Botosan Plumlee Wen 2011

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 alternativeproxies for firm-specific cost of equity capital or expected return (hereafter Et)1(rt)). Thefirst approach involves examining the association between the proxy for Et)1(rt) andfuture realized returns. The second approach focuses on the association between theEt)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 associa-tion between alternative proxies for Et)1(rt) and future realized returns and conclude thatnone of the proxies they examine provide valid estimates of the construct of interest. Incontrast, Botosan and Plumlee (2005) (hereafter BP) conclude that two common proxiesfor 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 atheoretically predictable and stable manner. Furthermore, Pastor, Sinha, and Swamina-than (2008) document a positive association between market-level implied cost of capitaland risk as measured by the volatility of market returns, consistent with the estimates cap-turing time-varying Et)1(rt).

In this paper, our goal is to reconcile the conflict between these two streams of litera-ture and provide additional evidence pertaining to the construct validity of the proxiesemployed in extant research. Contrary to the results documented in EM and GKS, wedocument a positive association between ten of the twelve Et)1(rt) proxies included in ourstudy and future realized returns after controlling for new information.1 We reconcile ourfindings to those in EM and GKS by demonstrating that the prior results are due toempirical misspecification. Finally, we show that two of the proxies, rDIV and rPEG, dem-onstrate not only the expected relation with future realized returns, but also with firm-spe-cific risk.

We also address several other issues regarding the use of implied cost of capital esti-mates 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 orearnings. Our evidence suggests that deviations between analysts’ expectations and thoseof 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 Uni-

versity, 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

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 anenhanced metric. Finally, substituting realized values for analysts’ forecasts of cash flowsyields systematically biased estimates, which might yield biased and inconsistent resultswhen such estimates are employed in empirical research.

Given the current state of the literature, the validity of the various cost of capital esti-mates is unclear and it is not uncommon for similar studies to document dissimilar resultsbecause they employ different cost of capital estimates. For example, Ogneva, Subraman-yam, and Raghunandan (2007) (hereafter OSR) conclude that firms with internal controlweaknesses do not bear a higher cost of equity capital, while Ashbaugh-Skaife, Collins,Kinney, and LaFond (2009) (hereafter ACKL) conclude the opposite. These contradictoryresults 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 tohelp guide researchers’ proxy selection.

Based on our evidence, we recommend that researchers requiring a valid proxy forEt)1(rt) employ either rDIV or rPEG. We caution against the use of realized returns or theother implied cost of capital estimates we examine to proxy for Et)1(rt). Finally, we sug-gest that researchers introducing new proxies for Et)1(rt) to the literature subject theirproposed 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 estimatingEt)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 exam-ines the impact of financial reporting and disclosure on required returns, to financeresearch that investigates market anomalies, asset pricing theory, and capital budgeting.These areas of research produce findings of interest to standard setters, regulators, inves-tors, preparers, and auditors. Accordingly, the validity of the Et)1(rt) proxies employed inresearch is an important issue with pervasive implications.

We organize the remainder of our paper as follows. Section 2 reviews the related liter-ature and sets forth the development of our hypotheses. Section 3 presents our empiricalmodels and proxies. Section 4 delineates our sample selection procedure and providesdescriptive statistics for our sample. We discuss the results of our construct validity assess-ment in section 5. In section 6 we provide evidence pertaining to several other issuesrelated to implied cost of capital estimates. Section 7 reconciles the results of our realizedreturn analysis with those documented in prior literature. Finally, section 8 summarizesour 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 con-

structs) 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.

1086 Contemporary Accounting Research

CAR Vol. 28 No. 4 (Winter 2011)

The preceding quote describes the classic, well-accepted method routinely employed to exam-ine construct validity.3 Consistent with standard practice, we rely on the preceding quote toguide our approach to examining construct validity. Specifically, we examine the relationshipamong alternative proxies for Et)1(rt) and future realized returns, which are a function ofEt)1(rt). In addition, we examine the relationship among alternative proxies for Et)1(rt) andcontemporaneous risk characteristics finance theory suggests are predictably associated withEt)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 conditionalon information available at t ) 1 (Et)1(rt)) plus the unexpected (or abnormal) return dueto new information (URt):

rREAL;t ¼ Et�1ðrtÞ þURt ð1Þ:

Relying on prior research (e.g., Campbell 1991;Vuolteenaho 2002) further decomposesthe unexpected return to new information (URt) into two components — the unexpectedreturn due to cash flow news (Ncf,t), and the unexpected return due to expected returnnews (Nr,t). This gives rise to equation 2:

rREAL;t ¼ Et�1ðrtÞ þ ðNcf ;t �Nr;tÞ 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; andNr,t = return due to expected return news from t)1 to t.

Traditionally, research that employs realized returns to proxy for expected returnsrelies on the assumption that URt is mean zero, and that in-sample averaging of realizedreturns across firms or time purges URt to produce a valid proxy for Et)1(rt). Some morerecent research goes further by using firm-specific (i.e., not averaged) realized returns toproxy 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 aproxy for Et)1(rt). Elton (1999) argues that averaging does not eliminate URt becauseunexpected returns tend to be large and correlated across firms and time. Vuolteenaho(2002) demonstrates that the unexpected component is the dominant factor driving firm-level stock returns, and that cash flow news is largely firm-specific, whereas expected returnnews 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 poorproxies for Et)1(rt). At the firm level the URt due to firm-specific cash flow news, as wellas 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 cashflow news, but it is less likely to mitigate the URt due to systematic, macroeconomicexpected 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 con-

trary, 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.

Expected Returns, Realized Returns, and Firm Risk Characteristics 1087


component of the URt. Attempts to mitigate the problem by averaging over increasinglylarger samples or longer periods invoke unpalatable stationarity assumptions (Chan andLakonishok 1993).

(2) and the research discussed in the preceding paragraph suggest that an examinationof 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 correlatedomitted variable bias could result in biased and inconsistent results. Even if Et)1(rt) is notcorrelated with Ncf,t or Nr,t, however, omitting the latter two variables reduces the powerof the analysis. In this case, no statistically significant correlation between rREAL,t andEt)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 positivecorrelation between the proxy and rREAL,t after controlling for Ncf,t and Nr,t. This givesrise to our first hypothesis.4

HYPOTHESIS 1. After controlling for Ncf,t and Nr,t, a positive correlation between a proxyfor 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 periodas a function of the risk free rate (rf) plus the risk premiums arising from K risk factors:

Et�1ðrtÞ ¼ rf ;t�1 þXK

k¼1kkðEt�1ðrkÞ � rf ;t�1Þ: ð3Þ

Ross’s APT does not identify the risk factors, although existing research suggests sev-eral candidates. The capital asset pricing model (CAPM) suggests that Et)1(rt) is increas-ing 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) arguesthat market value of equity is systematically decreasing in priced risk such that Et)1(rt) isinversely related to the market value of equity and positively related to the book-to-priceratio. Finally, Beaver, Kettler, and Scholes (1970) assert that abnormal earnings arisingfrom growth opportunities are inherently more risky, leading to a positive associationbetween Et)1(rt) and growth. Equation 3 above and this body of research gives rise to oursecond 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 correlationwith 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. 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.

5. Readers interested in a more in-depth discussion of these risk characteristics are referred to Botosan and

Plumlee 2005.



findings from this research are mixed. GKS regress realized returns on five alternativeproxies for Et)1(rt).

6 The authors do not document the expected positive associationbetween realized returns and their proxies, but their analysis does not control for Ncf,t orNr,t. EM control for Ncf,t and Nr,t in their examination of the association between realizedreturns and seven proxies for Et)1(rt). Even so, EM find that none of the proxies are posi-tively associated with realized returns. GKS and EM conclude that their results do notprovide support for the construct validity of the proxies they examine. In contrast, BPexamine the association among five proxies for Et)1(rt) and firm-specific risk characteris-tics. They conclude that rDIV and rPEG, are valid proxies for Et)1(rt) as both are correlatedwith firm risk characteristics in a theoretically predictable manner.

While GKS, EM, and BP examine different sets of Et)1(rt) proxies, rPEG is examinedby all three. Accordingly, the findings of GKS and EM versus those of BP present anexplicit conflict in the evidence regarding this metric’s construct validity. The conflict withrespect to rDIV is implied as opposed to explicit since neither GKS nor EM include rDIV intheir analyses. In addition, since 2005 there has been an explosion in Et)1(rt) proxiesemployed in the literature, without a rigorous construct validity assessment of the same.Accordingly, the primary objectives of the construct validity portion of this study arethreefold: first, to investigate the source of the disparate results noted above; second, toaugment BP’s risk-based construct validity analysis of rDIV with a realized return analysisand extend their findings over an additional period of time; and third, to use both the real-ized return and risk-based approaches to examine the construct validity of the more recentadditions 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 b1ERit�1 þ b2CFN 1it þ b3CFN TVit þ b4EWER Nit þ b5FSER Nit þ eit ð4Þ;

where:rREALit = 12-month buy and hold return, beginning the month after estimation of ER;ERit)1 = expected return proxy at t conditional on information at time t)1;CFN_1it = 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; andFSER_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 flownews (Ncf,t) and expected return news (Nr,t) received from t)1 to t. In our specificationERit)1 is one of a number of alternative expected return estimates intended to proxy forEt)1(rt).

7 Hypothesis 1 states that, after controlling for Ncf,t and Nr,t, a positive correla-tion between a given proxy for Et)1(rt) and rREAL,t (i.e., a positive ß1 coefficient) providessupport for the validity of that Et)1(rt) proxy.

