Are Information Attributes Priced?

Christine A. Botosan*Associate Professor of Accounting

C. Roland Christensen Faculty FellowEmail: actcb@business.utah.edu

Marlene A. Plumlee* a

Associate Professor of AccountingEmail: actmp@business.utah.edu

*David Eccles School of BusinessUniversity of Utah

Salt Lake City, UT 84112a corresponding author

January 2006

We wish to thank Stephen Brown for his generous assistance in the calculation of the PIN variable used in this study. We also wish to thank the workshop participants at the University College Dublin, University of Utah, New York University, Toronto University, Wharton and University of Wisconsin-Madison for their helpful comments. The authors gratefully acknowledge the financial support of the David Eccles School of Business and the contribution of I/B/E/S Inc. for providing earnings per share forecast data, available through the Institutional Brokers Estimate System. These data have been provided as part of a broad academic program to encourage earnings expectations research.

Are Information Attributes Priced?

Abstract

Easley and O’Hara (EO) (2004) model the impact of information attributes on the cost of equity

capital. We empirically test three implications of the EO model and document results consistent with its

predictions. Specifically we find that cost of equity capital is increasing in the proportion of the

information set that is private versus public, decreasing in the fraction of investors who are informed and

decreasing in the overall precision of the information set. Accordingly we conclude that Easley and

O’Hara’s conjecture that public and private information have a role to play in affecting firms’ required

returns is supported by the data.

1. Introduction

Easley and O’Hara (EO) (2004) model the impact of information attributes on the cost of equity

capital. They conclude that cost of equity capital is affected by the following attributes of information: (1)

the proportion of the information set that is private versus public (hereafter composition), (2) the fraction

of investors who are informed (hereafter dissemination), and (3) the overall precision of the information

set (hereafter precision). EO demonstrate that cost of equity capital is increasing in the composition of the

information set and decreasing in its dissemination and precision. We empirically test these three

implications of the EO model and document results consistent with the model’s predictions.

We employ two alternative proxies for the cost of equity capital – rDIVPREM and rPEGPREM. rDIVPREM is

derived from the dividend discount model and is the internal rate of return that equates a firm’s current

stock price to analysts’ forecasts of future dividends and target price (Botosan and Plumlee (2002);

Botosan et al. (2004)). rPEGPREM is similarly derived from the dividend discount model, but after imposing

the assumption that both dividends prior to the earnings forecasts and growth in abnormal earnings

beyond the forecast horizon are zero (Ohlson and Juettner-Nauroth (OJ) (2003); Easton (2004)). Botosan

and Plumlee (2005) assess the empirical validity of five alternative methods of estimating cost of equity

capital including rDIVPREM and rPEGPREM and conclude that, among those examined, only these estimates are

predictably and robustly related to risk.1

Our proxies for the composition and precision of information are drawn from Barron et al. (BKLS)

(1998). BKLS demonstrate how observable attributes of analysts’ forecasts can be employed to estimate

the precision of the analysts’ public and private information sets. We employ these measures to derive

estimates of the overall precision of the information set (labeled PRECIS), and the proportion of the

information set that is private versus public (labeled COMPOS). We compute a proxy for the fraction of

1 For other research that examines possible proxies for expected cost of equity capital see Botosan (1997), Gebhardt

et al. (2001), and Gode and Mohanram (2003).

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investors who are informed (labeled DISSEM) using the estimated arrival rates of informed and

uninformed investors, both of which are components of the probability of an informed investor (i.e. PIN)

metric developed in Easley et al. (1997).

We find that both proxies for cost of equity capital are increasing in COMPOS and decreasing in

DISSEM and PRECIS, consistent with the EO model and EO’s conjecture that information attributes are

priced. The magnitudes of our coefficients suggest that an increase in COMPOS of 10 points (e.g. from

20% to 30%) is associated with an increase in cost of equity capital of about 7 basis points, whereas a

similar increase in DISSEM is associated with a decrease in cost of equity capital of about 38 basis

points, on average. In addition, the sample firm providing the most precise information enjoys a cost of

equity capital that is 114 basis points lower than the sample firm providing the least precise information.2

One implication of our findings is that managers can realize a lower cost of equity capital by reducing

private information relative to public information. Most existing research (including the EO model)

assumes that public information supplants private information, which suggests that managers might

realize cost of equity capital benefits by providing more public disclosures. However, a relatively early

stream of research suggests that some types of public disclosure might generate private information (see

Barron et al. (2005), and Botosan et al. (2004)), indicating that further research is needed to help

managers evaluate their optimal reporting strategy. Another implication of our findings is that managers

can procure lower costs of equity capital by adopting corporate reporting strategies that mitigate

investors’ costs of becoming informed thereby encouraging greater dissemination of private information.

For example, managers might increase the transparency of their disclosures to reduce investors’

information processing costs. Managers might also hold conference calls or host analyst “road-shows” to

encourage a greater analyst following. Finally, managers can achieve cost of equity capital benefits by

choosing accounting policies and disclosure practices that increase the overall precision of information.

Our study contributes to a growing body of empirical literature which focuses on the association

between information and cost of equity capital. For example, several papers examine the relationship

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between corporate financial reporting practices and cost of equity capital (see Botosan (1997), Botosan

and Plumlee (2002), Brown et al. (2004), and Richardson and Welker (2001)). In addition, a number of

papers relate attributes of earnings to cost of equity capital (see Affleck-Graves et al. (2002), Francis et al.

(2004), Hribar and Jenkins (2004), and Mikhail et al. (2004)). Common to all of these studies is a focus

on public information. Two more recent studies focus on proxies for private information and so are most

closely related to this endeavor. First, Botosan et al. (BPX) (2004) show that rDIVPREM is increasing in the

precision of private information, but decreasing in the precision of public information. Second, Easley et

al. (EHO) (2002) document a positive association between realized returns and PIN, their proxy for

COMPOS.

