Comparable firms and the precision of equity valuations

Journal of Banking & Finance 25 (2001) 1367±1400 www.elsevier.com/locate/econbase

Comparable ®rms and the precision of equity valuations Allan C. Eberhart

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The McDonough School of Business, Georgetown University, 411 New North, Washington, DC 20057, USA Received 13 June 1999; accepted 16 February 2001

Abstract I investigate the relationship between the amount of information provided by a ®rm's comparables (i.e., ®rms in the same line of business as the ®rm being valued) and the precision of the ®rm's equity valuation. When investors have more information, previous studies argue that investors can make a more precise estimate of a ®rm's true equity value and this implies a lower (excess) stock return volatility around corporate events such as earnings announcements. I develop a simple model that shows a negative relationship between the amount of information provided by a ®rm's comparables and the ®rm's stock return volatility. Using alternative measures of information provided by comparables and di€erent de®nitions of comparables, I consistently ®nd a negative and signi®cant relationship between these information measures and stock return volatility, ceteris paribus. Ó 2001 Elsevier Science B.V. All rights reserved. JEL classi®cation: G30; G14 Keywords: Valuation; Corporate ®nance; Information

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Tel.: +1-202-687-4584; fax: +1-202-687-4031. E-mail address: [email protected] (A.C. Eberhart).

0378-4266/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 4 2 6 6 ( 0 1 ) 0 0 1 7 1 - 6

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1. Introduction Why are some stocks more precisely valued than others? Some scholars posit that when investors have more information about a stock, they can make a more precise estimate of its true value. For example, Atiase (1985) argues that there is more information on large ®rms and implies that this should increase the precision of their stock valuation. In support of this argument, he ®nds that large ®rms have a lower stock price reaction to earnings announcements than small ®rms. More information means the pre-announcement price of the stock more accurately forecasts the information contained in the announcement, ceteris paribus. Therefore, the announcement is less surprising and the stock price reaction to the announcement is reduced. Other information proxies besides size have been considered in the literature. For example, Barry and Brown (1984) propose the ®rm's period-of-listing (POL) as a proxy for the amount of information on the stock. They focus on the relationship between information and stock returns and ®nd that a longer POL is associated with lower returns after controlling for size, beta and interactive e€ects. 1 Their results suggest an inverse relationship between POL and the magnitude of stock price reactions to corporate announcements, ceteris paribus. The number of analysts following a ®rm has also been posited as a proxy for the amount of information on a stock (i.e., di€erential information across securities). For instance, Brennan et al. (1993) ®nd that stocks followed by many analysts react more quickly to common information than stocks followed by fewer analysts. I propose a new proxy for di€erential information that explains cross-sectional di€erences in the magnitude of security price reactions to corporate announcements beyond that previously suggested in the literature. This proxy follows from the regular use of comparables (i.e., ®rms in the same industry as the ®rm being valued) in stock valuation. For example, in a survey of investment ®rms, Carter and Van Auken (1990) report on the popularity of comparables' multiples in valuation. This technique can be as simple as multiplying the comparables' average price±earnings (PE) ratio times the ®rm's earnings to get an estimate of the ®rm's stock value. Besides the survey data cited above, everyday discussions of valuation in the popular press and valuation books attest to the popularity of using comparables' multiples in valuation. 2 Moreover, Kaplan and Ruback (1995) ®nd that, in their sample, the use of comparables' multiples is about as accurate as 1

Consistent with Barry and Brown's results, Clarkson and Thompson (1990) ®nd that the betas for IPO ®rms decline signi®cantly as time passes and information increases. In particular, there is an abrupt decline in betas after the ®rst earnings announcement. 2 Other popular multiples include book-to-market, price-to-cash ¯ow, etc. (see Damodaran, 1994).

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discounted cash ¯ow (DCF) analysis. Kim and Ritter (1999) examine the usefulness of multiples for IPO valuation and report that PE multiples with forecasted earnings provide more accurate valuations than multiples using trailing earnings. Comparables are also useful in DCF analysis, however. For example, the betas of comparables can be used to estimate a ®rm's cost of capital (Fuller and Kerr, 1981). Therefore, comparables are useful with a variety of valuation techniques. 3 The importance of comparables in valuation is also revealed in studies that document a contagion e€ect, where an announcement a€ecting the value of one ®rm in an industry is shown to a€ect the value of other (comparable/competitor) ®rms in the same industry. For example, Lang and Stulz (1992) ®nd that bankruptcy announcements reduce the stock value of the ®rm announcing bankruptcy and the value of its competitors. Fenn and Cole (1994) report that the announcement of an insurance company writing down the value of its bond portfolio decreases its stock value and the value of its competitors. As a result of the support for contagion e€ects and the prominent role of comparables in valuation, I argue that comparables comprise a signi®cant portion of the information investors use to value a stock. One simple measure of how much information comparables provide is the number of comparables. Ceteris paribus, more comparables suggests there is more information on the stock. Using the number of comparables as a di€erential information proxy is analogous to using the number of analysts and both measures may be needed to capture the various facets of di€erential information. The correlations from my sample, however, show that the number of analysts is more highly correlated with variables that represent more information on the stock (such as size and period-of-listing) than the number of comparables and tends to have a larger negative correlation with measures of the stock's intrinsic risk (such as the ®rm's debt ratio and the volatility of its return on assets). Therefore, the number of analysts may be at least partly re¯ecting the e€ect of other proxies for di€erential information or estimates of the stock's intrinsic risk. In fact, Bhushan (1989) argues that analysts may be attracted to high volatility stocks. To determine if more comparables imply more information, I examine the relationship between the number of comparables and the magnitude of stock price reactions to earnings announcements. I use the excess stock return volatility for the 21-day period surrounding the earnings announcement as the measure of the magnitude of stock price reactions to these announcements. 4 As with Atiase's (1985) ®nding that large ®rms have a smaller reaction, there 3 Gilson et al. (2000) use comparable ®rms' multiples and betas to estimate the value of ®rms emerging from bankruptcy. 4 To be succinct, I use the term volatility interchangeably with the term excess stock return volatility.

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should be a negative relationship between the number of comparables and the stock price reaction to earnings announcements if more comparables imply more information. I also develop a simple model in Appendix A that shows, ceteris paribus, a negative relationship between the number of comparables and excess stock return volatility (resulting from the greater information more comparables provide). The negative relationship illustrated in the model is in a general one-period framework and is not restricted to earnings announcement tests. Therefore, I perform additional tests on the relationship between the number of comparables and volatility measured each month (i.e., the monthly volatility tests). To mitigate the possibility of ®nding a negative relationship between the number of comparables and volatility merely because ®rms with more comparables tend to have lower intrinsic risk, I include control variables for each sample ®rm's business risk, ®nancial risk and its industry structure. Moreover, because previous studies (e.g., Karpo€, 1987) report a positive relationship between volatility and trading volume, I include trading volume as an additional control variable. I also include the information proxies discussed above (i.e., size, POL and number of analysts) to see if the number of comparables provides additional information beyond that contained in these established proxies for di€erential information. 5 Besides these primary control variables, I include some other control variables to mitigate further the possibility that the number of comparables is correlated with some other factor(s) that reduces volatility. I include the ®rm's dividend yield as an additional control variable because ®rms with higher dividend yields may have less risk; of course, a high dividend yield does not cause the ®rm's risk to be lower but less risky ®rms may choose a high dividend yield and this lower risk may not be captured by the main control variables. In the earnings announcements tests, I also control for the analysts' earnings forecast error, the standard deviation of the analysts' forecasts, the ®rm's market-to-book ratio and the existence of previous earnings announcements in the same quarter by a ®rm's comparables. Of course, despite these e€orts, I cannot rule out the possibility that there is some other factor I should control for but this is a common problem among empirical studies and I have more control variables than previous studies in this area. 6 After accounting for the possible confounding e€ects discussed above, I consistently ®nd a signi®cantly negative relationship between the number of 5 The studies cited above use POL and the number of analysts as information proxies in the context of di€erent tests (POL is shown to have a negative relationship with returns and number of analysts has a negative relationship with the speed of reaction to common information) but I include them in my tests because they are established as information proxies. 6 I thank one of the referees for suggesting these additional control variables and this caveat about the possibility of not having a complete list of control variables.

