Efect of auditing:Evidence from variability of stock returns and trading volume

Chrles J.P.Chen,Bin Srinidhi,X iji Su

aChina Europe International Business School,699 Hongfeng Road,Pudong,Shanghai,PR China

bUniversity of Texas A rlington,USA

Efect of auditing:Evidence from variability of stock returns and trading volume

Charles J.P.Chena,Bin Srinidhib,*,X ijia Sua

aChina Europe International Business School,699 Hongfeng Road,Pudong,Shanghai,PR China

bUniversity of Texas A rlington,USA

A R T IC L E I N F O

Article history:

Received 22 October 2014

Accep ted 3 November 2014

Availab leonline3December2014

Auditing

A lthough the benef ts o f auditing are uncontroversial in developed markets, there isscantevidenceabout its ef ect in emerging econom ies.Auditing derives its value by increasing the credibility o f f nancial statements,which in turn increases investors’reliance on them in developed markets.Financial statement in formation is common to all investors and therefore increased reliance on it should reduce divergence in investors’assessmentof f rm value.W eexamine theefect of interim auditing on inter-investor divergencew ith a large sample o f listed Chinese f rms and f nd that it decreases more for f rms whose reports are audited com pared to non-audited f rm s.This f nding suggests that investors relymore on audited f nancial information.Resu lts o f this study are robust to variations in event w indow length and specif cation o f em pirical measures.

?2014 Sun Yat-sen University.Production and hostingby Elsevier B.V.Thisis an open accessarticleunder the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/3.0/).

1.Introduction

G lobal com petition fo r scarce f nancial resou rces has m ade it im po rtan t for em erging econom ies to stim u late the investm ent environm ent by im proving the info rm ation that is available to ord inary investors. Emerging econom ies like China have responded by undertaking two app roaches to reducing the divergence between sophisticated and other investors both in the pub lic information made available to all investors and making iteasier for the pub lic to invest:improvingmarket and legal institutions;and regu lating auditing and related institutions to imp rove the credibility of fnancial statements.China set up the Shanghai and Shenzhen stock exchanges in the early 1990’s and undertook major legal and market reforms in 1992.Onthe regulato ry side,it re-established the aud iting p rofession in 1980,allowed in ternational aud it f rm s to practice in China in 1992,established legal penalties for vio lating audit standards in 1992,promulgated the f rst set o f independent auditing standards in 1995,made audit f rms independent of local governments in 2000,m ade auditors responsible for dam ages su fered by investors from audit negligence from1The Act about the Acceptance of Tort Cases Caused by Fraudulent Financial Reporting in Security M arket enacted by the Chinese Supreme Court in 2002 def ned individualauditor’s liability for dam ages to investors for undetectedm aterialm isstatem entsand the Act of Security,passed in 2005mandates that auditors be held liable for damages to investors.2005 and adopted international accounting and auditing standards in 2007.Sim ilar measures have been adopted by other developing econom ies.

Improving the reliability o f fnancialstatementsby better auditing isbenef cial to ordinary investorson ly if such improvementm akesa discernib le dif erence in asset pricing.Otherw ise,the dem and for auditingw ill collapse and even if auditing ismandatory,audit quality w ill race to the bottom.W hile the benef cial ef ectso f aud iting in developed econom ieswhere investors are sophisticated and aud ito rs face high legaland repu tation costsarew idely recognized(see US based evidence such as in Brown and Pinello,2007),there is little evidence2Chinese and other emergingmarkets exhibit somemarket tensions because of weak country-level governance,weak legal and extralegalinstitutionsand po liticaleconom y variables(Craig,2005;Leahy,2004)thatm ight reduce theoverall reliability of fnancialstatements (LaPorta et al.,1998;H aw et al.,2004;D yck and Zingales,2004).A strand of recent literature,however,has addressed the diferential efect of auditing on the reliability of f nancial statem ents and suggests that auditing substitutes fo rweakness in the institutional variables mentioned above(Srinidhiet al.,2008;Choietal.,forthcoming).The resultsof this study are consistentw ith theargument that the efect of auditing in these emergingmarkets is in fact,stronger than in themore developed markets.that aud iting benef ts investo rs in em erging econom ies w ith less developed m arkets.

From a policy perspective,for developing econom ies that face competing demands for scarce resources,it is not clearwhether establishing auditing as an independent institution3Establishing the audit institution and m ak ing it efective is costly.The cost includes the costs o f training and certifying competen t auditors and setting up a structure in which they can provide independen t op inions in addition to the cost incu rred by all listed f rm s in getting their fnancialstatements audited.prior to establishing ef ective legal and market institutions4The issue is NOT whether auditing should be p romoted atall.The issue is the sequence in which reforms are undertaken.If auditing has a d irect efect on asset p ricing even when the legal and m arket institutions are weak,a reform of the auditing institutions shou ld be undertaken early in the sequence of reform s.On theother hand,ifauditing ison ly efective in a sophisticated marketw ith strong legaland market institutions,audit reform is best undertaken after building those institutions.w ill lead to a lower divergence between investorsand greater con fdence among ordinary investors.A resolution o f this issue demands the collection o f systematic evidence on the efect o f auditing in emerging markets.Such evidence is scarce.This paper provides evidence supporting the benef cial ef ects o f auditing in an emerging econom y.

Financialstatement information af ects stock prices in two ways.The f rst is the price ef ect.Beaver(1968) points out that p rice changes in response to earnings announcements ref ect the average change in traders’beliefs.However,the average hides d if erential reactionsbetween traderswho rely solely on public info rm ation and sophisticated investors who develop private in form ation in an ticipation o f the earnings announcem en t (K im and Verrecchia,1997).This divergence between investors is cap tured by stock return variability and trading vo lume(Callen,forthcom ing;Beaver,1968).A comp lete analysis of the efect o f auditing calls for an exam ination of inter-investor divergence5We use the term“inter-investor divergence”instead of“in formation asymmetry”in this paper to denote inter-investor diferences in inform ation,because the term“info rmation asymm etry”has the connotation of information diferences between m anagers and investors, which is not the focus of this study.in addition to average p rice changes.We argue that a reduction in inter-investor divergence–amore level p laying f eld–createsgreater con fdence among ordinary investors and creates an environment that stimu lates investment.

Haw et al.(2008)exam ines the price efect of auditing in China using a window of opportunity in which num erous listed Chinese f rms had their semi-annual statements voluntarily audited by external auditors (annualauditsaremandatory).They show thatearnings response coef cients(ERC)o faudited f rmsarehigher than those fo r non-audited f rm s.In con trast,we investigate the ef ect of aud iting on inter-investor d ivergence, using twom easu res:variability o f risk-ad justed abno rm alstock returnsand trad ing vo lum e.Thisapp roach differs from the ERC app roach in th ree im portan t ways.First,it cap tures the diferential ef ects of aud iting whereasERC captures theaverageef ect.Second,returnsvariability and trading volumeencompass theoverallin fo rm ational ef ect of audited in terim f nancial repo rts,whereas ERC focuses on the efect o f aud iting on earningsonly.Third,testso f variability do not rely upon an expected interim earningsmodelwhich isdif cult to model,given thatneither audited annual reportsnor non-audited interim reportsof the last year p rovide a justif ab le p roxy for expected interim earnings.