Our paper extends this stream of research in general and the research conducted by BPX and EHO in

particular, in several respects. First, BPX focus on the separate impacts of public and private information

precision on cost of equity capital, whereas our study considers the relationship between overall precision

and cost of equity capital in tandem with proxies for composition and dissemination. Second, EHO

employ realized returns for cost of equity capital. In contrast we employ measures of implied cost of

equity capital in the analysis. Third, ours is the first study to consider the relationship between cost of

equity capital and all three of the information attributes suggested by the EO model.

We organize the remainder of our paper as follows. We outline the theory that underlies our

hypotheses and discuss prior research related to this study in Section I. We describe our research design

and empirical proxies in Section II, and our sample and descriptive statistics in Section III. We present the

results of our analysis in Section IV, and Section V concludes the paper.

2. Hypotheses development and prior research

2.1. Hypotheses development

Easley and O’Hara (2004) (EO) develop a multi-asset, rational expectations, equilibrium asset-pricing

model that incorporates public and private information, as well as informed and uninformed risk-averse

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investors. Within this framework EO consider the impact of cross-sectional differences in (1) the

composition of information between public and private information, (2) the dissemination of private

information across traders, and (3) the overall precision of information on firms’ costs of equity capital.3

In the EO model uninformed investors perceive stocks to be risky due to information risk and demand

higher returns to compensate for this additional risk. In contrast, informed traders perceive less

information risk and, therefore, are willing to take larger positions in securities about which they are

informed. Trading by informed investors can have two beneficial effects on the firm’s cost of equity

capital. First, since informed investors take larger positions in the firm’s stock, demand for the firm’s

securities may be increased thereby reducing the cost of equity capital. Second, uninformed investors

partially infer private information from stock price; they perceive less information risk when the trading

activities of informed investors reveal their private information with greater precision.

The impact of the composition, dissemination, and precision of information on cost of equity capital

results from the interplay among the effects outlined above. With respect to the composition of the

information set, EO demonstrate that stocks with more private information and less public information

face a higher cost of equity capital. This is because uniformed investors can not perfectly infer private

information from stock price, such that firms with relatively more private information are viewed as more

risky by uninformed investors and are charged a higher cost of equity capital as a result. This gives rise to

our first hypothesis, stated below.

H1: Cost of equity capital is increasing in the proportion of information that is private.

With respect to the dissemination of information, EO demonstrate that when private information is

more widely disseminated across investors, cost of equity of capital is reduced via the demand effect and

the information revelation effect. First, when more investors are informed, demand for the stock is

greater, price is higher, and cost of equity capital is lower. Second, when more investors are informed

their private information is revealed to uninformed investors with greater precision. This makes the stock

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less risky for uninformed traders and further reduces the cost of capital. This gives rise to our second

hypothesis.

H2: Cost of equity capital is decreasing in the dissemination of private information across investors.

With respect to the overall precision of information, EO demonstrate that greater precision lowers cost

of equity capital by making the stock less risky for the uninformed investors. Uninformed investors

perceive less information risk because the public information they observe directly and the private

information revealed to them indirectly via stock price are both more precise. This gives rise to our third,

and final, hypothesis.

H3: Cost of equity capital is decreasing in the overall precision of information.

2.2. Prior Research

A large body of empirical research investigates the association between public information and cost of

equity capital. One segment of this research broaches this issue indirectly by examining the effect of

disclosure on variables believed to be related to cost of equity capital. For example, Frankel et al. (1995)

find that managers of firms that access the capital markets provide management earnings forecasts more

frequently. Welker (1995) and Leuz and Verrecchia (2000) document a negative association between

disclosure levels and bid-ask spreads. Healy et al. (1999) find that firms that increase disclosure

experience an increase in stock performance, institutional ownership, and analyst following, and a

decrease in bid-ask spreads. Brown et al. (2004) find that a policy of regularly holding conference calls

mitigates information asymmetry. Finally, Affleck-Graves et al. (2002) demonstrate a favorable

association between earnings predictability and reduced information asymmetry.

Another segment of this research broaches the association between public information and cost of

equity capital by examining the effect of disclosure on the cost of raising equity capital via a secondary

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offering or on estimates of cost of equity capital. For example, Lang and Lundholm (2000) conclude that

hyping a stock in anticipation of a secondary offering increases price and allows the firm to raise capital

at a lower cost. Botosan (1997) finds that among firms with low analyst following, greater annual report

disclosure is associated with a lower cost of equity capital and Botosan and Plumlee (2002) extend this

result to large, heavily followed firms. Finally, several recent papers document a negative association

between earnings “quality” and cost of equity capital (e.g. Francis et al. (2004), Hribar and Jenkins

(2004), and Mikhail et al. (2004)).

All of the research discussed above focuses on public information. Two more recent studies, Botosan

et al. (2004) (BPX) and Easley et al. (2002) (EHO), consider the effects of public and private information

on cost of equity capital, and, as such, are most closely related to this study. BPX use separate empirical

proxies for the precision of public and private information to examine the effect of private information

precision on cost of equity capital, after controlling for the negative association between cost of equity

capital and public information established in the prior literature. BPX find that cost of equity capital is

increasing in the precision of private information and that the precision of private information is

positively correlated with the precision of public information. They find that, for the average firm, the

cost of capital reduction achieved through more precise public information is almost entirely offset by the

cost of capital increase associated with more precise private information.

BPX consider the precision of private and public information as separate constructs. While the EO

model allows the precisions of private and public information to differ, the model is silent as to the

separate effects of each of these precisions on cost of equity capital. Moreover, BPX’s finding of a

positive correlation between the precisions of private and public information is not consistent with EO’s

assumption that the precisions of private and public information are perfect substitutes. BPX do not

examine the effect of overall precision or dissemination of information on cost of equity capital, nor do

they examine the impact of composition in tandem with precision or dissemination.

