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Are Information Attributes Priced?


                                        Christine A. Botosan*
                       ...
Are Information Attributes Priced?



Abstract

        Easley and O’Hara (EO) (2004) model the impact of information attr...
1. Introduction



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

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

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

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

informed. Trad...
With respect to the overall precision of            information, EO demonstrate that greater precision

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

(2004), and Mikhail...
This may explain why EHO find no association between cost of equity capital and beta and book-to-

price and a positive as...
derived from growth opportunities are more risky                 and La Porta (1996) provides empirical evidence

that gro...
E0 (  ) = the expectations operator.
             d t = dividends per share, t=1 to 5.


   The data and procedures we em...
equity capital, we triangulate our analysis by           examining the estimates produced by the PEG

method as well. Acco...
We compute market value of equity by                multiplying the number of common shares

outstanding by stock price at...
α k I kγ k
   αk =                                                                                                (4)
    ...
information). BKLS then reverse these relationships to solve for unobservable public and private

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

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

information event ...
Our sample consists of 3,896 firm/year              observations from 1993-2003. Observations are

included in the sample ...
informed traders. Based on data presented                graphically in Easley et al. (EHO) (2002), we

estimate that in t...
The univariate correlations between rDIVPREM and rPEGPREM and COMPOS are positive, as expected.

COMPOS is positively rela...
emphasize the need to examine the relationship                 between cost of equity capital and the attributes of

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

are added to the model...
Finally, managers might achieve cost of equity         capital benefits by choosing accounting policies and

disclosure pr...
Table 1
Descriptive statistics for the period 1993-2003a

    Variable                    Mean            Std. Dev.       ...
Table 2
Average cross-sectional correlations of firm characteristics
                       rDIVPREM          rPEGPREM    ...
Table 3
Time-series averages of the coefficients in 11 annual cross-sectional regressions (1993-2003).
   Panel A: Regress...
REFERENCES
   Abarbanell, J., and V.L. Bernard, 2000, Is the U.S. Stock Market Myopic? Journal of Accounting
Research 38, ...
Easley, D., and M. O’Hara, 2004. Information and the cost of capital. Journal of Finance 59,
1552-1583.

   ________, Engl...
Lee, C.M., and M. Ready, 1991. Inferring trade direction from intraday data. Journal of Finance 46,
733-746.

  Leuz, C., ...
30
1
    For other research that examines possible proxies for expected cost of equity capital see Botosan (1997), Gebhardt e...
and 1998, respectively.
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Marlene A. Plumlee* a