The variability o f risk-ad justed stock returns has been shown to refect divergence between informed and uninformed investors(Ro ll,1988;M orck etal.,2000;Durnevetal.,2003;Ferreiraand Laux,2007).In particular, a selectgroup o f privately informed investors increase their return by buying(selling)securitieswhen in form ation ispositive(negative)and participating in theop tionsand futuresm arkets.On theotherhand,most investors depend on public f nancial information for their trades.Auditing should reduce this divergence if the m arket allow s o rdinary investors to benef t from the quality im provem en t in public fnancial in form ation. The use of trading volum e as our second m easure of in ter-investo r divergence is also suppo rted by a num ber o f studies.K im and Verrecchia(1991)use a two-period rationalexpectationsm odeland show that theexpected trading volume ispositively associated w ith information divergence.Atiase and Bamber(1994)and Lobo and Tung(1997)provide empiricalevidence that trading vo lume isassociated w ith information divergence.

Investors aggregate fnancial and non-f nancial in formation available to them in pricing stocks.The f ndings of Banker and Datar(1989)suggest that investors could benef t from improved audited fnancial inform ation quality if they correspondingly increase theweight they place on fnancial in formation and reduce the weight on other information.Using a sim ilar Bayesian theory-based reasoning,Yeung(2009)argues that greater uncertainty in ex-ante earnings resu lts in investors putting a greater weight on reported earnings. Financial statement information isavailable to all investorsat thesame timewhereasother in formation cou ld vary bo th across investo rs and in the tim e atwhich it becom es available to d if erent investors.H igherweighting o f comm on in fo rm ation reduces inter-investor divergence.M o reover,fnancial statem en t info rm ation (sem i-annual)is released less frequently than other public and private information into themarket.A higher weighting o f the less frequent fnancial information also contributes to reduction in variability.A t theextreme, if accounting information is theonly information availab le for pricing the stock,thestock pricewould change only tw ice in a year,reducing the price variability to nearly zero(except around the earningsannouncement times).It is themore frequent and cross-sectionally variant non-accounting in formation that contributes to stock p rice variability on a daily basis.Stock p rice variability w ill be reduced if non-accounting information isweighted less.

However,more informative announcements cou ld increase the variability in stock returns temporarily after the announcem ent because o f the diference between the announced inform ation and p rio r investo r beliefs. This diferencew ill also be sharper and m o re pronounced for aud ited earnings announcem ents that arem o re accurate.Therefo re,we expect a tem porary increase in the variability of stock retu rns(or trading volum e)followed by a more permanent decrease after earnings announcements for audited f rms compared to nonaudited f rms.Consistentw ith our expectation,we fnd that subsequent to the announcement of sem i-annual reports both the variability of stock returns and trading vo lumes are higher for a short period of two days between t=0 and t=1 and are then signif cantly smaller for the group o f audited observations compared to the group of non-audited ones.6The bid-ask-spread which is a comm on m easure of in ter-investor info rm ation divergence is not available in the Chinese market context.In a sensitivity test,we fnd that the daily high-low spread is sign if cantly lower for audited f rm s(not tabulated).In efect,these fndings show that audited fnancial in formation decreases inter-investor divergencemore than non-audited in form ation.

Our study contributes to the literature by showing that auditing o f fnancial statementshas the discernible efect of reducing inter-investor divergence even in an emerging economy such as China.In ef ect,the policy m akers in em erging econom ies are justif ed in investing resou rces in auditing and seek ing im provem en ts in f nancial statem ent quality.In con trast to am andato ry annualaudit context,this study exp loits a context that allows us to d irectly com pare diferences between the ef ects o f vo luntarily aud ited and non-aud ited interim f nancial statements.Furthermore,this study also complements the average p rice level efects of auditing found by Haw et al.(2008).

The remainder of the paper is organized as fo llows:Section 2 provides the background and literature review;Section 3 develops the theory for the p roposition that auditing af ects the variability o f stock returnsand trad ing vo lum e,and presen ts research questions and propositions;Section 4 gives the sam p le,research method and empirical resu lts;fnally,Section 5 concludes the paper.

2.Background and literature review

2.1.Context of the study:semi-annual auditing in China

Chinese regu lation requiresmandatory audit of annual fnancial statements for all listed f rms.Further,it also mandates the audit of interim sem i-annual statements for f rmsw ith poor performance records or weak fnancial positions,aswellas for f rms that p lan to issue rightso feringsor pay dividends in thesecond half o f the year.Other f rms can have their sem i-annual reports audited voluntarily.7In general,voluntary auditing of semi-annualstatements in China and quarterly statements in the USisnot forbidden.However,our setting is diferent as som e f rm s are required to have their sem i-annual statem en ts aud ited.This sensitizes investors and f rm s to the possibility and benef ts o f a sem i-annual audit.Nevertheless,in the period between 1997 and 2000,over seventy percento f f rms that did not require to beaudited got their interim statements voluntarily audited.W e note here three implications of voluntary audits for our study.The efects o f sem i-annual aud its could be attenuated by annualaudits via ex-post settling up o f accoun ts,m aking them less detectab le.By imp lication,an empirical detection o f reduced information divergence in thissetting shows that auditing of sem i-annual reportshas an efect beyond the dilutive ef ects of ex-post settling by annual audits. Second,auditorsw ith whom we held follow-up interviews to ld us that the scope,reporting requirementsand audit procedures they emp loyed in sem i-annual audits were substantially sim ilar to those used in annual audits,which makes our resu lts generalizable to annual audits.Third,some f rmsm ight systematically selfselect to be voluntarily audited.W e have taken many steps in this study to contro l for self-selection,such as Heckman(1976)correction,two-stage regression and change-model specif cation.

2.2.Related work

Two strandso f literature are relevant to this study.The f rst one exam ines the efect o f auditing in the US. While studies on direct com parison o f audited and non-audited reports are scarce,several o f these studies exam ine the ef ect o f aud it quality d if erences on fnancial statem en ts.The second strand o f literature is on the audit structu re in China that p rovides an understanding of why som e f rm s voluntarily choose to be aud ited and o thers do not.This helps us in developing con trols fo r self-selection bias.

Chow(1982)takesadvantageofa historical regulation in theUSin 1926,prior to securities laws,when externalauditwasoptionalin pub lic f rms.Hestudied thecharacteristicso f f rms thatvo luntarily chose to have their fnancial statements audited,but did not exam ine the dif erences between audited and non-audited f nancial statements.Other papersexam inevo luntaryusesofauditorexpertisein f rms thatwerenotmandated to get their statementsaudited.For examp le,Givoly et al.(1978)focuson the audit review function(notmandated)and exam ine auditor-reviewed and non-reviewed f rms.Their conclusionswere not defnitive due to small sample and data lim itations.In a fo llow-up study,A lford and Edmonds(1981)replicated Givolyetal.(1978)and found sim ilar results.As thescopeand p roceduresapp licab leto reviewsaresubstantially diferent from thoseofannual aud its,the resu lts from these stud ies canno t be generalized to other aud iting contexts.

Several o ther studies have exam ined the ef ect o f aud it quality on f nancial reporting by using research designs other than direct comparison.Becker et al.(1998)show that the Big 6 auditors constrain earnings managem ent.Teoh and W ong(1993),Choi and Jeter(1992)and Loudder et al.(1992)show that earnings of f rms thatare audited by largeauditorsexhibithigher stock return responses to earnings.Thesestudieshave focused on the efect of audit quality(typically proxied by auditor size)on earningsmanagement and stock returns and have found that higher quality audits improve the reliability o f fnancial statements.

