Analyst coverage, optimism, and stock price crash risk: Evidence from China

Pacific-Basin Finance Journal 25 (2013) 217–239

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Pacific-Basin Finance Journal

j ourna l homepage: www.e lsev ie r .com/ locate /pacf in

Analyst coverage, optimism, and stock price
crash risk: Evidence from China
Nianhang Xu a,⁎, Xuanyu Jiang a, Kam C. Chan b, Zhihong Yi a

a School of Business, Renmin University of China, Beijing, Chinab Department of Finance, Western Kentucky University, Bowling Green, KY 42101, USA

a r t i c l e i n f o

⁎ Corresponding author.

0927-538X/$ – see front matter © 2013 Elsevier B.V.http://dx.doi.org/10.1016/j.pacfin.2013.09.001

a b s t r a c t

Article history:Received 24 January 2013Accepted 10 September 2013Available online 30 September 2013

We examine the relations among analyst coverage, analyst optimism,and firm-specific stock price crash risk. Using a unique Chinesedatabase, we find that an increase in a firm's analyst coverage leads toan increase in stock price crash risk and this positive relation is morepronounced when analysts are more optimistic analysts and areaffiliated with investment banks and brokerage firms with mutualfunds relation.We also find someweak evidence to suggest that analystoptimism on crash risk is less pronounced when analysts have highpersonal reputations or are affiliated with reputable brokerage firms.

© 2013 Elsevier B.V. All rights reserved.

JEL classification:G00G24

Keywords:Analyst optimismCrash riskConflict of interestReputation

1. Introduction

The determinants of stock price crash risk have drawn the attention of investors, regulators, and policymakers. For instance, Jin and Myers (2006) provide empirical evidence from 40 countries showing apositive correlation between stock market opaqueness and market-wide stock price crash risk. At the firmlevel, Hutton et al. (2009), using data from US firms, find a positive correlation between stock price crashrisk and the opaqueness of financial reports. Kim et al. (2011a,b) find that stock price crash risk ispositively correlated with corporate tax avoidance and the value of CFO option portfolios. Kim and Zhang(2011) document that accounting conservatism reduces the likelihood of stock price crashes. A basicargument of these studies is that managers have a tendency to withhold bad news, causing it to stockpile.When the accumulation of bad news passes a threshold, it is revealed to the market all at once, leading to alarge drop in the stock price. Firm-level stock price crash risk studies, however, primarily focus on theimpact of accounting characteristics on crash risk. Few studies consider determinants other than a firm'saccounting characteristics.

A separate strand of the literature on analyst coverage suggests that analysts indeed tend to beoptimistic in their recommendations and earnings forecasts. It also considers several incentives for analyst

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218 N. Xu et al. / Pacific-Basin Finance Journal 25 (2013) 217–239

optimism, including (1) the maximization of trading commissions (Hayes, 1998; Irvine, 2001; Jackson,2005; Cowen et al., 2006; Beyer and Guttman, 2011), (2) currying favor with management (Lim, 2001),and (3) the promotion of an investment banking business (Dugar and Nathan, 1995; Lin and McNichols,1998; Michaely and Womack, 1999).

Despite the literature on analyst coverage, analyst optimism, and stock price crash risk, few studies linkthese major research areas together. The role of analyst coverage and analyst optimism bias in individualfuture stock price crash risk is unclear. The objective of this paper is to examine the relation betweenanalyst coverage, analyst optimism, and firm-specific stock price crash risk (hereafter crash risk). Wecontend that analyst coverage, through their optimistic forecasts, can increase the crash risk of the firmsthey cover. If analysts are overly optimistic, negative information about the firms they cover cannot berevealed in a timely manner to outside investors. When the accumulated negative information reaches atipping point, it will be revealed to the market, bursting the bubble and resulting in a stock price crash.While our crash risk argument is similar to that in the literature, the cause is different. The explanation ofcrash risk in the literature stems from a firm's internal factors, such as accounting conservatism, but ourfocus relates crash risk to external factors, such as analyst coverage and analyst optimism. Hence, ourstudy offers a new perspective on the determinants of crash risk.

The relevant literature, with the exception of the work of Jin and Myers (2006), uses US data. We useinstead a rich database on the emerging Chinese stock market to examine several hypotheses. Such adetailed study using the Chinese stock market will shed light on crash risk in an emerging market and thefindings could be particularly useful to investors, regulators, and policy makers in China and otheremerging markets in terms of understanding the contributing factors of stock price crashes. In addition,the Chinese stock market offers unique features for testing several hypotheses.

First, China's financial market and listed firms are associated with a poor information environment(Piotroski et al., 2011). For instance, Ball et al. (2000) document that despite the introduction ofinternational accounting standards and their adoption by listed firms in China, timely loss recognitionpractices still lag behind those of common law countries. The opaque nature of the Chinese stock marketmakes analyst coverage particularly important in terms of providing information to investors. Severalstudies (e.g., Firth et al., 2013; Gu et al., 2013), argue that analyst forecasts and recommendations areinfluential in China due to analysts' role in information production. The Shenzhen Stock Exchange (2011)conducted a survey of individual investors and concluded that a significant portion of retail investors relyon analyst recommendations to make investment decisions. Second, several reports have raised concernsabout optimism bias among analysts in China. Li (2008), Liu and Zhang (2008), and Wang (2009) reportthat displeasing institutional clients in China can hurt an analyst's future career.1 As Piotroski et al. (2011),we argue that it is part of Chinese culture not to release negative information unless absolutelyunavoidable. Therefore, to the extent possible, analysts value social conformity and maintain goodrelationships with the firms they cover. Overall, analyst's optimism is a concern in China. Third, theChinese database permits us to identify analyst characteristics such as whether an analyst is (1) from aninvestment bank, (2) from a brokerage firm that has business relations with mutual funds or (3) a staranalyst. The rich database allows us to disentangle potential conflicts of interest between different analystaffiliations and the impact of analysts' personal and investment bank/brokerage firm reputations on therelation between analyst optimism and crash risk.

For our empirical analysis, following Chen et al. (2001) and Kim et al. (2011a,b), we use the negativecoefficient of skewness (NCSKEW), down-to-up volatility (DUVOL), and weekly returns severely below themean (Crash) to measure the crash risk. Using a sample of 8201 firm–years, our findings suggest thatanalyst coverage and analyst optimism contribute to crash risk in China. We find that a firm's increase inanalyst coverage leads to an increase in its crash risk and this positive relation is more pronounced whenthe analysts are more optimistic. In addition, the impact of analyst optimism on crash risk is morepronounced when analysts are from investment banks or analysts' brokerage firms having businessrelations with mutual funds. In contrast, we find weak evidence to suggest that the impact of analystoptimism on crash risk is less pronounced when analysts have a high personal reputation or are affiliated

1 Several news reports in China state that analysts are under pressure to provide optimistically biased opinions. A detailed surveystudying this issue was presented at Sina.com (http://finance.sina.com.cn/stock/qsth/20081129/03485569032.shtml, accessed onNovember 27, 2011).

http://finance.sina.com.cn/stock/qsth/20081129/03485569032.shtml

219N. Xu et al. / Pacific-Basin Finance Journal 25 (2013) 217–239

with reputable brokerage firms. Our results are robust to alternative variable measures, different samples(with and without zero analyst coverage), and different regression model specifications.

We make several contributions to the literature. First, our research extends the emerging literature offorecasting crash risk. This paper identifies a new negative effect of analyst coverage and analystoptimism: They can increase crash risk. Our evidence suggests that, at the firm level, there exists adeterminant of crash risk beyond internal characteristics (financial report opaqueness, the value of CFOoption portfolios, corporate tax avoidance, and accounting conservatism). Second, we provide additionalinsight into the role of conflicts of interest (Ljungqvist et al., 2007; Mehran and Stulz, 2007; Firth et al.,2013; Gu et al., 2013) and reputation (Hong et al., 2000; Cowen et al., 2006; Fang and Yasuda, 2010)within the vast body of sell-side analyst research.2 We find, on the one hand, that conflicts of interest canbias analyst research upward and aggravate crash risk. On the other hand, both personal reputation andbrokerage firm reputation can work as a disciplinary mechanism against analysts' tendency to issueoptimistic reports and ultimately attenuate crash risk. Third, our findings offer a new, informationproduction agent (analysts) view of the release of bad news in stock price crashes. While our bad newsrelease view is similar to the bad news hoarding theory of stock price crashes (Jin and Myers, 2006; Bleckand Liu, 2007), we focus on analysts' behavior rather than corporate insiders'. Our results suggest thatanalysts, through their optimistic information production, contribute to the slow release of bad news onthe firms they cover. By delaying the release of bad news, analyst coverage and analyst optimism renderfirms prone to future stock price crashes.

2. Hypothesis development

Sell-side analysts' supposed role is to act as an information intermediary, channeling informationfrom firms to investors in the form of earnings forecasts, recommendations, and detailed reports. Ifanalysts reveal firm-specific information (especially bad news) to investors, then a firm's informationtransparency would increase. Recent studies show that lack of information transparency increases astock's crash risk by enabling managers to hide and accumulate bad news (e.g., Jin and Myers, 2006;Hutton et al., 2009; Kim et al., 2011a,b).

Analysts, however, are not bound to fully and truthfully report their private information (Beyer et al.,2010). Generally, sell-side analysts tend to issue optimistic earnings forecasts and recommendations.3

Thus, if analysts tend to make optimistic earnings forecasts and recommendations, the negativeinformation of the firms they cover cannot be revealed in a timely fashion to outside investors. Whenthe accumulated negative information reaches a tipping point, it will suddenly be released to the stockmarket, bursting the bubble and resulting in a stock price crash (Jin and Myers, 2006; Hutton et al., 2009).Thus, analyst coverage can increase crash risk. Whether analyst coverage is positively or negatively relatedto the crash risk is a research question. Recent research findings, such as those of Chan and Hameed(2006), suggest that analysts in emerging markets provide more market-wide information thanfirm-specific information. Given that China exhibits typical emerging market characteristics, we expectanalyst coverage to be positively related to crash risk. We put forth the following hypothesis.

