TheReviewofFinancialStudies/v15n12002conditions[see,.,ShleiferandVishny(1986),Admati,Pfleiderer,andZechner(1994),KahnandWinton(1998),andMaug(1998)].However,asingle,“relationship”investmentstrategiesthatinvolvefirstmakingasubstantialinvestmentinafirmandtheninterveningtomonitoritsmanagement[ChernoffandStar(1993)].Infact,someinvestorssuchasWarrenBuffet,LENS,andBennetLeBowspe-cializeinstrategicor“relationship”investmentstrategies—,theLENSfund’sinvestmentstrategyhasbeendescribedbysomecommentatorsas“investinginahandfulofpoorperform-ersandthenrelentlesslypesteringtheirmanagerstoadoptabetterstrategy”[Economist(1997)].Interventionthroughsuchblocksharepurchaseshasbeenshowntoimprovecorporateperformance[Bethel,Liebeskind,andOpler(1998)].Otherinvestors,primarilyinstitutions,althoughtheydonotdelib-eratelybuyunderperformingfirmswithaviewtoimprovingmanagement,believethattheycancreatevaluebothforthemselvesandforthecompaniestheyinvestinthroughapolicyofintensemonitoringcombinedwithselectiveinterventioninexceptionalcases[CalPERS(1998)].Theevidencesupport-ingthevalueofthissortofmonitoringismixed[Gillan(1995),OplerandSokobin(1995)].Nevertheless,institutionsdopursueactivistpoliciesand,asParino,Sias,andStarks(2000)document,,theirpurchasesarecoincidentwithchangesinfirmperformance[D’Mello,Schlingemann,andSubramaniam(2000)].Theaimofthisarticleistoexplainwhy,despitetheobstaclesofshare-holderinterventiondiscussedpreviously,,whentheypur-chaseshares,,initial-ownershippositionacquiredforreasonsunrelatedtorelationshipinvesting,suchasmon-itoringbyafamilytrustownedbythedescendantsofafirms’,weassumethat,beforetheytrade,(startinginSection2),whomweterm“strategicinvestors,”areabletoengageincostlymonitoringofthefirm’’,strategicinvestors290
,,,,weanalyzethismodelanddemonstratethat,byexploitingprivateinformationregardingthecorrelationbetweentheirowntradingandmonitoringactivities,,,,informa-tionproductioniscircumscribedbyequilibriumincentiveconditions,whichrequirethatstochasticmonitoringis,exante,,,,whomweterm“core”monitors,,,“voice”and“exit”are,exante,complementarystrate-giesforinvestors,,whomweterm“fringe”monitors,,,theprofitsfromcapitalappreciationandtradingcannotoffsetmonitoringcosts,,theactivistcoremonitorswillalsogenerallynotbetheinvestorswiththegreatestwealthorthelargestinitialpositionsinthefirm’,whenmultipleinvestorsmonitor,,forfringemonitors,,-itoringnottobeanticipated,,in291
TheReviewofFinancialStudies/v15n12002equilibrium,conjecturesarealwayscorrect,(i)onlyoneinvestorneedmonitorand(ii)nocostsavingsorscaleeconomiesresultfromjointmonitoring,(1)monitoringeffortsmaybeundertakenbyanumberofdifferentstrategicinvestorswithmoderatewealthandshareholdingsratherthanexclusivelybythelargeststrategicinvestor,and(2)aninvestor’,,analyzedinSection3,,analyzedinSection4,,acomparativestaticsanalysisisusedtorelatemonitoringeffectivenessandbid-askspreadstothewealthofstrategicinvestors,marketdepth,-turemodels,inwhichstrategicinformedinvestorsarenotactivists,,inmostmicrostructuremodelswithexogenousuncertainty,increasedownershipbystrategicinvestors,relativetoliquidityinvestors,,KiniandMian(1993),,ceterisparibus,,thereisacountervailingeffect:Higherlevelsofstrate-gicownershipincreaseoptimallevelsofmonitoring,,asinKiniandMian’stests,,weconsider,inSection5,,aresultproducedbyBhattacharyaandreportedinSpatt(1988)showsthatwhenentryintotakeovercontestsiscostly,,
InvestorActivismandFinancialMarketStructurethesecuritydemandsofliquiditytraders,modifyingthemanagerialmoni-toringtechnology,incorporatinguncertaintyregardingmonitoringcosts,-reticalresearchonmarketstructure,corporategovernance,,itsnearestneighborsappeartobeWinton(1993)andCornelliandLi(1999).LikeWinton(1993),butincontrasttomuchoftherestoftheliterature,,ourassumptionthatmonitoringimprovesperformancealsotracksWinton(1993).However,inmanywaysourworkisquitedis-tinctfromWinton’,(1993),whichfocusonrelationshipinvesting,CornelliandLi(1999),asinourarticle,inCornelliandLi,,,theendogenousinfor-mationiseacharbitrager’(a)canoperateonboththebuyandsellsidesofthemarketand(b),agentsareendowedwithownershipstakes,,agentshavenoinitialownershipstake,,-sideactivismandsell-sidetradingarerelatedis,infact,-dateeconomy,withtimeindexedbyt=0 1,populatedbyasetof = 1 2 N strategicinvestors,nonstrategicinvestors,amarket3Foranothermodeloftradingandtakeoverswithastrategictraderanduninformedtraders,seeKyleandVila(1991).293
TheReviewofFinancialStudies/v15n12002maker,afirm,,theyhavetheoptionofinvestingeitherinarisklessliquidassetor“bond”paying$,orinthefirm’,,eachshareisworth$$,inordertoblockperkconsumption,,thenoneofourimportantlaterresults—thatsmallershareholdersmaysharetheburdenofmonitoringinequilibriumwithlargershareholders—wouldbeengenderedpurelybythemonitoringtechnology,,,firstconsidertheoptimalportfolio/’scon-−ijectureregardingtheprobabilitythatasharewillpayout$
sharesofthefirm’sstockposttrade,theniitis(sub)optimalforitomonitorwhenever
−c> <
v ii−iAtthestartoftheperiod,,themarketmakerpostsanorderedpairofprices,p= p p ,consistingofanaskprice,p,rep-ABAresentingthepriceatwhichthemarketmakersells,andabidprice,p,,takingthesepostedpricesasgiven,=
b ,whichconsistsof
,thetotalexpenditurebyano+o+4investorforpurchasingsecuritiesis b−b +
−
+−Alsonotethat · representsthefunctionx→max x 0 and · representsthefunctionx→max −x 0 .294
InvestorActivismandFinancialMarketStructureo−o−stock-and-bondendowment, b−b +
−
+o+assetsarethesumofbondandstockpurchases, b−b +
−
-balancingconstraintthusimpliesthato+o+o−o− b−b +
−
p= b−b +
−
p iiAiiBiiiiBondholdingsaftertradearegivenbyoo−o+b=b+
−
p−
−
p iiBiAiiiThesmallestpossibleterminalsecurityholdingis0andresultsfromatotalliquidationoftheinvestors’¯forinvestori,whichwerepresentby