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Marlene A. Plumlee* a

  1. 1. Are Information Attributes Priced? Christine A. Botosan* Associate Professor of Accounting C. Roland Christensen Faculty Fellow Email: actcb@business.utah.edu Marlene A. Plumlee* a Associate Professor of Accounting Email: actmp@business.utah.edu *David Eccles School of Business University of Utah Salt Lake City, UT 84112 a 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.
  2. 2. 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.
  3. 3. 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 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). 3
  4. 4. 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 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 4
  5. 5. 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 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 5
  6. 6. 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 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. 6
  7. 7. 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 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 7
  8. 8. 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. 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)). 8
  9. 9. 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. rit = α 0 + γ 1 BETAit + γ 2 LGROWit + γ 3 LMKVLit + γ 4 BPit + (1) + γ 5COMPOSit + γ 6 DISSEM it + γ 7 PRECISit + ε it 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. 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 9
  10. 10. 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 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. 5 P0 = ∑ (1 + rDIV ) − t E0 [ dt ] + (1 + rDIV ) − 5 E0 ( P5 ) (2) t =1 Where: Pt = price at time t=0 or t=5. rDIV = estimated cost of equity capital. 10
  11. 11. E0 (  ) = the expectations operator. d t = 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 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 11
  12. 12. 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). E0 ( eps2 ) − E0 ( eps1 ) rPEG = (3) P0 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. 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) 12
  13. 13. 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 3.3.1. Composition In the EO model, composition is measured by αk, the fraction of stock k’s information set that is private. We cannot observe αk directly. However, it can be shown that αk 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 αkIkγk, where Ιk is the number of signals in the information set and γk 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-αk)Ikγk. Accordingly, it is straightforward to demonstrate that αk equals the ratio of private precision to private plus public precision as given by equation (4) below. 13
  14. 14. α k I kγ k αk = (4) α k I k γ k + (1 − α k ) I k γ k 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 αkIkγk and (1-αk)Ikγk, respectively in equation (4). Accordingly, COMPOS is given by equation (5) below. PRIVATEit COMPOSit = (5) PUBLICit + PRIVATEit 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. 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 14
  15. 15. 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.  D  SE −  PUBLIC =  N 2 (6)  D   SE − N  + D     D PRIVATE = 2  D  (7)  SE − N  + D     Where: SE = squared error in the mean forecast. = ( Fit − Ait ) 2 D = forecast dispersion. 2 ∑ ( Fit − Fijt ) 1 N = N − 1 i =1 N = number of forecasts. Fit = 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. 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. 15
  16. 16. 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 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 16
  17. 17. 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 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 µ DISSEM = (8) µ + 2ε 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 17
  18. 18. 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% (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% 18
  19. 19. 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. 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. 19
  20. 20. 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. 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 20
  21. 21. 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 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 (1 + φ ) 2φ (1 − φ n ) adjustment factor, − , where n is the number of years (11) and φ is the first-order (1 − φ ) n(1 − φ ) 2 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% 21
  22. 22. 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 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. 22
  23. 23. 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, 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. 23
  24. 24. Table 1 Descriptive statistics for the period 1993-2003a Variable Mean Std. Dev. 25% 50% 75% rDIVPREM 0.092 0.082 0.037 0.078 0.128 rPEGPREM 0.057 0.043 0.032 0.049 0.072 BETA 1.020 0.557 0.666 0.943 1.275 GROW 0.142 0.084 0.096 0.123 0.162 MKVL 6893.8 19571.0 792.9 1915.8 5131.1 BP 0.465 0.355 0.259 0.407 0.593 COMPOS 0.208 0.279 0.000 0.054 0.360 DISSEM 0.311 0.065 0.238 0.302 0.374 PRECIS 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+2ε), 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. 24
  25. 25. Table 2 Average cross-sectional correlations of firm characteristics rDIVPREM rPEGPREM BETA LGROW LMKVL BP COMPOS DISSEM rPEGPREM 0.682 1.00 (11/0) BETA 0.144 0.279 1.000 (8/0) (11/0) LGROW 0.287 0.653 0.316 1.000 (11/0) (11/0) (11/0) LMKVL -0.231 -0.321 -0.046 -0.134 1.000 (0/11) (0/11) (0/3) (0/8) BP 0.135 0.237 -0.075 -0.108 -0.365 1.00 (9/0) (11/0) (0/4) (0/7) (0/11) COMPOS 0.117 0.146 -0.062 -0.025 -0.187 0.267 1.00 (9/0) (8/0) (1/4) (3/3) (0/7) (10/0) DISSEM 0.090 0.171 0.083 0.119 -0.793 0.239 0.127 1.00 (10/0) (10/0) (2/0) (9/0) (0/11) (8/0) (6/0) RPRECIS -0.068 -0.121 0.042 0.038 0.180 -0.291 -0.359 -0.115 (0/4) (0/9) (3/0) (3/0) (7/0) (0/10) (0/11) (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+2ε), 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. 25
  26. 26. Table 3 Time-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 0.037 -0.018 0.007 0.007 -0.121 -0.010 21.0% (4.56)** (9.76)** (-3.40)** (0.88) (2.17)* (-2.96)** (-3.69)** 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 0.049 -0.006 0.022 0.007 -0.038 -0.014 59.2% (3.95)** (10.85)** (-3.74)** (3.97)** (5.57)** (-2.98)** (-3.25)** 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 (1 + φ ) 2φ (1 − φ n ) based on an AR(1) autocorrelation structure. Standard errors are multiplied by an adjustment factor, − , where n is the number of (1 − φ ) n(1 − φ ) 2 years (11) and φ 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+2ε), 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). 26
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  30. 30. 30
  31. 31. 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). 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). 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. 4 See Litner (1965), Mossin (1966) and Sharpe (1964). 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. 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)). 8 The form of the log likelihood function we estimate is given in EEOW (2001). It is ( L({ y } T t t =1 )) Θ = ∑t =1[−2ε + M ln x + ( B + S ) ln(µ + ε )] T + ∑t =1 ln[α (1 −δ )e − µ x S − M + αδe − µ x B − M + (1 − α ) x B + S − M ] T 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. 10 Mean (median) values for μ and ε (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 ε=46.9) and Easley, et al. (2002) (mean μ = 31.1 and mean ε=24.0). Our higher values are consistent with our estimation 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
  32. 32. and 1998, respectively.

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