H1. All else being equal, analyst coverage is positively associated with future stock price crash risk.

Following H1, we argue that the positive impact of analyst coverage on crash risk should be morepronounced for firms covered by more optimistic analysts. This leads to the second testable hypothesis.

H2. All else being equal, the positive association between analyst coverage and crash risk is morepronounced when firms are covered by more optimistic analysts.

Empirical results consistent with H2 corroborate the analyst optimism explanation of H1 for thepositive relation between analyst coverage and crash risk. That is, if the positive relation between analyst

2 Mehran and Stulz (2007) offer an excellent review of the conflicts of interest in financial institutions.3 For example, from 1995 through 2001, only 4% of all recommendations on seasoned stocks were rated underperform or sell. Most

recommendations issued during that period were favorable, up to the rating of strong buy. In addition, since 2002, analyst tendencytoward optimism has persisted and stock recommendations are still biased upward (Mola and Guidolin, 2009).


coverage and crash risk is not caused by analyst optimism, we will not observe evidence consistent withH2.

With the next two hypotheses, we propose that the factors that influence analyst optimism also impactthe relation between analyst coverage and crash risk. Specifically, we consider these factors from twoperspectives: the presence of conflict of interest in sell-side research (i.e., the conflict of interesthypothesis) and the role of reputation (i.e., the reputation hypothesis).

For the conflict of interest hypothesis, we argue that there are two ways that sell-side analysts canincur conflicts of interest in their earnings forecasts and recommendations. First, sell-side analysts whowork for investment banking houses could come under pressure to publish more favorable research abouttheir employers' current or potential clients to help boost investment banking fee revenue (Dugar andNathan, 1995; Lin and McNichols, 1998; Michaely and Womack, 1999; Agrawal and Chen, 2008). Ifanalysts provide optimistic research to attract lucrative underwriting business to their firms, then analystsworking at investment banks that provide underwriting services should issue more optimistic earningsforecasts and recommendations compared with those employed in places that do not provideunderwriting services. Therefore, under the conflict of interest argument, firms covered by analystsfrom investment banks face greater crash risk.

Second, analysts are under pressure to help their brokerage firms to satisfy institutional investors. Thereare anecdotal evidences (e.g., Li, 2008; Liu and Zhang, 2008; and Wang, 2009) suggesting that displeasinginstitutional clients in China can hurt an analyst's future career. For instance, Li (2008) reports a case of ananalyst whomade negative comments on KweichowMoutai, a major liquor producer in China. His employerimmediately received substantially fewer trading commissions as institutional investors directed less tradingto the brokerage firm. After a fewweeks, the analyst changed the tone of his comments regarding KweichowMoutai's future stock price from “negative” to “uncertain.” The KweichowMoutai case suggests that analystsare likely to inflate their recommendations and earnings forecasts in hopes of satisfying institutionalinvestors. In a study of Chinamutual funds, Firth et al. (2013) document that an analyst's recommendation ona stock relative to consensus is significantly higher if the stock is held by the mutual fund clients of theanalyst's brokerage firm. Gu et al. (2013) find similar results when they examine mutual fund tradingcommissions to brokerage firms in China. Thus, we follow Firth et al. (2013) and Gu et al. (2013) to use thebusiness relations between an analyst's brokerage firm andmutual funds as a proxy for an analyst's conflict ofinterest.We argue that analysts at brokeragefirmswith business relations tomutual funds have a tendency toissue optimistic research report. Therefore, under the conflict of interest hypothesis, firms covered by analystsfrom brokerage firms with business relations to mutual funds face greater crash risk. Our testable hypothesisis as follows.

H3. All else being equal, the positive association between analyst coverage and crash risk is morepronounced when firms are covered by analysts who face greater conflict of interest.

Regarding the reputation hypothesis, prior studies show that individual and institutional reputationscan curtail analyst optimism. At the personal level, analysts face a trade-off between generating revenuesfor their employers' brokerage and investment banking businesses and their own future career concerns.In the short run, analysts may gain substantial underwriting or trading-related compensation bypublishing optimistic research. In the long run, however, their biased research can damage theirreputation and long-term career prospects (Hong et al., 2000; Hong and Kubik, 2003). Because analystswith better personal reputation have greater long-term benefits to lose, they are less likely to succumb toinvestment banking or brokerage pressure in the short run (Fang and Yasuda, 2010; Ljungqvist et al.,2007).

Similarly, at the employer level, a brokerage firm's reputation capital is also important for its long-termsuccess. Brokerage firms have strong incentives to build and preserve their reputation, motivating them tobetter supervise the actions of individual analysts (Fang and Yasuda, 2010). Cowen et al. (2006) find thatthe analysts at the six largestWall Street investment banks in the underwriting market give less optimisticforecasts and recommendations than those working at other investment banks, syndicates, or brokeragefirms. Ljungqvist et al. (2006) and Ljungqvist et al. (2007) find that analysts employed by highly reputedinvestment banks issue less aggressive recommendations. Therefore, under the reputation hypothesis, weargue that the reputation of both the analyst and the brokerage firm can curb analyst optimism and firms

Table 1Sample development and fiscal years. Panel A shows the sample development. Panel B shows the distribution of the sample by year.

Panel A: sample development

Number of firm–years

Beginning sample from 2004–2012 16,672Excluding firm fiscal years:With incomplete stock return data (fewer than 30 weeks) 1077B-Share stocks 954Financial services firms 179With insufficient data to calculate control variables 2015Without analyst coverage 4246Final sample 8201

Panel B: observations in each fiscal year

Year 2004 2005 2006 2007 2008 2009 2010 2011 2012 Total

# 293 538 741 831 884 945 1138 1233 1598 8201% 3.57 6.56 9.04 10.13 10.78 11.52 13.88 15.03 19.49 100.00


covered by star analysts and analysts from high-reputation brokerage firms face less crash risk, as shownin the following testable hypotheses.

H4. All else being equal, the positive association between analyst coverage and crash risk is lesspronounced when firms are covered by analysts with high personal reputation or associated withreputable brokerage firms.

3. Sample development, variable measurement, and research design

This section presents the empirical methods, sample selection, and variable definitions.

3.1. The sample

We use two sources to construct our variables: the China Stock Market and Accounting Research(CSMAR) database and the Wind Financial Database (Wind). The CSMAR and the Wind contain analystearnings forecast from domestic brokerage firms. The CSMAR database has comprehensively collectedanalyst earnings forecast data since 2003, which was the same year analyst forecast data first becameavailable in the Wind. Consequently, we start collecting data in 2003 and continue through the end of2012. To maximize our sample coverage, we follow Firth et al. (2013) to integrate analyst earnings forecastdata from these two sources based on firm stock codes, analyst and brokerage firm names, and forecastissuance dates. Firm stock return and financial data are extracted from the CSMAR database and the Wind,respectively.

Our sample period actually begins with fiscal year 2004 because we need analyst coverage in year t −1 to predict crash risk in year t.4 We have 16,672 firm–year observations in the period from 2004 to 2012.We exclude (1) firms with fewer than 30 weeks of stock return data, (2) B-share stocks,5 (3) financialservices firms,6 (4) firm–year observations with insufficient financial data to calculate control variables,and (5) firm–year observations without analyst coverage. We are left with a final sample of 8201 firms.We present the details of the sample development and the fiscal years of the sample in Table 1.

4 We measure the stock price crash risk from 2004 to 2012 and measure the control variables from 2003 to 2011.5 China trades both A-share stocks (denominated in local currency) and B-share stocks (denominated in Hong Kong or US dollars).

The trading volume for B-share stocks has been low since 1993.6 We use a number of balance sheet variables in the regression. Financial firms have different nature of income statements and

balance sheet compared with non-financial firms. Therefore, we follow Hutton et al. (2009) to exclude financial services firms.


3.2. Measuring firm-specific crash risk

We construct three measures of crash risk following Chen et al. (2001) and Kim et al. (2011a,b). Wefirst estimate firm-specific weekly returns, denoted by W, as the natural log of one plus the residual returnfrom the expanded market model regression for each firm and year:

ri;t ¼ α þ β1irm;t−2 þ β2irm;t−1 þ β3irm;t þ β4irm;tþ1 þ β5irm;tþ2 þ εi;t ð1Þ

ri,t is the return on stock i in week t and rm,t is the value-weighted A-share market return in week t.
whereThe firm-specific weekly returns for firm i in week t are represented by Wi,t = Ln(1 + εi,t), where εi,t isthe residual in Eq. (1).
The first measure of crash risk is the negative coefficient of skewness, NCSKEW, calculated by taking thenegative of the third moment of firm-specific weekly returns for each sample year and dividing it by thestandard deviation of firm-specific weekly returns raised to the third power. Specifically, for each firm i inyear t,

NCSKEW i;t ¼ −n n−1ð Þ3=2X

W3i;t= n−1ð Þ n−2ð Þ

XW2

i;t

� �3=2� �

ð2Þ

n is the number of observations of firm-specific weekly returns of firm i during year t.
whereThe second measure of crash risk is down-to-up volatility, DUVOL, which is computed as follows. For
any stock i in year t, we separate all the weeks with firm-specific weekly returns below the annual mean(down weeks) from those with firm-specific weekly returns above the period mean (up weeks) andcompute separately the standard deviation for each of these subsamples. We then take the log of the ratioof the standard deviation of the down weeks to the standard deviation of the up weeks. Thus we have

DUVOLi;t ¼ ln nu−1ð ÞXDown

W2i;t

" #= nd−1ð Þ

XUp

W2i;t

" #( )ð3Þ

nu and nd are the numbers of up and down weeks, respectively. Both NCSKEW and DUVOL are used
wherein the crash risk literature.
For a third measure of crash risk, we use the likelihood of the occurrence of extremely negativefirm-specific weekly returns to proxy for crash risk. Following Hutton et al. (2009), we define crash weeksin a given fiscal year for a given firm as those during which the firm experiences weekly returns that are3.09 standard deviations below the mean firm-specific weekly returns over the entire fiscal year. Theindicator variable Crash equals one for a firm–year that experiences one or more crash weeks during thefiscal year; otherwise Crash is equal to zero.