6. The Appendix summarizes the Et)1(rt) proxies examined in GKS, EM, BP, and the current study.

7. We enumerate the expected return estimates included in our study in the Appendix and in section 3.



In theory ß1 should equal 1. Such a test is not only a test of the extent to which theproxy captures cross-sectional variation in Et)1(rt), but also the extent to which it cap-tures the magnitude of Et)1(rt). Most empirical research employing Et)1(rt) proxies isconcerned with cross-sectional variation in Et)1(rt). Accordingly, an Et)1(rt) proxy thatcaptures cross-sectional variation in Et)1(rt) (i.e., ß1 > 0) might be valid for use in empiri-cal research even if the magnitude of the proxy is biased (ß1 „ 1). Under such circum-stances, a test of ß1 = 1 is an unnecessarily rigorous test of construct validity. For thisreason, in testing our first hypothesis we do not require ß1 to meet the more stringent testof 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 flownews related to near-term cash flows, and is measured as the earnings surprise during therealized return period. Our second proxy, CFN_TVt, is the revision in analysts’ forecastsof target prices during the realized return period. We include this variable to capture cashflow news related to long-horizon cash flows. Since realized returns are increasing in cashflow 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 functionof the risk free rate, we include the change in the risk free rate between t)1 and t to proxyfor 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 stockpresents, we include the change in firm-specific market beta between t)1 and t to proxyfor 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 realizedreturns. Accordingly, we expect both ß4 and ß5 to be significantly negative.

Target prices, which we employ in the computation of CFN_TVt, reflect the presentvalue of infinite horizon cash flows beyond the forecast horizon. As noted above, our pri-mary objective for including CFN_TVt in our empirical model is to capture long-horizoncash flow news. Nevertheless, analysts’ revisions of target prices reflect changing beliefsabout discount rates as well as future cash flows.8 Since target prices are increasing infuture cash flows but decreasing in the discount rate, we expect the association betweenCFN_TVt and realized returns to be positive regardless of whether CFN_TVt captures cashflow news, expected return news, or both. As both types of news are important to thetheoretical model, CFN_TVt is a particularly important control variable.

The following paragraphs provide details of the measurement of all variables includedin (4) except for the Et)1(rt) proxies. The Et)1(rt) proxies are outlined following our dis-cussion of the empirical model we employ in our risk analysis.

Realized returns. We calculate realized returns using CRSP data as the buy and holdrealized return computed over the 12 months beginning the month after we estimateexpected returns.

Cash flow news. To calculate our cash flow news proxies we rely on Value Line ana-lysts’ forecasts of annual earnings per share for the current year (Year t) and target pricesat 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 thereported annual earnings per share for year t announced during the 12-month period weestimate realized returns, less analysts’ forecasts of those annual earnings issued the daywe estimate Et)1(rt). Thus, CFN_1 captures ‘‘earnings surprise’’ similar to that employedin numerous other studies. We compute CFN_TV as the difference between the midpointof the forecasted target price range made 12 months after we estimate our expected returnproxies 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).



our Et)1(rt) proxies. In our analyses, we scale our cash flow news variables by stockprice on the day we estimate expected returns. We obtain actual earnings per share fromCOMPUSTAT and forecast and stock price data, which is stock price as of the publica-tion date or within three days after publication, from Value Line. Panel A of Table 1 pro-vides 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 per-iod. Specifically, EWER_N is the rf during the last month of the realized return estimationperiod less rf twelve months earlier.9 We measure rf as the five-year treasury constantmaturity 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 inmarket beta (MBETA) over the 12-month realized return period.10 We use CRSP data toestimate MBETA via the market model with a minimum of 20 out of 60 monthly returnsand a market index return equal to the value weighted NYSE ⁄AMEX return. Each betaestimation period ends in June. Panel B of Table 1 provides a description of the expectedreturn 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:

ERit�1 ¼ v0 þ c1rft�1 þ c2UBETAit�1 þ c3DMit�1 þ c4LMKVLit�1 þ c5LBPit�1

þ c6EXGRWit�1 þ git�1 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 forEt)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. Specifi-cally, we expect ERit)1 to be increasing in the risk-free rate, market beta, leverage, book-to-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. 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 economy-

wide 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.

10. 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.



TABLE 1

Variable descriptions: cash flow news, expected return news, and firm-specific risk factors

Panel A: Cash flow news proxies

Variable Descriptiona

CFN_1 = 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).

CFN_TV = 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 = 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.FSER_N = Firm-specific expected return news = Change in market beta =

mbetat+1 – mbetat.

Panel C: Risk proxies

MBETA = 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.

UBETA = unlevered CAPM beta = MBETA ⁄ (1 + Debt ⁄Equity) wheredebt 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.

DM = 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.

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.

BP = 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.

EXGRW = 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.



proxy for expected return. In theory c1 should equal 1, although a test of c1 = 1 is a par-ticularly rigorous construct validity test. Nevertheless, we also report the results of a testof c1 = 1.

We do not infer construct validity from the magnitude of the R2 of the cost ofequity capital models because assumptions regarding the terminal value imposed by theresearcher in the derivation of some implied cost of capital estimates can lead to inducedspurious correlation between the proxy and certain risk characteristics, yielding a highR2 by construction. For example, if an assumption related to long-range growth in earn-ings is used to derive the terminal value (as in the PEG model), it is not surprising thatgrowth, a firm-specific risk factor, explains a significant portion of the variation in thatexpected return proxy. Thus, it is particularly important to assess the associationbetween the expected return estimates and various firm-specific risk factors after control-ling for risk factors that are potential candidates for spurious correlation (primarilygrowth).

Finally, Berk (1995) argues that book-to-price and market value of equity play similarroles in an incomplete model of expected returns, in that both variables capture otherwiseunmeasured risk. Accordingly, it is unclear whether both variables should achieve signifi-cance in the empirical model. The ‘‘catch-all’’ nature of these variables, however, mitigatesthe concern that the model is susceptible to omitted risk factors.

Below is a detailed discussion of our measurement procedures for the risk proxiesemployed in our analysis. Panel C of Table 1 summarizes their descriptions.

Unlevered beta. We include unlevered beta (UBETA) to capture the theoretical relationbetween Et)1(rt) and CAPM beta. Including the traditional levered beta (MBETA) in themodel 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 proce-dure described in standard finance textbooks (e.g., Kester, Fruhan, Piper, and Ruback1997).11 Briefly,

MBETAi ¼ UBETAi þ DebtiEquityi

UBETA; which yields UBETAi ¼ MBETAi

1þ Debti=Equityi½ � :

MBETA is estimated as described earlier. We compute debt-to-equity by dividinglong-term debt by stockholders’ equity using COMPUSTAT data measured at the end ofthe 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 struc-ture increases, risk increases. As discussed above, estimating the model with UBETAallows us to predict unequivocally a positive coefficient on DM (c3). We measure DM asthe ratio of long-term debt (described above) to the market value of common equity mea-sured on December 31 prior to the year we estimate expected return. We collect marketvalue of common equity from CRSP, or from COMPUSTAT if the data are unavailableon CRSP.

Market value of equity. Our proxy for the market value of equity is the natural log ofthe market value of common equity (LMKVL) and is collected as described above. Consis-tent 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 thequarter 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 incor-

porates 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.



scaled by price per share. Price per share is the stock price on the Value Line publicationdate or closest date thereafter within three days of publication. We log transform thesedata to mitigate skewness (LBP).

Expected growth. We estimate expected earnings growth (EXGRW) using the fore-casted growth in earnings five years hence. We calculate EXGRW for each firm-year as theforecasted earnings for Year t+5 less forecasted earnings for Year t+4, scaled by theabsolute value of the Year t+4 forecast.

Before moving on to the measurement of the Et)1(rt) proxies, we emphasize theimportance of timing in our analyses. As noted in (2), realized returns (rREAL) are a func-tion of Et)1(rt) determined prior to the period over which realized returns and news aremeasured. 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 measuredat the end of the prior year. As noted in (3), however, firm-specific risks existing at t)1are part of the t)1 information set investors use to determine Et)1(rt). Thus, in our test ofHypothesis 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 impliedcost of capital proxies included in at least one of the three studies (GKS; EM; BP) thatcontribute 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 popularityof this measure, we also include estimates derived from the Fama-French four-factormodel (rFF), as well as two popular ‘‘composite’’ proxies not examined in any of the threeearlier studies (rHL and rDKL).

The implied cost of capital proxies are derived from the short-horizon form ofthe classic dividend discount model, which equates current stock price to a finite seriesof expected future cash flows and a terminal value, discounted to the present at the costof equity capital. Alternative estimates arise from models that deal with the terminal valuein different ways. Table 2 summarizes the assumptions that underlie the nine uniqueimplied cost of capital proxies and the Value Line forecasts needed to estimate eachproxy.12

We follow the estimation procedures employed in prior literature. Specifically, we fol-low 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 Mohanram2003 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 com-pute rDKL. We provide a brief description of each of the proxies below, with an emphasison key similarities and differences. Table 3 provides details that are not repeated in thetext below.

rDIV

The target price method relies strictly on current stock price and analysts’ forecasts of div-idends and target prices. It employs a short-horizon form of the dividend discount modelin which a forecasted terminal value truncates the infinite series of future cash flows at theend 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 fore-cast 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.



TABLE

2

Summary

offorecast

assumptionsanddata

requirem

ents

forim

plied

cost

ofcapitalexpectedreturn

proxiesa

Short-horizon

Terminalvalue

ValueLineforecasts

r DIV

•Duringtheforecast

horizon,analysts’

dividendforecastsequalthemarket’s

expectation.

•Beyondtheforecast

horizonanalysts’

forecastsofstock

price

equalthemarket’s

expectation.

•Dividendsper

share;currentyear,

oneyearahead,andlongrange.

•Longrangeminim

um

andmaxim

um

target

price.

r PEG

•Analysts’earningsforecastsin

Years

1and2equalthemarket’sexpectation.

•Zerodividendsin

Year1.

•Year1earningsandYear2

‘‘abnorm

alearnings’’(specification2b)

are

positive.


horizonzero

growth

in‘‘abnorm

alearnings’’.

