validity of rDIV and rPEG,
and accordingly our analysis of this issue focuses on these measures. Because the
market’s beliefs about future cash flows at the time the proxies are estimated are not
observable, we identify firm-years for which we have reason to believe that analysts’
beliefs might have deviated from those of market participants at the time rDIV and
rPEG are estimated. We split our sample into ‘‘consistent’’ and ‘‘inconsistent’’ subsamples. Consistent (inconsistent) firm-year observations are those for which the sign of
the earnings surprise is the same as (different from) the market reaction to the earnings
surprise. We expect the observations in the consistent (inconsistent) subsample to be
those with the least (greatest) risk of a deviation between analysts’ forecasts and the
market’s expectations. Employing the data in each subsample, we reestimate the realized return model (equation (4)) and expected return model (equation (5)) and present
the results in Table 8.
Panel A presents the realized return model, estimated with the consistent and inconsistent subsamples. Splitting the sample has little impact on the tenor of our conclusions.
The coefficients on the Et)1(rt) proxies continue to exhibit strong positive correlations
with rREAL after controlling for cash flow and expected return news in both subsamples.
Nevertheless, there is an increase (decrease) in the explanatory power of the model estimated with the subset of consistent (inconsistent) observations. This finding holds for both
proxies. The R2 of the rDIV specification estimated using the consistent subsample increases
by 14.5 percent from 29.7 percent (Table 6) to 34.0 percent; the R2 of the rPEG specification also increases by 14.5 percent from 27.6 percent (Table 6) to 31.6 percent. In contrast,
the R2 of the rDIV specification estimated with the inconsistent subsample decreases by 23
percent to 22.8 percent and the R2 of the rPEG specification decreases by 26 percent to
20.4 percent. These results suggest that deviations between analyst expectations and those
of the market do not lead to biased or inconsistent results with respect to the coefficients
on the proxies for Et)1(rt), but do reduce the power of the analysis.15
Panel B presents the results of estimating the risk model with the two subsamples. The
coefficients on the risk factors are similar for the consistent and inconsistent subsamples,
although a couple of risk factors that are statistically significant in Table 7 lose
significance when the sample is split. In the model estimated with rDIV (rPEG) DM
(UBETA) is no longer statistically significant. Since the findings are consistent across the
15.
The decrease in explanatory power might also be a result of a decreased relation between CFN_1 and
realized returns for the inconsistent sample.
CAR Vol. 28 No. 4 (Winter 2011)
Expected Returns, Realized Returns, and Firm Risk Characteristics
1113
TABLE 8
Impact of forecast bias
Panel A: Realized return regressions
Consistent forecasts (7527 obs.)
rDIV
rPEG
Intercept
ER
(+)
CFN_1
(+)
CFN_TV
(+)
EWER_N
())
FSER_N
())
Avg.
Adj. R2
)0.138
()1.44)
)0.109
()1.09)
1.007
(7.21**)
0.991
(3.80**)
0.016
(17.69**)
0.016
(15.02**)
0.002
(15.75**)
0.002
(14.88**)
)0.127
()1.90*)
)0.132
()1.94*)
0.007
(0.17)
)0.004
()0.09)
34.0
31.6
Inconsistent forecasts (6794 obs.)
rDIV
rPEG
Intercept
ER
(+)
CFN_1
(+)
CFN_TV
(+)
EWER_N
())
FSER_N
())
Avg.
Adj. R2
)0.164
()1.68)
)0.104
()1.36)
1.030
(4.68**)
1.200
(2.94**)
0.010
(9.88**)
0.009
(9.28**)
0.002
(13.14**)
0.002
(12.77**)
)0.141
()2.17**)
)0.132
()2.17*)
0.050
(0.44)
0.047
(0.70)
22.8
20.4
Panel B: Regression of expected return on risk factors
Consistent forecasts (7527 obs.)
rDIV
rPEG
Intercept (?)
rf
(+)
)3.21
()0.29)
3.07
(0.92)
1.59
(1.03)
0.40
(0.97)
UBETA
(+)
1.03
(4.71**)
0.31
(1.28)
DM
(+)
0.16
(0.82)
0.32
(5.01**)
LMKVL
())
)0.12
()0.81)
)0.13
()3.28**)
LBP
(+)
2.40
(7.92**)
1.56
(8.24**)
EXGRW
(+)
0.32
(9.12**)
0.41
(17.08**)
Avg.