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comparables and the volatility around earnings announcements. I also ®nd a signi®cantly negative relationship between the number of comparables and volatility measured each month, ceteris paribus. In contrast, the number of analysts is generally positively related to the volatility around earnings announcements and to the volatility measured each month. The other primary control variables are generally signi®cant and have a sign consistent with ®nancial theory or the ®ndings of previous studies. I de®ne comparable ®rms as those with the same primary 4-digit SIC code. To test the robustness of the results to an alternative industry de®nition, I use the Value Line (Investment Survey) industry de®nition. To gauge the robustness of the results to a di€erent measure of the amount of information provided by comparable ®rms, I develop an alternative (to the number of comparables) measure that recognizes that some comparables are more similar to the ®rm being valued than others and may provide more information. In other words, it is possible that one comparable ®rm that is highly similar to the ®rm being valued can provide more information than several comparables that are relatively dissimilar to the ®rm being valued. To account for this possibility, I develop an index of the amount of information provided by comparables called the degree of comparability (DOC) in Appendix A. When the comparables are highly similar to the ®rm being valued the DOC is higher and this implies that more information is provided by the comparables. The model I present in Appendix A shows a negative relationship between volatility and DOC, ceteris paribus. I consistently ®nd a highly signi®cant negative relationship between the volatility around earnings announcements and the number of comparables based on the Value Line industry de®nitions, ceteris paribus; the DOC measure has a similarly negative relationship (using the SIC code or the Value Line industry de®nitions). I also ®nd a signi®cantly negative relationship between the volatility measured each month and DOC (again, using the SIC code or the Value Line industry de®nitions) and with the number of comparables based on the Value Line industry de®nitions. The results in this paper are important for four reasons. First, this paper's explanation for cross-sectional di€erences in volatility beyond that provided in the literature has important implications for why some stocks' options are more valuable than others. Second, because some studies argue that di€erential information a€ects expected returns (e.g., Barry and Brown, 1984; Merton, 1987), the results in this paper may help explain di€erences in expected returns across securities (even though my focus is on volatility). Third, the number of analysts has been a popular proxy for di€erential information and the results in this study suggest that, after controlling for other factors (including the number of comparables or DOC), this variable may not be a good proxy. Finally, though the usefulness of comparable ®rms in valuation has been recognized, their signi®cance has not been fully investigated; the results in this paper highlight the importance of comparables in valuation.

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In Section 2, I discuss the data and methods. In Section 3, I analyze the empirical results and the summary and conclusions are presented in Section 4. 2. Data and methods 2.1. Data The initial sample consists of ®rms listed in both the Compustat ®les and the Center for Research in Security Prices (CRSP) daily NYSE/Amex and Nasdaq ®les anytime during 1986±1995. As in Kaplan and Ruback (1995) (among others), each ®rm must meet a minimum size requirement; in my sample, the ®rm must have sales of at least $100 million in 1986 dollars to be included in the count of comparable ®rms. To be included in the ®nal sample for the volatility tests, each ®rm must also have at least ®ve years of historical operating earnings and assets to measure the standard deviation of the ®rm's return on assets (where return on assets is earnings before interest and taxes divided by total assets). The ®rm also cannot have a missing value for total interestbearing debt (debt in current liabilities plus long-term debt). The ®nal sample consists of 2,890 ®rms with at least one observation in the tests. Descriptive statistics for the sample are provided in Table 1 using the average variables ± across time ± for each ®rm. Therefore, the sample size in Table 1 is the 2,890 ®rms with at least one observation in the tests and the descriptive statistics are the averages, medians and standard deviations across ®rms. In describing the measurement of each variable below, however, I will note whether it is measured monthly or annually. The number of comparables (N or NUMCOMP) using the SIC codes is computed at the beginning of each year and the average is 20.86 (median ˆ 11) with a standard deviation of 24.35. 7 As shown in the following equation, the DOC measure I use is based on the similarity in size between the ®rm and its comparables:     Ni DOCi ˆ LN 1 ‡ ; …1† Ni where DOC ˆ 0 when N ˆ 0, and N  is  Ni  X 1  Ni ˆ ; ‰1 ‡ jSi Sj j=Savg Š jˆ1

…2†

7 The SIC code is from CRSP and re¯ects the ®rm's primary line of business as of each year of interest.

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Table 1 Descriptive statisticsa Variable

Mean

Median

S.D.

NUMCOMP DOC POL DR ROAVOL Equity TVOLUME ANAL ANAL0 HERFINDX DY

20.86 0.61 22.69 36.86% 12.88% $1,411,872,000 3.88 7.78 10.77 0.21 2.87%

11 0.62 20 33.50% 4% $341,379,500 2.73 4.42 8 0.16 1.94%

24.35 0.08 16.87 27% 8.60% $3,808,561 5.06 9.07 9.04 0.17 18.77%

a NUMCOMP is the number of comparables and DOC is the degree of comparability using the 4-digit SIC code. POL is the period-of-listing, or age of the ®rm as of the beginning of the year (measured in years). DR is the book value of total interest bearing debt (short-term and long-term) to the sum of the book value of debt plus the market value of equity. Equity is the total market value of equity. The underlying business risk of the ®rm is estimated with the volatility of the return on assets (ROAVOL). TVOLUME is the total number of shares traded during the month divided by shares outstanding. ANAL is the number of analysts that make an annual earnings forecast each month as reported in I/B/E/S; if the ®rm is not listed in I/B/E/S, then no analysts are presumed to follow the ®rm. ANAL0 has the same de®nition as the previous variable except that only ®rms with analysts following the ®rm (as reported by I/B/E/S) are included. HERFINDX is the sum of each ®rm's squared market share within the industry (4-digit SIC code). DY is the ®rm's annual dividend yield. The descriptive statistics are computed based on the average variables across time ± for each of the 2,890 ®rms in the sample.

where Si is the log of the equity value of ®rm i, Sj is the log of the equity value of comparable ®rm j and Savg is the industry average log equity value. The ratio …Ni =Ni † is an index of comparability between ®rm i and all its comparable ®rms. If every comparable ®rm j is the same size as ®rm i, then N  ˆ N ; more generally, the more similar the size of the comparables to ®rm i, the higher the ratio. As this ratio rises, I posit that more information is provided by comparables and the ®rm's volatility declines, ceteris paribus. Appendix A provides a more complete discussion of this variable. The DOC has an average of 0.61 (median ˆ 0.62). As suggested earlier, I also hand collect data from Value Line each year over the same period and use their industry codes to de®ne comparable ®rms. With this de®nition, the average number of comparables is 18.14 (median ˆ 16) and the average DOC is 0.63 (median ˆ 0.64). The POL (or age, de®ned as the number of years listed on CRSP) is measured at the beginning of each year and the average is 22.69 years (median ˆ 20 years). Firms' debt ratios (i.e., total interest-bearing debt divided by the sum of total interest-bearing debt and the market value of equity) average 36.86%, with a median ratio of 33.50%. The market value of equity is measured at the

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beginning of the year and the average value is $1,411,872,000 (median ˆ $341,379,500). As noted above, I estimate business risk with the standard deviation of the ®rm's return on assets (ROAVOL) using annual data from the preceding ®ve years. This variable is measured at the beginning of each year and has an average value of 12.88% and the median is 4%. Trading volume (TVOLUME) is measured by the total number of a ®rm's shares traded during the month divided by its outstanding shares. This variable has an average value of 3.88 times and a median of 2.73 times. I also perform all the tests using the total number of shares traded and ®nd qualitatively similar results. The number of analysts following a ®rm is taken from I/B/E/S. Analyst coverage averages 7.78 analysts (median ˆ 4.42) when ®rms not included in I/B/ E/S are presumed not to have any analysts following them (ANAL is the variable name for this sample). For the subsample of ®rms included in I/B/E/S, the average number of analysts (ANAL0 is the variable name for this sample) following a ®rm is 10.77 (median ˆ 8). Unless otherwise noted, the number of analysts is estimated by the number of annual earnings forecasts reported each month by I/B/E/S. I include a measure of industry concentration as another control variable because this may a€ect volatility beyond what is captured in the other variables. Following Lang and Stulz (1992), among others, I use the Her®ndahl±Hirschman index (HERFINDX) to measure industry concentration. The index is the sum of each ®rm's squared market share within the industry (4-digit SIC code) and it ranges from 0, the lowest level of concentration, to 1, the highest level of concentration. To the extent that greater industry concentration implies less competition, I expect a negative relationship between this variable and volatility because less competitive industries (as suggested by a high HERFINDX) can more easily ®x their product prices and this should reduce the ®rm's cash ¯ow volatility and consequently its (excess stock return) volatility, ceteris paribus. The HERFINDX is a popular measure of competition but it is imprecise and potentially biased as some highly concentrated industries are highly competitive and vice versa (Scherer and Ross, 1990). Therefore, the coecient sign may be positive or negative; I only include it to control for industry concentration and any associated competitive e€ects. The coecient estimates for NUMCOMP and DOC remain negative and highly signi®cant with or without the inclusion of this control variable in all the empirical tests. For my sample, the average HERFINDX is 0.21 and the median is 0.16. Besides the main control variables discussed above and shown in Tables 1 and 2, I examine some additional control variables, as noted in the introduction, to reduce the possibility that the NUMCOMP or DOC is not correlated with some other variable that makes stocks less volatile. I include the annual

Table 2 Correlation coecients for main explanatory variablesa

NUMCOMP

POL DR ROAVOL S TVOLUME ANAL ANAL0 HERFINDX DY a

DOC

POL

DR

ROAVOL

S

TVOLUME

ANAL

ANAL0

HERFINDX

DY

1

0.090 (0.000) 1

0.021 (0.005) )0.120 (0.000) 1

0.257 (0.000) )0.011 (0.532) )0.029 (0.000) 1

)0.003 (0.662) 0.026 (0.247) )0.009 (0.242) 0.021 (0.005) 1

0.206 (0.000) 0.001 (0.000) 0.382 (0.000) )0.315 (0.000) )0.209 (0.000) 1

)0.087 (0.000) 0.029 (0.155) )0.179 (0.000) )0.071 (0.000) 0.263 (0.000) 0.028 (0.172) 1