•Earningsper

share;oneandtw

oyear

aheadandlongrange.

r MPEG


Years



‘‘abnorm


are

positive.


horizonzero

growth

in‘‘abnorm

alearnings’’.

•Earningsper

share;oneandtw

o

yearahead.

•Dividendsper

share;currentyear.

r PEGST


Years


•Zerodividendsin

Year1.


‘‘abnorm


are

positive.


horizonzero

growth

in‘‘abnorm

alearnings’’.

•Earningsper

share;tw

oyearahead.

(Thetable

iscontinued

onthenextpage.)



TABLE

2(C

ontinued)

Short-horizon

Terminalvalue

ValueLineforecasts

r OJN

andr G

M


Years

1and2andofdividendsin

Year

1equalthemarket’sexpectation.


‘‘abnorm


are

positive.

•Growth

in‘‘abnorm

alearnings’’isa

constantrate

forallt.

•Estim

atedabnorm

alearninggrowth

rate

equalsthemarket’sexpectation.

•Growth

rate

isless

thanthecost

ofequityandexceedszero.

•Dividendsper

share;currentyear.

•Earningsper

share;oneyearahead

andlongrange

r GOR


horizon,analysts’

dividendforecastsequalthemarket’s

expectation.


horizon,

each

firm

’sROE

equalsitscost

of

equitycapital.

•Dividendsper

share;currentyear,one

yearaheadandlongrange.

•Earningsper

share;longrange.

r GLS

•Duringtheanalysts’forecast

horizon,

analysts’forecastsofearningsand

bookvalueequalthemarket’s

expectation.


horizonwithout

forecasts,firm

ROE

fades

linearlyto

industry

ROE.

•Beyondtheforecasthorizon,firm

s

earn

theirindustry

ROEin

perpetuity.

•Beyondtheforecasthorizon,firm

s

havea100%

dividendpayoutratio.

•Earningsper

share;currentyear,one

yearahead,andlongrange.

•Dividendsper

share;oneyearahead

andlongrange.

•Bookvalueper

share;currentyear,

oneyearahead,andlongrange.

r CT

•Analysts’earningsforecastsfrom

Years

1to

5equalthemarket’s

expectations.

•Analysts’bookvalueforecastsfrom

Years

1to

4equalthemarket’s

expectation.

•BeyondYear5,‘‘abnorm

alearnings’’

grow

ataconstantrate,whichis

assumed

tobetheinflationrate.

•Bookvalueper

share;currentyear,

oneyearaheadandlongrange.

•Earningsper

share;oneyearahead

andlongrange.

Notes:

aTheassumptionsaboveare

statedin

generalterm

sandunderliethetheoreticalform

ofeach

model.Forem

piricalpurposes,additionalassumptions

are

imposedregardingthelength

oftheforecast

horizon.

bTwodefinitionsofabnorm

alearningsare

usedin

thevariousmodels.Specification1isdefined

asr)

1(eps 2

+rdps 1

)Reps 1).Specification2is

defined

asr)

1(eps 2

)Reps 1).



TABLE

3

Form

ulasforexpectedreturn

proxies

Variable

Commonnameformethodandoriginal

source

Form

ula

r DIV

Target

price

(BotosanandPlumlee2002).

P0¼P5 t¼

1ð1þ

r DIVÞ�

t ðdps

tÞþð1þ

r DIVÞ�

5ðP

5Þ

r PEG

Price-earnings-growth

ratio(Easton2004).

r PEG¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ðeps

5�

eps 4Þ=

P0

pr M

PEG

bModified

price-earnings-growth

(Easton2004).

r MPEG¼

Aþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

A2þðe

ps2�

eps 1Þ=

P0

p;A¼

dps 1=ð2

P0Þ

r PEGST

Price-earnings-growth

ratio(Easton2004).

r PEG

ST¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ðeps

2�

eps 1Þ=

P0

p

r OJN

Economy-w

idegrowth

(OhlsonandJuettner-

Nauroth

2003).

r OJN¼

Aþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

A2þðe

ps1=P

0Þ�f½ðe

ps3�

eps 2Þ=

eps 2þðe

ps5�

eps 4Þ=

eps 4�=

2�ðc�

1Þg

q;

A¼ðc�

1Þþ

dps 1=P

0ð

Þ=2

r GM

cModified

economy-w

idegrowth

(GodeandMohanram

2003).

r GM¼

Aþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

A2þðe

ps1=P

0Þ�ðe

ps2�

eps 1Þ=

eps 1�ðc�

1Þ

½�

p;A¼ðc�

1Þþ

dps

1=P

0ð

Þ=2

r GOR

Finitehorizon(G

ordonandGordon1997).

P0¼P4 t¼

11þ

r GO

Rð

Þ�t ðd

pstÞþ

r GO

Rð1þ

r GO

RÞ4

��

1ðe

ps5Þ

r GLS

aIndustry

method(G

ebhart

etal.2001).

P0¼

b 0þP11 t¼

1ð1þ

r GLSÞ�

t ððro

e t�

r GLSÞb

t�1Þþðr

GLSð1þ

r GLSÞ1

1Þ�

1ðð

roe 1

2�

r GLSÞb

11Þ

r CT

Economy-w

ide(C

lausandThomas2001).

P0¼

b 0þP5 t¼

1ð1þ

r CTÞ�

t ðroe

t�

r CTÞb

t�1þðr

CT�

gÞ�

1ð1þ

r CTÞ�

5ðr

oe5�

r CTÞb

4ð1þ

gÞ

r FF

Fama-French

andmomentum

four-factormodel

(Barthet

al.2010).

r FF¼

Rf tþ

bR

MR

Fði;

tÞðR

M�

RfÞðtÞþ

b SM

Bði;

tÞSM

Btþ

b HM

Lði;

tÞH

ML

tþ

bM

OMði;

tÞM

OM

t

r HL

Meanim

plied

cost

ofcapital(H

ailand

Leuz2006).

Theaverageofr C

T,r G

LS,r M

PEG,andr O

JN

r DKL

Mean,adjusted

implied

cost

ofcapital

(Dhaliwalet

al.2007).

Theaverageofr C

T,r G

LS,andr G

Mafter

limitingeach

implied

estimate

to0.5



of cash flows beyond the forecast horizon are permitted to vary across firms as a functionof analysts’ beliefs embedded in target prices.

rPEG, rMPEG, and rPEGST

The primary assumption underlying the models used to estimate these proxies is that themarket expects zero growth in abnormal earnings beyond the forecast horizon. Thisassumption simplifies the dividend discount model sufficiently that it can be solved forexpected return directly. The rPEG model also assumes that the market expects dividendsin Year t+1 to be zero, whereas rMPEG relaxes this assumption. Following BP we employlong-range earnings forecasts (Year t+5 and Year t+4) in lieu of the short-range earningsforecasts (Year t+2 and Year t+1) to estimate rPEG. Doing so increases our sample sizeand, we believe, is more in keeping with the assumption regarding future cash flows. Incontrast, consistent with many studies (including EM), we employ near-term earnings fore-casts (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 thatimposes 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, consis-tent with prior research, set the infinite growth in abnormal earnings equal to rf less 3 per-cent. The sole difference between rOJN and rGM lies in the empirical procedures employedin estimating the model: rGM is estimated with short-term growth in earnings, whereasrOJN 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 torevert 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 discountmodel (Ohlson 1995) to specify prices in terms of forecasted ‘‘return on equity’’ andexpected return. The two approaches deal with the terminal value issue in a different man-ner, however. CT assume that the market expects abnormal earnings beyond the forecasthorizon to grow at a constant rate, which they set equal to the inflation rate. GLS assumethat the market anticipates ROE will linearly fade to an industry-based ROE 12 yearshence, which GLS estimate based on historical industry ROE.

rFF

Barth et al. (2010) among others (e.g., Kothari, Li, and Short 2009) employ expectedreturn estimates based on the Fama-French four-factor model. The four factors includedin the model are a market factor, size factor, book-to-market-factor, and price momentumfactor. These factors explain some of the variation in realized returns, but use of thismodel 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 demandcompensation. This is a distinct difference vis-a-vis implied cost of capital approaches,which do not presuppose the set of priced risks. We estimate the expected annual factorreturns (bRMRF(i,t), bSMB(i,t), bHML(i,t), and bMOM(i,t)) by first calculating each factor’s



average monthly return over the 60 months prior to month m, and then compounding theresulting average monthly returns over the twelve months prior to the beginning of firm i’sfiscal year. rFF is calculated as an annualized predicted return computed using com-pounded monthly returns, consistent with Barth et al. 2010.

rHL and rDKL

The final two proxies we examine are averages of certain other proxies. Specifically, Hailand Leuz (2006, 2009) calculate rHL as the mean of rCT, rGLS, rMPEG, and rOJN, whereasDhaliwal 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 withmarket participants’ beliefs imbedded in stock price. All of the other implied cost of capi-tal approaches assume market participants’ expectations regarding infinite horizon cashflows are consistent with the assumptions imposed by the researcher. Because rDIV doesnot constrain the behavior of infinite growth in expected cash flows to be the same acrossfirms, we expect rDIV to display the greatest cross-sectional variation. Whether this reflectsvariation in the underlying Et)1(rt) however, depends on whether analysts’ forecasts ade-quately proxy for the market’s expectations. Moreover, as discussed previously, researcherimposed assumptions about the behavior of infinite horizon growth in cash flows can cre-ate a spurious correlation between the Et)1(rt) estimates produced and growth. Neverthe-less, if the researcher-imposed assumptions mirror those of market participants, suchcorrelations need not be spurious. Finally, rFF limits the set of priced risk factors to a pre-determined set resulting in an association between rFF and the predetermined set of riskfactors 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 Lineforecasts required to estimate expected return and cash flow news proxies, (3) currentstock 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 proxiesand firm-specific risk factors consists of 17,904 firm-years drawn from 1984–2004. The pri-mary sample for our analysis of the association among realized returns and the expectedreturn proxies includes 14,521 firm-years from the same period. Fewer observations appearin our realized return analysis because our cash flow news and expected return news vari-ables are change variables, such that a firm must have sufficient data in adjacent years tobe 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 twelveEt)1(rt) proxies and realized returns (rREAL). Mean (median) estimates of expectedreturn range from 7.36 (7.27) percent for rGLS to 15.60 (14.50) percent for rFF. The highvolatility 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 thereturn swamping variation in the expected return component. This underscores theseverity of the power issue that could arise if cash flow and expected return news areignored.