Adj. R2
22.4
68.4
Inconsistent forecasts (6794 obs.)
rDIV
rPEG
Intercept (?)
rf
(+)
)3.09
()0.27)
3.81
(1.32)
1.58
(1.02)
0.28
(0.78)
UBETA
(+)
1.06
(4.75**)
0.30
(1.21)
DM
(+)
0.18
(0.93)
0.39
(8.18**)
LMKVL
())
LBP
(+)
)0.12
2.39
()0.84)
(7.93**)
)0.13
1.49
()2.97**) (10.83**)
EXGRW
(+)
Avg.
Adj. R2
0.32
(9.18**)
0.43
(14.16**)
22.5
71.5
(The table is continued on the next page.)
CAR Vol. 28 No. 4 (Winter 2011)
1114
Contemporary Accounting Research
TABLE 8 (Continued)
Notes:
This table includes two robustness tests. Panel A includes the realized return regressions after splitting the sample into observations where the sign of the earnings surprise is consistent with the
sign of market response to earnings (consistent) and those where the sign of the earnings surprise is inconsistent with the sign of market response to earnings (inconsistent). We include the
time-series averages of the coefficients in the 21 annual cross-sectional regressions (1984–2004),
t-statistics using the standard error of the coefficient estimates across the 21 years (Fama and
MacBeth 1973), the number of times the coefficient on the ER proxy is (statistically positive
and equal to one ⁄ significantly positive ⁄ significantly negative) in the year-by-year regressions.
Panel B includes the risk model after splitting the sample into observations where the sign of
the earnings surprise is consistent with the sign of market response to earnings (consistent) and
those where the sign of where the sign of the earnings surprise is inconsistent with the sign of
market response to earnings (inconsistent). We include the time-series averages of the coefficients in the 21 annual cross-sectional regressions (1984–2004), t-statistics using the standard
error of the coefficient estimates across the 21 years (Fama and MacBeth 1973). **, * denotes
significance at the 0.01 and 0.05 or better levels, respectively (1-tailed t-test). Figures in bold
are significant at the 0.01 level or better. See Table 3 for detailed definitions of all variables.
subsamples, however, these results are also more consistent with a power issue than biased
and inconsistent results.
rREAL after controlling for cash flow news
Some recent studies use realized returns after controlling for cash flows news to proxy for
Et)1(rt) (e.g., Ogneva 2008). We examine the validity of this approach by estimating the
expected return model (equation (5)) with rREAL as the dependent variable and augmenting
the explanatory variables to control for cash flow and expected return news proxies.
Panel A of Table 9 presents the results of estimating this model. Even after controlling
for cash flow and expected return news, however, the association between rREAL and many
of the firm-specific risk factors contradicts theory. The coefficient on UBETA is not significant, and the coefficients on LBP and EXGRW are significant but the wrong sign.
As an alternative approach, we adopt a two-stage approach. In the first stage regression, we estimate the residuals (rRESID) from the baseline realized return model shown in
panel A of Table 6. In theory, rRESID should be rREAL purged of the unexpected component of realized returns. That is, rRESID should be a proxy for Et)1(rt). In the second stage
regression, we estimate the expected return model (equation (5)) with rRESID as the dependent variable. The results, presented in panel B, mirror those presented in panel A.
Taken together, we find no support for the construct validity of rREAL as a proxy for
Et)1(rt) after controlling for cash flow and expected return news. Moreover, since the data
needed to estimate the cash flow news proxies is the same data needed to estimate rDIV
and rPEG, there is no data advantage to using rREAL as a proxy for Et)1(rt). Accordingly,
we see no benefit to using realized returns as a proxy for expected returns, with or without
controlling for news.