0.151 (0.000) )0.017 (0.329) 0.358 (0.000) )0.161 (0.000) )0.016 (0.000) 0.603 (0.000) 0.153 (0.000) 1

0.202 (0.000) )0.034 (0.132) 0.387 (0.000) )0.132 (0.000) )0.009 (0.319) 0.745 (0.000) (0.156 (0.000) 0.999 (0.000) 1

)0.535 (0.000) )0.414 (0.000) )0.004 (0.586) )0.123 (0.000) )0.002 (0.811) )0.106 (0.000) )0.070 (0.000) )0.106 (0.000) 0.142 (0.000) 1

0.069 (0.000) 0.080 (0.000) 0.107 (0.000) 0.083 (0.000) )0.081 (0.000) 0.036 (0.130) )0.095 (0.000) 0.010 (0.682) 0.017 (0.535) )0.013 (0.600) 1

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NUMCOMP is the number of comparables using the SIC 4-digit code and DOC is the degree of comparability using the 4-digit SIC codes. POL is the period-of-listing, or age of the ®rm as of the beginning of the year (measured in years). DR is the book value of total interest-bearing debt (short-term and long-term) to the sum of the book value of debt and the market value of equity. S is the log of the market value of equity. The underlying business risk of the ®rm is estimated with the volatility of the return on assets (ROAVOL). TVOLUME is the total number of shares traded during the month during the month divided by shares outstanding. ANAL is the number of analysts that make an annual earnings forecast each month as reported in I/B/ E/S; if the ®rm is not listed in I/B/E/S, then no analysts are presumed to follow the ®rm. ANAL0 has the same de®nition as the previous variable except that only ®rms with analysts following the ®rm (as reported by I/B/E/S) are included. HERFINDX is the sum of each ®rm's squared market share within the industry. DY is the annual dividend yield. The correlations are computed based on the average variables ± across time ± for each of the 2,890 ®rms in the sample. P -values are listed in parentheses below each correlation coecient.

A.C. Eberhart / Journal of Banking & Finance 25 (2001) 1367±1400

DOC

NUMCOMP

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dividend yield (DY) in the monthly volatility and earnings announcement tests; the average DY is 2.87% and the median is 1.94%. For the earnings announcement tests, I include the market-to-book ratio (MB) as an additional control variable because ®rms with a high MB may have more growth opportunities; the greater risk in growth opportunities may imply a greater reaction to earnings announcements beyond that re¯ected in the main control variables. On average, the MB is 2.48 (median ˆ 1.67). If there is more volatility in analysts estimates of a ®rm's earnings (STDEST), then a greater stock price reaction to earnings announcements may be expected, ceteris paribus, and so I include this variable as an additional control; the average volatility is 10.07 and the median is 3. A greater di€erence between the analysts' forecasts of earnings and the ®rms' actual earnings (ERROR) implies a greater stock price reaction to earnings announcements and so I include this variable in the tests; I ®nd an average error of 0.79, median ˆ 0.10. If comparables provide information, then any earnings announcements by comparables that precede a ®rm's earnings announcement (outside the event window) in the same quarter suggests that more information has been provided and there should be lower volatility around earnings announcements; I divide the number of these previous announcements by NUMCOMP and call this variable PREVANN. Using the same sample as in Table 1, Table 2 contains the correlation coecients for the number of comparables, degree of comparability and each main control variable posited to a€ect volatility directly. The correlation between DOC and NUMCOMP is signi®cantly positive, suggesting that ®rms with many comparables tend to be more similar in size with their comparables than ®rms with fewer comparables. NUMCOMP has a significantly positive relationship with the POL, number of analysts, S (the log of the market value of equity) and DY; NUMCOMP also has a signi®cant negative relationship with TVOLUME. On the other hand, a higher NUMCOMP is (signi®cantly) associated with a less concentrated and possibly more competitive industry (i.e., lower HERFINDX) and a higher debt ratio. DOC has a signi®cantly negative correlation with the POL and HERFINDX but a signi®cantly positive relationship with S and DY. The negative relationship between DOC and HERFINDX suggests that ®rms in less competitive industries tend to have comparables that are less similar in size (i.e., low DOC). The number of analysts (ANAL or ANAL0 ) is positively related to S and POL; ANAL and ANAL0 are also negatively correlated with DR and ROAVOL. These correlations suggest that the number of analysts may be at least partly re¯ecting the e€ect of other proxies for di€erential information or estimates of the stock's intrinsic risk. More generally, all the correlations highlight the need to control for other factors when examining the relationship between NUMCOMP (or DOC) and volatility.

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2.2. Monthly volatility tests For the monthly tests, I use the following model: rit ˆ b0 ‡ b1 NUMCOMPi …or DOCi † ‡ b2 POLi ‡ b3 DRi ‡ b4 ROAVOLi ‡ b5 Si ‡ b6 TVOLUMEit ‡ b7 ANALit ‡ b8 HERFINDXi ‡ i ;

…3†

where rit is the log of the volatility of ®rm i's daily excess stock returns in month t. As noted above, I also use a log transformation of S. The log transformations reduce the positive skewness in these variables but they have no e€ect on the sign and signi®cance of the coecient estimates for NUMCOMP or DOC; with or without the log transformations of r and S, these coecient estimates are always negative and highly signi®cant. 8 The market model is used to compute the excess returns with parameters estimated during the last 150 trading days of the preceding year (the market index is the valueweighted NYSE/Amex index). Variables with a ``t'' subscript are measured each month; variables without a ``t'' subscript are measured at the beginning of each year or the end of the preceding year. I estimate the model each month and, following Fama and MacBeth (1973), compute the time-series averages of the coecient estimates and use the time-series standard deviation of these estimates to compute the standard errors. The DY variable is added as an additional control variable and the results are presented with this variable. To account for the possibility that the number of analysts is a€ected by volatility, I also use an iterated three-stage least squares model with Eq. (3) and the following equation: ! 5 X ANALit ˆ a0 ‡ a1 Si ‡ a2 rit ‡ ax‡2 INDx ‡ a8 INSTi ‡ li : …4† xˆ1

Following Bhushan (1989), this method posits that the number of analysts following ®rm i in month t depends on ®rm i's stock value, volatility, six industry dummy variables 9 …INDx ; where the sixth is captured in the intercept) and institutional ownership (INST). 10 The same model is also estimated with ANAL0 in place of ANAL. 8 I also estimate the results using logarithmic transformations of the number of comparables, volatility of return on assets, size, trading volume and the number of analysts and consistently ®nd a negative and signi®cant coecient estimate for the number of comparables. 9 Industry 1 is 2-digit SIC codes 10±14; industry 2 is 2-digit SIC codes 15±39; industry 3 is 2-digit SIC codes 40±49; industry 4 is 2-digit SIC codes 50±59; industry 5 is 2-digit SIC codes 60±67; industry 6 is 2-digit SIC codes greater than 67. 10 Standard and Poor's Stock Guide provides information on institutional ownership. I hand collect these data at the beginning of each year.

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2.3. Quarterly earnings announcement tests Using quarterly data for the 1987±1995 period (1986 data are not available), I estimate the following model: rCARi ˆ b0 ‡ b1 NUMCOMPi …or DOCi † ‡ b2 POLi ‡ b3 DRi ‡ b4 ROAVOLi ‡ b5 Si ‡ b6 TVOLUMEi;21 ‡ b7 ANALit ‡ b8 HERFINDXi ‡ i ;

…5†

where rCARi is the log of the squared cumulative abnormal return for ®rm i's stock in the 21-day period surrounding the quarterly earnings announcement (event days )10 to +10 where day 0 is the announcement date). The market model is used to estimate the excess returns and the market-model parameters are estimated ± using the NYSE/Amex value-weighted index ± over event days )210 to )31. 11 TVOLUMEi;21 is the total number of shares traded during the 21-day period divided by the ®rm's shares outstanding. As with the other tests, ANALit is used with the full sample and ANAL0it is used with the subsample of ®rms with data in I/B/E/S. The only di€erence is that, in this test, the number of analysts is computed as the number of quarterly earnings forecasts made before the quarterly earnings per share …EPSi † are announced. Again, the model is estimated using Fama and MacBeth (1973) and the iterated three-stage least squares estimation procedure (using a version of Eq. (4)). I also estimate the results with the additional control variables mentioned earlier (DY, ERROR, MB, STDEST, PREVANN). 3. Empirical results 3.1. Monthly volatility test results I ®rst present the results of the monthly volatility tests using the Fama and MacBeth (1973) method. Panels A±D of Table 3 show the results with the full sample (using ANAL for the number of analysts) and Panels E through H show the results with the sample limited to ®rms with data available on I/B/E/S. The SIC code de®nition of NUMCOMP is shown in Panels A, B, E and F; except for the number of analysts, every variable is highly signi®cant and has the predicted sign, including the negative coecient estimates for NUMCOMP. With the Value Line de®nition of NUMCOMP in Panels C, D, G and H, the coecient estimates for this variable remain negative and highly signi®cant. 11 The results are qualitatively unchanged if I estimate the market model parameters over the )90 to )31 period.