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EHO test the hypothesis put forward in EO regarding the composition of information. Consistent with

the EO model, EHO document a strong positive association between realized returns, their proxy for the

cost of equity capital, and PIN, their proxy for the fraction of information that is private. But, prior

research suggests that realized returns are not a powerful proxy for cost of equity capital when sample

size is limited in large part because “information about future cash flows is the dominant factor driving

firm-level stock returns” (Voulteenaho (2002)).

This may explain why EHO find no association between cost of equity capital and beta and book-to-

price and a positive association with firm size. Moreover, EHO’s PIN proxy for composition might also

capture dissemination. This is a significant issue because composition and dissemination have opposite

effects on cost of equity capital in the EO model. Finally, EHO focus on one information attribute –

composition. If composition, dissemination and/or precision are correlated, including one attribute in the

analysis without controlling for the other attributes may result in a correlated omitted variables bias.

Our study complements and extends existing research by (1) employing implied cost of equity capital

estimates in the analysis, (2) employing an alternative proxy for composition that is suggested by the EO

model, and (3) examining all three information attributes simultaneously.

3. Research design and empirical proxies

3.1. Empirical model

To examine the relationship between cost of equity capital and the composition, dissemination and

precision of information we estimate the following regression equation.

(1)

Where: rit = equity risk premium (i.e. cost of equity capital less the risk free rate) for firm i, year t. BETAit = market model beta for firm i, year t.

LGROWit = log of long range expected growth in earnings, year t.LMKVLit = log of market value of common equity for firm i, year t.BPit = book-to-price for firm i, year t.COMPOSit = percentage of total precision attributed to private information for firm i, year t.

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DISSEMit = percentage of trades by informed traders. PRECISit = total information precision for firm i, year t.

Based on the theory set forth in EO, we hypothesize that the coefficient on COMPOS (γ5) is positive,

and the coefficients on DISSEM (γ6) and PRECIS (γ7) are negative.

We include market beta, growth, firm size, and book-to-price in the analysis to control for other

sources of risk that could confound our analysis, and to validate our proxy for cost of equity capital. We

expect the coefficient on BETA to be positive since the Capital Asset Pricing Model indicates that cost of

equity capital is increasing in market beta.4 Beaver et al. (1970) argue that abnormal earnings streams

derived from growth opportunities are more risky and La Porta (1996) provides empirical evidence that

growth and risk are positively related. Accordingly we expect to observe a positive coefficient on

LGROW. Berk (1995) argues that, market value of equity (book-to-price) is inversely (positively)

associated with risk in general, and that cost of equity capital is negatively related to market value of

equity and positively related to book-to-price in an incomplete model of expected returns. Thus, we

expect the coefficient on LMKVL to be negative and the coefficient on BP to be positive. The procedures

we employ in estimating our variables are described in detail below.

3.2. Empirical proxies – cost of equity capital and control variables

3.2.1. Cost of equity capital (rDIVPREM and rPEGPREM)

The dependent variable in our model is the expected risk premium, or cost of equity capital net of the

risk free rate of interest. Botosan and Plumlee (2005) evaluate the construct validity of five popular

methods of estimating firm-specific cost of equity capital and find that the target price method and the

price-earnings-growth (PEG) method generate estimates (rDIVPREM and rPEGPREM, respectively), which are

consistently and predictably related to risk, while the alternative methods do not. Based on their results,

BP conclude that researchers requiring firm-specific estimates of expected cost of equity capital are

4 See Litner (1965), Mossin (1966) and Sharpe (1964).

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justified in using either rDIVPREM or rPEGPREM to proxy for cost of equity capital. To assess the robustness of

our results to the proxy employed, we estimate cost of equity capital using both methods.

The target price method estimates the internal rate of return that equates current stock price to the

present value of forecasted dividends and target price. It employs the short-horizon form of the dividend

discount formula given in equation (2). In this specification of the dividend discount model the forecasted

terminal value truncates the infinite series of future cash flows at the end of year 5.

(2)

Where: = price at time t=0 or t=5. rDIV = estimated cost of equity capital.

= the expectations operator.

= dividends per share, t=1 to 5.

The data and procedures we employ in estimating rDIV mirror those employed by Botosan and Plumlee

(2005). Dividend forecasts for the current fiscal year (i.e., t=1), the following fiscal year (i.e., t=2), the

long run (i.e., t=5), and maximum and minimum long-run target price estimates are collected from

forecasts published by Value Line during the third quarter of the calendar year. These data are collected

from the Value Line database, available in machine-readable form.

Value Line does not provide dividend forecasts for years 3 and 4. Accordingly, we assume linear

growth in dividends from year 2 to year 5, and interpolate between these years to generate dividend

forecasts for years 3 and 4. Forecasted target price is the 50th percentile of Value Line’s forecasted long-

run price range. Current stock price (P0) equals the stock price reported on CRSP on the Value Line

publication date or closest date thereafter within 3 days of publication.

We use the values for P0, E0[P5] and the E0[dt]’s (t=1 to 5) in a numerical approximation program that

identifies the annual firm-specific rDIV that equates the right and left-hand sides of the equation to within a

$0.005 difference between the actual- and fitted-value of P0.5 rDIVPREM is rDIV less the risk free rate of

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interest. We use the 5-year Treasury Constant Maturity Rate as of the end of the month in which the

expected cost of equity capital estimates are determined as our estimate of the risk free rate of interest.

We collect these data from the US Federal Reserve at www.federalreserve.gov.

The primary assumption underlying this method is that analysts’ forecasts of future dividends and

target prices accord with those of market participants. If this assumption is violated, the link between

current stock price and analysts’ forecasts of future cash flows is strained and the link between the

resulting estimates of cost of equity capital and the underlying construct is weakened. This mitigates

against finding results.

Since cost of equity capital is inherently unobservable and Botosan and Plumlee (2005) conclude that

the PEG method also produces estimates that behave as if they capture cross-sectional variation in cost of

equity capital, we triangulate our analysis by examining the estimates produced by the PEG method as

well. Accordingly, our second estimate of cost of equity capital is based on the formula below, drawn

from Easton (2004).