3.3. Measuring analyst optimism

We use analysts' earnings forecasts to gauge analyst optimism. Following Gu and Wu (2003), we firstcalculate analyst forecasting bias as

ForecastBiasi; j;T;t ¼ AnalystForecasti; j;T;t−ActualEPSi;t� �

=Pricei;T−1

ð4Þ

earnings forecast for firm i, by analyst j, in year t, and on day T. If an analyst issues more than one
for anearnings forecastin a calendar year, we calculate the average Forecast Biasi,j,T,t. The forecast bias for firm iin year t for each analyst j is
ForecastBiasi; j;t ¼1N

XNT¼1

ForecastBiasi; j;T;t: ð5Þ

If Forecast Biasi,j,t is above zero, then we define analyst j as an optimistic analyst for firm i in year t andvice versa.


3.4. Measuring analyst coverage

We measure the intensity of analyst activity as the number of analysts, denoted Analyst. Furthermore,we divide analyst coverage into optimistic analyst coverage (Analyst_OPT) and non-optimistic analystcoverage (Analyst_NOPT). Optimistic analyst coverage is the number of optimistic analysts as defined inSection 3.3 for firm i in year t and non-optimistic analyst coverage is the difference of analyst coverage andoptimistic analyst coverage.

3.5. Measuring analyst conflict of interest

We use two methods to measure an analyst's conflict of interest. The first involves differentiatingbetween investment bank and non-investment bank analyst coverage. Following Dugar and Nathan(1995), Lin and McNichols (1998), Michaely and Womack (1999), and Agrawal and Chen (2008), we splitanalyst coverage into investment bank and non-investment bank analyst coverage. Operationally, if ananalyst's employer has an investment banking department, then the analyst is defined as an investmentbank analyst. Thus, Analyst_IB denotes the number of analysts from investment banks. The differencebetween the number of all analysts and the number of investment bank analysts is the number ofnon-investment bank analysts (Analyst_NIB). According to H3, we expect firms covered by analysts frominvestment banks to face greater crash risk.

The second method involves differentiating between analyst coverage of the brokerage firms withbusiness relations to mutual funds and that of the other brokerage firms without such business relations.Following Firth et al. (2013), and Gu et al. (2013), we split analyst coverage into that of the brokeragefirms having business relations with mutual funds and that of the other brokerage firms. The Winddatabase has a mutual fund database covering the details on stock trading commission payments toindividual brokerage firms from each mutual. We combine the above data with our analyst forecast databy manually matching the names of the brokerage firms. If an analyst j's brokerage receives commissionfees in year t − 1 from any mutual fund that has hold stock i at the end of year t − 1, and analyst j coverstock i in year t, then we consider analyst j as an analyst with mutual funds affiliation (Analyst_Affiliated) inyear t. The difference between the number of analysts and the number of mutual funds affiliated analystsis the number of non-mutual funds affiliated analysts (Analyst_NAffiliated). According to H3, we expect thepositive association between analyst coverage and crash risk to be more pronounced when firms arecovered by analysts with mutual funds affiliation.

3.6. Measuring analyst reputation

To examine H4, we measure an analyst's reputation by two methods. The first involves differentiatingbetween star and non-star analyst coverage. We follow Xu et al. (2013) and split analyst coverage into star andnon-star analyst coverage to measure analysts' personal reputation. We consider the coverage of an analystselected by New Fortunemagazine as the best analyst in year t as star analyst coverage (Analyst_Star) since yeart + 1.7 The difference between the number of analysts and the number of star analysts is the number of non-staranalysts (Analyst_NStar). We expect the positive association between analyst coverage and crash risk to be lesspronounced when firms are covered by star analysts.

The secondmethod involves differentiating between the coverage of analysts from top five and non-top fivebrokerage firms in terms of size. We split analyst coverage into that of the top five and non-top five brokeragefirms in terms of size to measure employer reputation. For each year, we sort brokerage firms in descendingorder according to the number of analysts they employ. We define the top five brokerage firms as the five thatemploy themost analysts in year t. We then consider analyst j being a top five analyst (Analyst_Top5) in year t ifthe analyst works for one of these top five brokerage firms. The difference between the number of analysts andthe number of top five analysts is the number of non-top five analysts (Analyst_NTop5). If H4 is valid, we expect

7 The selection process is similar to that of the All American Research Team. To select star analysts in the current year, New Fortunesent questionnaires covering all industries to institutional investors. The questionnaire does not pre-list any analysts' names. Allrespondents write in the names of analysts for whom they wish to vote. If the respondent votes for more than one analyst, the namesare ranked. New Fortune then adds up the scores and identifies the star analyst selections.


the positive association between analyst coverage and crash risk to be less pronouncedwhen firms are coveredby analysts from these high reputation brokerage firms (Analyst_Top5).

3.7. Control variables

Following Chen et al. (2001), Hutton et al. (2009), and Kim et al. (2011a,b), we include a set of controlvariables deemed to be potential predictors of crash risk. The variable DTURN is the detrended stock tradingvolume, which is a proxy for investor heterogeneity, or the difference in opinions between investors. The laggedNCSKEW variable is the negative skewness of past firm-specific stock returns, which is included to capture thepotential persistence of the third moment of stock returns. The variable SIGMA is the standard deviation of pastfirm-specific stockweekly returns, and RET is the averagefirm-specificweekly return over the past year.We alsoinclude standard control variables such as SIZE, defined as the logarithm of a firm's total assets; MB, defined asthe ratio of themarket value of equity to the book value of equity; LEV, defined as the book value of all liabilitiesscaled by the book value of assets; and ROA, defined as the income before extraordinary items divided by totalassets.We further control for one information transparency variable (ABACC) in our analysis, which is defined asdiscretionary accruals as estimated from themodified Jonesmodel (Dechow et al., 1995).8 Prior studies find thatlaggedNCSKEW, SIGMA,RET, SIZE,MB, andABACC are positively related to future crash risk,while LEV andROA areboth negatively related to future stock crash risk.We also include firm and year dummies to control for firm andyear fixed effects. Detailed variable definitions are given in the Appendix A.

3.8. Empirical models

3.8.1. Analyst coverage and crash riskTo investigate the effect of analyst coverage on stock crash risk, we estimate the regression equation

8 Weheighteal., 200

CrashRiski;t ¼ α þ β1Analysti;t−1 þ γ � ControlVariablesþ εi;t ð6Þ

we use NCSKEW, DUVOL, or Crash as a proxy for crash risk and Analysti is the number of analysts
wherefollowing firm i. The dependent variable is measured in year t, while all the independent variables aremeasured in year t − 1. We also include a series of control variables (discussed in Section 3.7). If H1 isvalid, β1 in Eq. (6) will be positive and significant.
3.8.2. Analyst coverage, analyst optimism, and stock crash riskTo test whether analyst optimism is the main mechanism that leads to the positive relation between

analyst coverage and crash risk, we estimate the regression equation

CrashRiski;t ¼ α þ β1AnalystXOPT i;t−1 þ β2AnalystXNOPT i;t−1þγ � ControlVariablesþ εi;t

ð7Þ

we decompose analyst coverage into optimistic and non-optimistic analyst coverage (Analyst_OPT
whereand Analyst_NOPT). The control variables are the same as those in Eq. (6). If H2 holds, β1in Eq. (7) will bepositive and significant and its magnitude should be larger than that of β2.
3.8.3. Testing the conflict of interest and reputation hypothesesTo test H3, we modify Eq. (6) to include the conflict of interest variables. We run the following regression

equations:

CrashRiski;t ¼ α þ β1AnalystXIBi;t−1 þ β2AnalystXNIBi;t−1 þ γ � ControlVariablesþ εi;t ð8Þ

CrashRiski;t ¼ α þ β1AnalystXAffiliatedi;t−1 þ β2AnalystXNAffiliatedi;t−1 þ γ � ControlVariablesþ εi;t:

ð9Þ

also include lagged share turnover (DTURNt − 1) in the regressions to control for momentum and behavioral factors (i.e.,ned investor sentiment, irrational exuberance, and bubbles) that can produce price reversals in the subsequent year (Chen et1). The coefficient is expected to be positive.

Table 2Descriptive statistics. Table 2 presents descriptive statistics for the sample in 2004–2012. Panel A reports the summary statistics for allvariables. Panel B reports the summary statistics for the zero, low, medium, and high analyst coverage groups according to the number ofanalysts in the sample. Here Q1 and Q3 are the first and third quartile values. All variables are as defined in the Appendix A.

Panel A: summary statistics for all variables

Variables Mean Std. Q1 Median Q3

Crash risk measuresNCSKEW −0.142 0.659 −0.502 −0.129 0.242DUVOL −0.099 0.476 −0.412 −0.099 0.210Crash 0.093 0.291 0 0 0

Analyst coverageAnalyst 10.590 11.000 2 7 15

Analyst optimismAnalyst_OPT 5.949 7.936 1 3 8Analyst_NOPT 4.642 7.969 0 1 5

Control variablesDTURN −0.093 0.451 −0.311 −0.031 0.183SIGMA 0.049 0.017 0.036 0.047 0.060RET −0.134 0.093 −0.177 −0.109 −0.065SIZE 21.888 1.168 21.045 21.736 22.567MB 2.466 1.819 1.284 1.819 2.987LEV 0.483 0.193 0.343 0.497 0.631ROA 0.048 0.050 0.021 0.043 0.072ABACC 0.134 0.199 0.036 0.078 0.149

Panel B: paired t-tests for crash risk measures

Zero Low Medium High Combined low, medium,and high groups (for firmswith at least one analyst)

N 4246 2778 2681 2742 8201Analyst 0 1.869 7.457 22.490 10.590NCSKEW −0.098 −0.185 −0.154 −0.088 −0.142t-Test for zero vs. low 5.1625***t-Test for zero vs. med 3.3362***t-Test for zero vs. high −0.6381t-Test for zero vs. combined 3.4833***t-Test for Low vs. High −5.4652***t-Test for low vs. med 1.6436DUVOL −0.051 −0.121 −0.108 −0.069 −0.099t-Test for zero vs. low 5.8525***t-Test for zero vs. med 4.7898***t-Test for zero vs. high 1.5309t-Test for zero vs. combined 5.3184***t-Test for low vs. high −4.0280***t-Test for low vs. med 0.9741Crash 0.100 0.098 0.087 0.096 0.093t-Test for zero vs. low 0.3311t-Test for zero vs. med 1.9075*t-Test for zero vs. high 0.6547t-Test for zero vs. combined 1.2449t-Test for low vs. high 0.2967t-Test for low vs. med 1.4517

⁎ 10% significant⁎⁎⁎ 1% significant.