Substituting realizations for analysts’ forecasts
When analyst forecasts are unavailable some prior work employs realized values of future
earnings and ⁄ or cash flows in the estimation of implied cost of equity capital. For
example, in Chen, Chen, Lobo, and Wang 2011 the authors substitute future realizations
of ROE for the market’s expectations in estimating rPEG. This can be quite problematic,
CAR Vol. 28 No. 4 (Winter 2011)
0.011
(11.94**)
1.54
(1.40)
0.002
(15.25**)
CFN_TV
(+)
FSER_N
())
0.017
(0.25)
EWER_N
())
)0.077
()1.13)
)14.66
()1.06)
rf
(+)
0.02
(0.81)
UBETA
(+)
0.02 (0.78)
)13.02 ()2.05#)
1.19 (2.87**)
0.04 (5.13**)
DM (+)
)0.02 ()3.49**)
LMKVL ())
LBP (+)
)0.02
()3.16**)
LMKVL
())
)0.14 ()8.93#)
0.04
(5.97**)
DM
(+)
)0.01 ()7.54#)
35.4
Avg.
Adj. R2
15.4
Avg. Adj. R2
)0.01
()4.69#)
EXGRW
(+)
EXGRW (+)
)0.15
()9.45#)
LBP
(+)
This table includes two robustness tests. Panel A is based on regressing realized returns on the cash flow and expected return news variables (as controls)
and the risk factors included in Table 7. Panel B is based on regressing the residuals from regression of realized returns on the cash flow news and
expected return news variables. The values presented are the time-series averages of the coefficients in the 21 annual cross-sectional regressions
(1984–2004), t-statistics using the standard error of the coefficient estimates across the 21 years (Fama and MacBeth 1973). **, * denotes significance
in the predicted direction at the 0.01 and 0.05 or better levels, respectively (1-tailed t-test). # denotes significant in the wrong direction. Figures in
bold are significant at the 0.01 level or better. See Table 3 for detailed definitions of all variables.
Notes:
rRESID
UBETA (+)
rf (+)
Intercept (?)
Panel B: Cost of capital estimate (= residuals from realized returns) regressed on risk proxies
rREAL
CFN_1
(+)
INTERCEPT
Panel A: Controlling for CFN
TABLE 9
Additional analyses
Expected Returns, Realized Returns, and Firm Risk Characteristics
1115
CAR Vol. 28 No. 4 (Winter 2011)
1116
Contemporary Accounting Research
because it leads to systematic error in the estimates that is related to ex post cash flow
news. The implied cost of capital estimates are biased upward (downward) for firms with
ex post good (bad) cash flow news. Employing these estimates in empirical research might
yield biased and inconsistent results if other variables of interest (e.g., growth) vary systematically with firms’ cash flow news.
7. Reconciliation with prior research
Almost all the implied cost of capital proxies we examine are positively correlated with
realized returns after controlling for cash flow and expected return news, whereas GKS
and EM find that none of the proxies they examine are positively associated with realized
returns. This difference is particularly stark with respect to rPEG, since all three studies
examine close variants of this proxy.
Our results differ from GKS because their model does not include necessary controls
for new information. Consistent with this, we document little or no correlation between
rREAL and the expected return proxies in a univariate setting, but, after controlling for
cash flow and expected return news, we find the expected relation. EM also conclude that
the GKS results suffer from a severe omitted variable bias.
A more complicated issue explains the difference between our results and those of EM.
The theoretical specification of our realized return model is the same, although our empirical
specifications are critically different. We employ the change in the risk-free rate to proxy for
macroeconomic expected return news, and the change in market beta to proxy for firm-specific expected return news. EM’s proxy for expected return news is a scaled measure of the
difference in consecutive implied cost of capital estimates. In the remainder of this section of
the paper, we demonstrate that although EM’s proxy for expected return news is theoretically defensible, it is empirically problematic because it provokes circularity in the empirical
model, which confounds the coefficient on the Et)1(rt) proxy included in the model.
All implied cost of capital estimates (ICC) are internal rates of return that equate current stock price (P) to some series of expected future cash flows (CF). As noted earlier,
ICCs vary across approaches as different CF assumptions arise from different terminal
value assumptions. Nevertheless, by construction, all ICC f(CF, P), and therefore, all
DICC f(DCF, DP).