A.C. Eberhart / Journal of Banking & Finance 25 (2001) 1367±1400

1379

The only notable di€erence in the results is that HERFINDX has a signi®cantly positive coecient estimate (recall that this estimate may be positive or negative). Of course, the key ®nding is that NUMCOMP is an important factor in explaining di€erences in volatility, after controlling for other factors that should explain these di€erences. Moreover, the negative and signi®cant coef®cient estimate for NUMCOMP is robust to di€erent de®nitions of a ®rm's industry. The positive coecient estimate for the number of analysts reported in Table 3 is consistent with Bhushan's (1989) argument that analysts may be attracted to high volatility stocks. To account for the endogenous relationship between the number of analysts and volatility, I use an iterated three-stage least squares procedure as shown in Table 4. Panels A and B show the results with the SIC code industry de®nition and Panels C and D show the Value Line sample. The results show a positive relationship between the number of analysts and volatility in the ®rst and second equations, after accounting for the other e€ects on volatility. The other control variables have coecient estimates that have a sign and signi®cance similar to the results presented in Table 3. Most important, the coecient estimates for NUMCOMP are negative and highly signi®cant in every case. Table 5 contains the monthly volatility tests using DOC as a measure of the amount of information provided by comparable ®rms. To be succinct, I only present the remaining results using the iterated three-stage least squares method; the Fama and MacBeth (1973) results are qualitatively similar. For this table, I look at the full sample using ANAL as the measure of the number of analysts following the ®rm; the coecient estimate for this variable remains positive and signi®cant. The other control variables are consistent with ®nancial theory and the ®ndings of previous studies. The primary variable of interest, DOC, has a negative and highly signi®cant coecient estimate every time using the SIC code or the Value Line sample. I ®nd qualitatively similar results when I use ANAL0 as the measure of the number of analysts following the ®rm. 3.2. Earnings announcement test results The earnings announcement test results are displayed in Tables 6 and 7. Again, the coecient estimates for NUMCOMP (Panels A and B) and DOC (Panels C and D) are negative and signi®cant; when there is more information provided by comparable ®rms (measured by the number of comparables or the degree of comparability), the earnings announcements are less surprising, after controlling for other factors that may e€ect the volatility around earnings announcements. The other control variables have coecient estimates with a sign and signi®cance generally similar to the results presented with the monthly volatility tests. I use ANAL0 in this table to be consistent with Table 7 (where

1380

Variables

Panel A

Panel B

NUMCOMP (with SIC) NUMCOMP (with VL) POL

)0.004 ()24.59)

)0.004 ()23.36)

)0.005 ()29.10) 0.20 (10.25) 4.79 (54.45) )0.26 ()54.98) 0.05 (23.64) 0.006 (14.25)

)0.004 ()24.62) 0.24 (11.08) 4.52 (52.37) )0.25 ()52.02) 0.05 (22.11) 0.005 (13.51)

DR ROAVOL S TVOLUME ANAL

Panel C

)0.006 ()21.59) )0.003 ()17.58) 0.074 (3.51) 5.634 (40.66) )0.234 ()46.16) 0.065 (20.57) 0.005 (10.62)

Panel D

)0.004 ()12.73) )0.002 ()12.07) 0.15 (6.22) 5.08 (45.48) )0.21 ()37.47) 0.06 (18.80) 0.004 (9.50)

Panel E

Panel F

)0.005 ()30.10)

)0.004 ()27.11)

)0.005 ()29.11) 0.11 (5.04) 4.72 (47.89) )0.28 ()53.81) 0.05 (24.11)

)0.004 ()23.62) 0.17 (7.16) 4.43 (48.01) )0.27 ()50.59) 0.04 (22.03)

Panel G

Panel H

)0.007 ()25.87) )0.003 ()18.73) )0.03 (1.37) 5.52 (39.57) )0.26 ()45.27) 0.06 (20.06)

)0.004 ()12.17) )0.002 ()10.85) 0.09 (3.46) 4.90 (36.45) )0.24 ()37.85) 0.05 (18.33)

A.C. Eberhart / Journal of Banking & Finance 25 (2001) 1367±1400

Table 3 Monthly volatility tests using Fama and MacBeth method with SIC code and Value Line de®nitions of the number of comparablesa

ANAL0 HERFINDX DY

)0.03 ()1.86) )0.04 ()10.56)

0.32 (18.00)

0.22 (10.71) )0.05 ()10.93)

0.01 (24.96) 0.02 (1.10) )0.05 ()12.86)

0.01 (19.96) 0.38 (19.39)

0.01 (18.68) 0.26 (11.27) )0.07 ()14.33)

Regression estimates of the model rit ˆ b0 ‡ b1 NUMCOMPi ‡ b2 POLi ‡ b3 DRi ‡ b4 CVEBITi ‡ b5 Si ‡ b6 TVOLUMEit ‡ b7 ANALit ‡ b8 HERFINDXi ‡ b9 DYi ‡ i ;

where rit is the log of the standard deviation of the daily excess rates of return during month t. NUMCOMP is the number of comparables. POL is the period-of-listing, or age of the ®rm as of the beginning of the year (measured in years). DR is the book value of total interest bearing debt (short-term and long-term) to the sum of the book value of debt and the market value of equity. S is the log of the market value of equity. The underlying business risk of the ®rm is estimated with the volatility of the return on assets (ROAVOL). TVOLUME is the total number of shares traded during the month during the month divided by shares outstanding. ANAL is the number of analysts that make an annual earnings forecast each month as reported in I/B/E/S; if the ®rm is not listed in I/B/E/S, then no analysts are presumed to follow the ®rm. ANAL0 has the same de®nition as the previous variable except that only ®rms with analysts following the ®rm (as reported by I/B/E/S) are included. HERFINDX is the sum of each ®rm's squared market share within the industry. DY is the annual dividend yield. The sample size for Panels A and B is 208,207; 146,433 for Panels E and F; 93,607 for Panels C and D; 78,079 for Panels G and H. I estimate the model each month over the 1986±1995 sample period and, following Fama and MacBeth (1973), compute the time-series averages of the coecient estimates and use the time-series standard deviation of these estimates to compute the standard errors. The t-statistics are reported in parentheses.

A.C. Eberhart / Journal of Banking & Finance 25 (2001) 1367±1400

a

)0.01 ()0.87)

0.01 (26.24) 0.03 (1.71)

1381

1382

Dependent variable: rit

Dependent variable: ANALi

Variables

Panel A

Panel B

NUMCOMP (with SIC) NUMCOMP (with VL) POL

)0.004 ()29.88)

)0.004 ()30.12)

)0.004 ()21.36) 0.23 (18.65) 4.15 (61.94) )0.49 ()36.86) 0.05 (64.39) 0.06 (19.53)

)0.003 ()19.77) 0.24 (18.58) 4.08 (60.95) )0.49 ()35.74) 0.05 (63.35) 0.06 (18.89)

DR ROAVOL S TVOLUME ANAL

Panel C

)0.003 ()10.72) )0.002 ()12.48) 0.11 (7.72) 5.34 (46.42) )0.336 ()13.38) 0.06 (39.58) 0.03 (5.14)

Panel D

)0.003 ()10.55) )0.002 ()10.72) 0.11 (7.66) 5.41 (47.10) )0.31 ()12.44) 0.06 (40.34) 0.02 (4.02)

Variables

Panel A

Panel B

Panel C

Panel D

ri

1.38 (24.75) 4.66 (239.01) 2.57 (23.24) 0.84 (19.13) 0.36 (4.20) 1.69 (25.77) )0.58 ()8.81) )0.03 ()2.50)

1.45 (25.70) 4.65 (237.13) 2.53 (22.93) 0.84 (19.22) 0.36 (4.12) 1.64 (25.15) )0.66 ()9.90) )0.03 ()2.53)

2.54 (31.97) 5.50 (213.56) 1.78 (11.22) 0.21 (3.33) )0.33 ()2.71) 0.81 (8.35) )0.66 ()6.66) 0.49 (8.53)

2.59 (32.28) 5.48 (211.24) 1.54 (9.51) 0.10 (1.48) )0.39 ()3.07) 0.54 (5.44) )0.98 ()9.61) 0.573 (9.60)

Si IND1 IND2 IND3 IND4 IND5 INSTi

A.C. Eberhart / Journal of Banking & Finance 25 (2001) 1367±1400

Table 4 Monthly volatility tests using iterated three-stage least squares method with SIC code and Value Line industry de®nitions of the number of comparablesa