p w =
+ b/p ,,’spayoffis()oo−o+maxb+
−
p−
−
p+max
−c
v iBiAii−iiii¯
∈ 0
p w iioViewedasafunctionof
,thisexpressionisconvexover 0
andoverio¯
p w .¯0,or
,or
.Inotherwords,thestrategicinvestorwilleitherliquidateheroholding,orstandpat,,weobtain¯thefollowingsetofpossibleportfoliopositions: p w = 0
p w .oThisanalysisindicatesthatifnostrategicinvestorhasliquidwealthandnostrategicinvestor’sshareendowmentexceedsthecostsofmonitoring,,>0ormax
>c iiiiNext,,andletM= 1 0 ,=-strategysetofanindividualinvestorigivenpricespisgivendefby p = p w .Thevectorofallportfoliostrategiesforallstrategicii∏defiinvestorsisgivenby
p = p . M→ 0 1 betheindicatorMfunctionformonitoring,thatis,I m =1ifatleastoneinvestormonitorsM295
TheReviewofFinancialStudies/-askpricepair,p,theutilityfunctionforinvestorsisrepresentedbythemapmapu · p
p ×M→ givenbyi()oo−o+iu
m p =
I m +b+
−
p−
−
p−cI m iiMiBiAiiiMThestrategyspaceforinvestori,S p ,isM× p .ThepurestrategyiispaceforinvestorsisN∏S p =S p ii=1Thenumberofsharesstrategicinvestorschoosetobuyisgivenbythe+mapd → ,whereBN∑+d
=
−
Bioi=1ThedemandofstrategicinvestorsindollartermsisgivenbyD · =pd · .BABSimilarly,thenumberofsharesstrategicinvestorschoosetosellisgivenbyN∑+d
=
−
"Soii=1dollarsell-sidedemandisgivenbyD · =pd · .,letrv S M andtradingstrategiesdefinedonrv .Theunderlyingprobabilityspaceisassumedtoberichenoughtoipermittheconstructionofalljointprobabilitydistributionsover ×’,nonstrategicliquidityinvestorsalsotradethefirm’.˜˜Let# p (# p )representthenumberofsharesliquidityinvestorsdemandBStobuy(sell).Thisquantitycanbeafunctionofthebidandaskprices,p= p p ,’sprofitsfromtheaskmarketaregivenby[()]˜˜Ed
+# p p−I m˜ BBAMBecausemarketmakersquotefixedpricesindependentoforderflow,allorderswillbeplacedwiththemarketmakerwhoprovidesthemostfavorable296
,[()]˜˜Ed
+# p p−I m˜ =0 (1)BBAMThesameBertrandconditionappliedtothebidmarketensuresthatequilib-riummarket-makerprofitequalszerointhismarketaswell.[()]˜˜Ed
+# p I m˜ −p =0 (2)-side˜liquidityinvestorsdemandarandomdollaramount,X,inthefirm’˜Thusliquidityinvestorbuy-sidedemandintermsofshares,#,isgivenasBfollows:˜# p =X/p (3)BBASell-sideliquidityinvestorssellanexogenouslygivenrandomnumberofshares,x˜;thusliquidityinvestorsell-sidedemandisgivenasfollows:S# p =x˜ (4)SS˜Weassumethattherandomliquidityinvestordemandparameters,Xandx˜,BSarestatisticallyindependentofthetrading/monitoringstrategyofinformed˜=E X representexpectedbuy-sidedollardemandBBandweletl=E x˜ ,asSSweshallsee,onlytheexpectedlevelofliquiditydemandaffectsassetprices,wewill,inthesubsequentanalysis,refertoexpectedliquiditydemandsimply6as“liquiditydemand.” y∈ ,letdefx=y=x=y ∀mj =i −ijj∗∗∗˜Anequilibriumisthree-tuple,
m˜ p ,consistingoftradingstrategies∏∗∗N˜
∈rv p ,monitoringstrategiesm˜∈rv M ,,wherequotesareresponsivetoorderflow,tradersmay,inequilibrium,(1997).,inearlierdrafts,