(3)

Where: rPEG = estimated cost of equity capital. E0 = the expectations operator.epst = earning per share at time t.

This formula is derived from a special case of the dividend discount model that assumes no changes in

abnormal earnings beyond the forecast horizon, and no dividend payments prior to the earnings forecasts.

Consistent with Botosan and Plumlee (2005), we use long-run earnings forecasts (eps5 and eps4) in place

of eps2 and eps1 in the above model for two reasons. First, in some instances eps2 is less than eps1, but in

no instance is eps5 less than eps4. Since we cannot solve the model if eps2 is less than eps1 using eps5 and

eps4 maximizes our sample size. Second, and more importantly, using long-run earnings forecasts

increases the likelihood that changes in abnormal earnings beyond the forecast horizon will equal zero.

rPEGPREM is rPEG less the risk free rate of interest.

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3.2.2 Market beta (BETA)

Market beta is estimated using the market model with a minimum of 30 out of 60 monthly returns and

a market index return equal to the value weighted NYSE/AMEX return. We obtain the data to estimate

BETA from CRSP. The estimation period for BETA ends on June 30th of the year cost of equity capital is

estimated.

3.2.3. Long-term growth in earnings (LGROW)

Our estimate of long-range growth in earnings is the 3-5 year annual rate of change in expected

earnings included in the Value Line database.6 We use a natural log transformation of the data to mitigate

skewness in the distribution of long- range growth in earnings.

3.2.4. Market value of equity (LMKVL)

We compute market value of equity by multiplying the number of common shares outstanding by

stock price at the quarter-end immediately prior to June 30th of the year cost of equity capital is estimated.

We draw these data from the quarterly Compustat tape. If these data are unavailable, we substitute the

market value of the firm reported on CRSP as of June 30th of the Value Line publication year. Market

value of equity is stated in millions of dollars. We use a natural log transformation of the data to mitigate

skewness in the distribution of market value of equity.

3.2.5. Book-to-price (BP)

We compute book-to-price by scaling the book value of the firm’s common equity by its market value.

Both the numerator and the denominator of the ratio are measured at the quarter-end immediately prior to

June 30th of the year cost of equity capital is estimated. We collect these data from the quarterly

Compustat tape. If these data are unavailable, we substitute data for the fiscal year-end immediately prior

to June 30th of the year cost of equity capital is estimated. These data are collected from the annual

Compustat tape.

3.3. Empirical proxies – attributes of information

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3.3.1. Composition

In the EO model, composition is measured by k, the fraction of stock k’s information set that is

private. We cannot observe k directly. However, it can be shown that k is equal to the precision of

private information divided by the sum of the precision of private and public information. In EO’s model

the precision of private information is given by kIkk, where k is the number of signals in the

information set and k is the precision of the distribution from which the public and private signals are

drawn. Further, the precision of public information is given by (1-k)Ikk. Accordingly, it is

straightforward to demonstrate that k equals the ratio of private precision to private plus public precision

as given by equation (4) below.

(4)

Our proxy for the fraction of information that is private (COMPOS) is based on equation (4). We

substitute the precision of private (PRIVATE) and public (PUBLIC) information measures derived by

Barron et al. (BKLS) (1998) for kIkk and (1-k)Ikk, respectively in equation (4). Accordingly,

COMPOS is given by equation (5) below.

(5)

3.3.2. Estimating PRIVATE and PUBLIC

BKLS demonstrate how observable properties of analysts’ forecasts (squared error in the mean

forecast, forecast dispersion and the number of analysts providing forecasts) can be used to infer

unobservable attributes of analysts’ information environment. In their analysis BKLS make the following

assumptions: (1) analysts observe a signal common to all analysts (i.e. the public signal); (2) each analyst

also observes a signal unique to the individual analyst (i.e. the private signal); and (3) analysts’ forecasts

of earnings are unbiased and are based only on their public and private signals.

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Given these assumptions, BKLS show how error in analysts’ public and private information sets is

reflected differently in the squared error in the mean forecast and forecast dispersion. Specifically, error

arising from analysts’ reliance on public information is fully reflected in the squared error in the mean

forecast, while idiosyncratic error arising from analysts’ reliance on private information is captured only

to the extent that it is not diversified away by the process of averaging across analysts. In contrast,

forecast dispersion reflects idiosyncratic error only. BKLS further demonstrate that when the precision of

private information is similar across analysts, squared error in the mean forecast and forecast dispersion

can be expressed as functions of the precision of public and private information.

With this structure in place, BKLS begin by defining observable variables (squared error in the mean

forecast and forecast dispersion) in terms of unobservable constructs (the precision of public and private

information). BKLS then reverse these relationships to solve for unobservable public and private

information precision in terms of the observable variables. The resulting formulas derived by BKLS for

the precision of public and private information are given by equations (6) and (7), respectively.

(6)

(7)

Where: SE = squared error in the mean forecast.

D = forecast dispersion.

N = number of forecasts.= mean forecast for firm i, quarter t.

Ait = actual earnings for firm i, quarter t.Fijt = analyst j’s forecast of earnings for firm i, quarter t.

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We estimate SE, D, and N quarterly using analysts’ most recent one-quarter-ahead forecasts of

quarterly earnings. We collect forecast and actual earnings data from IBES. A minimum of three

individual analysts must provide forecasts of earnings for a given firm-quarter for that firm-quarter to be

included in our sample. To obtain our final measures of the precision of public and private information,

we take a time-series average of the four successive quarterly values of PUBLIC and PRIVATE that

precede the third quarter of the calendar year in which rDIVPREM and rPEGPREM are estimated. This generates

an estimate of the average level of precision of public and private information for each firm, for each

year. Since PUBLIC and PRIVATE are, in theory, the inverse of the variance of analysts’ public and

private information signals, non-negative values of PUBLIC and PRIVATE are not meaningful.