The theoretical specification of the realized return model (i.e., equation (2)) is shown
below for convenience.
rREAL;t ¼ Et1 ðrt Þ þ ðNcf ;t Nr;t Þ
ð6Þ:
Empirically, rREAL,t f(DP) and Ncf,t f(DCF). In EM’s empirical specification
Nr,t = DICC f(DCF, DP). Consequently, the model EM estimate can be described by
the following set of relationships:
f ðDPÞ ¼ Et1 ðrt Þ þ f ðDCFÞ f ðDCF; DPÞ
ð7Þ:
EM’s proxy for expected return news (DICC) is by construction a function of DCF and
DP, which are also included in the model as dependent and explanatory variables, respectively. Stated another way, solving (7) for Et)1(rt) yields:16
Et1 ðrt Þ ¼ f ðDCFÞ f ðDCFÞ þ f ðDPÞ f ðDPÞ
ð8Þ:
The right hand side of (8) implies a product that is close to zero. Expected return
is not likely to explain realized returns under this empirical specification. Thus, while it
16.
Expected returns are increasing in cash flows (holding price constant) and decreasing in price (holding
cash flows constant).
CAR Vol. 28 No. 4 (Winter 2011)
Expected Returns, Realized Returns, and Firm Risk Characteristics
1117
is theoretically defensible to use the change in true Et)1(rt) to capture expected
return news, it is empirically problematic to use the change in an Et)1(rt) proxy
measured via an implied cost of capital approach for this purpose. The resulting
provoked circularity in the empirical model provides no role for Et)1(rt) to contribute
to the explanation of rREAL,t, and as a result, any ICC estimate included in the model
to proxy for Et)1(rt) will be statistically insignificant, regardless of the validity, or lack
thereof, of the ICC estimate employed. Moreover, the circularity we are concerned
with not only manifests in no association between rREAL,t and the Et)1(rt) proxies,
but in a strong association between rREAL,t and EM’s expected return news proxies
(i.e., DICC).17
To provide further evidence of the impact of EM’s empirical specification for expected
return news on the coefficient on the Et)1(rt) proxy, we reestimate our realized return
model using EM’s cash flow and expected return news proxies (hereafter CFN_EM and
ERN_EM, respectively). We estimate the model with the five implied cost of capital proxies that overlap with the prior work (rPEG, rMPEG, rGM, rCT, and rGLS) plus rDIV, since we
find strong support for the construct validity of the latter proxy.
Panel A of Table 10 presents these results. As predicted by our analysis above, and
consistent with EM’s results, the coefficient on EM_ERN is positive and highly significant
in all specifications (t-statistics ranging from 3.86 to 15.56). In addition, except for the
coefficients on rCT and rDIV, which are significantly positive and negative, respectively, the
coefficients on the Et)1(rt) proxies are statistically insignificant.
Finally, we estimate the regression model using EM’s cash flow news proxy, but our
measure of expected return news. Because our measures of expected return news are independent of the derivation of the implied cost of capital estimates, they do not provoke circularity in the empirical specification of the model. These results, presented in Table 10,
panel B, demonstrate that, once the circularity issue is resolved, the coefficients on the
Et)1(rt) proxies are significantly positive.
Finally, it is interesting to note the difference in the R2s of the models estimated in
Table 10 panel B versus Table 6. For example, the rDIV model in Table 6 has an R2 of
29.7 percent – 68 percent higher than the R2 of 17.7 percent in Table 10, panel B for the
rDIV specification. The only difference between these models is the empirical proxy for cash
flow news. The former employs our empirical proxy, while the latter employs EM’s proxy.
The higher R2 achieved with our cash flow news proxy provides evidence of its greater
explanatory power.
8. Conclusions
Existing literature employs two approaches to assess the validity of alternative proxies for
firm-specific cost of equity capital or expected return (Et)1(rt)). One approach relies on
the theoretical link between realized returns and Et)1(rt), while the second approach relies
on the theoretical relation between Et)1(rt) and priced risk characteristics. Based on
results from both approaches we conclude that there is support for the construct validity
of two of the Et)1(rt) proxies we examine: rDIV and rPEG.