TheReviewofFinancialStudies/v15n12002∗∗∗p= p p .Thisthree-tuplesatisfiesthefollowingconditions:(i)Thecol-AB∗∗˜lection
m˜ ispairwiseindependent;(ii)Themarket-makerbreakeveniiiEquations(1)and(2)aresatisfied;and,(iii)foralli=1 2 N,thefollow-∏N∗˜˜˜ingconditionholds:∀m
∈rv p m˜∈rv M suchthat
=
,jj−i∗∗∗˜˜m˜=m˜,and
m˜ isindependentof
m˜ ,itisthecasethat−iiij =ijj∗∗∗∗˜˜E u
m˜ p ≥E u
m˜ p (5)˜,letv m˜ representthevalueofoneshareofthefirm’sstockunderm˜;thatis,v m˜ =E I m˜ M−iForanyvectorm∈M,let m n representthevectorobtainedfrommbyreplacingtheithcomponentofmby0,−iv m˜ =E I m˜ 0 "−iMthatis,vrepresentsthevalueofashareofthefirm’sstockundermonitoring−ivectorm˜,giventhatallstrategicinvestorsotherthaninvestorifollowm˜and∗∗+=P m˜=1 ,Lemmas1and2,characterizeequilibriumbid-askpricesasfunctionsof(a)thecorrelationbetweeninformeddemand,D,andmonitoringactivity,and(b)∗∗˜˜E D I=0 +LB∗∗BMp=1− 1−v A∗˜E D +LBB∗-makerbreakevenconditionfortheaskmarket,Equation(1),bytheaskprice,p;Athismultiplicationyields[()]∗∗˜˜Epd
+p# p p−I =0 (6)ABABAM∗˜Bydefinition,dollarbuy-sidedemandbystrategicinvestors,D,isgivenbyB∗˜
InvestorActivismandFinancialMarketStructure∗˜dollardemandfromliquidityinvestors,p#,isgivenbyX;thusEqua-ABBtion(6)canbereexpressedas[()]∗∗˜˜ED+X p−I =0 (7)BAM˜Notingthat,bydefinition,L=E X ,andnotingthattheliquidityinvestorBBdemandparameter,X,isindependentofthestrategicinvestors’monitoringB˜˜˜˜˜˜strategies,andusingthecovarianceidentityE YZ =E Y E Z +cov Z Y ,weobtain()∗∗∗∗˜˜E D +L p−E I +cov I D =0 (8)BAMMBBecauseourzero-onenormalizationoffirmvalueimpliesthattheexpected∗˜valueofthefirm,E I ,equalstheequilibriumprobabilityofmonitoring,M∗v,wecansimplifyEquation(8)toobtainthefollowingexpression.∗∗˜cov I D ∗∗MBp=v+ (9)A∗E D +LBBTechnicalLemma1inAppendixAshowsthat∣[]∗∗∗∗∗∗˜∣˜cov I D =− 1−v ED−E D I=0 (10)MBBBMThus,combiningEquations(9)and(10)weobtain∗∗∗˜E E D −D I=0 ∗∗∗BBMp=v+ 1−v A∗E D +∗∗˜˜E d I=0 +lS∗∗SMp=1− 1−v B∗˜E d +,asthedepthofthemarketincreasesto∗infinity,thebidandaskpricesconvergetov,(measuredbyliquidityvolume)falls,,thespreadsneednotconvergetounity(bidpriceto0,askpriceto1)’
TheReviewofFinancialStudies/,aswewillsee,althoughspreadsdonotconvergetounityasuninformedtradersexit,,,,strategicsell-sidedemandisposi-tivewhenallinvestorshaveinitialshareendowments,andstrategicbuy-sidedemandispositivewheneverallinvestorshavepositiveliquidwealth.∗∗∗∗∗˜˜=
m˜ p I=0 =1,-maker∗breakevenconditions[Equations(1)and(2)]thusimpliesthatp= 0 0 .oBecausethestockisfree,thisinturnimpliesthat,forallisuchthat(i)b>0,,suchthat(ii)
>c,(1),either(i)or(ii)∗thatmonitoringdoesnotoccurine.∗˜Next,supposethatP I=0 =,Msayinvestor1,-makerbreakeven∗∗conditions[Equations(1)and(2)]impliesthatp= 1 1 .Becausep=1 1 1 ,thepayofftoinvestor1frommonitoringis
+b−