To test H4, we modify Eq. (6) to include variables that measure analyst reputation. We run the followingregression equations:

CrashRiski;t ¼ α þ β1AnalystXStari;t−1 þ β2AnalystXNStari;t−1 þ γ � ControlVariablesþ εi;t ð10Þ

where

9 For(2011a)(medianbe usedsamples1995–210 Thecoveragupon re


CrashRiski;t ¼ α þ β1AnalystXTop5i;t−1 þ β2AnalystXNtop5i;t−1 þ γ � ControlVariablesþ εi;t ð11Þ

all the variables are defined earlier and in the Appendix A.

4. Empirical results

4.1. Descriptive statistics

Table 2 presents the sample's descriptive statistics. In Panel A, two of the three crash risk measures,MCSKEW and DUVOL, have different profiles in terms of mean, standard deviation, and median. For Crash,9.3% of firm–years are associated with at least one crash event. The crash risk measures in China, comparedwith those in the United States of Kim et al. (2011a,b), are lower.9 At the firm–year level, 10.59 analystsfollow a firm in a given year. There are about 5.95 optimistic and 4.64 non-optimistic analysts in a year,suggesting that, generally, analysts' earnings forecasts suffer from an optimism bias.

Panel B of Table 2 compares the crash risk measures of the sample with regard to the extent of analystcoverage. For each year, we divide the samples equally into low, medium, and high analyst coveragecategories, as well as firms with zero coverage to conduct t-tests on the mean values of crash riskmeasures. When we compare crash risk measures using low versus high analyst coverage, we find that thehigh analyst coverage group has a significantly higher crash risk than the low analyst coverage group,using NCSKEW and DUVOL. Hence, higher analyst coverage also suggests higher crash risk. We also notethat, with the exception of the CRASH, firms with zero analyst coverage generally have higher crash riskmeasures than firms with low and medium analyst coverage and these differences in crash measuresbetween zero and low/medium categories of analyst coverage are statistically significant (as in Panel B) inthe univariate t-tests, suggesting that it may be not consistent with H1. We, however, should be cautiousin interpreting the results from the univariate t-tests. As stated earlier, whether analyst coverage ispositively or negatively related to the crash risk is a research question. It is because analysts have aninformation production role (reduce crash risk) as well as hoarding information if they chose to makeoptimistic earnings forecasts and recommendations. The zero analyst coverage results in Table 2 Panel Bare based on univariate analysis without controlling for other factors that may impact crash risk. Hence,the univariate t-tests cannot show a genuine picture on the relation between analyst coverage and crashrisk. For firms with and without analyst coverage, they may have different firm characteristics. Thesedifferent firm characteristics can also contribute to the crash risk. Another possibility for the results inPanel B of Table 2 that crash risk for firms with no analyst coverage is higher than crash risk for firms withlow and medium analyst coverage is due to a nonlinear relation between analyst coverage and crash risk.

4.2. Analyst coverage and crash risk

Table 3 presents the impact of analyst coverage on crash risk. The use of the NCSKEW, DUVOL, and Crashmeasures offers three different regression models for a robust test of H1. The coefficients associated withAnalyst in all three models are positive and significant at the 1% level, suggesting that crash risk ispositively correlated with analyst coverage in China. The findings support H1.10 The result is consistentwith that of Chan and Hameed (2006), who find that analysts collect more market-wide information thanfirm-specific information in an emerging market. Given the general optimism bias of analyst earningsforecasts, an increase in analyst coverage is associated with an increase in crash risk for the average firm inChina. While greater analyst coverage increasing crash risk appears to be counterintuitive, we argue that

instance, our crash risk variable, NCSKEW, has a mean (median) of −0.142 (−0.129) in 8201 firm-year samples. Kim et al.report an average (median) NCSKEW in the United States of about −0.079 (−0.077); Kim et al. (2011b) report an average) NCSKEW in the United States of about 0.034 (−0.001). It seems that Chinese firms face crash risk. However, caution shouldwhen comparing these crash risk measures between Chinese and US firms, since these variables are measured for differentand different periods. For example, Kim et al. (2011a) use a sample of 87,162 firm–year observations for the period

008 and Kim et al. (2011b) use a sample of 29,638 firm–year observations for the period 1993–2009.results are qualitatively the same when we include a square term of analyst coverage in Table 3. The square term of analyste is not statistically significant, suggesting no nonlinear relation between analyst coverage and crash risk. They are availablequest.

Table 3Impact of analyst coverage on future stock price crash risk. This table presents the impact of analyst coverage on crash risk. Allvariables are as defined in the Appendix A. The p-values reported in parentheses are based on standard errors clustered by both firmand time. The superscripts *, **, and *** indicate statistical significance at the10%, 5% and 1% levels, respectively.

NCSKEW DUVOL Crash

Analystt − 1 0.008** 0.005** 0.019***(0.011) (0.011) (b0.001)

DTURNt − 1 0.009 0.045 0.029(0.795) (0.404) (0.804)

NCSKEWt − 1 0.032*** 0.014* 0.068(0.001) (0.064) (0.331)

SIGMAt − 1 4.350* 2.854 5.094(0.085) (0.145) (0.598)

RETt − 1 0.839** 0.631** 2.687*(0.030) (0.041) (0.085)

SIZEt − 1 −0.067*** −0.054*** −0.243***(b0.001) (0.006) (b0.001)

MBt − 1 0.014*** 0.008** 0.016(b0.001) (b0.001) (0.552)

LEVt − 1 0.010 0.006 −0.179(0.910) (0.922) (0.500)

ROAt − 1 0.275 0.177 −0.860(0.627) (0.693) (0.381)

ABACCt − 1 0.010 0.009 0.165(0.814) (0.619) (0.382)

Constant 1.343*** 1.131*** 3.524***(0.020) (0.009) (0.001)

Year fixed effects Yes Yes YesFirm fixed effects No No NoN 8201 8201 8201Adjusted R2/Pseudo-R2 10.10% 10.36% 7.06%


greater analyst coverage in China only means more noise or bias, since the earnings forecasts are overlyoptimistic.

For the control variables, lag value of crash risk (NCSKEWt − 1), standard deviation of stock returns(SIGMAt − 1), stock mean returns (RETt − 1), and market-to-book ratio (MBt − 1) are positive andsignificant, which are consistent with the prior literature (e.g., Chen et al., 2001 and Kim et al., 2011a).That is, past return skewness, past return, and past total risk on stock return, and past market-to-bookratio are all positively related to crash risk. We find that the firm size (SIZEt − 1) variable is negative andsignificant, which is in contrast to the findings in the literature. That is, a larger Chinese firm, on average,tends to have a lower crash risk or vice versa. We contend that the Size variable likely captures someunobserved firm characteristics that are unique to China. Thus, it may be useful to control for firm fixedeffect in the regression models.

4.3. Robustness checks for analyst coverage and crash risk

4.3.1. Causal effect of analyst coverage on crash riskAnalyst coverage and crash risk may be endogenously determined. To address the potential

endogeneity problem (i.e., analyst coverage may not be exogenously determined) between analystcoverage and crash risk, we follow Yu (2008) and add an instrumental variable when estimating therelation between analyst coverage and crash risk. Specifically, we use EXP_COVi,t (the expected analystcoverage of firm i in year t) as an instrumental variable for analyst coverage. Our logic is that when abrokerage house reduces (increases) its size, it employs fewer (more) analysts and tends to drop (add)some of its existing coverage to reduce (expand) its total workload. Therefore, EXP_COVi,t is calculatedbased on the change in size of brokerage houses and we treat it as an exogenous variable because it isunlikely to be affected by firm characteristics.

Table 4Robustness checks for the impact of analyst coverage on future stock price crash risk. This table presents the results ofseveral robustness checks for the impact of analyst coverage on crash risk. Panel A shows the results of an instrumentalvariable approach estimation of the impact of analyst coverage on crash risk. Panel B shows the results of usingLn(1 + number of analysts) rather than the raw number of analysts. Panel C shows the results for the sample with zeroanalyst coverage. If a firm is not covered by any analysts, Analyst equals zero and one otherwise. Panel D shows the resultscontrolling for firm fixed effects. Panel E shows the results using Crash_1% and Crash_0.01% to measure crash risk. Forbrevity, we do not report the results for the coefficients of the control variables in Panels B to E but they are available uponrequest. All the variables are as defined in the Appendix A. The p-values reported in parentheses are based on standarderrors clustered by both firm and time. The superscripts *, **, and *** indicate statistical significance at the10%, 5% and 1%levels, respectively.