The Chinese stock market has attracted increasing attention from accounting and auditing researchers. Chen et al.(1999)provide a descriptive analysis of the auditing requirements and environment in China. DeFond et al.(2000)present evidence that the frequency of modifed audit opinions(M AOs)increased signif cantly after the adoption of the auditing standards in 1995,which was imm ed iately fo llowed by“f igh tfrom aud it quality.”Chen et al.(2000)presen t em p irical evidence on a negativem arket reaction to m odifed audit opinions in China.Chen et al.(2001)f nd that auditors aremore likely to issue MAOs for regulationinduced earningsmanagem ent.Haw et al.(2003)show that the timelinesso f f nancial reporting isnegatively associated w ith modifed audit opinions.These fndings document the institutional background in which our study is conducted.

2.3.Voluntary semi-annual audits in China

The reason as towhy amajority of f rmsvoluntarily undertakesem i-annualaudits isparticularly intriguing in China because the fees for sem i-annualauditing,based on our investigationsw ith localaudit f rms,typically are 30–50%o f annual audit fees.M oreover,the audit could lead to an unfavorable audit opinion that cou ld impactmanagerial reputation and increase regulatory scrutiny.For the f rms that vo luntarily get their sem iannual statem entsaudited,the expected benef tsof aud iting shou ld be higher than the above-m entioned costs.

W e conducted several interview sw ith audit partners and m anagers of listed com panies to identify facto rs that m o tivated them to choose volun tary sem i-annual audits.Som e f rm s wan ted to im prove their m arket image(signaling),which in turn could help in their future share issuance or business negotiations,such as those for strategic alliancesor joint ventures.M anagersof a Shanghaicompany told us,for examp le,that they were negotiating a joint venture w ith a mu ltinational company and believed that a voluntary audit wou ld m ake their companymore transparent and attractive to the potential partner.Some f rms chose sem i-annual auditsw ith a view to making annual audits less tim e consum ing and moremanageable.Aseach listed f rm is assigned a date by the Stock Exchange for pub lishing its annual report,it is important that they have the f nancial statements ready on tim e.A sem i-annual audit reduces theworkload o f the annual audit and facilitates timely reporting.M anagers also suggested that this wou ld be particu larly useful if the audit f rm was sm all and had lim ited resources.Third,som e f rm s chose external auditing to com p lem ent their internal aud iting.Fourth,better perfo rm ing f rm s that had signif cant increases in revenue and p rof ts in the f rst half o f the year were m o re likely to choose volun tary aud iting to convey this inform ation credibly to the investment community.These interviews helped us identify determ inants of vo luntary audits and develop a self-selection m odel to contro l for potential bias.

3.Theoretical development and research questions

The theoreticalbasis for the efect of auditing on returns’variance(or stock p rices’variance)in steady state is obtained from the follow ing reasoning that is formally developed in Appendix A.

1.In valuation decisions,investorsaggregateaccounting and non-accounting information.The relativeweight p laced on each of the two information sources is p roportional to its performance sensitivity and precision (Banker and Datar,1989).

2.Audit could decrease the biasand increase the precision of accoun ting in fo rm ation.If investors discern this im provem ent in the quality,they w ill p lace higher weight on f nancial statem en t in form ation relative to non-fnancial info rm ation in audited f rm s com pared to non-audited f rm s.This is shown in the f rst part o f Appendix A.

3.Accounting information,whether it is audited or not,is common across all investors.Non-accounting information can either be public and common across investors(such as public disclosures of new product introductions,managem ent changes,and strategic initiatives)or p rivate(generated by the private insights o f the analyst or the investor).If investors increase the weight on common accounting information,it reduces the inter-investor divergence regarding the estimated stock p rice for the f rm.This is formally shown in the second part o f Appendix A.

4.W hen compared to non-audited f rm s,audited f rms’valuesareassessedmorehomogeneously across investo rs.This resu lts in a sm aller variability of stock retu rns and a lower trad ing vo lum e fo r aud ited f rm s.

The above reasoning app liesonly in the steady state afterm ost o f the investo rshave fu lly inco rpo rated the earnings information in their belief revision p rocess.However,in the short period immediately after earningsannouncem ents,the stock return variability increases(Beaver,1968;Rajgopal et al.,2002;M ay,1971;Patell and Wo lfson,1981;Gillette etal.,1999;Ederington and Lee,1996)becauseof thedeviation between the information in the earningsannouncement and prior investor beliefs.Audited information ismore likely to accentuate the deviation between reported information and prior investor belief,resu lting in higher transitory variability for audited f rms.

Weexam ine theef ectof auditing by comparing thevariability o f stock returnsand trading volum ebetween the audited and non-audited f rms.Our hypotheses stated in alternate form are: H1.Audited f rms exhibit a signif cantly lower variability in stock returns than non-audited f rm s after the announcement o f sem i-annual reports. H2.Aud ited f rm sexhibit a signif cantly lower trad ing volum e than non-aud ited f rm safter the announcem en t of sem i-annual reports.

4.Sample,researchmethod and results

4.1.The samp le

We selected years 1997–2000 as our sample period becausemany observations had m issing values before 1997 and quarterly fnancial reporting becamem andatory after 2000.Table 1 summarizes the auditing status of listed f rmsduring thisperiod.Firms in China cou ld either be restricted to domestic ownership(A shares)or cou ld haveboth domestic and foreign ownership(A and B shares).Firmscross-listed in Hong Kong also issue H-shares to trade in Hong Kong.Themotivationso f f rms issuing B or H-shares in seeking sem i-annualvoluntary auditsare diferent from those issuing only A-shares.For examp le,B and H-share f rmscould get theirin terim fnancial repo rts aud ited to attract foreign investors and to m inim ize their cost o f capital.Therefore, we lim ited our samp le to f rms that issue only A-shares.Our samplewas retrieved from the A-share f le o f the Taiwan Econom ic Journal database.Out o f a total o f 3679 f rm-year observations that were available,we excluded 396 non-A-share-on ly observations and 482 w ith m issing values,and were leftw ith 2801 f rm-year observations.Out o f these,883were audited and 1918 were not.To exam ine the ef ect of voluntary auditing, we removed 101 observationso f Special Treatment(ST)and Particu lar Treatment(PT)f rms and 374 observationsw ith rights issues during the yearwhere sem i-annualauditing ismandatory.This f ltering process left usw ith a f nal sam ple of 2326 f rm-year observations,of which 616 observationswere voluntarily audited.

Table 1 Auditing status of listed A-share f rms and samp le selection results.

4.2.Control for self-selection bias–Heckman correction

To contro l fo r self-selection,we use the Inverse M ill’s Ratio(IM R)estim ated by a probitm odel of voluntary audit choice as an additional contro l variable when comparing the efects between audited and nonaudited f rms(Johnston and D iNardo,1997;Heckman,1976).In additional analysis,we also complement these results using othermethods.W e discuss below the p robitmodel.