+∗,-sidemustbesubmittedbystrategicinvestorswithliquidwealth,notethatifpositivedemandisnotsubmittedintheaskmarket,,inthis∗∗case,p=v<,sayinvestorA∗’spayofffrommonitoringandbuyingshares, 1/v b+
−c,11ooexceedsherpayofffrommonitoringandnotsubmittingdemand,b+
−
InvestorActivismandFinancialMarketStructurethereisnoinformeddemandonthesellside,thenLemma1showsthat∗∗p=,sayinvestor1,,∗∗∗thenherpayoffwhenshechoosesnottomonitorisv<v=,−. ,exante,investorswhomonitorearnacompetitivereturnontheirmoni-toringactivity:thatis,thetradingprofitsfrombuyingintothefirmandthenmonitoringareexactlyoffset,inexpectedvalueterms,,TP,byoo˜TP
m˜ p =b 1/p−1 +
1−max p v m˜ (11)iAB−-handsideofEquation 11 ’ssharesto$’sstockfromthemarketmaker,thereturnoninvestingnewfundsinthefirmandthenmonitoringis1/p−’sAooinitialwealthbalance,b,givesb 1/p−1 ,-handsideofEquation(11)representsthenetgaininvalueofthefirm’$,theinvestorcaneitherholdontohersharesandrelyonthemonitoringactivitiesofotherinvestors,therebyreceiv-ingv m˜ ,−iBgain,perinitialshare,frommonitoringisthus1−max p v m˜ .ThetotalB−ionetvalueincreaseontheinitialholdingisthus
1−max p v m˜ .B−iiSummingthetwotermsontheright-handsideofEquation(11).∗,themaximumgrosstradingprofitfromstra-tegicinvestingequalstheadditionalassociatedmonitoringcosts,thatis,∗∗∗˜maxTP
m˜ p =c ii∈ ,,notethatthevalueofashareconditionalonmonitoringis$
TheReviewofFinancialStudies/v15n12002∗priceisp<1,’spayofffrommonitoringisoo∗¯
−c=
+b/p −c iiAIfaninvestordecidesnottomonitor,,givenadverseselection,theequilibriumaskpriceforthefirm’,afortiori,thepriceishigherthanthepriceconditionedoni’,shewilleitherretainherinitialpositiono∗oorsellout,dependingonwhetherthepayofffromsellingout,b+p
,oriBioo∗thepayofffromretainingtheposition,b+
v,−ifromnotmonitoringis[]oo∗∗b+
maxp v iiB−iThisimpliesthatinvestoriwillbeindifferenttomonitoringifandonlyifTP= 0 1 ,which,byLemma1,,ifforsomei,TP>c,theniwillmonitorwithiprobability1,∗maxTP=c. i∈ iLemma3showsthat,netoftradingcosts,strategicinvestorsearnafairrateofreturnontheirmonitoringactivity;:fringeversuscoremonitorsTheaboveresults,althoughstraightforward,,,werepresentthefractionoftotalexpectedstrategicsellingactivitygeneratedi∗,foragivenequilibriume,leto∗˜
P
=0 ∗ii0= ∑io∗˜
P
=0 jjj∗∗˜LetR=l/E d representmarketdepth,theratioofuninformedtoSS∗∗informedsell-sidedemandinequilibriume;let+representtheprobabil-i∗∗investoriisacoremonitorineif()∑∗1R+0∗jj11−+j> (12)∗∗1−+R+1i302