First stage Second stage

Analystt − 1 NCSKEWt DUVOLt Crasht

Panel A: instrumental variable approach estimationPredicted_Analystt − 1 0.005*** 0.003** 0.002**

(0.003) (0.023) (0.021)DTURNt − 1 −0.035 0.074** 0.075*** 0.024*

(0.759) (0.010) (b0.001) (0.086)NCSKEWt − 1 0.206*** −0.128*** −0.090*** −0.039***

(0.001) (b0.001) (b0.001) (b0.001)SIGMAt − 1 65.831*** −0.030 0.009 −0.901

(b0.001) (0.992) (0.997) (0.219)RETt − 1 9.320*** 0.346 0.335 0.113

(b0.001) (0.477) (0.346) (0.273)SIZEt − 1 1.638*** 0.081*** 0.062*** 0.010

(b0.001) (0.008) (0.003) (0.414)MBt − 1 0.265*** 0.041*** 0.028*** 0.008**

(b0.001) (b0.001) (b0.001) (0.028)LEVt − 1 −0.607 −0.176 −0.137* −0.057

(0.380) (0.120) (0.088) (0.259)ROAt − 1 30.034*** 1.092*** 0.955*** 0.025

(b0.001) (0.005) (b0.001) (0.885)ABACCt − 1 −0.568*** −0.007 −0.005 −0.002

(0.006) (0.871) (0.867) (0.940)EXP_COVt − 1 0.573***

(b0.001)Year fixed effects Yes Yes Yes YesFirm fixed effects Yes Yes Yes YesN 7768a 7768 7768 7768R2 87.15% 12.84% 13.12% 5.51%F-statistics for the joint significance of the instruments 1581.73***

NCSKEW DUVOL Crash

Panel B: using Ln(1 + number of analysts) rather than the raw number of analystsLn Analystt − 1 0.075** 0.049* 0.118**

(0.047) (0.055) (0.048)N 8201 8201 8201Adjusted R2/Pseudo-R2 9.81% 10.12% 6.83%

Panel C: including sample with zero analyst coverageAnalystt − 1 0.008** 0.005** 0.017***

(0.011) (0.012) (0.001)N 12447 12447 12447Adjusted R2/Pseudo-R2 9.53% 10.68% 6.54%

Panel D: controlling for firm fixed effectsAnalystt − 1 0.005*** 0.003*** 0.023***

(b0.001) (0.002) (0.005)Year fixed effects Yes Yes YesFirm fixed effects Yes Yes YesN 8201 8201 3399b

Adjusted R2/Pseudo-R2 12.65% 12.97% 15.95%


Table 4 (continued)

NCSKEW DUVOL Crash

Panel E: different measures for Crashc

Crash_1% Crash_0.01%(1) (2)

Analystt − 1 0.008** 0.024**(0.012) (0.013)

N 8201 8201Pseudo-R2 4.85% 5.93%

a There were groups (in firms) with only one observation. We cannot use these observations in these firm fixed effect models.Therefore, the number of observations reduces from 8201 to 7768 (433 observations not used).

b We use conditional (firm fixed effects) logistic regressions here. There were 1312 groups (4802 observations) with all positiveor all negative outcomes. Therefore, the sample size reduces from 8201 to 3399.

c Following Hutton et al. (2009), we use the 0.1% cutoff of the normal distribution (3.09 standard deviations) to measure thevariable Crash in Panel A. Here we use the 1% and 0.01% cutoffs of the normal distribution (2.33 and 3.72 standard deviations,respectively) for the robust test.

Table 4 (continued)


To be specific, we first use the following equations to construct EXP_COVi,t:

11 In othe signcontrol

EXPXCOV i;k;t ¼ Brokersizek;t=Brokersizek;initial� �

� Analysti;k;initial ð12Þ

EXPXCOV i;t ¼Xnk¼1

EXPXCOV i;k;t

� �ð13Þ

EXP_COVi,k,t is the expected analyst coverage of firm i from broker k in year t, Brokersizek,t is the
wherenumber of analysts employed by broker k in year t, Brokersizek,initial is the number of analysts employedby broker k in the first year, and Analysti,k,initial is the analyst coverage for broker k's initial coverage offirm i.
In the first stage of the regression analysis, we estimate the predicted analyst coverage based on theinstrumental variable regression:

Analysti;t−1 ¼ bt þ bi þ ϕ1EXPXCOV i;t−1 þ λ� ControlVariablesi;t−1 þ ηi;t: ð14Þ

After we obtain the predicted value of analyst coverage (Predicted_Analysti,t − 1), we use it to replace theAnalysti,t − 1 variable in our main equation, Eq. (15), in the second stage of the regression analysis; that is,

CrashRiski;t ¼ at þ ai þ β1PredictedXAnalysti;t−1 þ γ � ControlVariablesi;t−1 þ εi;t ð15Þ

at and bt are the year fixed effects and ai and bi are the firm fixed effects.
wherePanel A of Table 4 shows the results of the instrumental variable regression equations with firm fixed
effect. The coefficients associated with the instrumented variable (Predicted_Analysti,t − 1) are positive andsignificant. In addition, the F-statistics (for testing the appropriateness of the instrumented variable) aresignificant at the 1% level, suggesting that our instrumented variable is a strong instrument. That is, ourmain results for H1 are qualitatively the same as those in Table 3. Using the instrumental variableapproach, our findings are not due to the potential endogeneity of crash risk and analyst coverage. For thecontrol variables, the signs are similar to those of Table 3 with two exceptions. First, after controlling forfirm fixed effect, the Size variable becomes positive and significant, a finding that is consistent with theliterature. Thus, our contention about the negative sign associated with the Size variable in Table 3 is likelydue to some unobserved unique firm characteristics in Chinese firms.11 Second, the past return skewness

ur abbreviated results for H3 and H4 in Tables 5, 6, 8 and 9 later, we also find similar scenarios for the Size variable. That is,for the variable is significantly negative without controlling for firm fixed effect and it changes to significantly positive after

ling for firm fixed effect. The results are available upon request.


variable (NCSKEWt − 1) has a negative sign in Table 4 Panel A, suggesting that, after controlling for firmfixed effect, the third moment of stock returns is negatively related to crash risk.

4.3.2. Other robustness checks related to H1We conduct a number of robustness checks on our results for H1 in Table 3, including (1) using

Ln(1 + number of analysts) instead of the raw number of analysts, (2) including samples with zeroanalyst coverage in addition to the current sample of only firms with analyst coverage, (3) controlling forfirm fixed effects,12 and (4) a different measure of the Crash variable. The findings are shown in Panels B toE of Table 4, respectively. For brevity, we only present the coefficients associated with the Analyst variable.These coefficients are all positive and significant, suggesting that our findings supporting H1 are robust.

4.4. Effect of analyst optimism on the relation between analyst coverage and crash risk

The results in Tables 3 and 4 reveal amore generalfinding regarding the positive correlation between analystcoverage and crash risk. To be precise about the association between analyst optimism and crash risk, weexamine the validity of H2 by separating the impact of optimistic and non-optimistic analysts, using Eq. (7). Thefindings are presented in Table 5. The coefficients associated with optimistic analysts (Analyst_OPTt − 1) arepositive and significant while those associated with non-optimistic analysts (Analyst_NOPTt − 1) are notsignificant. Hence, the findings in Table 5 are supportive of H2, that is, the positive association between analystcoverage and crash risk is more pronounced when firms are covered by more optimistic analysts. The signs ofthe control variables in Table 5 are the same as those in Table 3. In addition, the tests for the difference betweenestimated coefficients of (Analyst_OPTt − 1) and (Analyst_NOPTt − 1) are significant in the NCSKEW and DUVOLequations.

4.5. Robustness checks for the effect of analyst optimism on the relation between analyst coverage and crash risk

We apply similar robust checks to Table 5 as those in Sections 4.3.1 and 4.3.2, using an instrumental variableapproach to mitigate endogeneity and various alternative measures of analyst coverage and crash risk. For theinstrumental approach, we divide expected analyst coverage (EXP_COVi,t) into expected optimistic analystcoverage (EXP_COV_OPTi,t) and expected non-optimistic analyst coverage (EXP_COV_NOPTi,t). That is, we use thefollowing equations to construct EXP_COV_OPTi,t:

12 Sincfrom thcontrol

EXPXCOVXOPT i;k;t ¼ Brokersizek;t=Brokersizek;initial� �

� AnalystXOPT i;k;initial ð16Þ

EXPXCOVXOPT i;t ¼Xnk¼1

EXPXCOVXOPT i;k;t

� �ð17Þ

EXP_COV_OPTi,k,t is the expected optimistic analyst coverage of firm i from broker k in year t,
whereBrokersizek,t is the number of analysts employed by broker k in year t, Brokersizek,initial is the number ofanalysts employed by broker k in the first year, and Analyst_OPTi,k,initial is the extent of the optimisticanalyst coverage of firm i when broker k's initial optimistic analyst coverage of firm i.
Similarly, we use the following equations to construct EXP_COV_NOPTi,t:

EXPXCOVXNOPT i;k;t ¼ Brokersizek;t=Brokersizek;initial� �

� AnalystXNOPT i;k;initial ð18Þ

EXPXCOVXNOPT i;t ¼Xnk¼1

EXPXCOVXNOPT i;k;t

� �ð19Þ

e the empirical literature on forecasting crash risk is relatively recent, it is possible that our analysis omits some variablese regression equations that are correlated with other included variables. To mitigate such a potential problem, we need tofor firm fixed effects.

Table 5Effects of analyst optimism on the relation between analyst coverage and stock price crash risk. Table 5 presents the results of analystoptimism on the association between analyst coverage and crash risk. All the variables are as defined in the Appendix A. The p-valuesreported in parentheses are based on standard errors clustered by both firm and time. The superscripts *, **, and *** indicatestatistical significance at the10%, 5% and 1% levels, respectively.