Our choice of variables for themodel isbased both on earlier empirical testsand our interviewsw ithmanagers and auditors in China.W hile there is no published study thatmodels vo luntary audit choice,two p rior studiesare helpful in identifying relevant variab les.Francisetal.(1999)study exam ines the choicebetween Big 6 and non-Big 6 auditors in the USby f rms to signalbetter fnancialstatementquality.Signaling by voluntary audit choice is sim ilar to signaling by voluntary choice of a high quality auditor and has been mentioned as one o f the factors in ou r interview sw ith m anagers.However,because Francis et al.(1999)is conducted in the US,we also rely on Chen et al.(2001)who fnd that earningsm anagem ent incentives in Chinam ightm otivate voluntary audit decisions.In addition to these two studies,Chow(1982)and Ettredge et al.(2000)p rovide additional guidance in the choice of variab les.Our interviewso fmanagerso f listed f rmswho had the choice to be audited and of auditorswho audited some of those f rmsalso yielded some important factors.Based on the f ndings o f p rior studies and our interviews,we developed the fo llow ing p robit model to control for self-selection:

We give below the def nitionsand then discuss the rationale for selection o f the variables in the abovem odel.

Defnitions:

OPCYCLE=Operating Cycle:[365*(average inventory/cost o f goods sold)+365*(average accounts receivab le/sales)]/30.

CAPINT=Capital Intensity:G ross PP&E/sales.

Size:natu ral logarithm of to tal assets.

Leverage:to tal long-term deb t to total asset ratio.

PE=P/E Ratio:Stock price over EPS.

ROA=sem i-annual net income over beginning total assets.

Loss:1 for net income less than 0 and 0 otherw ise.

TACCR=Total Accrual:annual total accruals.

Top5=Top 5 Auditor:1 if the auditor is among the top 5 in China(bymarket share)and 0 otherw ise.

SalesGrwth=Sales growth:(sales in year t–sales in year t-1)/sales in year t–1.

Beta:Beta estimated by themarketmodel over the period between t=-150 to t=-30.

Nontrade:Percentage of non-tradable shares outstanding.

y98,y99 y00,indicator variables for years 1998,1999 and 2000,respectively.

IND:Twen ty-one Industry dumm ies based on Chinese industry classif cation.

i:f rm indicato r.

t:interim period indicator,t-1 for beginning of the year.

The inclusion o f OPCYCLE,CAPINT,Size,Leverage,PE and Loss in themodel isbased on Francisetal. (1999).Firm sw ith longer operating cyclesdevelop accrualestimatesover a longer timehorizon and are therefore likely to havemoremeasurem ent errors(seeDechow and D ichev,2002).This resu lting skepticism among investors increases the need felt by the f rm to send a positive audit signal.Accordingly,we expect f rm sw ith longer operating cycles to opt more frequently for vo luntary auditing.Firms w ith high capital intensity (defned as gross property,p lant and equipment divided by sales)have relatively high depreciation,and their m anagers can choose the depreciation m ethod aswell as estim ated usefu lasset lives to tim e the recognition o f related expenses.Here again,aud iting can im prove the perceived reliability o f repo rted earnings and asset values.8As our test context is diferent from that of Francis et al.(1999),who em p loyed operating cycle and cap ital in tensity to exam ine Big 6 auditors’role in the credible reporting of accruals,we do not expect allvariables adop ted from theirmodel to afect the choice of sem iannual auditing in the sameway that they afect the choice of Big 6 auditors.W e include f rm size in our m odel to control for f rm-level diferences in innate credibility and their in formation environment.We expect large f rms to have less need for sem i-annual auditing,ceteris paribus, since their fnancial reports arem ore carefu lly scrutinized by the public than those of smaller f rms.Consequently,their f nancial reports are generally perceived to bemore reliable.As a f rm’s debt level increases, its debt ho ldersmay need to monitor itsmanagement team more closely.Therefore,f rmsw ith high leverage ratios are more likely to em ploy sem i-annual audits.Firms w ith low Price Earnings(PE)ratios are often undervalued.M anagerso f these f rms aremore likely to resort to external auditing in their attempts to communicate to investors that their f rmsare good investment opportunities.Thus,we expect f rmsw ith lower PE ratios to optmore frequently for interim auditing.

The selection of four o ther variables,nam ely ROA,Top5,SalesGrwth,and Loss,was based on ou r in terview sw ith partners of audit f rm s and m anagers of listed com panies.ROA is the ratio o f the sem i-annual period income over thep reviousyear-end’s totalassets.Some partnerssuggested that f rms that do well in the f rst part of theyear choose to be audited to signal thegood newsearly to themarket.Based on this rationale, we expect the audited f rms to have a signif cantly higher ROA than non-audited f rms.Large(Top5)auditors aremore independent,have high reputation and aremore likely to issuemodifed audit opinions(DeFond et al.,2000,2002;Ashton and Kennedy,2002).9Identifying a group o f large auditors as high quality in Chinam ay be arb itrary.Therefo re,we also used other classif cation schemes such as Top 10(DeFond et al.,2000)instead of Top 5 and did not fnd qualitatively diferent emp irical resu lts.In anticipation o f being held to higher standards by large auditors,f rmsm ight be less willing to be vo luntarily audited by them.Another factor is auditor workload. Smallauditorshave lim ited resources thatarestretched during annualauditsandm ightencourage their clients to op t for sem i-annual audits to sm ooth out theirwork load.A t the sam e time,the vo luntary audit choice signalw illbe even m o re powerfuland the benef tsm ight be seen to be higher if a Top5 auditor is chosen.Therefo re,we do no t pred ict a sign on this variab le bu t recognize that it isan im portant contro l variab le.Firm sw ith low sales grow th or losses repo rted in them ost recent f scal period are expected to be lessw illing to have their sem i-annual reports audited.

Further,high-risk f rms(thosew ith high accrualsand high beta values)are likely toweigh thenegative consequences o f audit more than its incremental benef ts;but low-risk f rms are more likely to choose to be audited.A variable that isunique to China is thepercentageo f outstanding non-tradab le shareswhich proxies for government control of the f rm.Usually,managers in government-controlled f rmshave lessneed to communicatew ith investors,as these f rms depend lesson themarket for fnance and receive government protection from regu latorsand investors.Therefore,we expect f rmswithmorenon-tradable shares to show a lower propensity to have their sem i-annual reportsaudited.In ourmodel,we employ an indicator variab le for each year and each industry to contro l fo r industry and year ef ects.

In o rder to construct a parsim onious m odel,we exclude variables that are trivial in ou r sam p le or no t repo rted to be signif cant in prior studies.For exam p le,the p ropo rtion of comm on stock owned by o f cers and directors is not included because both themean and median values o f this variab le in our sample aretoo low to af ect the aud it choice.The ratios o f invento ry and receivables over total assets are captu red by total accruals in ourmodel.The number o f business segments is not relevant formost f rms.

We report the probitmodel resu lts in Tab le 2.The results are generally consistentw ith our expectations. They show that the decision for sem i-annual auditing is negatively associated w ith PE ratio,loss reported in the p revious year,large auditor(Top5),risk(Beta)and percentage of non-tradab le shares outstanding. Leverage,pro f tability(ROA)and sales grow th are positively associated w ith the choice for sem i-annual auditing.Firm size hasa negative coef cient but isnot statistically signif cant,and the likelihood ratio is very signif cant,which indicates that the p robitmodel efectively dif erentiates between audited and non-audited observations.