TABLE4

Descriptivestatistics

Panel

A:Expectedreturn

proxiesa

r REAL

r DIV

r PEG

r MPEG

r PEGST

r OJN

r GM

r GOR

r GLS

r CT

r FF

r HL

r DKL

Mean

15.27%

15.26%

11.63%

12.36%

11.23

11.55%

13.20%

9.23%

7.36%

10.65%

15.60%

10.48%

10.39%

Median

11.72

14.35

11.09

11.31

10.22

11.14

12.11

8.93

7.27

10.37

14.50

10.13

9.99

Perc. 1%

)67.39

2.52

4.94

5.92

4.34

5.42

5.89

3.92

0.98

4.98

0.91

5.48

5.12

25%

)8.19

10.49

9.20

9.53

8.48

9.49

10.11

7.48

5.27

8.82

9.45

8.62

8.39

75%

33.19

19.01

13.41

13.96

12.80

13.11

14.98

10.79

9.17

12.11

20.48

11.90

11.91

99%

143.65

36.89

23.48

28.61

27.54

21.20

30.54

17.59

15.39

18.66

41.25

19.11

19.83

STD

39.91

7.02

3.76

4.61

4.63

3.67

4.99

2.98

3.57

3.17

8.73

2.92

3.06

N17,904

17,904

17,904

17,904

17,904

17,904

17,904

17,904

17,904

17,904

15,608

17,904

17,904

Panel

B:Cash

flow

new

sbandexpectedreturn

new

sproxiesc

Cash

flownew

s(scaledbyprice)

Cash

flow

new

s(scaledbyforecast)

Expectedreturn

new

s

CFN_1

CFN_TV

CFN_1A

CFN_TVA

EWER_N

FSER_N

Mean

)0.76%

**

0.69%

*)0.99%

*2.43%

*)0.32**

)0.03**

Median

)0.16**

0.00

)2.44

0.00

)0.42**

)0.02**

Percentiles

1%

)16.11

)133.33

)268.00

)57.89

)3.01

)0.72

25%

)2.36

)23.26

)36.67

)13.33

)0.98

)0.14

75%

1.25

25.02

20.38

16.13

0.50

0.09

99%

11.18

134.02

321.54

84.21

2.06

0.63

STD

4.50

49.64

1.20

26.94

1.20

0.24

N14,521

14,521

14,521

14,521

14,521

14,521

(Thetable

iscontinued

onthenextpage.)



TABLE

4(C

ontinued)

Panel

C:Firm-specificrisk

proxiesd

MBETA

UBETA

DM

MKVL

BP

EXGRW

Mean

1.02

0.73

0.42

4106.62

0.55

13.54

Median

0.98

0.64

0.22

909.14

0.50

12.50

Notes:

ar R

EAListhebuyandhold

realizedreturn

computedover

the12monthsbeginningafter

themonth

expectedreturn

proxiesare

estimated.See

detailed

descriptionsandcalculationsforeach

proxyin

Tables2and3.

bCFN_1AandCFN_TVAare

analogousto

CFN_1andCFN_TV

exceptforthescaling.Theoriginalvalues

are

scaledbyrecentstock

price,butthe

variableslabeled

‘A’are

scaledbytheabsolute

valueoftheoriginalforecast.

cCash

flow

new

s,firm

-specificrisk

proxiesvariablesare

defined

inTable

1.

dNumber

ofobservationsforthesevariablesis17,904.**,*denotessignificance

atthe0.01and0.05orbetterlevels,respectively(2-tailed

t-test).



Explanatory variables

Panel B of Table 4 provides descriptive statistics for our cash flow and expected returnnews 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 opti-mism. CFN_1A measures the earnings surprise as a percentage of beginning earnings fore-cast. 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’ expecta-tions of target price over the 12-month realized return period. The mean change in the tar-get price is significantly positive (0.69 percent of stock price), while the median value is0.0. This is consistent with ‘‘good’’ news on average with respect to infinite horizon dis-counted expected cash flows.

The mean (median) value of our economy-wide expected return news proxy issignificantly negative at )0.32 ()0.42) indicating an annual decline in the risk free rate ofone-third to almost one-half of one percent. Similarly, the mean (median) value of ourfirm-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 firm-specific risk factors including MBETA, UBETA, DM, MKVL, BP, and EXGRW. Thesestatistics describe a sample similar in average market risk to that of the market portfoliowith a mean debt-to-market ratio of 42 percent and a market value of equity that is heav-ily skewed to larger firms. The average book-to-price ratio of 55 percent is consistent withthe 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 regres-sion analyses. We present the mean value of the year-by-year correlations along with thenumber 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 realizedreturns and the twelve proxies for Et)1(rt). The correlations are quite small, ranging from0.00 (rPEGST and rFF) to 0.09 (rGOR). Four of our Et)1(rt) proxies (rOJN, rGOR, rGLS, andrCT) 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. None-theless, this analysis fails to consider critical controls for cash flow and expected returnnews as modeled in (2).

Except for the correlation between rDIV and rGLS, where the correlation is statisticallypositive in ‘‘only’’ 19 years, the pair-wise correlations among the implied cost of capitalproxies 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 alter-native 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 sameunderlying construct. In contrast, the correlation between rFF and the implied cost of capi-tal estimates is almost as likely to be negative as positive. This suggests that rFF and theimplied 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 testingHypothesis 1. Consistent with cash flow news playing an important role in explainingrealized 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 scal-

ing each component by the absolute value of the relevant forecast at the beginning of the period. We pro-

vide these data to convey the economic magnitude of the revisions in cash flows.



TABLE

5

Correlations

Panel

A:Correlationsamongexpectedreturn

proxies

r DIV

r PEG

r MPEG

r PEGST

r OJN

r GM

r GOR

r GLS

r CT

r FF

r HL

r DKL

r REAL

0.04

(6⁄6)

0.01

(8⁄5)

0.02

(6⁄4)

0.00

(5⁄5)

0.05

(10

⁄3)

0.01

(5⁄4)

0.09

(12

⁄2)

0.08

(12

⁄5)

0.08

(13

⁄3)

0.00

(4⁄4)

0.06

(9⁄2)

0.05

(9⁄3)

r DIV

—0.61

(21

⁄0)

0.46

(21

⁄0)

0.46

(21

⁄0)

0.56

(21

⁄0)

0.44

(21

⁄0)

0.57

(21

⁄0)

0.22

(19

⁄0)

0.55

(21

⁄0)

)0.04

(2⁄7)

0.56

(21

⁄0)

0.49

(21

⁄0)

r PEG

—0.51

(21

⁄0)

0.62

(21

⁄0)

0.73

(21

⁄0)

0.51

(21

⁄0)

0.60

(21

⁄0)

0.22

(21

⁄0)

0.56

(21

⁄0)

0.00

(21

⁄6)

0.64

(21

⁄0)

0.54

(21

⁄0)

r MPEG

—0.91

(21

⁄0)

0.40

(21

⁄0)

0.98

(21

⁄0)

0.62

(21

⁄0)

0.39

(21

⁄0)

0.51

(21

⁄0)

0.00

(5⁄7)

0.79

(21

⁄0)

0.86

(21

⁄0)

r PEGST

—0.29

(21

⁄0)

0.91

(21

⁄0)

0.50

(21

⁄0)

0.25

(21

⁄0)

0.43

(21

⁄0)

0.00

(7⁄6)

0.66

(21

⁄0)

0.74

(21

⁄0)

r OJN

—0.38

(21

⁄0)

0.68

(21

⁄0)

0.36

(21

⁄0)

0.63

(21

⁄0)

)0.01

(3⁄3)

0.70

(21

⁄0)

0.52

(21

⁄0)

r GM

—0.53

(21

⁄0)

0.30

(21

⁄0)

0.43

(21

⁄0)

)0.01

(5⁄7)

0.73

(21

⁄0)

0.80

(21

⁄0)

r GOR

—0.70

(21

⁄0)

0.87

(21

⁄0)

0.04

(8⁄3)

0.90

(21

⁄0)

0.84

(21

⁄0)

r GLS

—0.54

(21

⁄0)

0.07

(9⁄2)

0.72

(21

⁄0)

0.72

(21

⁄0)

r CT

—0.04

(9⁄3)

0.80

(21

⁄0)

0.74

(21

⁄0)

r FF

—0.03

(7⁄3)

0.03

(8⁄3)

r HL

—0.96

(21

⁄0)

(Thetable

iscontinued

onthenextpage.)



TABLE

5(C

ontinued)

Panel

B:Correlationsamongrealizedreturns,cash

flow

new

s,andexpectedreturn

new

sproxies.