HERFINDX DY Adjusted R2

)0.09 ()5.30) )0.001 ()7.44) 0.18

0.18

0.15 (6.29) 0.25

0.13 (5.51) )0.00 ()11.65) 0.265

Adjusted R2

0.48

0.50

0.49

0.50

Regression estimates of the model rit ˆ b0 ‡ b1 NUMCOMPi ‡ b2 POLi ‡ b3 DRi ‡ b4 ROAVOLi ‡ b5 Si ‡ b6 TVOLUMEit ‡ b7 ANALit ‡ b8 HERFINDXi ‡ b9 DYi ‡ i ; ! 5 X ANALi ˆ a0 ‡ a1 Si ‡ a2 ri ‡ ax‡2 INDx ‡ a8 INSTi ‡ li ; xˆ1

where rit is the log of the standard deviation of the daily excess rates of return during month t. NUMCOMP is the number of comparables using the SIC 4-digit code. POL is the period-of-listing, or age of the ®rm as of the beginning of the year (measured in years). DR is the book value of total interest bearing debt (short-term and long-term) to the sum of the book value of debt and the market value of equity. S is the log of the market value of equity. The underlying business risk of the ®rm is estimated with the volatility of the return on assets (ROAVOL). TVOLUME is the total number of shares traded during the month during the month divided by shares outstanding. ANAL is the number of analysts that make an annual earnings forecast each month as reported in I/B/E/S; if the ®rm is not listed in I/B/E/S, then no analysts are presumed to follow the ®rm. ANAL0 has the same de®nition as the previous variable except that only ®rms with analysts following the ®rm (as reported by I/B/E/S) are included. HERFINDX is the sum of each ®rm's squared market share within the industry. DY is the annual dividend yield. The sample size for Panels A and B is 157,068 and 93,607 for Panels C and D. The t-statistics are reported in parentheses.

A.C. Eberhart / Journal of Banking & Finance 25 (2001) 1367±1400

a

)0.07 ()4.17)

1383

1384

Dependent variable: rit Variables DOC (with SIC) DOC (with VL) POL DR ROAVOL S TVOLUME ANAL

Dependent variable: ANALi

Panel A

Panel B

)0.22 ()6.55)

)0.20 ()5.91)

)0.003 ()18.28) 0.16 (12.75) 4.02 (59.36) )0.66 ()45.65) 0.05 (55.71) 0.10 (27.50)

)0.003 ()17.24) 0.16 (13.19) 3.99 (58.74) )0.65 ()45.53) 0.05 (56.13) 0.10 (27.20)

Panel C

)0.46 ()8.70) )0.003 ()14.41) 0.10 (6.79) 5.93 (50.75) )0.16 ()6.23) 0.06 (41.88) )0.01 ()1.86)

Panel D

)0.45 ()8.51) )0.002 ()12.40) 0.09 (6.69) 5.96 (50.76) )0.15 ()5.92) 0.06 (42.00) )0.01 ()2.23)

Variables

Panel A

Panel B

Panel C

Panel D

ri

1.54 (26.73) 4.70 (236.93) 2.73 (28.07) 1.07 (28.35) 0.56 (7.95) 1.79 (31.27) )0.42 ()6.66) )0.04 ()3.90)

1.55 (26.77) 4.68 (234.50) 2.69 ()0.48) 1.06 (28.00) 0.55 (7.65) 1.76 ()5.89) )0.52 ()8.11) )0.04 ()3.79)

2.75 (34.40) 5.54 (213.21) )0.08 ()0.88) )0.82 ()11.82) )1.03 ()7.52) )0.63 ()7.15) )1.62 ()15.49) 0.95 (15.10)

2.76 (34.22) 5.51 (210.77) )0.15

Si IND1 (28.65) IND2 IND3 IND4 (32.07) IND5 INSTi

)0.81 ()11.60) )0.96 ()6.85) )0.77 )1.81 ()16.97) 0.97 (15.36)

A.C. Eberhart / Journal of Banking & Finance 25 (2001) 1367±1400

Table 5 Monthly volatility tests using iterated three-stage least squares method with SIC code and Value Line industry de®nitions of the degree of comparabilitya

HERFINDX DY Adjusted R2

0.07 (3.92) )0.001 ()7.99) )0.07

)0.08

0.16 (5.77) 0.28

0.13 (4.87) )0.003 ()12.37) 0.28

Adjusted R2

0.50

0.50

0.50

0.50

Regression estimates of the model rit ˆ b0 ‡ b1 DOCi ‡ b2 POLi ‡ b3 DRi ‡ b4 ROAVOLi ‡ b5 Si ‡ b6 TVOLUMEit ‡ b7 ANALi0 t ‡ b8 HERFINDXi ‡ b9 DYi ‡ i ; ! 5 X ANALi ˆ a0 ‡ a1 Si ‡ a2 ri ‡ ax‡2 INDx ‡ a8 INSTi ‡ li ; xˆ1

where r is the log of the standard deviation of the daily excess rates of return during month t. DOC is the degree of comparability using the 4-digit SIC codes. POL is the period-of-listing, or age of the ®rm as of the beginning of the year (measured in years). DR is the book value of total interest-bearing debt (short-term and long-term) to the sum of the book value of debt and the market value of equity. S is the log of the market value of equity. The underlying business risk of the ®rm is estimated with the volatility of the return on assets (ROAVOL). TVOLUME is the total number of shares traded during the month during the month divided by shares outstanding. ANAL is the number of analysts that make an annual earnings forecast each month as reported in I/B/E/S; if the ®rm is not listed in I/B/E/S, then no analysts are presumed to follow the ®rm. ANAL0 has the same de®nition as the previous variable except that only ®rms with analysts following the ®rm (as reported by I/B/E/S) are included. HERFINDX is the sum of each ®rm's squared market share within the industry. DY is the annual dividend yield. The sample size for Panels A and B is 157,068 and 93,607 for Panels C and D. The t-statistics are reported in parentheses.

A.C. Eberhart / Journal of Banking & Finance 25 (2001) 1367±1400

a

0.07 (4.25)

1385

1386

Dependent variable: ANAL0i

Dependent variable: rCARi Variables

Panel A

Panel B

NUMCOMP

)0.005 ()14.48)

)0.006 ()15.56)

)0.005 ()12.84) 0.35 (10.60) 6.61 (25.23) )0.61 ()14.98) 17.27 (13.33) 0.10 (13.27)

)0.005 ()12.18) 0.35 (10.96) 6.69 (17.45) )0.53 ()13.18) 17.84

DOC POL DR ROAVOL S TVOLUME ANAL0

0.08 (11.26)

Panel C

)0.33 ()5.47) )0.003 ()9.33) 0.20 (6.23) 4.92 (11.67) )0.81 ()17.10) 12.66 (10.31) 0.13 (14.75)

Panel D

)0.34 ()5.28) )0.003 ()9.40) 0.20 (6.91) 5.28 (12.99) )0.74 ()16.16) 13.85 (11.28) 0.11 (13.65)

Variables

Panel A

Panel B

Panel C

Panel D

rCAR

2.22 (13.44) 5.65 (117.12) 3.85 (14.32) 0.85 (6.90) )0.02 ()0.11) 1.52 (8.94) 0.98 (6.71) 0.19 (1.62)

2.29 (13.99) 5.64 (117.72) 3.89 (14.22) 0.67 (5.28) )0.20 ()1.01) 1.26 (7.19) 0.57 (3.75) 0.17 (1.34)

3.45 (17.70) 5.91 (108.96) 2.72 (10.05) 0.81 (7.12) )0.04 ()0.22) 1.22 (7.94) 0.47 (3.86) 0.25 (3.14)

3.40 (17.68) 5.87 (109.73) 2.92 (10.80) 0.76 (6.70) )0.13 ()0.78) 1.17 (7.54) 0.28 (2.17) 0.25 (2.85)

S IND1 IND2 IND3 IND4 IND5 INST

A.C. Eberhart / Journal of Banking & Finance 25 (2001) 1367±1400

Table 6 Earnings announcement tests using iterated three-stage least squares method with SIC code de®nitions of the number of comparables and degree of comparabilitya

HERFINDX DY Adjusted R2

0.05

)0.23 ()4.75) )0.01 ()8.44) 0.13

)0.07 ()1.28) )0.16

)0.08 ()1.47) )0.004 ()7.90) )0.07

Adjusted R2

0.68

0.68

0.64

0.65

Regression estimates of the model rCARi ˆ b0 ‡ b1 DOCi ‡ b2 POLi ‡ b3 DRi ‡ b4 ROAVOLi ‡ b5 Si ‡ b6 TVOLUMEi;21 ‡ b7 ANALi0 t ‡ b8 HERFINDXi ‡ b9 DYi ‡ i ; ! 5 X 0 ax‡2 INDx ‡ a8 INSTi ‡ li ; ANALi ˆ a0 ‡ a1 Si ‡ a2 rCARi ‡ xˆ1

where rCAR is the log of the squared cumulative abnormal return for ®rm i's stock in the 21-day period surrounding the quarterly earnings announcement (event days )10 to +10 where day 0 is the announcement date). The market model is used to estimate the excess returns and the marketmodel parameters are estimatedBusing the NYSE/Amex value-weighted index ± over event days )210 to )31. NUMCOMP is the number of comparables using the 4-digit SIC codes. POL is the period-of-listing, or age of the ®rm as of the beginning of the year (measured in years). DR is the book value of total interest bearing debt (short-term and long-term) to the sum of the book value of debt and the market value of equity. S is the log of the market value of equity. The underlying business risk of the ®rm is estimated with the volatility of the return on assets (ROAVOL). TVOLUMEi;21 is the total number of shares traded during the 21-day period divided by shares outstanding. ANAL0 is the number of analysts that make an annual earnings forecast each month as reported in I/B/E/S, where the ®rms must be listed in I/B/E/S. HERFINDX is the sum of each ®rm's squared market share within the industry. DY is the annual dividend yield. The sample size for Panels A and B is 117,078 and 78,079 for Panels C and D. The t-statistics are reported in parentheses.