The Heckm an(1976)co rrection for self-selection bias is an appropriate m ethod to use in this particu lar context for the follow ing reasons.The m ethod is robust in cases where the two sets of variab les overlap (one used fo r the probit m odel and the o ther to determ ine the ef ect o f aud it on in form ation d ivergence). Johnston and D iNardo(1997)argue that this correction is less sensitive to normality assum ptionswhen these two sets o f variables dif er.In this study,the variables that afect the outcome include the variability of the returnsprior to theannouncementand other variables that difer from variablesused in thep robitmodel.This m akes the IMR method less sensitive to normality assump tions.Second,in most situations,it is dif cu lt to f nd variab les that af ect probability but do not factor in the equation that tests the diferences(Johnston and D iNardo,1997).In our study,we use a number o f variab les that afect stockmarket variability and trading vo lume but they do not necessarily predict the choice o f vo luntary auditing.For example,random arrival o f value relevant information may afect both return variability and trading vo lume.However,it is not expected to af ect the choice fo r sem i-annual aud it.W e include the absolute value of cum u lative abno rm al retu rns during the announcem ent period to con trol for this factor in the m odel fo r testing the ef ect o f auditing,but not in the probitmodel.10Larcker and Rusticus(2005)show lim itations of using instrumental variables in accounting research.As an exercise of cau tion in interpreting our results,extensive robustness checksare performed and discussed in a subsequent section.

4.3.Efect of auditing on stock-return variability and trading volume

4.3.1.Auditing and stock-return variability

The follow ingmodel is employed to compare the standard deviationso f the risk-adjusted abnormal daily returnsbetween audited and non-audited sub-samples fo llow ing theannouncemento f interim f nancial reports:

where vpostis the standard deviation of f rm’s risk-adjusted abnormal daily returns after sem i-annual audit, Audit=1 if audited and 0 if not audited,vpreis the standard deviation of f rm’s risk-adjusted abnormal daily returns before sem i-annual audit,vannualis the standard deviation of f rm’s returns after announcement o f annual earningsmade p rior to each sem i-annual audit,Size is the natural logarithm o f equity’s beginning m arket value,IM R is the Inverse M ills Ratio from the p robit model,ABS_CAR is the abso lute value o f risk-adjusted cumulativeabnormal returnsover thepost-announcement period and y98,y99,y00 are indicator variab les fo r the years 1998,1999 and 2000,respectively.

Post-announcem ent retu rn variability ism easu red by the standard deviation o f risk-ad justed11W eestimate the alpha and beta of each f rm yearover the period between 150 and 30 daysbefore theannouncementof itssemi-annual report.In order to add ress concernsabou t the reasonableness of them arketm odel in China and other em ergingmarkets,wehave repeated all the tests w ith m arket-ad justed return data and found qualitatively sim ilar results.daily abno rm al returnsover three diferent eventw indowsafter the sem i-annual earningsannouncement date(+1 to+7, +1 to+15 and+1 to+30).Likew ise,pre-announcem ent return variability ismeasured by the standard deviation o f risk-ad justed abnormal returns over three dif erent time w indows before the sem i-annual earnings announcement dates(-7 to-1,-15 to-1 and-1 to-30).The announcement date is excluded from both p re-and post-announcement periods.Thismodelisestimated separately over each of the threeeventw indows. A signif cant negative coef cient on the indicator variab le,Audit,would indicate that audited sem i-annual f nancial statements are associated w ith less return variability than non-audited f rms.

Table 2Control for self selection–probit regression results.

W e contro l fo rm arket size(natu ral logarithm of them arket value o f equity at t=-30)because larger f rm s resem ble diversifed portfo lios and consequently have lower return variability.The pre-announcem en t standard deviation of retu rns(respectively over the th ree even tw indow s)is a contro l fo r o ther f rm-specif c facto rs that af ect the variability of returns.It also captures the level o f p re-announcement information divergence among investors as A tiase and Bamber(1994)fnd it to be positively related with trading volume reaction to announcementso f accounting information.Additionally,A tiase and Bam ber(1994)also fnd that trading volum e reaction is positively associated w ith the abso lute value o f cumulative abnormal returns during the announcement period.Therefore,ABS_CAR is included to control for this efect.As a further contro l for f rm-specif c factors,we include the post-annual-announcement return variability of the previous year when all fnancial reports are audited.This control variab le is necessary because o f the possibility that the trading behavior o f investorscou ld bediferentbetween theaudited and non-audited groups in our samp le irrespectiveo f the ef ect of sem i-annualaud its.W e con tro l fo r year-specif c efectsby year dumm ies.Finally,we con tro l fo r self-selection bias by including the IM R from the probitmodel as an additional control variable.

4.3.2.Auditing and trading volume

W e em p loy the follow ing m odel to exam ine the ef ects of auditing on average daily trad ing vo lum e in the threew indows def ned earlier:

where TVpostis theaveragedaily trading vo lumeafter sem i-annualannouncements,Audit=1 if audited and 0 if not aud ited,TVpreis the average daily trading volum e befo re sem i-annual announcem en ts,Size is the natu ral logarithm of equity’sbeginningm arket value,TVannualis the average daily trading volum e after annual announcem ents,IM R is the Inverse M ills Ratio from the p robit m odel,M TV is the average daily m arket trading vo lume,ABS_CAR is the absolute value o f risk-ad justed cumu lative abnormal returns over the post-announcement period and y98,y99,y00 are indicator variables for the years 1998,1999 and 2000, respectively.

Wemeasure trading volume as the average daily percentage of outstanding shares traded for a given f rm. Themarket-w ide trading volum e is the averagedaily totalnumber of all trades divided by the totalnumber o f all outstanding shares for the stock exchange.

We control for f rm-specif c ef ects by including the natural logarithm o f themarket value o f equity at t=-30,the pre-announcement trading vo lume and the post-annual announcement trading volume in the regression.W e usem arket-w ide average daily trad ing vo lum e to con trol fo r them arket-w ide trading intensity efect on the trading volum e o f the f rm.W e em p loy TVpreand ABS_CAR to contro l for the efect o f the positive association between these two variablesand the trading volume reaction to disclosureo f accounting inform ation as reported in A tiase and Bamber(1994).Finally,weuseyear indicator variables,and include the IM R to control for f xed efects and self-selection bias,respectively.

4.4.Univariate analysis

Panel A of Tab le 3 p resents the descrip tive statisticso f the variab les,vpre,vpost,vannual(standard deviations o f f rm returns before and after sem i-annual earnings announcements,and after the p revious annual announcements,respectively)andm arket size.The variability after the announcement o f sem i-annual reports (vpost)is signif cantly(p＜0.01)lower for the audited group than for the non-audited group in all the three eventw indows.