CFN_1

CFN_TV

EWER_N

FSER_N

r REAL

0.33(21

⁄0)

0.35(21

⁄0)

)0.01(7

⁄8)

0.01(10

⁄4)

CFN_1

—0.46(21

⁄0)

)0.01(0

⁄1)

0.00(4

⁄5)

CFN_TV

—)0.01(0

⁄1)

)0.01(2

⁄3)

EWER_N

—)0.01(2

⁄4)

Panel

C:Correlationsamongexpectedreturn

andcash

flow

new

sandexpectedreturn

new

proxies.

r DIV

r PEG

r MPEG

r PEGST

r OJN

r GM

r GOR

r GLS

r CT

r FF

r HL

r DKL

CFN_1

)0.06

(0⁄8)

0.00

(2⁄3)

0.04

(6⁄1)

0.05

(8⁄1)

)0.04

(0⁄6)

0.06

(7⁄1)

)0.07

(0⁄6)

)0.04

(0⁄7)

)0.08

(0⁄6)

0.01

(2⁄2)

)0.01

(2⁄4)

0.01

(4⁄4)

CFN_TV

)0.25

(0⁄21)

)0.14

(0⁄18)

)0.06

(0⁄8)

)0.06

(0⁄5)

)0.16

(0⁄19)

)0.06

(0⁄7)

)0.13

(0⁄15)

)0.05

(3⁄10)

)0.14

(0⁄19)

0.00

(2⁄3)

)0.12

(0⁄13)

)0.09

(0⁄11)

EWER_N

)0.02

(4⁄7)

)0.04

(2⁄4)

)0.01

(0⁄3)

)0.03

(1⁄6)

)0.03

(0⁄5)

)0.03

(0⁄6)

0.00

(4⁄3)

0.01

(5⁄3)

)0.03

(1⁄4)

)0.01

(3⁄3)

)0.02

(3⁄3)

)0.02

(4⁄4)

FSER_N

)0.01

(6⁄9)

)0.01

(5⁄6)

0.01

(4⁄4)

0.00

(5⁄6)

0.01

(4⁄5)

0.01

(3⁄3)

0.00

(7⁄6)

0.01

(7⁄5)

0.01

(6⁄4)

)0.13

(3⁄14)

0.01

(6⁄5)

0.01

(6⁄6)

(Thetable

iscontinued

onthenextpage.)



TABLE

5(C

ontinued)

Panel

D:Correlationsamongexpectedreturn

andrisk

proxies.

r REAL

r DIV

r PEG

r MPEG

r PEGST

r OJN

r GM

r GOR

r GLS

r CT

r FF

r HL

r DKL

MBETA

)0.05

(8⁄9)

0.18

(17

⁄0)

0.31

(21

⁄0)

0.08

(11

⁄0)

0.27

(21

⁄0)

)0.02

(2⁄4)

0.10

(12

⁄0)

)0.02

(3⁄7)

)0.16

(0⁄20)

0.03

(6⁄4)

0.19

(14

⁄2)

)0.01

(3⁄4)

0.00

(4⁄4)

UBETA

)0.04

(8⁄10)

0.11

(15

⁄0)

0.19

(19

⁄0)

)0.05

(1⁄7)

0.14

(18

⁄0)

)0.09

(0⁄15)

)0.02

(2⁄6)

)0.15

(0⁄18)

)0.25

(0⁄21)

)0.09

(1⁄13)

0.10

(10

⁄4)

)0.14

(0⁄18)

)0.14

(0⁄17)

DM

0.03

(10

⁄8)

0.05

(7⁄1)

0.09

(12

⁄0)

0.30

(21

⁄0)

0.16

(19

⁄0)

0.20

(21

⁄0)

0.26

(21

⁄0)

0.39

(21

⁄0)

0.43

(21

⁄0)

0.23

(21

⁄0)

0.07

(10

⁄1)

0.39

(21

⁄0)

0.39

(21

⁄0)

LMKVL

0.02

(7⁄5)

)0.16

(1⁄17)

)0.29

(0⁄21)

)0.25

(0⁄21)

)0.29

(0⁄21)

)0.16

(0⁄ 18)

)0.24

(0⁄21)

)0.24

(0⁄20)

)0.17

(0⁄18)

)0.12

(1⁄13)

0.06

(10

⁄5)

)0.25

(0⁄20)

)0.24

(0⁄20)

LBP

0.07

(8⁄3)

0.24

(20

⁄0)

0.30

(21

⁄0)

0.46

(21

⁄0)

0.33

(21

⁄0)

0.37

(21

⁄0)

0.40

(21

⁄0)

0.63

(21

⁄0)

0.69

(21

⁄0)

0.35

(21

⁄0)

0.01

(7⁄5)

0.62

(21

⁄0)

0.61

(21

⁄0)

EXGRW

)0.05

(4⁄10)

0.36

(20

⁄0)

0.78

(21

⁄ 0)

0.20

(20

⁄0)

0.36

(21

⁄0)

0.45

(21

⁄0)

0.27

(20

⁄0)

0.06

(9⁄3)

)0.23

(0⁄21)

0.08

(11

⁄1)

)0.03

(6⁄9)

0.18

(17

⁄1)

0.09

(13

⁄1)

Notes:

Table

values

are

themeanofyear-by-yearcorrelations.Figuresin

parentheses

are

thenumber

ofyears

thecorrelationissignificantly

(positive

⁄negative)

at5%

level

inyear-by-yearcorrelations.Allvariablesare

defined

inTables1or3.



(greater than 0.30) and significantly positive in all 21 years. We also document a strongpositive correlation between our cash flow news proxies (0.46), suggesting that ‘‘good’’ cur-rent period cash flow news tends to be associated with ‘‘good’’ long-horizon cash flownews. 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 thatneither is strongly correlated with rREAL supports the conclusion in prior research thatcash flow news is the primary driver of realized returns. Finally, the expected return newsproxies are not highly correlated with the cash flow news proxies, suggesting that cash flownews is distinct from expected return news.

Panel C of Table 5 presents correlations between the Et)1(rt) proxies, and our proxiesfor cash flow and expected return news. There is a fairly strong negative correlationbetween CFN_TV and several of the Et)1(rt) proxies (rDIV, rPEG,, rOJN, rGOR, rCT, andrHL), which suggests that terminal values tend to decline when cost of equity capital ishigh at the beginning of the realized return period. The low correlation among most of theEt)1(rt) proxies and our two proxies for expected return news is reasonable since there isno obvious basis for expected return news to be correlated with the initial level of expectedreturns.

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 regressionmodel, 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 least11 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) arenegatively 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 correlatedwith MBETA but not UBETA, highlights the importance of separating leverage risk andmarket risk.

Except for an unexpected negative association between rGLS and EXGRW ()0.23) andan unexpected positive association between rFF and LMKVL, the remaining correlationsamong the Et)1(rt) proxies and the risk factors accord with expectations. Despite thecounterintuitive nature of the negative association between rGLS and EXGRW, this findingis consistent with prior research (e.g., BP 2005; Gebhardt et al. 2001). The particularlystrong correlation between EXGRW and rPEG (q = 0.78) is explained in part by the alge-braic relationship between rPEG and growth, and serves to underscore the importance ofcontrolling for growth in our firm-specific risk analysis. Nevertheless, EXGRW is alsohighly correlated with rDIV (q = 0.36), which does not have an algebraic relationship withgrowth, 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 toexpectations 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 pre-dictable manner. With respect to rDIV and rPEG this finding is consistent with BP, whostudy 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 associa-tion 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.



5. Empirical results

Test of Hypothesis 1

Baseline model

Panel A of Table 6 provides the results of estimating a baseline realized return model thatincludes 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 theEt)1(rt) proxies. We report the time-series averages of the coefficients from annual cross-sectional regressions and t-statistics based on the standard error of the coefficient (Famaand MacBeth 1973).

The average R2 of the baseline model is 25.9 percent, indicating that our proxies forcash flow and expected return news capture one-quarter of the variation in rREAL. We doc-ument 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 Voulteenaho2002. We document a significant negative relation between rREAL and economy-wideexpected 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 con-cludes that expected return news is driven by macroeconomic, not firm-specific factors(Vuolteenaho 2002; Campbell and Ammer 1993). Alternatively, CFN_TV might capturefirm-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 realizedreturn model with the various Et)1(rt) proxies. In all specifications the coefficients onCFN_1 and CFN_TV are significantly positive, the coefficient on EWER_N is significantlynegative, and the coefficient on FSER_N is not statistically different from zero. Thus, add-ing Et)1(rt) proxies to the model has no effect on the associations between realized returnsand cash flow and expected return news.

Below the coefficient on the Et)1(rt) proxy, we present t-statistics related towhether the mean proxy coefficient is significantly positive and whether the mean proxycoefficient 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 positivein 19 of 21 years). Moreover, in all but one specification (rFF) adding Et)1(rt) to the base-line models improves explanatory power. The models employing rDIV and rGOR show thegreatest 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 averagecoefficient 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, ifthe empirical model is well-specified, the intercept should be zero, which is the case in allbut one of the specifications (rGOR), providing further support for the appropriateness ofour 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 coefficienton rDIV is significantly positive, but statistically indistinguishable from 1. It is significantlypositive in the greatest number of years (19) and indistinguishable from one in close tohalf the years (9). The model estimated with rDIV is also tied for the greatest increase inR2 (15 percent increase).



TABLE 6

Regressions of realized returns on cash flow news and expected return news proxies.

Panel A: Model 1: rREALit ¼ a0 þ b1CFN 1it þ b2CFN TVit þ b3EWER Nit þ b4FSER Nit þ eit

Intercept CFN_1 (+) CFN_TV (+) EWER_N ()) FSER_N ()) Avg. Adj. R2

)0.018 ()0.18) 0.014 (14.22**) 0.002 (15.31 **) )0.144 ()1.85*) 0.008 (0.15) 25.9

Panel B: Model 2:

rREALit ¼ a0 þ b1ERit�1 þ b2CFN 1it þ b3CFN STit þ b4CFN TVit þ b5EWER Nit þ b6FSER Nit þ eit

Intercept ER (+)

CFN_1

(+)

CFN_TV

(+)

EWER_N

())FSER_N

())Avg.