A.C. Eberhart / Journal of Banking & Finance 25 (2001) 1367±1400

a

)0.19 ()4.00)

1387

1388

Dependent variable: ANAL0i

Dependent variable: rCARi Variables

Panel A

Panel B

Panel C

Panel D

Variables

Panel A

Panel B

Panel C

Panel D

NUMCOMP

)0.005 ()12.40) )0.005 ()11.80) 0.44 (9.65) 6.31 (14.08) )0.70 ()15.08) 20.59 (13.79) 0.11 (14.12) )0.17 ()3.81) )0.000 ()0.82)

)0.005 ()8.47) )0.006 ()9.41) 0.11 (2.39) 6.80 (13.06) )0.48 ()10.22) 27.85 (9.98) 0.07 (8.71) )0.31 ()4.06)

)0.01 ()15.01) )0.005 ()13.19) 0.36 (10.83) 6.76 (17.27) )0.58 ()14.20) 17.69 (13.59) 0.09 (12.29) )0.19 ()3.61)

)0.006 ()15.17) )0.005 ()12.92) 0.37 (11.00) 6.83 (17.67) )0.59 ()14.62) 18.35 (13.02) 0.09 (13.02) )0.18 ()3.76)

rCARi

2.57 (15.86) 5.65 (108.13) 3.52 (12.76) 0.86 (7.69) 0.33 (1.82) 1.55 (9.56) 0.99 (0.14) 0.15 (1.50)

2.48 (8.95) 5.99 (71.84) 6.10 (11.96) 0.77 (3.37) )0.49 ()1.40) 1.99 (6.39) 0.97 (3.48) 0.03 (0.15)

2.19 (13.30) 5.67 (117.35) 3.90 (14.39) 0.79 (6.17) )0.21 ()1.09) 1.39 (7.96) 0.91 (6.01) 0.20 (1.65)

2.02 (12.51) 5.60 (117.55) 3.94 (14.66) 0.85 (6.77) )0.01 ()0.06) 1.49 (8.64) 0.97 (6.47) 0.23 (1.88)

POL DR ROAVOL S TVOLUME ANAL0 HERFINDX MB

Si IND1 IND2 IND3 IND4 IND5 INSTi

A.C. Eberhart / Journal of Banking & Finance 25 (2001) 1367±1400

Table 7 Earnings announcement tests using iterated three-stage least squares method with SIC code de®nition of the number of comparablesa

STDEST

0.00 (1.27)

PREVANN ERROR )0.03

0.12

0.10

)0.03 ()6.80) 0.08

Adjusted R2

0.64

0.66

0.68

0.68

Regression estimates of the model rCARi ˆ b0 ‡ b1 NUMCOMPi ‡ b2 POLi ‡ b3 DRi ‡ b4 ROAVOLi ‡ b5 Si ‡ b6 TVOLUMEi;21 ‡ b7 ANALi0 t ‡ b8 HERFINDXi ‡ b9 …Other Control Variables† ‡ i ; ANALi0 ˆ a0 ‡ a1 Si ‡ a2 rCARi ‡

5 X xˆ1

ax‡2 INDx

! ‡ a8 INSTi ‡ li ;

where rCAR is the log of the squared cumulative abnormal return for ®rm i's stock in the 21-day period surrounding the quarterly earnings announcement (event days )10 to +10 where day 0 is the announcement date). The market model is used to estimate the excess returns and the marketmodel parameters are estimated using the NYSE/Amex value-weighted index ± over event days )210 to )31. NUMCOMP is the number of comparables using the 4-digit SIC codes. POL is the period-of-listing, or age of the ®rm as of the beginning of the year (measured in years). DR is the book value of total interest bearing debt (short-term and long-term) to the sum of the book value of debt and the market value of equity. S is the log of the market value of equity. The underlying business risk of the ®rm is estimated with the volatility of the return on assets (ROAVOL). TVOLUMEi;21 is the total number of shares traded during the 21-day period divided by shares outstanding. ANAL0 is the number of analysts that make an annual earnings forecast each month as reported in I/B/E/S, where the ®rms must be listed in I/B/E/S. HERFINDX is the sum of each ®rm's squared market share within the industry. DY is the annual dividend yield. ERROR is the analysts earnings forecast error. MB is the market-to-book ratio for the ®rm. STDEST is the standard deviation of the analysts earnings forecast. PREVANN is the number of earnings announcements made by comparable ®rms that precede the ®rm's earnings forecast in the same quarter. The sample size is 117,078. The t-statistics are reported in parentheses.

A.C. Eberhart / Journal of Banking & Finance 25 (2001) 1367±1400

Adjusted R2 a

)0.10 ()5.49)

1389

1390

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I need to use ANAL0 because I use data on analysts' earnings forecasts). The results are also qualitatively unchanged using ANAL as the measure of the number of analysts and with the Value Line sample. Four additional control variables in the earnings announcement tests are considered in Table 7. The MB and STDEST coecient estimates are insigni®cant but the PREVANN estimate is signi®cantly negative. Therefore, when a ®rm's comparable announces its earnings, this announcement provides information to the market about the ®rm's earnings; more previous announcements by a ®rm's comparables suggests more information and this is manifested in the lesser magnitude of the ®rm's stock price reaction to an earnings announcement (i.e., a signi®cantly negative coecient estimate). The signi®cantly negative coecient estimate for ERROR is not consistent with its predicted sign but NUMCOMP remains negative and highly signi®cant for the regression with this control variable, as well as the regression with the other three additional control variables. The tests are also conducted with DOC and these coecient estimates are also negative and signi®cant. 12 3.3. Additional robustness tests With the NUMCOMP variable, there is the possibility that some industries are driving the results. For example, utilities have many comparables and tend to be low risk ®rms. Therefore, it is possible that the negative relationship between volatility and the number of comparables is merely due to the fact that there are a lot of utility ®rms that tend to have, for example, lower business risk and consequently lower volatility. Though I control for business risk with the ROAVOL measure, this control variable may be inadequate. Therefore, I estimate the results with utilities removed. I also estimate the results with the top four industries (in terms of the average number of comparables over the sample period) removed to ensure that outliers are not driving the results; these industries are SIC codes 6021, 4813, 4911, 6022 and Value Line codes 5600, 4912, 2000, 6000. I also estimate the results with utilities and the top four industries removed. In each case, the results are qualitatively unchanged (speci®cally, the NUMCOMP coecient estimates remain negative and highly signi®cant). Besides the control variables I include in my reported test results, I check for the other possible confounding e€ects. For example, ®rms in high growth in12 I also model the number of analysts following a ®rm as a function of the ®rm's squared CAR around the 21-day period surrounding the ®rm's earnings announcement in the previous quarter (which would be known with certainty by the analysts at the time of their forecast of the ®rm's earnings in the current quarter) and the other control variables. The results are qualitatively similar to those reported. I also estimate the ratio of the squared CAR to the volatility over the quarter and regress this ratio on NUMCOMP and the control variables and ®nd a signi®cantly negative coecient estimate for NUMCOMP.

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dustries (as revealed by the high ratio of, say, the average market-to-book ratio for the ®rm's industry) may have higher risks than captured by my business risk or Her®ndahl measures. Therefore, I estimate the results using di€erent industry multiples as a control variable: price-to-earnings, market-to-book and market-to-sales. None of these variables has a consistently signi®cant coecient estimate and the sign and signi®cance of the other variables that I report in my tests are qualitatively unchanged (e.g., the coecient estimates for NUMCOMP and DOC remain negative and highly signi®cant). 13 4. Summary and conclusions Previous studies suggest that greater information about a stock increases the market's precision in valuing the stock and this implies a lower stock price reaction to events such as earnings announcements, ceteris paribus. I argue that comparables comprise a signi®cant portion of the information investors use to value a ®rm because of their widespread use in valuation and the well-documented existence of contagion e€ects. I use the number of comparables as a simple measure of di€erential information and posit that more comparables imply more information and lower stock price reactions to earnings announcements (de®ned as the excess stock return volatility around earnings announcements), ceteris paribus. Comparable ®rms are those in the same 4-digit SIC code as the ®rm being valued. The intuition is similar to that used with another popular proxy for di€erential information, the number of analysts following a ®rm. The number of analysts, however, has two notable problems as a proxy for di€erential information. First, the correlations from my sample show that the number of analysts may be re¯ecting the e€ect of other proxies for di€erential information (such as size and period-of-listing) and estimates of the stock's intrinsic risk. Second, the number of analysts can be a€ected by the volatility around earnings announcements; for example, Bhushan (1989) shows that analysts may be attracted to high volatility stocks. I address both problems by including other proxies for di€erential information and estimates of the stock's intrinsic risk (e.g., period-of-listing, size, trading volume, measures of business and ®nancial risk and a measure of concentration in the ®rm's industry). I also use an 13 As a ®nal check, I estimate the earnings announcement tests with the volatility outside the event window as an additional control variable. The monthly volatility tests I conduct above imply a signi®cant relationship between the primary control variables and this additional control variable but it is possible that this volatility measure controls for some additional risk not fully captured in the primary control variables. I continue to ®nd a highly signi®cant coecient estimate for NUMCOMP (and DOC) with this additional control variable. I thank one of the referees for suggesting this additional test.