Consistent with prior research, we limit our analyses to non-negative values of PUBLIC and PRIVATE.

Barron et al. (2002) conduct extensive analyses to investigate the sensitivity of their results to

violations of the BKLS assumptions with no impact on their conclusions. Venkataraman (2000) conducts

similar analyses, also with no impact on his conclusions. Moreover, the measures developed by BKLS are

employed in a number of prior empirical studies including Barron et al. (1999), Venkataraman (2000),

Botosan and Harris (2000), Barron et al. (2002), Byard (2001), Byard and Shaw (2002), and Botosan et

al. (2004). Accordingly, we believe that the BKLS assumptions are sufficiently descriptive to render the

BKLS measures useful in empirical research.

While the measures derived by BKLS use observable properties of analyst forecasts to assess the

underlying attributes of analysts’ information environment, Barron et al. (BHS) (2005) find that investors’

trade volume responses to quarterly earnings announcements are predictably associated with changes in

analysts’ information environment estimated with the BKLS measures. Thus, BHS conclude that the

BKLS measures are a good proxy for investors’ information environment with respect to a given firm. If

this assumption is not valid and the characteristics of analysts’ information environment differ from those

of investors, PUBLIC and PRIVATE represent noisy measures of the underlying constructs we seek to

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capture. While this measurement error may mitigate against finding results, we do not expect it to induce

bias.

3.3.2. Dissemination

We use the proportion of informed traders to total traders as our proxy for the fraction of investors

who are informed (DISSEM). We derive the inputs into DISSEM from the PIN measure developed in

Easley et al. (EKO) (1997). 7 EKO model a market maker’s beliefs as a function of α (the probability of an

information event), δ (the probability the new information is bad news), μ (the arrival rate of informed

traders), εb (the arrival rate of uninformed buyers), and εs (the arrival rate of uninformed sellers). In brief,

the EKO model interprets a normal level of buys and sells as uninformed trades, which allows for

estimates of the arrival rate of uninformed traders (εb and εs). Abnormal buy or sell order volume is

considered information-based trading and is used to estimate the arrival rate of informed traders (μ). The

number of days on which there is abnormal buys or sells is used to identify both the probability of an

information event (α) and the probability the news is bad (δ).

We estimate buys and sells using TAQ data and the Lee-Ready algorithm known as the tick test (Lee

and Ready (1991)). Then, using a maximum likelihood procedure, we estimate the parameters of the

model (α, δ, μ, εb, and εs) simultaneously. We use the estimates of μ, εb, and εs produced by this procedure

to compute our measure of dissemination.

Different researchers have adopted different methods to deal with the truncation error that arises when

one attempts to estimate the parameters of PIN with a large number of daily buys and sells. For example,

Easley et al. (2001) (EEOW) set the arrival rate of uninformed buyers and sellers equal to each other (i.e.

εb = εs = ε) and factor out a common factor to simplify the log likelihood function and mitigate the

problem. In contrast, Vega (2004) allows εb and εs to differ, but she alters the form of the log likelihood

7 In prior research, PIN is used as a proxy for the risk of information based trading (Easley et al. (1996a)), the

probability of information based trading (Easley et al. (1996b)), a measure of information asymmetry (Brown et al.

(2001)), and a measure of the composition of the information set (Easley et al. (2002)).

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function to mitigate truncation error. For completeness, we estimate the parameters using the empirical

methods employed by EKO, EEOW and Vega. Empirically, we find that the estimates from the three

methods are highly correlated (on average, the correlations exceed 0.70). We use the parameter estimates

from EEOW (2001) in equation (8) to estimate DISSEM, because the EEOW method results in the largest

number of observations.8

DISSEM = (8)

3.3.3. Precision

Our proxy for the overall precision of information for a given firm (PRECIS) is computed by

taking the sum of the PUBLIC and PRIVATE estimates described previously. Consistent with the notion

that PRECIS captures the quality of the overall information set, BKLS refer to this sum as a measure of

informedness.

4. Sample selection and descriptive statistics

4.1. Sample selection

Our sample consists of 3,896 firm/year observations from 1993-2003. Observations are included in the

sample if we have sufficient data from Value Line, IBES, Compustat, CRSP, and TAQ to estimate the

variables described above. The number of observations varies by year and increases across time except

for the last two years of the sample period where we lose more observations due to truncation error

because the number of daily buys and sells is larger in these years than in earlier years.

4.2. Descriptive statistics

Table I provides descriptive statistics pertaining to our cost of capital estimates and independent

variables. We compute our descriptive statistics using all observations in our sample pooled across the

years 1993-2003. The mean (median) values of our estimates of the risk premium are 9.2% (7.8%) for

rDIVPREM and 5.7% (4.9%) for rPEGPREM. In comparison, Botosan and Plumlee (2005) employ a sample

spanning 1983 through 1993 and estimate mean (median) values of 6.4% (5.7%) for rDIVPREM and 5.0%

18

(4.4%) for rPEGPREM. Our rDIVPREM estimates exceed those reported in BP because we use the 50th percentile

of Value Line’s forecasted long-run price range whereas BP use the 25th percentile.9

Mean (median) BETA for our sample is approximately 1.02 (0.94). These data indicate that our

average (median) sample firm presents a level of market risk slightly greater (lower) than that of the

market portfolio. Mean (median) expected long-term growth in earnings (GROW) is 14.2% (12.3%).

These growth statistics are similar, albeit lower, than the 15.1% mean and 13.7% median long-term

growth in IBES earnings documented by Gode and Mohanram (2003) for an earlier time period. Mean

MKVL is $6893.8 million; the median is $1915.8 million, which indicates a sample populated by

relatively large firms and a skewed distribution. Mean (median) book-to-price (BP) equals 0.47 (0.41),

indicating that our sample is characterized by firms trading at a substantial premium above book value.

This is consistent with the relatively high rate of growth noted earlier.