Adj. R2

rDIV )0.131 0.883 0.014 0.002 )0.126 0.018 29.7

>0 ()1.13) (6.67**) (17.99**) (16.22**) ()1.91*) (0.44)

=1 (0.40)

=1 ⁄+ ⁄ ) {9 ⁄ 19 ⁄ 0}rPEG )0.104 0.893 0.014 0.002 )0.131 0.008 27.6

>0 ()1.34) (3.50**) (15.51**) (15.09**) ()1.95*) (0.17)

=1 (0.69)

=1 ⁄+ ⁄ ) {7 ⁄ 13 ⁄ 3}rMPEG )0.056 0.434 0.014 0.002 )0.133 0.008 26.7

>0 ()0.53) (2.44**) (16.67**) (15.66**) ()1.88*) (0.17)

=1 ()2.77**)=1 ⁄+ ⁄ ) {5 ⁄ 10 ⁄ 2}rPEGST )0.044 0.322 0.014 0.002 )0.137 0.002 26.9

>0 ()0.43) (1.54) (16.29**) (15.69**) ()1.95*) (0.05)

=1 ()3.05**)=1 ⁄+ ⁄ ) {7 ⁄ 10 ⁄ 2}rOJN )0.124 1.157 0.014 0.002 )0.125 0.014 27.3

>0 ()1.44) (4.46**) (16.47**) (15.42**) ()1.94*) (0.29)

=1 (0.60)

=1 ⁄+ ⁄ ) {9 ⁄ 14 ⁄ 0}rGM )0.045 0.304 0.014 0.002 )0.136 0.008 26.6

>0 ()0.42) (1.83*) (16.33**) (15.48**) ()1.87*) (0.15)

=1 ()2.68**)=1 ⁄+ ⁄ ) {4 ⁄ 9 ⁄ 2}rGOR )0.177 2.141 0.015 0.002 )0.114 0.007 29.8

>0 ()2.14**) (6.99**) (18.16**) (16.14**) ()2.06*) (0.17)

=1 (3.33**)

=1 ⁄+ ⁄ ) {5 ⁄ 17 ⁄ 0}rGLS )0.056 0.964 0.015 0.002 )0.118 0.017 28.0

>0 ()0.67) (3.23*) (17.63**) (14.90**) ()1.94*) (0.37)

=1 (0.92)

=1 ⁄+ ⁄ ) {4 ⁄ 12 ⁄ 0}rCT )0.161 1.581 0.015 0.002 )0.122 0.016 28.2

>0 ()1.57) (5.07**) (17.68**) (16.13**) ()1.90*) (0.36)

=1 (1.52)

=1 ⁄+ ⁄ ) {8 ⁄ 16 ⁄ 0}

(The table is continued on the next page.)



Our results provide support for the construct validity of all the proxies we examineexcept rPEGST and rFF. This conclusion is inconsistent with GKS and EM, who documentinsignificant, and in some cases significantly negative relationships between the impliedcost of capital estimates they examine and realized returns. We investigate the source ofthe difference in our results in section 7.

Although the results in Table 6 provide support for the construct validity of 10 of theEt)1(rt) proxies, rREAL is only one of the ‘‘other measures’’ that can be used to assess theconstruct validity of alternative Et)1(rt) proxies. A second set of ‘‘other measures’’ alsouseful for this purpose is the set of firm-specific risk factors that theory predicts should beassociated 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 therisk-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 proxiesincluded in the model. rPEG and rPEGST are related to all of the proxies consistent with the-ory. rDIV is related to all but LMKVL, but this is expected if LMKVL and LBP both serveto capture unmeasured risk (Berk 1995). No other expected return proxy performs as wellas 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 thesethree specifications, and the coefficient on the risk-free rate should be indistinguishablefrom 1, which it is in the models estimated with rDIV and rPEGST. rREAL is not correlated

TABLE 6 (Continued)

Intercept ER (+)

CFN_1

(+)

CFN_TV

(+)

EWER_N

())FSER_N

())Avg.

Adj. R2

rFF 0.032 )0.051 0.014 0.002 )0.111 0.009 25.2

>0 (0.45) ()0.56) (15.56**) (16.83**) ()1.89*) (0.45)

=1 ()6.04**)=1 ⁄+ ⁄ ) {1 ⁄ 5 ⁄ 7}rHL )0.131 1.430 0.014 0.002 )0.117 0.014 28.0

>0 ()1.36) (4.33**) (18.17**) (16.04**) ()1.95*) (0.33)

=1 (0.30)

=1 ⁄+ ⁄ ) {5 ⁄ 13 ⁄ 0}rDKL )0.107 1.177 0.014 0.002 )0.120 0.013 27.7

>0 ()1.08) (3.74**) (17.64**) (15.92**) ()1.93*) (0.29)

=1 (0.65)

=1 ⁄+ ⁄ ) {8 ⁄ 12 ⁄ 0}

Notes:

This table includes the time-series averages of the coefficients of the 21 annual cross-sectional regres-

sions (1984–2004) and t-statistics for whether that mean coefficient is statistically positive ⁄nega-tive (>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-by-

year regressions is (significantly positive and equal to one ⁄ significantly positive ⁄ significantlynegative) (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.



TABLE 7

Regression of expected return specifications on firm-specific risk factors.

Intercept (?)rf

(+)UBETA(+)

DM(+)

LMKVL())

LBP(+)

EXGRW(+)

Avg.Adj. R2

rREAL )111.08 14.45 1.12 1.36 )0.14 2.40 )0.07 8.3

>0 ()1.52) (1.61) (0.34) (1.43) ()0.28) (2.17**) ()0.60)=1 (2.57**)

=1 ⁄+ ⁄ ) {7 ⁄ 6 ⁄ 0}rDIV )2.34 1.59 1.59 0.33 )0.16 2.51 0.27 22.3

>0 ()0.19) (0.98) (5.42**) (2.25**) ()0.87) (8.36**) (7.03**)

=1 (0.49)

=1 ⁄+ ⁄ ) {6 ⁄ 7 ⁄ 1}rPEG 4.92 0.29 0.45 0.37 )0.16 1.60 0.37 67.3

>0 (1.65) (0.81) (3.30**) (8.71**) ()4.82**) (9.12**) (7.56**)

=1 ()3.07**)=1 ⁄+ ⁄ ) {6 ⁄ 6 ⁄ 5}rMPEG 7.38 0.61 0.17 0.86 )0.18 2.43 0.16 28.5

>0 (3.35**) (2.16**) (1.19) (7.97**) ()3.98**) (8.07**) (11.99**)

=1 ()1.85**)=1 ⁄+ ⁄ ) {3 ⁄ 2 ⁄ 2}rPEGST 4.30 0.63 1.07 0.96 )0.31 1.85 0.21 30.5

>0 (1.19) (1.55) (4.01**) (7.96**) ()9.12**) (8.21**) (13.85**)

=1 ()1.40)=1 ⁄+ ⁄ ) {4 ⁄ 2 ⁄ 2}rOJN 6.40 0.45 )0.91 )0.06 0.10 1.51 0.22 41.2

>0 (4.77*) (2.55**) ()9.71#) ()1.06) (1.81#) (9.75**) (9.62**)

=1 ()4.16**)=1 ⁄+ ⁄ ) {5 ⁄ 0 ⁄ 3}rGM 5.59 0.90 0.08 0.81 )0.18 2.27 0.21 28.0

>0 (2.35**) (3.28**) (0.48) (7.30**) ()4.01**) (8.51**) (12.38**)

=1 ()0.49)=1 ⁄+ ⁄ ) {3 ⁄ 0 ⁄ 1}rGOR 7.73 0.31 )0.07 0.48 )0.06 2.13 0.02 39.3

>0 (3.15**) (0.97) ()0.70) (15.36**) ()1.24) (8.27**) (2.46**)

=1 ()4.18**)=1 ⁄+ ⁄ ) {4 ⁄ 6 ⁄ 2}rGLS 9.81 )0.07 )0.21 0.56 0.00 2.54 )0.07 40.8

>0 (4.21**) ()0.18) ()1.06) (7.22**) (0.07) (6.94**) ()10.78#)=1 ()2.78**)=1 ⁄+ ⁄ ) {4 ⁄ 5 ⁄ 2}rCT 6.52 0.57 )0.03 0.37 )0.00 1.11 0.02 15.6

>0 (3.17**) (2.11**) ()0.26) (7.02**) ()0.09) (12.19**) (1.43)

=1 ()2.16*)=1 ⁄+ ⁄ ) {7 ⁄ 0 ⁄ 6}rFF 16.34 )0.74 4.07 2.34 0.15 0.30 )0.06 17.9

>0 (4.07**) )1.59 (2.36**) (2.80**) (0.23) (1.04) ()2.72#)=1 ()2.63**)=1 ⁄+ ⁄ ) {4 ⁄ 6 ⁄ 2}




in a reasonable manner with any of the risk factors except for LBP, further supporting theconclusion 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, rPEGand rPEGST, while the results of the realized return analysis provide support for the con-struct validity of all of the Et)1(rt) proxies except rPEGST and rFF. Taken together, the twosets of analyses provide support for the validity of rDIV and rPEG alone, since these are theonly proxies associated with future realized returns and firm-specific risk in the mannerpredicted by theory.

Amalgamated proxies

rHL and rDKL attempt to control for noise in the Et)1(rt) proxy by averaging several prox-ies, but our analysis suggests that neither is superior to their inputs. Nonetheless, we aresympathetic to concerns regarding noise and the argument that averaging several validestimates, each individually measured with error, could yield a superior proxy. To addressthis issue, we focus on rDIV and rPEG because we find the greatest support for their con-struct validity. To combine these measures into one proxy we use factor analysis (to isolatethe 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 measureyields 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 litera-ture regarding Et)1(rt) proxies: (1) the impact of analyst forecast bias, (2) the efficacy ofrealized returns for expected returns after controlling for cash flow news, and (3) substitut-ing realizations for analysts’ forecasts.