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iterated three-stage least squares method, where the number of analysts is affected by volatility and other factors posited by Bhushan. After accounting for the other variables a€ecting the stock price reaction to earnings announcements and the endogeneity of the number of analysts, I ®nd that the number of analysts is consistently positively related to the volatility around earnings announcements. In contrast, the number of comparables is consistently negatively related to the volatility around earnings announcements. Because the number of comparables depends on how an industry is de®ned and the number of comparables is just one way to measure the amount of information provided by comparables, I test the results using the Value Line industry de®nitions to compute the number of comparables. I also construct a separate measure of the amount of information provided by comparables that I call the degree of comparability. The more similar the comparables are to the ®rm being valued, the greater the degree of comparability and the more information they provide. I also develop a simple model that shows a negative relationship between excess stock return volatility (i.e., volatility) and the degree of comparability; the model also shows a negative relationship between volatility and the number of comparables. Because the model is in a general one-period framework and is not restricted to earnings announcement tests, I perform additional tests on the relationship between the number of comparables (and the degree of comparability) and excess stock return volatility measured each month. Using alternative de®nitions of comparables (SIC code and Value Line) and di€erent measures of the amount of information provided by comparables (number of comparables and degree of comparability), I consistently ®nd a highly signi®cant negative relationship between a ®rm's volatility (measured each month and around earnings announcements) and the amount of information provided by a ®rm's comparables, ceteris paribus. These results help answer a fundamental question in ®nance: Why are some stocks more volatile than others? Answering this question helps explain why some stock's options are more valuable than others and possibly why some stocks have higher expected rates of returns. Comparable ®rms appear to be an important part of the answer.

Acknowledgements I thank Jim Angel, Jim Bodurtha, Lisa Fairchild, John Mayo, Cathy Niden, David P. Brown, Akhtar Siddique, Dick Sweeney, Michael Walker and especially Aswath Damodaran (who provided some of the data) for comments and suggestions. I received support from a Georgetown University (and School of

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Business) summer research grant and a Goldman, Sachs & Co. Fellowship. The Capital Markets Research Center at Georgetown also provided support. I thank I/B/E/S for providing data and my research assistants for their help. Finally, I thank the editor, Georgio P. Szeg} o, and two referees for their comments.

Appendix A. A simple model of excess stock return volatility A.1. The model The NUMCOMP and DOC variables are proxies for di€erential information that I posit in the spirit of other proxies previously used in the literature because of their intuitive appeal (e.g., number of analysts, POL, size). 14 To motivate the empirical tests more formally, I use the following simple model. 15 I begin with a conventional assertion that a stock's price at time t is equal to its expected price based on the information available at time t 1, Xt 1 , and a forecast error: Pit ˆ E…Pit jXt 1 † ‡ lit ;

…A:1†

where Pit is the logarithm of stock i's actual market price at date t and lit is an i.i.d. random variable that has a zero mean, ®nite variance r2li and is uncorrelated with E…Pit jXt 1 ). Consider the following decomposition of Xt 1 into two subsets: Xt

1

ˆ …/t 1 ; ht 1 †;

…A:2†

where /t 1 is the information on comparables and ht 1 represents all other relevant information. Suppose that the market separately forecasts the price based on each information subset and weights the forecasted prices as shown below: E…Pit jXt 1 † ˆ x/i E…P/it j/t 1 † ‡ xhi E…Phit jht 1 †;

…A:3†

where x/i is the weight assigned to the forecasted price based on the comparables' information, xhi ˆ …1 x/i † is the weight assigned to the forecasted price based on other information, E…P/it j/t 1 † is the expected price based on the comparables' information set and E…Phit jht 1 † is the expected price based on the 14 As noted earlier, the empirical results I report suggest that these previously used proxies may be partly re¯ecting intrinsic risk; more generally, NUMCOMP and DOC explain cross-sectional di€erences in volatility beyond what these previously used proxies explain. 15 Of course, the model I present is just one way of illustrating an inverse relationship between excess stock return volatility and NUMCOMP (or DOC); other models could show a similar relationship.

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other information set. 16 The price based on the comparables is de®ned as relative valuation whereas the price based on the other information set is de®ned as absolute valuation (e.g., DCF analysis). 17 These forecasted prices are assumed to be rational: P/it ˆ E…P/it j/t 1 † ‡ l/it ;

…A:4†

Phit ˆ E…Phit jht 1 † ‡ lhit ;

…A:5†

where P/it is the true realization of the forecasted price based on the comparables' information, Phit is the true realization of the forecasted price based on the other information and l/it and lhit are i.i.d. random variables with zero means and ®nite variances r2l/i and r2lhi . The error terms are assumed to be independent of each other and are uncorrelated with E…P/it j/t 1 † and E…Phit jht 1 †, respectively. I use a one-period framework where the weights may vary cross-sectionally but not over the period; speci®cally, x/i ˆ DOCi is the degree of comparability, a measure of how similar the comparables are to the ®rm being valued; so the more similar the comparables are to the ®rm being valued, the more weight applied to the forecasted price based on the comparables. I substitute the expressions for the expected values in Eqs. (A.4) and (A.5) into Eq. (A.3) and then substitute Eq. (A.3) into Eq. (A.1). If I de®ne Pit ˆ x/it P/it ‡ xhit Phit , then these substitutions provide the following expression for the error term: lit ˆ x/i l/it ‡ xhi lhit :

…A:6†

The total forecast error, or excess return, is a weighted average of the forecast error from the relative valuation, l/it , and the forecast error from the absolute valuation, lhit . With the assumed independence of l/it and lhit , r2li ˆ x2/i r2l/i ‡ x2hi r2lhi ;

…A:7†

where rli is the excess stock return volatility (i.e., volatility), rl/i is the volatility of the forecast error from the relative valuation and rlhi is the volatility of the forecast error from the absolute valuation. Because absolute valuation is typically considered more dicult than relative valuation, asserting rl/i < rlhi is plausible (though this assumption is not necessary as shown below). As the

16 Averaging stock values obtained with di€erent techniques appeals to the uncertainty surrounding valuation under any one technique (Damodaran (1994) discusses the use of absolute and relative valuation techniques). Moreover, this averaging circumvents the circularity of the market only looking to comparables' multiples to value a ®rm. 17 As noted earlier, comparables can be used in DCF analysis. For example, comparables' betas (sometimes called ``pure plays'') can be used to estimate the expected return. To the extent that this is true, this information is contained in the comparables' information set.

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number of comparable ®rms that are imperfectly correlated grows, rl/i becomes smaller (I illustrate this point below). Without loss of generality, suppose that /t 1 is composed entirely of the weighted average PE ratio for the ®rm's comparables. 18 " # Ni X E…P/it j/t 1 † ˆ wj E‰PEjt Š ; …A:8† jˆ1

where wj is the weight assigned to comparable ®rm j, E‰PEjt Š is the expected price/earnings ratio in period t, given the information available in t 1, for comparable ®rm j and Ni is the number of comparables. 19; 20 If I de®ne the true realization of the forecasted price based on the comparables' information as the weighted P average of the true P realization of the comparables' PE ratios (i.e., P/it ˆ wj PEj ), then l/i ˆ wj …PEj E…PEj ††. These expressions lead to the following expression for rl/i : v u Ni Ni Ni X X uX …A:9† w2m r2PEm ‡ wm wj qmj rPEm rPEj ; rl/i ˆ t mˆ1

m6ˆjˆ1 j6ˆmˆ1

where rPEm is the volatility of the unexpected change in the PE ratio for comparable ®rm m, rPEj is the volatility of the unexpected change in the PE ratio for comparable ®rm j, and qmj is the correlation coecient between the unexpected change in the PE ratio for ®rms m and j. The correlation coecients can be interpreted as comparability measures. Comparability measures likely di€er within the industry. In the relative valuation in Eq. (A.8), the weight …wj † assigned to each comparable ®rm j's PE ratio should depend on how similar it is to ®rm i; less similar ®rms should be assigned lower weights. This similarity should also a€ect the correlation coecient between ®rms m and j; the more similar these ®rms are to each other, the higher should be the correlation coecient (or comparability measure). Equity capitalization, or size, is a common variable used in assessing comparability within an industry; for example, the matched stock method of estimating expected stock returns in long-term event studies (e.g., Lyon et al., 18 The PE ratio for the comparables is assumed to be exogenous. I illustrate the point using the PE ratio because it is the most popular multiple used in comparables' valuation but the point is easily made with any other multiple (e.g., price/book, price/sales, etc.). 19 Of course, the PE ratio must be multiplied by the ®rm's earnings to get the stock price estimate. However, the ®rm's earnings are not part of the comparables' information set and many practitioners view valuation in terms of multiples (e.g., IBM is selling at 15 times earnings). Therefore, the relative and absolute valuation are in terms of the multiple applied to earnings (from a DCF perspective, the appropriate ``multiple'' to apply to current earnings for a constant growth ®rm is ‰…1 ‡ g†DPRŠ=…r g†; where DPR is the dividend payout ratio, r is the cost of equity and g is the expected growth rate in dividends). 20 This type of forecasting does occur in practice; for example, Value Line forecasts PE ratios.