Themagnitude o f the diference in the variability after announcements is about 10%in each o f the three w indows.The p re-announcem ent period retu rn variability(vpre)is also higher fo r the non-aud ited group in the 15 and 30-day even tw indow s,bu t no t in the 7-day w indow.The change in retu rn variability(vpost-vpre) is positive only in the 7-day eventw indow for the non-aud ited group.Its negative value in all other cells indicatesa general decrease in the variability o f stock returns for both audited and non-audited groupsafter the announcement of interim reports.M oreover,the decrease in the variability is signif cantly larger for the audited group in all event w indows.Though these resu lts are consistent w ith our expectations,we do not attempt to d raw conclusions based on the univariate resu lts w ithout contro lling for other factors thatmay afect the diference between the audited and non-audited groups.The abso lute value of cumu lative abnormal returns is signif cantly smaller at conventional levels for the audited group on ly in the 7-day and 15-day event w indows,which indicates that the ef ect o f auditing on the abnormal returns doesnot persist into the future. Audited observations are larger in terms ofmarket capitalization.The IMR,by construction,is signif cantly d iferen t between aud ited and non-aud ited observations.Noting that all f rm s need to be audited annually,a com parison o f vannualbetween audited and non-aud ited f rm s fails to show signif cant diferences in any o f the th ree even tw indow s.This corrobo rates the interpretation that the d if erencesafter sem i-annualaud its are no t d riven by systematic diferencesbetween audited and non-audited f rms,becausewhen annual f nancial reportsare required to be audited for all listed f rm s,there isno system atic d if erence in stock retu rn variability during any of the post-announcem en t periods(+1 to+7,+1 to+15,+1 to+30).

Table 3 Descriptive statistics and univariate comparisons of stock-return variab ility and trading vo lum e between aud ited and non-audited f rm s.

Figure 1.

Figu re 2.

Comparison of trading volume in PanelB o f Table3 shows that theaveragedaily post-announcement trading vo lume for the audited group is signif cantly smaller than that of the non-audited group in all the three event w indows.The magnitude of the diference varies from 22%to 24%,which is econom ically material. The decrease in average trading volume over the pre-and post-announcem ent periods is signif cantly larger for the audited group than for the non-audited groups in all three event w indows.Specif cally,between-7 and+7 days relative to the announcement o f sem i-annual reports,the average trading vo lume increases slightly for both audited(from 1.501 to 1.580)and non-audited groups(from 1.685 to 2.038),but the change ismuch smaller for theaudited(0.079)than for thenon-audited group(0.647).In the-15 to+15window,the average trad ing volum e o f the audited group drops from 1.526 to 1.467(3.8%),but it increases for the nonaud ited group from 1.738 to 1.931(11.1%).In the-30 to+30 period,the average trading vo lum e for the aud ited group d rops from 1.721 to 1.305(24.2%),overshadow ing that of the non-aud ited group,which ison ly 11.2%from 1.948 to 1.729.A comparison o f TVRannualbetween audited and non-audited groups does not exhibit signif cant or consistent diferences across the threew indows.This resu lt further augm ents the interp retation that the diference in trading vo lume after sem i-annualaudits isnot d riven by systematic dif erences between audited and non-audited f rm s.

We also p lot the three-daymean and median values of variability o f returns and trading vo lume over the period between-30 and+30 in Figs.1–4.Consistentw ith our expectations,there isam arked increase in both m easures o f inter-investor information divergence immediately follow ing the announcement o f sem i-annual reports(0 to+2),but a sustained decrease thereafter.The decreases in the return variability and trading volum e are consistently greater in the aud ited group than in the non-audited group.

Figure 3.

Figu re 4.

In efect,these fgures show patterns after earnings announcements that are consistentw ith(i)short-term increases in variability and volum e repo rted in the literatu re,(ii)a steady state decrease in inter-investor belief divergence fo r all f rm s and(iii)a relatively higher decrease in d ivergence for the audited f rm s.

4.5.M ultivariate analysis

Table4 summarizes regression resultscomparing return variability and trading volum ebetween theaudited and the non-audited groups.PanelA o f Table 4 show s the retu rn variability resultso f M odel2;and panel B o f Table 4 show s the trad ing vo lum e resu lts of M odel 3.Audit coef cients in bo th m odels are signif can tly (p＜0.01)negative across three diferent w indow lengths,which indicates that audited fnancial statements areassociated w ith smaller standard deviationsof stock returnsand lower averagedaily trading volume.Compared to themean value of the standard deviation of returns in non-audited f rms,the coef cients of Audit suggest a reduction o f 31%in the 7-day w indow,35%in the 15-day w indow and 30%in the 30-day w indow. Sim ilarly,the turnover reductions are 87%,94%and 93.7%respectively in the 7,15 and 30-day w indows.12These computations are performed as follows.Consider the standard deviation of returns,Vpostfor non-audited f rms in the 7-day w indow in Table 3=2.115.The coef cient of Audit in Tab le 4 for the 7-day w indow is-.654.The reduction is com puted as.654/ 2.115=31%.These reductions are both statistically signif cant and econom icallymaterial.

The ad justed R2of the variabilitymodel increases for longer eventw indows,mainly because o f increased association between post-and p re-announcement standard deviations.The IM R coef cientsare signif cant in all cases.Consisten tw ith our expectations,the post-announcem en t return variability and trading vo lum e aresignif cantly and positively associated w ith pre-announcementand post-annualannouncement return variability and trading volume,respectively.Size hasa negativeassociationw ith return variability and trading volume in all three event w indows.Consistent w ith resu lts reported by A tiase and Bam ber(1994),the estimated coef cients of ourmeasures of p re-announcement level o f belief divergence(vpre,TVpre)and ABS_CAR are signif cantly(p＜0.01)positive.Results in both Panel A(variability)and Panel B(trading vo lum e)are consisten t w ith our p rio r expectations;they suggest greater in form ation convergence in the audited group than in the non-audited group after controlling for self-selection(IM R),general in formation environment(Size), other inherent dif erences in thevariability(vpre,vannual,TVpre,M TV),and year-specif c ef ects(year dumm ies).

Table 4 M ultivariate analysis of the efect of audit on stock-retu rn variab ility and trading volum e.

4.6.Alternative control for self-selection:two-stage regression

We employ a two-stage regression analysis through estimation of a simu ltaneous system o f equations in which the post-announcem en t return variability(o r trading vo lum e)is determ ined sim u ltaneously w ith the choice of sem i-annual aud it.W e then use all the contro l variables that we have iden tifed in M odels 1–3 to so lve them odel.Since one of the endogenous variab les(Audit)is d icho tom ous and the o ther(Vpost)is con tinuous,we adapt the p rogram suggested by K eshk(2003),which is specif cally designed to solve this type o fsystem of equations.The second stage results are given in Panels A and B o f Tab le 5.A fter we correct for simu ltaneity,we continue to f nd signif cant negative associations between the audit variable and return variability(or trading vo lume)in all threew indows.

Table 5 A lternative control fo r self-selection bias:two-stage regression.

4.7.The changemodel

To check the sensitivity of our resu ltsagainst alternativemodelspecif cations,we test the follow ing change model:

where Change is vpost-vprefor the return variability test and TVpost-TVprefor the trading volum e test.Similarly,Changeannualis thechange in return variability(or trading volume)over theannual reportannouncement period in the p rior year.The resu ltsare reported in Table 6.The estimated coef cient o f the audit variable is signif cantly negative acrossall th reew indow s fo r bo th variability and trad ing volum em odels.In add ition,we tested a size-defated variability m odel by dividing bo th the left-hand side variab le(V-pre)and the right-hand side variab le(V-post)by Size and kept all o ther con trol variab les unchanged.A fter running thism odel in all three eventw indows,we found that the resu ltswere not qualitatively diferent from that reported in Panel Ao f Table 4.Sim ilarly,we constructed a size-def ated trad ing vo lum em odel and d id not fnd results that were qualitatively dif erent from that reported in PanelB o f Tab le4.Therefore,weconclude there isno evidence that ourmain resultswere d riven by size.