TABLE 7 (Continued)

Intercept (?)rf

(+)UBETA(+)

DM(+)

LMKVL())

LBP(+)

EXGRW(+)

Avg.Adj. R2

rHL 7.41 0.39 )0.17 0.55 )0.02 1.93 0.08 39.9

>0 (4.50**) (1.70) ()1.87#) (3.90**) ()0.37) (9.99**) (7.71**)

=1 ()3.55**)=1 ⁄+ ⁄ ) {5 ⁄ 1 ⁄ 4}rDKL 7.20 0.47 )0.04 0.61 )0.06 1.98 0.05 34.5

>0 (4.08**) (1.89**) ()0.32) (7.02**) ()1.53) (10.77**) (7.38**)

=1 ()2.57**)=1 ⁄+ ⁄ ) {6 ⁄ 2 ⁄ 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.



Impact of analysts’ forecast bias

Most Et)1(rt) estimates employ analysts’ forecasts to proxy for the market’s expectationsof future cash flows, which gives rise to the concern that deviations between the market’sexpectations embedded in stock price and analysts’ forecasts lead to measurement error inthe Et)1(rt) proxies. GKS and Hou, van Dijk, and Zhang (2009) express the concern thatstale forecasts and ⁄or bias in analysts’ forecasts could lead to measurement error in theEt)1(rt) proxies.

It is important to note that error or bias in analysts’ forecasts relative to reportedearnings is not the issue. The issue is whether analysts’ beliefs are consistent with those ofthe market at the time expected returns are estimated. In addition, even though systematicbias in analyst forecasts (e.g., optimism relative to the market’s beliefs) might lead tobiased (e.g., overstated) Et)1(rt) estimates, it need not induce spurious correlations whenemploying the resulting Et)1(rt) proxy in empirical analyses. For this to occur, measure-ment error in the Et)1(rt) proxy would need to be systematic and correlated with othervariable(s) of interest. Even so, unsystematic deviations between analysts’ and the market’sexpectations 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 themarket’s beliefs about future cash flows at the time the proxies are estimated are notobservable, 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 andrPEG are estimated. We split our sample into ‘‘consistent’’ and ‘‘inconsistent’’ subsam-ples. Consistent (inconsistent) firm-year observations are those for which the sign ofthe earnings surprise is the same as (different from) the market reaction to the earningssurprise. We expect the observations in the consistent (inconsistent) subsample to bethose with the least (greatest) risk of a deviation between analysts’ forecasts and themarket’s expectations. Employing the data in each subsample, we reestimate the real-ized return model (equation (4)) and expected return model (equation (5)) and presentthe results in Table 8.

Panel A presents the realized return model, estimated with the consistent and inconsis-tent 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 correlationswith 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 esti-mated with the subset of consistent (inconsistent) observations. This finding holds for bothproxies. The R2 of the rDIV specification estimated using the consistent subsample increasesby 14.5 percent from 29.7 percent (Table 6) to 34.0 percent; the R2 of the rPEG specifica-tion 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 23percent to 22.8 percent and the R2 of the rPEG specification decreases by 26 percent to20.4 percent. These results suggest that deviations between analyst expectations and thoseof the market do not lead to biased or inconsistent results with respect to the coefficientson 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. Thecoefficients 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 losesignificance 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.



TABLE 8

Impact of forecast bias

Panel A: Realized return regressions

Consistent forecasts (7527 obs.)

InterceptER(+)

CFN_1(+)

CFN_TV(+)

EWER_N())

FSER_N())

Avg.Adj. R2

rDIV )0.138()1.44)

1.007

(7.21**)

0.016

(17.69**)

0.002

(15.75**)

)0.127()1.90*)

0.007

(0.17)

34.0

rPEG )0.109()1.09)

0.991

(3.80**)

0.016

(15.02**)

0.002

(14.88**)

)0.132()1.94*)

)0.004()0.09)

31.6

Inconsistent forecasts (6794 obs.)

Intercept

ER

(+)

CFN_1

(+)

CFN_TV

(+)

EWER_N

())FSER_N

())Avg.

Adj. R2

rDIV )0.164()1.68)

1.030

(4.68**)

0.010

(9.88**)

0.002

(13.14**)

)0.141()2.17**)

0.050

(0.44)

22.8

rPEG )0.104()1.36)

1.200

(2.94**)

0.009

(9.28**)

0.002

(12.77**)

)0.132()2.17*)

0.047

(0.70)

20.4

Panel B: Regression of expected return on risk factors

Consistent forecasts (7527 obs.)

Intercept (?)

rf

(+)

UBETA

(+)

DM

(+)

LMKVL

())LBP

(+)

EXGRW

(+)

Avg.

Adj. R2

rDIV )3.21()0.29)

1.59

(1.03)

1.03

(4.71**)

0.16

(0.82)

)0.12()0.81)

2.40

(7.92**)

0.32

(9.12**)

22.4

rPEG 3.07

(0.92)

0.40

(0.97)

0.31

(1.28)

0.32

(5.01**)

)0.13()3.28**)

1.56

(8.24**)

0.41

(17.08**)

68.4

Inconsistent forecasts (6794 obs.)

Intercept (?)

rf

(+)

UBETA

(+)

DM

(+)

LMKVL

())LBP

(+)

EXGRW

(+)

Avg.

Adj. R2

rDIV )3.09()0.27)

1.58

(1.02)

1.06

(4.75**)

0.18

(0.93)

)0.12()0.84)

2.39

(7.93**)

0.32

(9.18**)

22.5

rPEG 3.81

(1.32)

0.28

(0.78)

0.30

(1.21)

0.39

(8.18**)

)0.13()2.97**)

1.49

(10.83**)

0.43

(14.16**)

71.5




subsamples, however, these results are also more consistent with a power issue than biasedand inconsistent results.

rREAL after controlling for cash flow news

Some recent studies use realized returns after controlling for cash flows news to proxy forEt)1(rt) (e.g., Ogneva 2008). We examine the validity of this approach by estimating theexpected return model (equation (5)) with rREAL as the dependent variable and augmentingthe 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 controllingfor cash flow and expected return news, however, the association between rREAL and manyof the firm-specific risk factors contradicts theory. The coefficient on UBETA is not signifi-cant, 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 regres-sion, we estimate the residuals (rRESID) from the baseline realized return model shown inpanel A of Table 6. In theory, rRESID should be rREAL purged of the unexpected compo-nent of realized returns. That is, rRESID should be a proxy for Et)1(rt). In the second stageregression, we estimate the expected return model (equation (5)) with rRESID as the depen-dent 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 forEt)1(rt) after controlling for cash flow and expected return news. Moreover, since the dataneeded 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 withoutcontrolling for news.

Substituting realizations for analysts’ forecasts

When analyst forecasts are unavailable some prior work employs realized values of futureearnings and ⁄or cash flows in the estimation of implied cost of equity capital. Forexample, in Chen, Chen, Lobo, and Wang 2011 the authors substitute future realizationsof ROE for the market’s expectations in estimating rPEG. This can be quite problematic,

TABLE 8 (Continued)

Notes:

This table includes two robustness tests. Panel A includes the realized return regressions after split-

ting 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 sur-

prise 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 coeffi-

cients 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.



TABLE9

Additionalanalyses

Panel

A:ControllingforCFN

INTERCEPT

CFN_1

(+)

CFN_TV

(+)

EWER_N

())

FSER_N

())

rf(+

)UBETA

(+

)DM

(+

)LMKVL

())

LBP

(+

)EXGRW

(+

)Avg.

Adj.R2

r REAL

1.54

(1.40)

0.011

(11.94**)

0.002

(15.25**)

)0.077

()1.13)

0.017

(0.25)

)14.66

()1.06)

0.02

(0.81)

0.04

(5.97**)

)0.02

()3.16**)

)0.15

()9.45#)

)0.01

()4.69#)

35.4

Panel

B:Cost

ofcapitalestimate

(=residualsfrom

realizedreturns)

regressed

onrisk

proxies

Intercept(?)

rf(+

)UBETA

(+

)DM

(+

)LMKVL

())

LBP

(+

)EXGRW

(+

)Avg.Adj.R2

r RESID

1.19(2.87**)

)13.02()2.05#)

0.02(0.78)

0.04(5.13**)

)0.02()3.49**)

)0.14()8.93#)

)0.01()7.54#)

15.4

Notes:

Thistable

includes

tworobustnesstests.Panel

Aisbasedonregressingrealizedreturnsonthecash

flow

andexpectedreturn

new

svariables(ascontrols)

andtherisk

factors

included

inTable

7.Panel

Bisbasedonregressingtheresidualsfrom

regressionofrealizedreturnsonthecash

flow

new

sand

expectedreturn

new

svariables.Thevalues

presentedare

thetime-series

averages

ofthecoefficients

inthe21annualcross-sectionalregressions

(1984–2004),t-statisticsusingthestandard

errorofthecoefficientestimatesacross

the21years

(FamaandMacB

eth1973).**,*denotessignificance

inthepredicteddirectionatthe0.01and0.05orbetterlevels,respectively(1-tailed

t-test).#denotessignificantin

thewrongdirection.Figuresin

bold

are

significantatthe0.01level

orbetter.See

Table

3fordetailed

definitionsofallvariables.



because it leads to systematic error in the estimates that is related to ex post cash flownews. The implied cost of capital estimates are biased upward (downward) for firms withex post good (bad) cash flow news. Employing these estimates in empirical research mightyield biased and inconsistent results if other variables of interest (e.g., growth) vary sys-tematically with firms’ cash flow news.

7. Reconciliation with prior research

Almost all the implied cost of capital proxies we examine are positively correlated withrealized returns after controlling for cash flow and expected return news, whereas GKSand EM find that none of the proxies they examine are positively associated with realizedreturns. This difference is particularly stark with respect to rPEG, since all three studiesexamine close variants of this proxy.