COMPOS is 0.21 at the mean (0.05 at the median), suggesting that approximately 21% of the

information set for our average sample firm is comprised of private information. The interquartile range

of COMPOS is large, ranging from 0.00 at the 25th percentile to 0.36 at the 75th percentile. DISSEM has a

mean (median) value of 0.31 (0.30), which suggests that the average firm has approximately 31%

informed traders. Based on data presented graphically in Easley et al. (EHO) (2002), we estimate that in

the final year of their sample period (i.e. 1998), EHO’s mean values of μ, εb, and εs, are approximately

52%, 48% and 46%, respectively, suggesting a value of DISSEM of approximately 36%. This value lies

within the interquartile range of our data, which is approximately 24% at the 25th percentile and 37% at

the 75th percentile.10 Finally, the mean (median) value for PRECIS is 3296.8 (2166.9). The distribution of

PRECIS is skewed and has a large interquartile range – 684.8 at the 25th percentile and 5121.7 at the 75th

percentile. Consistent with prior empirical research employing the BKLS measures of the precision of

public and private information, we overcome the problem of skewness in the data by using the fractional

rank of PRECIS (RPRECIS) in our analysis.

19

Insert Table I here.

5. Empirical Results

5.1. Rank correlation among risk premium estimates and independent variables

Table II presents correlation statistics among our estimates of the risk premium and our independent

variables. To mitigate the impact of outlying observations we examine Spearman correlation coefficients.

The values reported in Table II represent the average of the year-by-year correlation coefficients across

the eleven years included in our sample. The values reported in parentheses are the number of years out of

the eleven sample years that the correlation between the variables is significantly positive/negative.

Consistent with prior research in this area, Table II documents a strong positive correlation between

rDIVPREM and rPEGPREM (0.68). This result indicates that these variables are related to the same underlying

construct. In addition, both rDIVPREM and rPEGPREM are positively correlated with the control variables

BETA, LGROW, and BP and negatively correlated with LMKVL. Similar to findings documented in

Botosan and Plumlee (2005), the correlation between rPEGPREM and the control variables is stronger than

with rDIVPREM, although the signs are the same. The correlations we document are consistent with theory

and suggest that our proxies capture required returns.

The univariate correlations between rDIVPREM and rPEGPREM and COMPOS are positive, as expected.

COMPOS is positively related to rDIVPREM in nine of eleven years and to rPEGPREM in eight years. The

univariate correlation between rDIVPREM and rPEGPREM and DISSEM is positive, which is contrary to our

expectations. However, DISSEM is highly negatively correlated with firm size, which is itself negatively

correlated with cost of equity capital, making it difficult to disentangle the effects using univariate

analysis. Finally, the univariate correlations between RPRECIS and rDIVPREM and rPEGPREM are negative as

expected. RPRECIS is significantly negatively related to rDIVPREM in four years and to rPEGPREM in nine

sample years.

20

Among our explanatory variables of interest we find that COMPOS is negatively related to RPRECIS

(ρ= - 0.359). This is not surprising given the manner in which the variables are computed. COMPOS is

positively related to DISSEM (ρ=0.127), which suggests that when a greater proportion of the

information set is private, private information is held by a greater proportion of the investor set. Finally,

there is a negative correlation between RPRECIS and DISSEM, which suggests that firms with less

precise information tend to have a greater proportion of informed investors.

All three of our explanatory variables, COMPOS, DISSEM and RPRECIS, are correlated with

LMKVL and BP, but we document a particularly strong correlation between DISSEM and LMKVL (ρ= -

0.793). This latter finding is consistent with prior research employing PIN (e.g., Easley et al. (2002) and

Brown et al. (2001)). The strength of this relationship raises the possibility of multicollinearity, which

could hamper our ability to document statistically significant results. In addition, DISSEM is positively

correlated with LGROW in nine of our eleven sample years.

In summary, our univariate correlation results provide support for the following preliminary

conclusions. First, rDIVPREM and rPEGPREM perform well in capturing cross-sectional variation in risk. Second,

we find evidence that cost of equity capital is related to the composition and precision of information, as

predicted by the EO model, but no evidence of the anticipated negative association between cost of equity

capital and dissemination. However, significant correlations among the explanatory and control variables

emphasize the need to examine the relationship between cost of equity capital and the attributes of

information in a multivariate setting.

Insert Table II here.

5.2. Regression of expected cost of equity on control variables and information attributes

Table III presents the results of estimating regression equation (1). Panel A reports the results with

rDIVPREM as the dependent variable. The parameter values reported in the table are the average parameter

values from eleven annual regressions with adjusted Fama-MacBeth t-statistics shown in parentheses. In

21

computing the t-statistics, we weight the coefficients by the square root of the annual sample size to

adjust for differences in the number of observations per year, and we adjust for autocorrelation in the

annual coefficients based on an AR(1) autocorrelation structure by multiplying the standard errors by an

adjustment factor, , where n is the number of years (11) and is the first-order

autocorrelation of the annual coefficient estimates (Abarbanell and Bernard, 2000).

The association between rDIVPREM and each of the control variables is consistent with our expectations.

Specifically, rDIVPREM is increasing in market beta and growth, and decreasing in market value of equity.

The coefficient on book-to-price is not statistically significant when LMKVL is included in the regression

equation, but it is significantly positive when LMKVL is removed from the analysis. These findings are

consistent with BP and LMKVL serving a similar role in the regression equation – that of capturing risk

in general when included in an incomplete model of expected returns.

rDIVPREM is increasing in COMPOS (coefficient of 0.007) and decreasing in DISSEM (coefficient of –

0.121) and RPRECIS (coefficient of – 0.010). Each of the coefficients is statistically significant at a p-

value less than 5%. These results suggest that cost of equity capital is higher when a greater proportion of

the information about a firm is private, but lower when private information is more widely disseminated

across investors and when the information set is more precise. In results not tabled, we document a 7.6%

increase in the overall explanatory power of the regression when COMPOS, DISSEM, and PRECIS are

added to the model.