Table 6 Analysis of the efect of aud it on the change between post-and p re-announcem ent stock-retu rn variab ility and trading volum e.

4.8.Robustness checks13In the interest of space,em pirical results reported in this section are no t tabulated.However,they are available from authors upon request.

4.8.1.Efect of auditing on frequency ofmodifed audit opinions

Financial statements that aremore reliable should be associated with a lower frequency ofmodif ed audit opinions(M AOs)ceteris paribus.W e adop t the logistic regression model constructed by Chen et al.(2001)to test whether f rm s w ith audited sem i-annual repo rts are less likely to receive M AOs at the year end as compared to those whose sem i-annual reports are no t audited.This m odel controls for the client’s f rm size, accoun ting perform ance(ROA),debt level,system atic risk(Beta)and o ther facto rs that afect the likelihood o f receiving MAOs in China.The resu lts show that the audited group has a signif cantly(p＜0.01)lower frequency o f receiving MAOs than the non-audited group.This evidence is consistent w ith the notion that auditing imp roves the reliability of f nancial statements and thereby decreases the likelihood of M AOs.

4.8.2.Analysis of f rms that discontinue sem i-annual audits

We compared a samp le of 435 observationswhose interim reportsare audited in the current yearw ith 377 observationswhose interim reportswere audited p reviously but not in the current year by estimating M odel (2)and f nd that the Audit variable issignif cantly negative in all three eventw indows.This indicates that f rms whose interim reports are audited in the current year show a lower return variability than f rmswho chose auditing o f interim reports in the past but have since discontinued it.This fnding is consistent w ith the argument that the reduced variability in returns arises from auditing o f interim statements that year rather than f rm characteristics or the auditing o f the interim statements in previous years.

4.8.3.Analysis of f rst-time sem i-annual audits

In this test,we focused on observations w ithout repeated sem i-annual aud its to test whether ou r results were driven by repeated ly audited observations.The resu lts rem ained qualitatively unchanged after we excluded repeated ly audited observations from our samp le.

4.8.4.Efect of auditing when alternative empirical proxiesare used

We performed additional tests to exam ine the robustness of the resultswhen alternative empirical proxies are emp loyed by repeating all regression analyses reported in Tab le 4.In the variability model,we replaced risk-adjusted returnsw ith market-index-ad justed returns to calculate the standard deviation.In the trading volum em odel,we rep laced average trading vo lumew ith total trading vo lume over the eventw indow.Results werenotqualitatively diferent.Furtherm ore,in addition to return variability and trading volume,weused the average d if erence between the daily high and low p rices of the stock(the bid-ask sp read in form ation is no t availab le to us)asa rough proxy for inform ation asymm etry and found a signif cantly larger reduction in this variab le for the audit group than for the non-audited group in all three eventwindows.

4.8.5.Examination of stock-return variability and volume using amatched sample

We also perform matched samp le tests to check the robustness of our resu lts as inherent f rm-specif c differencesbetween audited and non-audited f rmsmay afectboth preand post-announcement trading behavior. Audited observationsarematched w ith non-audited onesby year on the fo llowing f rm-specif c variab les individually:SIZE,beta,Vpreand TVpre.Thisapproach isessentially sim ilar to including these f rm characteristics ascontrolvariables in themodel.However,matched samp lesaremore homogeneousand thesubsequent comparison of the efect o f aud iting is conducted between two groupso f observationsw ith sim ilar size,system atic risk or pre-announcem en t belief d ivergence level,respectively.The resu lts are not qualitatively diferen t from those reported in Tab le 4.

4.8.6.Extended time period analysis

We exp lore thepersistent length of tim e in the diference between audited and non-audited groups.W e f nd no substantial diferences between the standard deviations of audited and non-audited observations before -30 and after+30.Even though some m inor dif erences continue for up to 180 days after the release o f sem i-annual f nancial statements,the system seems to typically reset itself after 30 days,w ith the inf ow o f more information.

4.8.7.Analysis after removing the period of variability and volume increase

As d iscussed earlier,the pattern o f variability and vo lum e changes show s an increase in the variability o f stock returns14The absence of a well-developed op tionsmarket in China precludes us from m easuring im p lied variability based on option prices. Further,since variances calculated over a shortw indow of two daysmay not be very reliable,we subtracted the variance calculated over the truncated post-announcement windows from that over the full post-announcementw indows and com pared the diferences between these variancew ith the variances in the corresponding p re-announcem ent w indow s and found them to be positive for both aud ited and non-audited f rms(show ing an increase in variance over a two-day post-announcem ent period).and vo lum e o f trad ing fo r two days follow ing the announcem ent.W e repeated ou r analysis removing the[-2,+2]time period from the samp le periods but this did not change our results.

5.Concluding remarks

Using a sampleo f Chinese f rms,wep rovideevidence thatauditing decreases in formation divergenceacross investorsm easured by reduced stock return variability and trading volume.W e fnd that the reduction in stock return variability and trading vo lume are both statistically signif cant and econom icallymaterial.Resultsare robust after contro lling for self-selection bias and several other factors.Our fndings are consistentw ith the argument that investors place more weight on audited f nancial statements than on non-audited ones in p ricing stocks.

Our resu lts show that auditing has the benef cial ef ect o f decreasing inter-investor divergence even in an em erging econom y such as China.Ou r fndings are consistentw ith the argum ent that the benef ts of aud iting in im p roving the conf dence o f ord inary investo rs who rely on pub lic info rm ation do not require a high ly developed m arket and legal infrastructu re.From a po licy perspective,em erging econom ies are justif ed in investing in auditing infrastructureand seeking to improve fnancial reporting quality to stimulate investments w ithout necessarily waiting for the fu ll development o f legal and market infrastructures.China has justif ab ly taken steps to increase investor con fdence by changes in regu lations that create a disciplined and regulated audit market(China Securities Regu lation Comm ission,2000).The actions taken by Chinese regulators include:revocation o f audit licenses for those invo lved in fraudulent fnancial reporting;closure of auditing f rms that providem isleading audit reports;imp lementation o f new audit standardsm odeled after international p ractices;and ef ecting more stringent disclosure requirements on f rms receiving modifed audit opinions.15Fo r exam p le,since1998,thenameso f f rm s that receive disclaim ers and adverseop inions are required to be exposed on the front page o fmajor securities new spapers once every two weeks.

A lthough this study is based on the Chinese context,we believe that investo rs in China arem otivated by sim ilar econom ic incentives as in other parts of theworld and to that extent the f ndings can be generalized to other emerging econom ies.However,institutional dif erences between countries should be considered when generalizing our results.

Acknowledgments

We exp ressour gratitude to Ashiq A li,Suraj Srinivasan,SunilDatta,Shyam Sunder,Sanjeev Bho jraj,Jere Francis,Dan Dhaliwal,Dan Simunic and JoeW einthrop for their excellent suggestionson an earlier version o f this paper.The paper hasalso benef ted from the commentsofworkshop participantsat City University o f Hong Kong,The Hong Kong University of Science and Techno logy and The Indian Schoo l o f Business.

AppendixA

In thisappendix,we present a formal developm ent o f our reasoning.W e show thatwhen auditing reduces the biasand/or improves the p recision of accounting information,there is less variability in stock returnsand less trading volume in audited f rms as compared to non-audited f rm s.