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1999) uses size as one variable in choosing a matched ®rm (which is analogous to a comparable ®rm). Therefore, I use size di€erences for the comparability measure, qmj ˆ

1 ‰1 ‡ jSm

Sj j=Savg Š

;

…A:10†

where Sm is the log of the equity value of comparable ®rm m, Sj is the log of the equity value of comparable ®rm j and Savg is the industry average log equity value. 21 Eq. (A.10) shows that the greater the di€erence in size between ®rm m and ®rm j, the lower the correlation coecient (i.e., the less similar, or comparable, ®rms m and j are to each other); note the comparability bounds, 0 < qmj 6 1. I now illustrate the construction of a size-weighted number of comparables. This number is used to compute two weights. First, the weight assigned to each of the comparables in the relative valuation estimation (i.e., wj in Eq. (A.8)). Second, the weight assigned to each ®rms' relative valuation component, x/it . Consider the case of ®rm i and Ni comparable ®rms Ni

ˆ

Ni  X jˆ1



1 ‰1 ‡ jSi

Sj j=Savg Š

:

…A:11†

If every comparable ®rm j is the same size as ®rm i, then the size-weighted number of comparables …Ni † equals the number of comparables …Ni †. 22 The larger the size di€erences between ®rm i and its comparable ®rms, the lower is Ni . The weight for each comparable ®rm j is then de®ned as follows: wj ˆ

1=‰1 ‡ jSi Sj j=Savg Š : Ni

…A:12†

If every comparable ®rm j is the same size as ®rm i, then the weight for each ®rm j collapses to …1=N †. 23 With Ni de®ned, I now propose a functional form for the weight assigned to the relative valuation component, x/i (i.e., DOCi †. 24

21 This point can apply to other ways of estimating comparability. For example, as a robustness check, I estimate the results shown below using the log of total sales instead of the log of equity value. The results are qualitatively the same is those that I present. I also perform the tests without using Savg in Eq. (A.10) and ®nd qualitatively similar results. 22 As with the PE ratios, the equity values are exogenous variables. 23 It is not necessary to make a distinction between comparable ®rm m and j for the computation of the w's and Ni . 24 This measure is not to be confused with qmj , the comparability measure for ®rms m and j. The degree of comparability, x/i , is a gauge of how similar all the comparable ®rms are to ®rm i.

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Fig. 1. This ®gure shows how the inverse relationship between the number of comparables and the volatility of the relative valuation forecast error becomes more pronounced as the correlation coecients decrease.

    Ni x/i ˆ DOCi ˆ LOG 1 ‡ ; Ni

…A:13†

where DOC ˆ 0 when N ˆ 0. The ratio …Ni =Ni † is an index of comparability between ®rm i and all its comparable ®rms. As this ratio rises, more weight …x/i † is assigned to the relative valuation component in Eq. (A.3). As Ni ! Ni ; x/i ! >0.301. This weighting is consistent with the assumption that the market considers information beyond that provided by the comparables. 25 A.2. Simulation analysis To show the intuition behind the model, I begin with a preliminary simulation analysis that focuses on the volatility of the relative valuation forecast error, rl/i . Suppose the weight assigned to each comparable ®rms' 25 I use the LOG (base 10) transformation to illustrate a ``monotonic'' (with some noise) decrease in rli as x/i rises in the simulation analysis below. More generally, any weighting scheme where x/i ! 0:5 as Ni ! Ni , leads to a ``monotonic'' decrease in rli as x/i rises. If I allow x/i to rise above 0.5 as Ni ! Ni , then there is still a negative relationship between rli as x/i until Ni is close to Ni ; at this point, it can turn positive. The DOC coecient estimate is consistently negative and signi®cant with the LOG (base 10) or natural log transformations, however. I present the natural log transformations in the empirical tests.

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PE ratio, as shown in Eq. (A.8), is the same and the correlation coecients (or comparability measures) between the comparables are the same (i.e., wm ˆ wj and qmj is constant 8m, j). Fig. 1 shows there is a negative relationship between Ni and r/i for a range of constant correlation coecients. The drop is more precipitous the lower the correlation coecient and this suggests that there is a greater bene®t (i.e., greater reduction in rl/i ) to having more comparables when they are less similar to each other. If the comparables are highly similar, then the addition of another ®rm to the ``portfolio'' of comparables provides relatively less additional information (and therefore less of a reduction in rl/i ). For the full simulation analysis, I allow the equity capitalizations …Si ; Sj ; Sm † and consequently the weights …w0j 's), correlation coecients …q0mj 's) and volatilities (rl/i and rli ) to vary stochastically. Speci®cally, the value of ®rm i and comparable ®rms m and j are the absolute value of a draw from a standard normal distribution multiplied by the LOG of 10,000. To avoid biasing the simulation results by choosing an arbitrarily high level of rlhi compared with rl/i , I assume that rl/i ˆ rlhi when there is just one comparable ®rm. To maintain the ceteris paribus conditions, I set the volatility of the unexpected change in the comparable ®rms' PE ratios equal to the volatility of the absolute valuation forecast error (i.e., rPEm ˆ rPEj ˆ rlhi ˆ 0:2†. The variable Ni varies from 1 to 30 and the simulation is conducted 12,000 times. 26 Panel A of Table 8 shows a positive relationship between DOCi and the volatility of the relative valuation forecast error, rl/i . 27 Intuitively, DOCi is high when the comparables are similar in size to ®rm i ± and therefore likely similar in size to each other ± and this implies a high qmj 8m; j. These high correlation coecients cause a smaller reduction in rl/i than when the comparable ®rms are more varied in size. In other words, the volatility of the relative valuation forecast error can be lower with many dissimilar comparables (which implies a low value for DOCi ) than with many similar comparables (which implies a high value for DOCi ). Part of this result is driven by the assumption that rPEm ˆ rPEj 8m; j. When I allow for the rPE 's to vary stochastically, the positive relationship between DOCi and rl/i is reduced. 28 Nevertheless, although the assumptions are stacked against the primary prediction of an inverse relationship between DOCi , and rli , the prediction still follows. When the comparables are similar, there is more weight assigned to the relative valuation component. Since rl/i is always less than rlhi whenever Ni > 1, the greater weight assigned to this less uncertain valuation implies less overall volatility (i.e., lower rli ). 26 Of course, cross-sectional di€erences in, for example, business or ®nancial risk also a€ect the r0 s and these e€ects are controlled for in the empirical tests. 27 There is a negative relationship between Ni and rl/i as shown in Table 8 regression results. 28 As noted earlier, I assume constant volatilities to appeal to the ceteris paribus conditions.

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Table 8 Simulation analysisa Model Panel A rl/i ˆ a ‡ bDOCi ‡ i Panel B rl/i ˆ a ‡ bNi ‡ i Panel C rli ˆ a ‡ bDOCi ‡ i Panel D rli ˆ a ‡ bNi ‡ i

Parameter estimates a

b

R2

0.164 (0.000)

0.092 (0.000)

0.075

0.193 (0.000)

)0.0002 (0.000)

0.173

0.186 (0.000)

)0.118 (0.000)

0.926

0.154 (0.000)

)0.00001 (0.000)

0.006

a

The value of ®rm i and comparable ®rms m and j are the absolute value of a draw from a standard normal distribution multiplied by the log of 10,000. To avoid biasing the simulation results by choosing an arbitrarily high level of rlhi (volatility of the absolute valuation forecast error) compared with rl/i (volatility of the relative valuation forecast error), I assume that rl/i ˆ rlhi when there is just one comparable ®rm. To maintain the ceteris paribus conditions, I set the volatility of the unexpected change in the comparable ®rms' PE ratios equal to the volatility of the forecast error for the absolute valuation (i.e., rPEm ˆ rPEj ˆ rlhi ˆ 0:2† and Ni (the number of comparables for ®rm i) varies from 1 to 30. Based on a random draw of ®rm values, the correlation coecients, weights and then the volatilities …rl/i and rli , the volatility of the excess returns) are computed; this simulation is conducted 12,000 times. DOC is the degree of comparability and the P -values are in parentheses.

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