We find it quite plausible that among the alternatives, rDIV and rPEG consistently demonstrate the greatest degree of construct validity. The primary assumption underlying rDIV
is that analysts’ beliefs regarding short-term cash flows and terminal value concur with
17.
The cash flow news proxy EM employ in the estimation of their realized return model differs from the
cash flow proxies EM employ in the estimation of ICC. This breaks the cycle of near perfect circularity
suggested by our analysis, but merely masks the underlying problem, and further complicates the interpretation of the results. That is, in the absence of this substitution we would expect to observe no association
between rREAL,t and the Et)1(rt) proxies, but with this substitution the expected outcome is less clear.
CAR Vol. 28 No. 4 (Winter 2011)
1118
Contemporary Accounting Research
TABLE 10
Regressions of various specifications of expected returnb on EM cash flow news and expected return
news proxies
Panel A: rREALit ¼ a0 þ b1 ER it 1 þ b2 CFN EM it þ b3 EM ER N it þ eit
ER
(+)
Intercept
rDIV
rPEG
rMPEG
rGM
rCT
rGLS
0.12
0.15
0.16
0.15
0.16
0.03
0.08
(6.25**)
(5.34**)
(4.01**)
(4.15**)
(4.24**)
(0.83)
(2.79**)
)0.29
)0.43
)0.31
)0.39
0.76
0.46
CFN_EM
(+)
()2.45#)
()1.72)
()1.29)
()1.64)
(1.83*)
(1.36)
0.50
0.49
0.41
0.45
0.44
0.56
0.57
EM_ERN
(+)
(4.27**)
(10.87**)
(11.10**)
(8.98**)
(8.94**)
(16.90**)
(16.18**)
0.04
0.07
0.03
0.03
0.11
0.18
(15.56**)
(7.59**)
(4.25**)
(3.86**)
(6.99**)
(6.46**)
Avg.
Adj. R2
10.4
31.2
25.4
17.3
16.7
26.3
32.9
Panel B: rREALit ¼ a0 þ b1 ERit1 þ b2 CFN EMit þ b3 EWER Nit þ b4 FSER Nit
ER
(+)
Intercept
rDIV
rPEG
rMPEG
rGM
rCT
rGLS
)0.03
)0.09
)0.09
)0.07
)0.06
)0.19
)0.08
()0.37)
()1.30)
()1.07)
()0.85)
()0.80)
()2.49**)
()1.17)
0.61
0.60
0.52
0.44
1.87
1.15
(6.23**)
(2.49**)
(2.83**)
(2.46**)
(5.83**)
(3.36**)
CFN_EM
(+)
0.30
0.51
0.31
0.48
0.48
0.52
0.49
(6.92**)
(14.05**)
(6.94**)
(13.67**)
(13.59**)
(16.34**)
(13.11**)
EWER_N
(+)
13.18
12.13
12.75
11.96
12.19
11.31
10.80
(1.94*)
(2.02**)
(2.01*)
(1.94**)
(1.93*)
(1.92*)
(2.04**)
FSER_N
(+)
Avg.
Adj. R2
0.003 (0.04)
0.01 (0.18)
0.01 (0.12)
0.01 (0.18)
0.01 (0.18)
0.01 (0.02)
0.00 (0.05)
11.9
17.7
13.8
16.6
16.5
18.0
17.9
Notes:
*, * denotes significance at the 0.01 and 0.05 or better levels, respectively (1-tailed t-test). # denotes
significant in the wrong direction. Figures in bold are significant at the 0.01 level or better.
See Table 3 for detailed definitions of all variables. t-statistics in the table are based on the
time-series averages of the coefficients in the 22 annual cross-sectional regressions 1984–2004
(Fama and MacBeth 1973).
those of market participants embedded in stock price. This assumption is not unique to
our study, and is supported by existing research (Barron, Harris, and Stanford 2005).
Importantly, because this is the only researcher assumption imposed on terminal value in
the estimation of rDIV, terminal values are free to reflect whatever assumptions analysts
make with regard to infinite horizon cash flows and future discount rates. Accordingly,
rDIV is not constrained across firms or industries by researcher-imposed assumptions
regarding the behavior of terminal values.