Step 1:Auditing increases theweight placed by investorson accounting information relative to non-accounting information in valuing stocks.

In this step,we consider only one investor and one stock.Oh lson(1995)and Easton(1999),posit a valuation m odel that com bines accounting and non-accounting in form ation.W e w rite the m arket p rice of the stock as P,a linear com bination of an accoun ting-based value as z,and a non-accounting based value as u:

In Eq.(A 1)the tim e t is supp ressed.Under the C lean su rp lusm odel in Oh lson(1995),zt=[yt-δ(R-1) yt-1]+δxt,where the subscript t rep resen tsa particu lar period,y is the book value,x is the earnings,R is the risk-free return andδisa scalar.In amoregeneral case,we can think o f z as thevaluation that resu lts from allaccounting inform ation inclusive of(bu t no t lim ited to)book values and earnings of cu rrent and p revious periods.On the other hand,u represents thevaluation that results from allnon-accounting information available in themarket during the relevant period.

For any particu lar individual investor,however,thevaluation o f thestock dependson how heor she aggregates the two sources of information.In particular,all non-accounting information is not available to all investors.Non-accounting in formation includesp rivate information that isdistributed am ong investors.Some investors receivemore in form ation than others.16There is considerable recent literature that recognizes this dif erencebetween informed and relatively uninformed investors(Easley and O’Hara,2004;Brockman and Chung,2003;Goel and Thakor,2003;Brennan and Subrahmanyam,1996).Given thesedif erences,thestock valuation by investor ican bew ritten as fo llows:

In Eq.(A 2),zRrep resents valuation that resu lts from the set o f reported fnancial statement in formation. Since f nancial statement in formation is public and common to all investors,there isno subscrip t i in the valuation o f that in form ation.17It is possible for investors to use diferent valuation functions to value common information and arrive at diferent valuations. A lternatively,the diferences in valuation function can also be viewed as d iferences in other information.Yet,zRmay still dif er from the true z(which is unobservable).We cap ture the dispersion o f the accounting information by the variance o f zR.In contrast,non-accounting information uidenotes investor i’s valuation of non-accounting in formation that he can access.18Even though much of the non-accounting information might be available publicly,its interpretation by diferent investors can be diferent.There isno common process like GAAP thatguides the production and communication ofnon-accounting in formation.W eseek to capture this aspect of non-accounting in formation in them odel by the term ui.The valuation component uicould vary across dif erent investors depending on the access,interpretation ability and the ef ort of the investors.19W eassum e the information risk to be comm on to all the investors,bu tdiferent for diferent sources of information.In otherwords,we assume thatall investorsharbor thesamedegree ofskepticism aboutaccounting information;and that they share similar skepticism about non-accounting information,which could difer from their skepticism about accounting information.W e denote dispersion in the valuation component based on non-accounting in formation by its varianceσ2.W e assum e that the stock value expected across investo rs,E(Vi)is the expected stock m arket price.

W e focus on the relative weights,γ1andγ2,that investors p lace on accoun ting and non-accoun ting valuation,respectively.In this analysis,we assume that auditing cou ld have two specif c ef ects on accounting in formation and,therefore,on valuation:(i)to screen f rmswhose fnancial reports are biased and/or unreliable by issuing qualifed reportsand(ii),to discip line the report production processand increase the precision and unbiasedness o f reported f nancial statement numbers.20W e show later that either one of these audit efects is suf cient to reduce the variance of the stock price(and returns)in them arket.

We assum e(w ithout loss of generality)thatwhen fnancial statements are not qualifed,investors do not expect statements to be biased and attribute a high reliability to numbers ref ected by a low variance of zRwhich we denote byψ21.However,when fnancial statements are qualif ed,this signals to investors the possibilitiesof biasand lower reliability in the reported accounting valuation zR,relative to unqualifed reports.W e denote the perceived bias by the variab le‘a’and the reduced perceived reliability21Th is is the signaling efect of auditing.W hile the bias and reliability of the num bersare not known,investorsw illassume that the bias and lack of reliability are at threshold levels that can be detected by an auditor after prescribed auditing practices.These threshold levels are‘a’for the bias and the increased varianceψ22.of f nancial statem en ts by an increased varianceThese notations are cap tured in the follow ing exp ressions of probability density functions22Only themean and the variance of the density function are shown in expressions(A 3).This is not meant to im p ly that the density function is fu lly defned by the f rst two m om ents.:

Further,if the f rm is not audited,the lack of audit in formation adds an additional varianceψ23.W e also denote the p rior probability o f an unqualif ed report by p.

W ith the above notation,the variance of the accounting com ponent o f the valuation in a non-audited f rm is given by

The investor optimally weighs the accounting and non-accounting sources o f valuation in formation by a m inimum variance aggregation p rocess(see Banker and Datar,1989,for a theoretical basis for the aggregation process)by solving the fo llow ing op tim ization problem23Th is prob lem is solved under theassumption that the two information sources do no t covary w ith each other.Add ing covariance does not change results,bu t com p licates the expressions.Therefore,we present the no covariance version.:

In the aboveexpression,γ1uis theweight p laced on accounting in formation andγ2uis theweight p laced on non-accounting information.The subscript‘u’denotes‘non-audited’fnancial statements.

This yields op timalweights

W ith the audit,the f rm m ight get a clean op inion w ith probability p o r a qualifed opinion w ith a p robability(1-p).The expected op tim alweigh ts w ill be as fo llow s:

In(A 7),subscrip t 1 stands for weight on accounting inform ation and subscrip t 2 for weight on nonaccounting inform ation.Subscrip t‘a’denotes audited fnancial statements.

An exam ination of(A 6)and(A 7)reveals thatγ1a＞γ1uandγ2a＜γ2u.In efect,audited fnancial statement numbers areweighted more than non-audited ones relative to theweighting of non-accounting in formation.

Step 2:Auditing reduces the variance in stock valuations by investors.

Heretofo re,we have focused on one investor.W e w ill now exam ine the d ivergence am ong investo rs.The valuation o f the stock by the i th investor is given by(A 2):

The f rst term is common to all investors.The second term consistso f non-accounting in formation,which could be dif erent for diferent investors.W hen we take the variance of Viacross investors,we have

From step 1,we know thatγ2a＜γ2u.Therefore,from(A 8)we see that the expected variance o f the stock values perceived by investors is less for audited f rms than for non-audited f rms,ceteris paribus.

Further,for a given market price of the previous period,(Pt-1),the expected return on the stock is given by(Vi-Pt-1)/Pt-1.The expected return w ill be equal to the market return.The expected variance o f the m arket retu rn w ill be equal to［Variance（Vi）］/P2t-1.Therefore,we expect audited f rm s to have a lower variance of m arket retu rns relative to non-audited f rm s.The diferences in valuation by diferen t investo rs also lead to a greater trad ing vo lum e.Therefo re,after we contro l for other determ inan ts o f trade volume,we expect the trade vo lume for audited f rms to be less than the expected trade vo lume for nonaudited f rms.

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*Corresponding author.

E-mail addresses:ccharles@ceibs.edu(C.J.P.Chen),srinidhi@uta.edu(B.Srinidhi),sxijia@ceibs.edu(X.Su).

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Inter-investor divergence

Variability of stock returns

Trading vo lume