NCSKEW DUVOL Crash

Panel A: basic results

Analyst_OPTt − 1 0.011** 0.007** 0.024***(0.013) (0.010) (0.002)

Analyst_NOPTt − 1 0.007 0.004 0.011(0.152) (0.235) (0.326)

DTURNt − 1 0.012 0.022 0.029(0.713) (0.478) (0.804)

NCSKEWt − 1 0.034*** 0.014* 0.078(0.001) (0.073) (0.269)

SIGMAt − 1 4.489* 3.077 4.854(0.076) (0.114) (0.616)

RETt − 1 0.870** 0.659** 2.649*(0.025) (0.041) (0.090)

SIZEt − 1 −0.055* −0.045** −0.196***(0.053) (0.036) (b0.001)

MBt − 1 0.017*** 0.010*** 0.023(0.001) (0.007) (0.383)

LEVt − 1 0.010 0.007 −0.242(0.908) (0.902) (0.425)

ROAt − 1 0.588 0.423 0.340(0.207) (0.245) (0.829)

ABACCt − 1 0.009 0.008 0.162(0.827) (0.644) (0.389)

Constant 1.055* 0.908* 2.480**(0.076) (0.052) (0.020)

Year fixed effects Yes Yes YesFirm fixed effects No No NoN 8,201 8,201 8,201Adjusted R2/Pseudo-R2 9.94% 10.19% 6.95%Test for OPT vs. non-OPT analyst P N F = 0.076 P N F = 0.047 P N χ2 = 0.250


EXP_COV_NOPTi,k,t is the expected non-optimistic analyst coverage of firm i by broker k in year t,
whereBrokersizek,t is the number of analysts employed by broker k in year t, Brokersizek,initial is the number ofanalysts employed by broker k in the first year, and Analyst_NOPTi,k,initial is the extent of the non-optimisticanalyst coverage of firm i when broker k's initial non-optimistic analyst coverage of firm i.
After constructing these two instrumented variables, we estimate the first stage of the regressionequations to obtain the predicted values of optimistic and non-optimistic analyst coverage as, respectively,

AnalystXOPT i;t−1 ¼ bt þ bi þ ϕ1EXPXCOVXOPT i;t−1 þ ϕ2EXPXCOVXNOPT i;t−1 þ λ� ControlVariablesi;t−1 þ ηi;t ð20Þ

AnalystXNOPT i;t−1 ¼ ct þ ci þ χ1EXPXCOVXOPT i;t−1 þ χ2EXPXCOVXNOPT i;t−1 þ κ � ControlVariablesi;t−1 þ μ i;t: ð21Þ

In the second stage of estimation, we use Predicted_Analyst_OPTt − 1 and Predicted_Analyst_NOPTt − 1 toreplace the Analyst_OPTt − 1 and Analyst_NOPTt − 1 variables in the crash risk equation, as follows:

CrashRiski;t ¼ at þ ai þ β1PredictedXAnalystXOPT i;t−1 þ β2PredictedXAnalystXNOPT i;t−1 þ γControlVariablesi;t−1 þ εi;t ð22Þ

at, bt, and ct are the year fixed effects and ai, bi, and ci are the firm fixed effects.
wherePanel A of Table 6shows that the coefficients associatedwith optimistic analysts (Predicted_Analyst_OPTt − 1)
are positive and significant, while those associated with non-optimistic analysts (Predicted_Analyst_NOPTt − 1)are not significant. Thus, our main results for H2 do not change after mitigating the endogeneity concern.

Table 6Robustness checks for the effects of analyst optimism on robustness checks of the relation between analyst coverage and stock pricecrash risk. Table 6 presents the results of several robustness checks for the effects of analyst optimism on the association betweenanalyst coverage and crash risk. Panel A shows the results of the instrumental variable estimation. Panel B shows the results usingLn(1 + number of analysts) rather than the raw number of analysts. Panel C shows the results controlling for firm fixed effects.Panel D shows the results using Crash_1% and Crash_0.01% to measure crash risk. All variables are as defined in the Appendix A. Thep-values reported in parentheses are based on standard errors clustered by both firm and time. The superscripts *, **, and *** indicatestatistical significance at the10%, 5% and 1% levels, respectively.

First stage Second stage

Analyst_OPTt − 1 Analyst_NOPTt − 1 NCSKEWt DUVOLt Crasht

Panel A: instrumental variable estimationPredicted_Analyst_OPTt − 1 0.006*** 0.003** 0.002**

(0.001) (0.018) (0.025)Predicted_Analyst_NOPTt − 1 0.001 0.0002 0.0008

(0.640) (0.894) (0.405)DTURNt − 1 0.961*** −0.605*** 0.070** 0.063*** 0.023

(b0.001) (b0.001) (0.015) (b0.001) (0.102)NCSKEWt − 1 0.178** −0.087 −0.128*** −0.072*** −0.038***

(0.039) (0.290) (b0.001) (b0.001) (b0.001)SIGMAt − 1 −12.521 −27.628 −0.025 0.976 −1.154

(0.468) (0.129) (0.993) (0.544) (0.108)RETt − 1 −0.005 −6.166** 0.343 0.457 0.067

(0.999) (0.037) (0.483) (0.100) (0.496)SIZEt − 1 0.928*** −0.632*** 0.085*** 0.050*** 0.012

(b0.001) (0.002) (0.006) (0.003) (0.340)MBt − 1 0.172*** −0.137** 0.041*** 0.023*** 0.008**

(0.001) (0.018) (b0.001) (b0.001) (0.029)LEVt − 1 −5.669*** 5.038*** −0.141 −0.095 −0.051

(b0.001) (b0.001) (0.222) (0.161) (0.324)ROAt − 1 −31.501*** 27.162*** 1.520*** 1.006*** 0.114

(b0.001) (b0.001) (b0.001) (b0.001) (0.560)ABACCt − 1 −0.469* 0.402 −0.004 −0.006 −0.001

(0.067) (0.123) (0.923) (0.792) (0.948)EXP_COV_OPTt − 1 1.574*** −0.262***

(b0.001) (b0.001)EXP_COV_NOPTt − 1 −0.070** 1.411***

(0.014) (b0.001)Year fixed effects Yes Yes Yes Yes YesFirm fixed effects Yes Yes Yes Yes YesN 7768 7768 7768 7768 7768R2 64.62% 61.79% 12.91% 13.37% 5.51%Test for OPT vs. non-OPT analyst P N χ2 = 0.037 P N χ2 = 0.092 P N χ2 = 0.365F-statistics for the joint significanceof the instruments

949.13***

NCSKEW DUVOL Crash

(1) (2) (3)

Panel B: using Ln(1 + number of analysts) rather than the raw number of analystsLn (Analyst_OPTt − 1) 0.059** 0.038*** 0.106**

(0.013) (0.007) (0.017)Ln (Analyst_NOPTt − 1) 0.029 0.016 0.033

(0.161) (0.234) (0.519)N 8201 8201 8201Adjusted R2/Pseudo-R2 9.88% 10.13% 6.90%Test for OPT vs. non-OPT analyst P N F = 0.023 P N F = 0.011 P N χ2 = 0.189

Panel C: controlling for firm fixed effectsAnalyst_OPTt − 1 0.007*** 0.003** 0.034***

(0.002) (0.041) (0.007)Analyst_NOPTt − 1 −0.001 −0.003 −0.003

(0.583) (0.190) (0.839)Year fixed effects Yes Yes Yes


Table 6 (continued)

NCSKEW DUVOL Crash

(1) (2) (3)

Firm fixed effects Yes Yes YesN 8201 8201 3399Adjusted R2/Pseudo-R2 12.64% 12.95% 16.04%Test for OPT vs. non-OPT analyst P N F = 0.0008 P N F = 0.002 P N χ2 = 0.017

Panel D: different measures for CrashCrash_1% Crash_0.01%(1) (2)

Analyst_OPTt − 1 0.019*** 0.047***(b0.001) (0.003)

Analyst_NOPTt − 1 −0.002 0.011(0.710) (0.612)

N 8201 8201Pseudo-R2 4.94% 6.12%Test for OPT vs. non-OPT analyst P N χ2 = 0.002 P N χ2 = 0.075

Panel C: controlling for firm fixed effects

Table 6 (continued)


Furthermore, we can draw the same conclusions from Panels B to D of Table 6 when usingLn(1 + number of analysts) rather than the raw number of analysts, controlling for firm fixed effects andusing a different measure of the Crash variable. As in Table 5, the tests for the difference betweenestimated coefficients in (Analyst_OPTt − 1) and (Analyst_NOPTt − 1) are significant in the NCSKEW andDUVOL equations. Overall, the results in Tables 5 and 6 support H2.

Table 7Analyst optimism in various groups. Table 7 compares analyst optimism in various groups sorted by investment bank or analystcharacteristics. The superscripts *, **, and *** indicate statistical significance at the 10%, 5% and 1% levels, respectively.

Panel A: investment bank analysts vs. non-investment analysts

Investment bank Non-investment bank t/Z-value

Forecast bias (mean) 0.0037 0.0032 2.01**Forecast bias (median) (0.0011) (0.00086) 2.86***Whether forecast bias N 0 56.35% 55.05% 2.63***N 75,152 11,700

Panel B: mutual fund affiliated analysts vs. non-mutual fund affiliated analysts

Affiliated Non-affiliated t/Z-value

Forecast bias (mean) 0.0038 0.0034 2.03**Forecast bias (median) (0.0011) (0.0010) 1.10Whether forecast bias N0 56.33% 55.91% 1.19N 54,549 32,303

Panel C: star analysts vs. non-star analysts

Non-star Star t/Z-value

Forecast bias (mean) 0.0037 0.0028 2.00**Forecast bias (median) (0.0011) (0.0012) −0.22Whether forecast bias N 0 56.15% 56.48% −0.49N 80,798 6054

Panel D: analysts from the top 5 brokerage firms with the most employees vs. analysts from non-top 5 brokerage firms

Non-top 5 Top 5 t/Z-value

Forecast bias (mean) 0.0037 0.0031 2.17**Forecast bias (median) (0.0012) (0.00078) 4.45***Whether forecast bias N0 56.50% 54.94% 3.78***N 68,457 18,395

Table 8Effect of conflict of interest on the relation between analyst coverage and stock price crash risk. This table presents the regression analyses ofthe effect of conflict of interest on the relation between analyst coverage and crash risk. Panel A presents the basic results while Panel Bpresents the robustness results, controlling for both firm and fixed year effects. In Models (1) to (3), we measure conflict of interest bywhether analysts are from investment bankswith underwriting services and test the effect of investment bank affiliation. InModels (4) to (6),wemeasure conflict of interest bywhether there are business relations between analyst's brokeragefirms andmutual fund sand test the effectof their brokerage business. All the variables are as defined in the Appendix A. The p-values reported in parentheses are based on standarderrors clustered by both firm and time. The superscripts *, **, and *** indicate statistical significance at the10%, 5% and 1% levels, respectively.