Further, the primary researcher-imposed assumption underlying rPEG is that, beyond
the forecast horizon, growth in abnormal earnings is zero. It is reasonable to expect this
researcher-imposed assumption mirrors the assumption frequently employed by analysts
and market participants, since it is commonly taught in financial statement analysis
courses. For example, in their discussion of terminal values, Palepu, Healy, and Bernard
(1999) state: ‘‘But in the face of competition, one would typically not expect a firm to
extend its supernormal profits to new additional projects year after year.. .. Each new project would generate cash flows with a present value no greater than the cost of investment
— the investment would be a ‘zero net present value’ project. Since the benefits of the
CAR Vol. 28 No. 4 (Winter 2011)
Expected Returns, Realized Returns, and Firm Risk Characteristics
1119
project are offset by its costs, it does nothing to enhance the current value of the firm, and
the associated growth can be ignored.’’18
The results of our realized return analysis differ markedly from those documented in
prior research. Consistent with EM and our univariate analysis we conclude that the
results in GKS are attributable to an omitted variable bias arising from a lack of adequate
controls for new information. With respect to EM, we demonstrate that their results are
prompted by circularity in their empirical model generated by their empirical approach to
measuring expected return news.
Finally, we consider several other issues raised in the literature regarding implied cost
of capital estimates, including (1) the impact of analysts’ forecast bias, (2) the efficacy of
realized returns for expected returns before and after controlling for cash flow news, (3)
the effectiveness of averaging several proxies to produce superior measures, and (4) the
substitution of realized values for analysts’ forecasts of cash flows or earnings.
Our evidence suggests that the impact of deviations between analysts’ expectations and
those of the market is limited to potentially less powerful proxies. On the second point, we
find that realized returns are not a reliable proxy for expected returns even after controlling for cash flow news. On the third point we find that the act of averaging several proxies does not yield an enhanced metric. Finally, we note that substituting realized values for
analysts’ forecasts in the estimation of implied cost of equity capital yields estimates that
are systematically biased upward (downward) for firms with ex post good (bad) cash flow
news, which could yield biased and inconsistent results if the resulting measurement error
is correlated with other variables of interest.
In conclusion, we recommend that researchers requiring a valid Et)1(rt) proxy employ
either rDIV or rPEG estimated with analysts’ forecasts and we caution against the use of
realized returns with or without controlling for cash flow news to proxy for Et)1(rt). We
advocate that researchers assess the validity of any new Et)1(rt) proxies by demonstrating
a consistent and predictable association between the proxy and future realized returns, as
well as established risk measures. Finally, we note that the primary difference between
rDIV and rPEG is that rDIV effectively allows the terminal value assumption to vary across
firms, while rPEG imposes an assumption of zero growth in abnormal earnings beyond the
forecast horizon on all firms regardless of their circumstances. This suggests that rDIV
might be superior even to rPEG for firms with nonzero growth in abnormal earnings
beyond the forecast horizon. We leave an investigation of this supposition for future
research.
18.
Palepu et al. (1999, 12–6). This is one example, but similar instruction can be found in almost any financial statement analysis text.
CAR Vol. 28 No. 4 (Winter 2011)
1120
Contemporary Accounting Research
Appendix
Summary of Et)1(rt) proxies examined in related research
Et)1(rt)
proxy
rDIV
rPEG
rMPEG
rPEGST
rOJN
rGM
rGOR
rGLS
rCT
rFF
rHL
rDKL
rdagr
rPE
Guay,
Kothari and
Shu (2005)
Easton and
Monahan
(2005)
x
x
x
x
x
x
x
Botosan and
Plumlee
(2005)
x
x
x
x
x
x
x
x
x
Current
study
x
x
x
x
x
x
x
x
x
x
x
x
x
x
Notes:
rdagr is the expected return estimate imputed from Easton’s 2004 implementation of the Ohlson and
Juettner-Nauroth 2005 model. rPE is the expected return estimate imputed from the price to
forward earnings model. All other expected return estimates are defined in Tables 2 and 3.
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