Panel B reports our results from estimating the regression equation with rPEGPREM as the dependent

variable. These results are similar to those reported in panel A – COMPOS, DISSEM, and RPRECIS as

well as the control variables are related to rPEGPREM as predicted.

In summary, our results support the predictions drawn by EO from their model in three respects. First,

all else equal, firms with a higher proportion of private information face a higher cost of equity capital.

Second, all else equal, firms enjoy a lower cost of equity capital when private information is more widely

22

disseminated across investors. Finally, firms with greater overall information precision also enjoy a lower

cost of equity capital.

6. Conclusion

We test three hypotheses related to the impact of information attributes on the cost of equity capital as

suggested by the model developed in Easley and O’Hara (2004). According to EO’s model (1) firms with

a greater proportion of private information face a higher cost of equity capital; (2) firms with more widely

disperse private information face a lower cost of equity capital; and (3) firms with greater information

precision also face a lower cost of equity capital. We regress two alternative measures of expected cost of

equity capital on proxies for these three information attributes and document results consistent with all

three hypotheses.

Our results suggest that managers might take actions that impact the composition, dissemination and

precision of their firm’s information set to achieve a lower cost of equity capital. For example, managers

might realize cost of equity capital benefits by providing greater public disclosure to reduce the share of

the information set that is private. Alternatively, managers might hold conference calls, host road-shows,

increase the transparency and availability of their disclosures, or take other actions to reduce investors’

information acquisition and processing costs and encourage greater dissemination of private information.

Finally, managers might achieve cost of equity capital benefits by choosing accounting policies and

disclosure practices that increase the overall precision of information.

A key assumption underlying much of the existing theoretical research that relates information to cost

of equity capital is that the precision of public information and the precision of private information are

inversely related. Even so, a relatively early stream of research suggests that some types of public

disclosure might generate private information (see Barron et al. (2005), and Botosan et al. (2004)). These

early findings are important because an inverse relationship is critical to managers’ ability to favorably

impact their cost of equity capital through greater public disclosure. In the absence of such a relationship,

23

the identification of a firm’s optimal disclosure policy is a much more complex problem than suggested

by the results presented herein. Given the important role cost of equity capital plays in the allocation of

resources among firms in the economy and among projects within a firm, additional research focused on

this issue is warranted.

24

Table 1Descriptive statistics for the period 1993-2003a

Variable Mean Std. Dev. 25%

50% 75%

rDIVPREM 0.092 0.082 0.037 0.078 0.128rPEGPREM 0.057 0.043 0.032 0.049 0.072BETA 1.020 0.557 0.666 0.943 1.275GROW 0.142 0.084 0.096 0.123 0.162MKVL 6893.8 19571.0 792.9 1915.8 5131.1BP 0.465 0.355 0.259 0.407 0.593COMPOS 0.208 0.279 0.000 0.054 0.360DISSEM 0.311 0.065 0.238 0.302 0.374PRECIS 3296.8 3142.0 684.8 2166.9 5121.7

a rDIVPREM is the estimated risk premium based on the target price method (BP 2005). rPEGPREM is the estimated risk premium based on the PEG method (Easton 2004). BETA is capital market beta estimated via the market model with a minimum of 30 monthly returns over the 60 months prior to June 30th of the year expected cost of equity capital is estimated using a value weighted NYSE/AMEX market index return. GROW is the Value Line long-range earnings growth forecasts. MKVL is the market value of equity as of the most recent quarter prior to the date cost of equity is calculated, stated in millions of dollars. BP is the book value of common equity scaled by the market value of common equity, both measured at the end of the most recent quarter prior to June 30th of the year cost of equity capital is estimated. COMPOS is the proportion of overall precision attributed to private information measured as PRIVATE/(PUBLIC + PRIVATE), where PUBLIC is the precision of analysts’ public information set and PRIVATE is the precision of analysts’ private information set, both based on the BKLS method. DISSEM is the dissemination of private information across traders measured the number of informed traders (μ), scaled by the sum of the informed and uninformed traders (μ+2), drawn from the calculation of PIN (EEOW (2001)). PRECIS is total information precision calculated as PUBLIC + PRIVATE. The table contains means, medians, 25th percentiles, 75th percentiles, and standard deviations of the variables included in the regressions for the 3,896 firm-year observations from 1993-2003. All statistics are calculated from the sample pooled across 11 years.

25

Table 2Average cross-sectional correlations of firm characteristics

rDIVPREM rPEGPREM BETA LGROW LMKVL BP COMPOS DISSEMrPEGPREM 0.682

(11/0)1.00

BETA 0.144(8/0)

0.279(11/0)

1.000

LGROW 0.287(11/0)

0.653(11/0)

0.316(11/0)

1.000

LMKVL -0.231(0/11)

-0.321(0/11)

-0.046(0/3)

-0.134(0/8)

1.000

BP 0.135(9/0)

0.237(11/0)

-0.075(0/4)

-0.108(0/7)

-0.365(0/11)

1.00

COMPOS 0.117(9/0)

0.146(8/0)

-0.062(1/4)

-0.025(3/3)

-0.187(0/7)

0.267(10/0)

1.00

DISSEM 0.090(10/0)

0.171(10/0)

0.083(2/0)

0.119(9/0)

-0.793(0/11)

0.239(8/0)

0.127(6/0)

1.00

RPRECIS -0.068(0/4)

-0.121(0/9)

0.042(3/0)

0.038(3/0)

0.180(7/0)

-0.291(0/10)

-0.359(0/11)