Test of H3(Investment bank affiliation)

Test of H3(Mutual fund affiliation)

NCSKEW DUVOL Crash NCSKEW DUVOL Crash

(1) (2) (3) (4) (5) (6)

Panel A: basic resultsAnalyst_IBt − 1 0.009*** 0.007*** 0.020***

(0.002) (0.001) (0.001)Analyst_NIBt − 1 −0.005 −0.006 −0.006

(0.543) (0.335) (0.869)Analyst_Affiliatedt − 1 0.009*** 0.006*** 0.023***

(0.004) (0.002) (b0.001)Analyst_NAffiliatedt − 1 0.001 0.0005 −0.010

(0.598) (0.832) (0.459)DTURNt − 1 0.008 0.020 0.028 0.007 0.018 0.018

(0.816) (0.546) (0.807) (0.857) (0.577) (0.879)NCSKEWt − 1 0.032*** 0.013* 0.071 0.030*** 0.012* 0.062

(0.001) (0.060) (0.317) (0.001) (0.078) (0.383)SIGMAt − 1 4.737* 3.295* 5.888 4.477* 3.041 6.401

(0.060) (0.097) (0.543) (0.080) (0.119) (0.506)RETt − 1 0.895** 0.682** 2.735* 0.844** 0.636* 2.735*

(0.026) (0.044) (0.081) (0.036) (0.053) (0.079)SIZEt − 1 −0.066** −0.053** −0.236*** −0.068** −0.055*** −0.245***

(0.017) (0.010) (b0.001) (0.013) (0.006) (b0.001)MBt − 1 0.015*** 0.009*** 0.015 0.013*** 0.007*** 0.008

(b0.001) (0.003) (0.556) (b0.001) (0.007) (0.757)LEVt − 1 0.006 0.003 −0.247 0.016 0.010 −0.213

(0.942) (0.960) (0.411) (0.857) (0.860) (0.479)ROAt − 1 0.304 0.202 −0.678 0.297 0.191 −0.633

(0.577) (0.639) (0.650) (0.594) (0.666) (0.672)ABACCt − 1 0.009 0.008 0.165 0.012 0.010 0.174

(0.844) (0.687) (0.381) (0.776) (0.563) (0.356)Constant 1.312** 1.093** 3.381*** 1.384** 1.150*** 3.603***

(0.024) (0.014) (0.002) (0.017) (0.008) (0.001)Year fixed effects Yes Yes Yes Yes Yes YesFirm fixed effects No No No No No NoN 8201 8201 8201 8201 8201 8201Adjusted R2/Pseudo-R2 10.15% 10.42% 7.07% 10.20% 10.44% 7.17%Test for difference in twogroups of analysts

P N F = 0.089 P N F = 0.068 P N χ2 = 0.488 P N F = 0.001 P N F = 0.008 P N χ2 = 0.023

Panel B: robust results, controlling for both firm and year fixed effectsAnalyst_IBt − 1 0.007*** 0.005*** 0.026***

(b0.001) (b0.001) (0.004)Analyst_NIBt − 1 −0.008 −0.010** −0.010

(0.197) (0.015) (0.808)Analyst_Affiliatedt − 1 0.007*** 0.004*** 0.031***

(b0.001) (b0.001) (b0.001)Analyst_NAffiliatedt − 1 −0.002 −0.002 −0.210

(0.524) (0.204) (0.226)Year fixed effects Yes Yes Yes Yes Yes YesFirm fixed effects Yes Yes Yes Yes Yes YesN 8201 8201 3399 8201 8201 3399Adjusted R2/Pseudo-R2 12.70% 13.05% 15.98% 12.78% 13.07% 16.34%Test for difference in twogroups of analysts



Table 9Effect of reputation on the relation between analyst coverage and stock price crash risk. Table 9presents the regression analyses of theeffect of reputation on the relation between analyst coverage and crash risk. Panel A gives the basic resultswhile Panel B provides a robustcheck by controlling for both year and firmfixed effects.Models (1) to (3) present the effects of personal reputation according towhetheranalysts are star analysts. Models (4) to (6) present the effects of brokerage reputation by brokerage size. All variables are as defined inthe Appendix A. The p-values reported in parentheses are based on standard errors clustered by both firm and time. The superscripts *, **,and *** indicate statistical significance at the10%, 5% and 1% levels, respectively.

Test of H4(Personal reputation)

Test of H4(Institutional reputation)

NCSKEW DUVOL Crash NCSKEW DUVOL Crash

(1) (2) (3) (4) (5) (6)

Panel A: basic resultsAnalyst_Start − 1 −0.00006 −0.004 −0.025

(0.997) (0.744) (0.592)Analyst_NStart − 1 0.008*** 0.006*** 0.021***

(0.002) (b0.001) (b0.001)Analyst_Top5t − 1 0.003 0.001 −0.018

(0.559) (0.785) (0.423)Analyst_NTop5t − 1 0.009** 0.006** 0.025***

(0.020) (0.014) (b0.001)DTURNt − 1 0.009 0.020 0.027 0.009 0.020 0.028

(0.802) (0.532) (0.817) (0.795) (0.524) (0.811)NCSKEWt − 1 0.033*** 0.014* 0.072 0.033*** 0.014* 0.073

(0.001) (0.061) (0.307) (0.001) (0.071) (0.301)SIGMAt − 1 4.411* 3.018 5.632 4.351* 2.950 5.399

(0.077) (0.113) (0.560) (0.085) (0.124) (0.577)RETt − 1 0.848** 0.642** 2.694* 0.841** 0.634** 2.701*

(0.030) (0.045) (0.084) (0.030) (0.045) (0.084)SIZEt − 1 −0.066** −0.053*** −0.235*** −0.066** −0.053*** −0.232***

(0.014) (0.007) (b0.001) (0.018) (0.009) (b0.001)MBt − 1 0.014*** 0.008*** 0.013 0.014*** 0.008*** 0.013

(b0.001) (0.005) (0.610) (b0.001) (0.004) (0.607)LEVt − 1 0.010 0.006 −0.240 0.011 0.007 −0.240

(0.912) (0.920) (0.425) (0.902) (0.907) (0.425)ROAt − 1 0.282 0.183 −0.670 0.299 0.197 −0.504

(0.618) (0.680) (0.654) (0.582) (0.651) (0.736)ABACCt − 1 0.009 0.007 0.154 0.011 0.009 0.168

(0.856) (0.730) (0.417) (0.810) (0.620) (0.373)Constant 1.330*** 1.105*** 3.352*** 1.334** 1.112** 3.329***

(0.018) (0.009) (0.002) (0.023) (0.012) (0.002)Year fixed effects Yes Yes Yes Yes Yes YesFirm fixed effects No No No No No NoN 8201 8201 8201 8201 8201 8201Adjusted R2/Pseudo-R2 10.10% 10.35% 7.07% 10.10% 10.34% %Test for difference in twogroups of analysts


Panel B: robust results, controlling both firm and year fixed effectsAnalyst_Start − 1 −0.023** −0.022*** −0.053

(0.012) (0.001) (0.370)Analyst_NStart − 1 0.007*** 0.005*** 0.027***

(b0.001) (b0.001) (0.002)Analyst_Top5t − 1 0.002 −0.002 −0.040

(0.656) (0.505) (0.218)AnalystnNTop5t − 1 0.006*** 0.004*** 0.035***

(0.001) (0.001) (b0.001)Year fixed effects Yes Yes Yes Yes Yes YesFirm fixed effects Yes Yes Yes Yes Yes YesN 8201 8201 3399 8201 8201 3399Adjusted R2/Pseudo-R2 12.76% 13.09% 16.03% 12.65% 12.95% 16.13%Test for difference analysts P N F = 0.002 P N F = 0.0002 P N χ2 = 0.197 P N F = 0.518 P N F = 0.126 P N χ2 = 0.048



4.6. Conflict of interest, analyst coverage, and crash risk

To show potential conflict of interest among analysts, we present summary statistics for analysts ininvestment banks versus those in non-investment banks, as well as for analysts with mutual fundaffiliation versus without mutual fund affiliation. The results are presented in Table 7, Panels A and B,respectively. In both panels, optimism bias is present in the mean and median earnings forecast bias, aswell as the proportion of analysts with positive earnings forecast bias, as suggested by the significant t-and Z-tests. For instance, in Panel A, investment bank analysts have a mean, median, and proportion ofanalysts with positive bias of 0.0037, 0.0011, and 56.35%, respectively. The respective statistics fornon-investment bank analysts are 0.0032, 0.00086, and 55.05%. Similarly, in Panel B, mutual fund affiliatedanalysts, on average, have statistically significant higher forecast bias than those of non-mutual fundaffiliated analysts.

4.6.1. Effect of investment bank and mutual fund affiliationWe examine the conflict of interest hypothesis (H3) with respect to the investment bank affiliation of

analysts in more detail. The findings are shown in Table 8, Panel A, Models (1) to (3). The investment bankanalyst variable (Analyst_IB) in all three models are positive and significant at the 1% or 5% level, while thenon-investment bank analyst variable (Analyst_NIB) are not significant, suggesting that crash risk ispositively associated with investment bank analyst coverage. The tests for the difference betweenestimated coefficients in (Analyst_IBt − 1) and (Analyst_NIBt − 1) are significant in the NCSKEW and DUVOLequations in the models for investment bank affiliation. Our findings support H3 in two out of three crashrisk measures.

Models (4) to (6) in Panel A of Table 8 present the conflict of interest hypothesis with respect to mutualfund affiliated analysts. Models (4) to (6) show the results of mutual fund vs. non-mutual fund affiliatedanalyst coverage. The findings in Models (4) to (6) consistently show that the coefficient associated withthe Analyst_Affiliatedt − 1 variable is positive and significant in all three models, suggesting that coverageby mutual fund affiliated analysts is associated with higher crash risk. The tests for the difference betweenestimated coefficients in (Analyst_Affiliatedt − 1) and (Analyst_NAffiliatedt − 1) are significant in all threemodels. Our findings support H3 in all three crash risk measures. Models (1) to (6) offer similar findingswhen we include a firm fixed effect (in Panel B of Table 8). Hence, our findings are robust to firm fixedeffects. Overall, we find five out of six crash risk models to offer support to H3.