Our results differ from GKS because their model does not include necessary controlsfor new information. Consistent with this, we document little or no correlation betweenrREAL and the expected return proxies in a univariate setting, but, after controlling forcash flow and expected return news, we find the expected relation. EM also conclude thatthe 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 empiricalspecifications are critically different. We employ the change in the risk-free rate to proxy formacroeconomic expected return news, and the change in market beta to proxy for firm-spe-cific expected return news. EM’s proxy for expected return news is a scaled measure of thedifference in consecutive implied cost of capital estimates. In the remainder of this section ofthe paper, we demonstrate that although EM’s proxy for expected return news is theoreti-cally defensible, it is empirically problematic because it provokes circularity in the empiricalmodel, 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 cur-rent 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 terminalvalue assumptions. Nevertheless, by construction, all ICC � f(CF, P), and therefore, allDICC � f(DCF, DP).

The theoretical specification of the realized return model (i.e., equation (2)) is shownbelow for convenience.

rREAL;t ¼ Et�1ðrtÞ þ ðNcf ;t �Nr;tÞ ð6Þ:

Empirically, rREAL,t � f(DP) and Ncf,t � f(DCF). In EM’s empirical specificationNr,t = DICC � f(DCF, DP). Consequently, the model EM estimate can be described bythe following set of relationships:

f ðDPÞ ¼ Et�1ðrtÞ þ f ðDCFÞ � f ðDCF;DPÞ ð7Þ:

EM’s proxy for expected return news (DICC) is by construction a function of DCF andDP, which are also included in the model as dependent and explanatory variables, respec-tively. Stated another way, solving (7) for Et)1(rt) yields:16

Et�1ðrtÞ 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 returnis 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).



is theoretically defensible to use the change in true Et)1(rt) to capture expectedreturn news, it is empirically problematic to use the change in an Et)1(rt) proxymeasured via an implied cost of capital approach for this purpose. The resultingprovoked circularity in the empirical model provides no role for Et)1(rt) to contributeto the explanation of rREAL,t, and as a result, any ICC estimate included in the modelto proxy for Et)1(rt) will be statistically insignificant, regardless of the validity, or lackthereof, of the ICC estimate employed. Moreover, the circularity we are concernedwith 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 expectedreturn news on the coefficient on the Et)1(rt) proxy, we reestimate our realized returnmodel using EM’s cash flow and expected return news proxies (hereafter CFN_EM andERN_EM, respectively). We estimate the model with the five implied cost of capital prox-ies that overlap with the prior work (rPEG, rMPEG, rGM, rCT, and rGLS) plus rDIV, since wefind strong support for the construct validity of the latter proxy.

Panel A of Table 10 presents these results. As predicted by our analysis above, andconsistent with EM’s results, the coefficient on EM_ERN is positive and highly significantin all specifications (t-statistics ranging from 3.86 to 15.56). In addition, except for thecoefficients on rCT and rDIV, which are significantly positive and negative, respectively, thecoefficients on the Et)1(rt) proxies are statistically insignificant.

Finally, we estimate the regression model using EM’s cash flow news proxy, but ourmeasure of expected return news. Because our measures of expected return news are inde-pendent of the derivation of the implied cost of capital estimates, they do not provoke cir-cularity 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 theEt)1(rt) proxies are significantly positive.

Finally, it is interesting to note the difference in the R2s of the models estimated inTable 10 panel B versus Table 6. For example, the rDIV model in Table 6 has an R2 of29.7 percent – 68 percent higher than the R2 of 17.7 percent in Table 10, panel B for therDIV specification. The only difference between these models is the empirical proxy for cashflow 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 greaterexplanatory power.

8. Conclusions

Existing literature employs two approaches to assess the validity of alternative proxies forfirm-specific cost of equity capital or expected return (Et)1(rt)). One approach relies onthe theoretical link between realized returns and Et)1(rt), while the second approach relieson the theoretical relation between Et)1(rt) and priced risk characteristics. Based onresults from both approaches we conclude that there is support for the construct validityof 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 dem-onstrate 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 interpre-

tation 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.



those of market participants embedded in stock price. This assumption is not unique toour study, and is supported by existing research (Barron, Harris, and Stanford 2005).Importantly, because this is the only researcher assumption imposed on terminal value inthe estimation of rDIV, terminal values are free to reflect whatever assumptions analystsmake with regard to infinite horizon cash flows and future discount rates. Accordingly,rDIV is not constrained across firms or industries by researcher-imposed assumptionsregarding the behavior of terminal values.

Further, the primary researcher-imposed assumption underlying rPEG is that, beyondthe forecast horizon, growth in abnormal earnings is zero. It is reasonable to expect thisresearcher-imposed assumption mirrors the assumption frequently employed by analystsand market participants, since it is commonly taught in financial statement analysiscourses. 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 toextend its supernormal profits to new additional projects year after year.. .. Each new pro-ject 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

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 b1ER it � 1þ b2CFN EM it þ b3EM ER N it þ eit

InterceptER(+)

CFN_EM(+)

EM_ERN(+)

Avg.Adj. R2

0.12 (6.25**) 0.50 (4.27**) 10.4

rDIV 0.15 (5.34**) )0.29 ()2.45#) 0.49 (10.87**) 0.04 (15.56**) 31.2

rPEG 0.16 (4.01**) )0.43 ()1.72) 0.41 (11.10**) 0.07 (7.59**) 25.4

rMPEG 0.15 (4.15**) )0.31 ()1.29) 0.45 (8.98**) 0.03 (4.25**) 17.3

rGM 0.16 (4.24**) )0.39 ()1.64) 0.44 (8.94**) 0.03 (3.86**) 16.7

rCT 0.03 (0.83) 0.76 (1.83*) 0.56 (16.90**) 0.11 (6.99**) 26.3

rGLS 0.08 (2.79**) 0.46 (1.36) 0.57 (16.18**) 0.18 (6.46**) 32.9

Panel B: rREALit ¼ a0 þ b1ERit�1 þ b2CFN EMit þ b3EWER Nit þ b4FSER Nit

Intercept

ER

(+)

CFN_EM

(+)

EWER_N

(+)

FSER_N

(+)

Avg.

Adj. R2

)0.03 ()0.37) 0.30 (6.92**) 13.18 (1.94*) 0.003 (0.04) 11.9

rDIV )0.09 ()1.30) 0.61 (6.23**) 0.51 (14.05**) 12.13 (2.02**) 0.01 (0.18) 17.7

rPEG )0.09 ()1.07) 0.60 (2.49**) 0.31 (6.94**) 12.75 (2.01*) 0.01 (0.12) 13.8

rMPEG )0.07 ()0.85) 0.52 (2.83**) 0.48 (13.67**) 11.96 (1.94**) 0.01 (0.18) 16.6

rGM )0.06 ()0.80) 0.44 (2.46**) 0.48 (13.59**) 12.19 (1.93*) 0.01 (0.18) 16.5

rCT )0.19 ()2.49**) 1.87 (5.83**) 0.52 (16.34**) 11.31 (1.92*) 0.01 (0.02) 18.0

rGLS )0.08 ()1.17) 1.15 (3.36**) 0.49 (13.11**) 10.80 (2.04**) 0.00 (0.05) 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).



project are offset by its costs, it does nothing to enhance the current value of the firm, andthe associated growth can be ignored.’’18

The results of our realized return analysis differ markedly from those documented inprior research. Consistent with EM and our univariate analysis we conclude that theresults in GKS are attributable to an omitted variable bias arising from a lack of adequatecontrols for new information. With respect to EM, we demonstrate that their results areprompted by circularity in their empirical model generated by their empirical approach tomeasuring expected return news.

Finally, we consider several other issues raised in the literature regarding implied costof capital estimates, including (1) the impact of analysts’ forecast bias, (2) the efficacy ofrealized 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) thesubstitution of realized values for analysts’ forecasts of cash flows or earnings.

Our evidence suggests that the impact of deviations between analysts’ expectations andthose of the market is limited to potentially less powerful proxies. On the second point, wefind that realized returns are not a reliable proxy for expected returns even after control-ling for cash flow news. On the third point we find that the act of averaging several prox-ies does not yield an enhanced metric. Finally, we note that substituting realized values foranalysts’ forecasts in the estimation of implied cost of equity capital yields estimates thatare systematically biased upward (downward) for firms with ex post good (bad) cash flownews, which could yield biased and inconsistent results if the resulting measurement erroris correlated with other variables of interest.

In conclusion, we recommend that researchers requiring a valid Et)1(rt) proxy employeither rDIV or rPEG estimated with analysts’ forecasts and we caution against the use ofrealized returns with or without controlling for cash flow news to proxy for Et)1(rt). Weadvocate that researchers assess the validity of any new Et)1(rt) proxies by demonstratinga consistent and predictable association between the proxy and future realized returns, aswell as established risk measures. Finally, we note that the primary difference betweenrDIV and rPEG is that rDIV effectively allows the terminal value assumption to vary acrossfirms, while rPEG imposes an assumption of zero growth in abnormal earnings beyond theforecast 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 earningsbeyond the forecast horizon. We leave an investigation of this supposition for futureresearch.

18. Palepu et al. (1999, 12–6). This is one example, but similar instruction can be found in almost any finan-

cial statement analysis text.



Appendix

Summary of Et)1(rt) proxies examined in related research

Et)1(rt)proxy

Guay,Kothari andShu (2005)

Easton andMonahan(2005)

Botosan andPlumlee(2005)

Currentstudy

rDIV x x

rPEG x x x

rMPEG x x

rPEGST x x

rOJN x x x x

rGM x x

rGOR x x x

rGLS x x x x

rCT x x x

rFF x

rHL x

rDKL x

rdagr x

rPE 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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