-0.115(0/6)

a rDIVPREM is the estimated risk premium based on the target price method (BP 2005). rPEGPREM is the estimated risk premium based on the PEG method (Easton 2004). BETA is capital market beta estimated via the market model with a minimum of 30 monthly returns over the 60 months prior to June 30th of the year expected cost of equity capital is estimated using a value weighted NYSE/AMEX market index return. GROW is the Value Line long-range earnings growth forecasts. MKVL is the market value of equity as of the most recent quarter prior to the date cost of equity is calculated, stated in millions of dollars. BP is the book value of common equity scaled by the market value of common equity, both measured at the end of the most recent quarter prior to June 30th of the year cost of equity capital is estimated. COMPOS is the proportion of overall precision attributed to private information measured as PRIVATE/(PUBLIC + PRIVATE), where PUBLIC is the precision of analysts’ public information set and PRIVATE is the precision of analysts’ private information set, both based on the BKLS method. DISSEM is the dissemination of private information across traders measured the number of informed traders (μ), scaled by the sum of the informed and uninformed traders (μ+2), drawn from the calculation of PIN (EEOW (2001)). PRECIS is total information precision calculated as PUBLIC + PRIVATE. The table contains the time-series means of annual bivariate rank correlations of the variables included in the regressions for the 3,896 firm-year observations from 1993-2003. The numbers in parentheses are the number of years (out of eleven) that the annual correlation coefficient is significantly positive/negative.

26

Table 3Time-series averages of the coefficients in 11 annual cross-sectional regressions (1993-2003).

Panel A: Regressions using rDIVPREM (estimated risk premium based on the target price method) as the proxy for risk.

BETA(+)

LGROW(+)

LMKVL(-)

BP(+)

COMPOS(+)

DISSEM(-)

RPRECIS(-)

Avg. Adj. R2

0.017(4.56)**

0.037(9.76)**

-0.018(-3.40)**

0.007(0.88)

0.007(2.17)*

-0.121(-2.96)**

-0.010(-3.69)**

21.0%

Panel B: Regressions using rPEGPREM (estimated risk premium based on the PEG method) as the proxy for risk.

BETA(+)

LGROW(+)

LMKVL(-)

BP(+)

COMPOS(+)

DISSEM(-)

RPRECIS(-)

Avg. Adj. R2

0.006(3.95)**

0.049(10.85)**

-0.006(-3.74)**

0.022(3.97)**

0.007(5.57)**

-0.038(-2.98)**

-0.014(-3.25)**

59.2%

The sample includes 3,896 firm-year observations from 1993-2003. The t-statistics are based on the standard error of the weighted coefficient estimates across the 11 years (Fama and MacBeth 1973). In calculating the t-statistics, the coefficients are weighted by the square root of the annual sample size to adjust for differences in the number of observations on a year-by-year basis and adjusted for autocorrelation in the annual coefficients

based on an AR(1) autocorrelation structure. Standard errors are multiplied by an adjustment factor, , where n is the number

of years (11) and is the first-order autocorrelation of the annual coefficient estimates (Abarbanell and Bernard, 2000). The dependent variable in Panel A is the estimated risk premium based on the target price method (BP 2005) (rDIVPREM). The dependent variable in Panel B is the estimated risk premium based on the PEG method (Easton 2004) (rPEGPREM). BETA is capital market beta estimated via the market model with a minimum of 30 monthly returns over the 60 months prior to June 30th of the year expected cost of equity capital is estimated using a value weighted NYSE/AMEX market index return. LGROW is natural log of the Value Line long-range earnings growth forecasts. LMKVL is the natural log of the market value of equity as of the most recent quarter prior to the date cost of equity is calculated. BP is the book value of common equity scaled by the market value of common equity, both measured at the end of the most recent quarter prior to June 30th of the year cost of equity capital is estimated. COMPOS is the proportion of overall precision attributed to private information measured as PRIVATE/(PUBLIC + PRIVATE), where PUBLIC is the precision of analysts’ public information set and PRIVATE is the precision of analysts’ private information set, both based on the BKLS method. DISSEM is the dissemination of private information across traders measured the number of informed traders (μ), scaled by the sum of the informed and uninformed traders (μ+2), drawn from the calculation of PIN (EEOW (2001)). RPRECIS is the fractional rank of total information precision calculated as PUBLIC + PRIVATE. T-values are given in parentheses.** (*) denotes significant at the 0.01 (0.05) level or better, < (1-tailed t-test).

27

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2 The figures quoted in the text are from the rPEGPREM regression. The corresponding figures from the rDIVPREM

regression are 7 basis points (for COMPOS), 121 basis points (for DISSEM), and 100 basis points (for RPRECIS).

5 We make appropriate adjustments for fractions of years and the portion of the current fiscal-year dividend forecast

distributed to investors prior to the forecast date. Botosan and Plumlee (2005) describe these adjustments in detail.

6 We eliminate 36 observations from our sample because long- range growth in earnings is in excess of 100%. In

each case, period two forecasted earnings per share is small and negative and the long-range earnings per share is

relatively large and positive. Our conclusions are not altered if these observations are included in our analyses,

although we ultimately eliminate several of the 36 observations as they are influential observations in the

regressions.

8 The form of the log likelihood function we estimate is given in EEOW (2001). It is

9 BP estimate rDIV using three alternative points in the target price range (the 50th percentile, the 25th percentile, and

the minimum value) and find their results are robust to all. BP employ rDIV estimated with the 25th percentile value in

their primary tests to reduce the magnitude of the average estimate; we employ the 50th percentile because doing so

maximizes our sample size.

3 EO also conclude that the existence of some information (even if it is all private) yields a lower cost of equity

capital than no information at all. We do not investigate the fourth prediction since some information exists for all of

the firms included in our analysis.

10 Mean (median) values for μ and (the components of DISSEM) are 88.7 (60.1) and 128.5 (67.5), respectively.

These values are greater than the mean values documented in Brown et al. (2001) (mean μ = 34.5 and mean =46.9)

and Easley, et al. (2002) (mean μ = 31.1 and mean =24.0). Our higher values are consistent with our estimation

31

method, which truncates observations with a large number of buys and sells to a lesser extent, and with a more

recent sample period characterized by greater trade volume. Our sample period ends in 2003, while the Brown et al.

and Easley et al. sample periods end in 1996 and 1998, respectively.

32