4.7. The reputation hypothesis, analyst coverage, and crash risk

Panels C and D of Table 7 show potential analyst optimism bias with moderation of personal andinstitutional reputation. In terms of earnings forecast bias, star analysts and analysts associated with thetop five brokerage firms in terms of the number of employees have a lower mean forecast bias thannon-star analysts and analysts associated with non-top five brokerage firms.

We present the impact of an analyst's personal reputation on crash risk in Table 9, Panel A, Models (1)to (3). All three models show positive and significant coefficients at the 1% or 5% level for non-star analystvariable. In contrast, all three coefficients associated with star analyst variable are not significantly relatedto crash risk. The findings suggest that an analyst's personal reputation matters. Non-star analyst coverageis associated with higher crash risk. However, the F-tests on the difference between the coefficients of staranalysts and non-star analyst coverage variables are not significant in all three models.

The results for the impact of institutional reputation on crash risk are shown in Table 9, Panel A, Models(4) to (6). As for the results in Models (1) to (3), analyst variables associated with non-top five brokeragefirms have positive and significant coefficients. That is, brokerage firm institutional reputation matters.Similar to Models (1) to (3), the F-tests do not show statistically significant difference between thecoefficients of top-five and non-top-five analyst coverage variables.

The firm fixed effect robust check in Panel B offers similar conclusions as those in Panel A regarding theindividual coefficients of non-star and non-top-5 brokerage firm analysts. The F-tests for the equality ofestimated coefficients between star and non-star and between top-5 brokerage and non-top-5 brokerage,however, are statistically significant in three out of six models. Overall, we can only find a weak supportfor H4.


5. Summary

We examine the relation among analyst coverage, analyst optimism, and firm-specific crash risk inChina. We contend that analysts' coverage, through their optimistic earnings forecasts, can increase thecrash risk of the firms they cover. If analysts are overly optimistic in their earnings forecast, the negativeinformation of the firms they cover cannot be revealed in a timely fashion to outside investors. When theaccumulated negative information reaches a tipping point, it will be revealed to the market, bursting thebubble and resulting in a stock price crash. Using a sample of 8201 firm–year analyst earnings forecasts,our findings suggest that analyst coverage and analyst optimism contribute to crash risk in China. We findthat an increase in a firm's analyst coverage leads to an increase in its crash risk and this positive relation ismore pronounced when analysts are more optimistic. In addition, the impact of analyst optimism on crashrisk is more pronounced when analysts are affiliated with investment banks or their brokerage firms arehaving business relations with mutual funds. We also find some weak evidence to suggest that analystoptimism on crash risk is less pronounced when analysts have high personal reputations or are affiliatedwith reputable brokerage firms. Our results are robust to an alternative crash risk measure and differentregression model specifications.

Appendix A. Variable definitions

A. Dependent variablesNCSKEWi,t NCSKEW is the negative coefficient of skewness and is calculated by taking the negative of

the third moment of firm-specific weekly returns for each sample year and dividing it bythe standard deviation of firm-specific weekly returns raised to the third power. See Eq. (2)for details.

DUVOLi,t DUVOL is the down-to-up volatility. For any stock i in year t, we separate all the weeks withfirm-specific weekly returns below the annual mean (down weeks) from those withfirm-specific weekly returns above the period mean (up weeks) and compute the standarddeviation for each of these subsamples separately. We then take the log of the ratio of thestandard deviation of the down weeks to the standard deviation of the up weeks. See Eq. (3)for details.

Crashi,t Crash is an indicator variable equal to one if, within its fiscal year, a firm experiences one ormore firm-specific weekly returns falling 3.09 or more standard deviations below the meanfirm-specific weekly return and zero otherwise.

B. Independent variablesAnalysti,t Number of analysts who issued earnings forecasts for a firm during year t.Ln Analysti,t Ln Analysti,t = Ln(1 + Analysti,t).Analyst_OPTi,t Number of optimistic analysts for firm i in year t. In each firm, we define an analyst as an

optimistic analyst if the analyst's forecast bias is above zero. If an analyst issues more thanone forecast during year t, we calculate the average of the bias. Forecast bias = (analyst'searnings forecast − actual earnings per share) / stock closing price on the day prior to the forecast.

Analyst_NOPTi,t Number of non-optimistic analysts for firm i in year t. For each firm, we define an analystas a non-optimistic analyst if the analyst's forecast bias is not greater than zero.

Ln Analyst_OPTi,t Ln Analyst_OPTti,t = Ln(1 + Analyst _OPTi,t).Ln Analyst_NOPTi,t Ln Analyst_NOPTi,t = Ln(1 + Analyst_NOPTi,t).Analyst_IBi,t Number of analysts from an investment bank for firm i in year t. If an analyst's firm began

its underwriting business since year t, then the analyst is classified as an investment bankanalyst since year t and as a non-investment bank analyst otherwise.

Analyst_NIBi,t Number of analysts from brokerage firms without underwriting services for firm i in year t.Analyst_Affiliatedi,t Number of analysts from brokerage firms having business relationships with mutual fund

in year t. If an analyst j's brokerage receives commission fees in year t − 1 from any mutualfund that has hold stock i at the end of year t − 1, and analyst j cover stock i in year t,then we consider analystj as an analyst with mutual funds affiliation in year t.

Analyst_NAffiliatedi,t Number of analysts from brokerage firms without business relationships with mutual fund in year t.Analyst_Stari,t Number of star analysts for firm i in year t. If an analyst is selected by New Fortune as the best

analyst in year t, we consider the analyst a star analyst in year t + 1 and a non-star analystotherwise.

(continued on next page)

(continued)

A. Dependent variablesAnalyst_NStari,t Number of non-star analysts for firm i in year t.Analyst_Top5i,t Number of analysts from the top five brokerage firms that employ the most analysts. For

each year, we sort brokerage firms in descending order according to their number of analysts.If an analyst's firm is a top five brokerage firm in year t, we consider that analyst a top fiveanalyst in year t and a non-top five analyst otherwise.

Analyst_NTop5i,t Number of analysts from non-top five brokerage firms in year t.

C. Control variablesDTURNt − 1 DTURN is the average monthly share turnover for the current fiscal year minus the average

monthly share turnover for the previous fiscal year, where monthly share turnover iscalculated as monthly trading volume divided by the total number of circulating sharesoutstanding during the month.

SIGMAt − 1 SIGMA is the standard deviation of firm-specific weekly returns over the fiscal year.RETt − 1 RET is the mean of firm-specific weekly returns over the fiscal year, times 100.SIZEt − 1 SIZE is the log of the firm's total assets.MBt − 1 MB is the market-to-book ratio.LEVt − 1 LEV is the book value of all liabilities scaled by the book value of assets.ROAt − 1 ROA is income before extraordinary items, divided by total assets.ABACCt − 1 ABACC is the absolute value of discretionary accruals, where discretionary accruals are

estimated using the modified Jones model (Dechow et al., 1995).EXP_COVi,t Expected analyst coverage of firm i in year t. Following Yu (2008), we use the following

equations to construct EXP_COVi,t:EXP _ COVi,k,t = (Brokersizek,t/Brokersizek,initial) ∗ Analysti,k,initial

EXPCOV i;t ¼ ∑n

k¼1EXPCOV i;k;t� �

where EXP_COVi,k,t is the expected analyst coverage of firm i by broker k in year t,Brokersizek,t is the number of analysts employed by broker k in year t, Brokersizek,initialis the number of analysts employed by broker k in the first year, and Analysti,k,initial isthe number of the analyst coverage of firm i.

EXP_COV_OPTi,t Expected optimistic analyst coverage of firm i in year t. We use the following equations toconstruct EXP_COV_OPTi,t:EXP _ COV _ OPTi,k,t = (Brokersizek,t/Brokersizek,initial) ∗ Analyst _ OPTi,k,initial

EXPCOVOPTi;t ¼ ∑n

k¼1EXPCOVOPTi;k;t� �

where EXP_COV_OPTi,k,t is the expected optimistic analyst coverage of firm i by broker kin year t, Brokersizek,t is the number of analysts employed by broker k in year t,Brokersizek,initial is the number of analysts employed by broker k in the first year, andAnalyst_OPTi,k,initial is the number of the optimistic analyst coverage.

EXP_COV_NOPTi,t Expected optimistic analyst coverage of firm i in year t. We use the following equationsto construct EXP_COV_NOPTi,t:EXP _ COV _ NOPTi,k,t = (Brokersizek,t/Brokersizek,initial) ∗ Analyst _ NOPTi,k,initialForecast Biasi,j,T,t = (Analyst Forecasti,j,T,t − Actual EPSi,t)/Pricei,T − 1

where EXP_COV_NOPTi,k,t is the expected non-optimistic analyst coverage of firm i bybroker k in year t, Brokersizek,t is the number of analysts employed by broker k in year t,Brokersizek,initial is the number of analysts employed by broker k in the first year, andAnalyst_OPTi,k,initial is the number of the non-optimistic analyst coverage.

Appendix A (continued)

B. Independent variables


Acknowledgments

We acknowledge the helpful comments from an anonymous reviewer, Tze Chuan (Chewie) Ang,Qingbo Yuan, Weining Zhang, and seminar participants at Jinan University, Sun Yat-Sen University, andthe University of International Business and Economics. An earlier version of the paper was presented atthe 2012 Conference on Cross Strait Banking and Finance and the 2012 Financial Management AssociationInternational Asian Conference. Financial support from the National Natural Science Foundation of China(Grant Nos. 71172180 and 71271251) and the Foundation for the Author of National ExcellentDoctoralDissertation of the People's Republic of China (Grant No. 201085) are gratefully acknowledged.


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Analyst coverage, optimism, and stock price crash risk: Evidence from China