InvestorActivismandFinancialMarketStructure∗IftheinequalityinEquation(12)isreversedand+>0,wewillcallinvestori∗,-handsideofEquation(12)∗marketbecomesdeeper,thatis,whenR→ ,theright-handsideofEqua-tion(12),asmarketdepthincreaseswithoutbound,all∗,becauseR>0,andbecausethefractionontheright-handsideofEquation(12)isdecreasing∗inR,()∑∗1R+0∗jj∑()1−+1j<0 j∗∗R+11−+jjThus,ifanyinvestormonitorsmorethantheweightedaverageofallinvestors,thatis,if()∑11≥0 j∗∗1−+1−+, 0 ,sumjto1,thislastobservationimpliesthatsomeoftheinvestorswhomonitorwithpositiveprobabilityarecoremonitors,andmoreoverthat,ifallstrategicinvestorsmonitorwithequalprobability,,,whenevertheirliquidwealthispositive,,,coremonitorssellinitialholdingswhentheydonotmonitor,,,notethatthevalueofashareconditionalonmonitoringis$$,thebidpriceislessthantheexpectedpayoffconditionedontheexanteexpectedlevelofmonitoringand,afortiori,lessthanthevalueoftheshareconditionedonagiveninvestor’’swealth,,then,becauseaskpricesreflecttheaveragelevelofmonitoring(seeLemmas1and2)andtheactuallevelofmonitoringconditionedontheinvestor’snotmonitoringissmaller,
TheReviewofFinancialStudies/v15n12002anddoesnotmonitor,herpayoffwillequalherinitialholdingtimesthevalueoftheshareunderthepolicyofnotmonitoring:o∗
v (13)i−iIfinvestoridoesnotmonitorandsellsherstake,herpayoffwillbeo∗
p (14)iBThusthedifferenceinthepayoffsfromselling(S)andnotselling(NS)hasthesamesignas∗˜l+E d S∗S 1−+ − (15)i∗∗˜˜l+E d I=0 SSMNext,notethat,foreachj,∗o∗˜˜E d =
P
=0 Sjjjando∗˜
P
=0 jj∗∗˜E d I=0 = SjM∗1−+(15)hasthesamesignasthediffer-encebetweentheleft-handsideandright-handsideexpressionsusedinthedefinitionofacoremonitorEquation(16). ThelogicbehindTheorem2isthatbecause,bymonitoring,strategicinvestorsensurepositiveperformanceoutcomes,,,thisinvestor’sfailuretomonitormaynotlowerthelikelihoodofsuccessfulmon-itoringsufficientlytosupportprofitableselling,“verysurprising”canprofitfromsellingoutwhenthemarketforthefirm’-torexante,asshownbyTheorem2,
,
,
Investor
11/22227/3863227/336443/64ooNotethat0 50=
<···<
≈0 ,14c,is1/-sidesharedemandfromliquiditytraders,l,is1/-rium:investor1:monitorandretainshareholdingwithprobability99/227,donotmonitorandselloutwithprobability128/227;investor2:monitorwithprobability1/8andnevertrade;investor3:monitorwithprobability1/24andnevertrade;investor4:nevermonitor,nevertrade;marketmaker:setanaskpriceof359/681andabidpriceof1/ b
b
,becauseinvestoriisacoremonitor,heroptimaltrading/∗∗o∗oTP= 1/p−1 b+ 1−p
=c (16)iAiBiooooIf b
b
,thenjjii∗o∗o∗o∗o 1/p−1 b+ 1−p
< 1/p−1 b+ 1−p
(17)AjBjAiBi305
TheReviewofFinancialStudies/v15n12002Equations(16)and(17)implythat∗o∗o 1/p−1 b+ 1−p
<c (18)AjBjBythedefinitionofthetradingprofitfunction,∗∗o∗oTP≤ 1/p−1 b+ 1−p
(19)jAjBj∗ThusTP<,andtherebycontradictstheassertionthatinvestorjisafringemonitor. ,,iftwofringemonitorshavethesameendowmentofbonds,,iftwofringemonitorshavethesameendowmentofstocks,,say,′ooband
>
,itmustbethecase,byLemma3andTheorem2,thattheijexantetradingprofitsofbothinvestorsareinducedbystrategiesthatinvolveholdinginitialendowmentswhennotmonitoring,,∗∗′∗o∗′∗o∗TP= 1/p−1 b+ 1−v
=c= 1/p−1 b+ 1−v
=TP iA−iiA−jjjooBecause0>
>
,thetwoextremetermsintheequalitycanbeequalonlyij∗∗∗∗∗∗∗if1−v<1−−v= 1−v 1−+ = 1−v 1−+ ,−i−j−ii−jjthiscanbethecaseonlyifinvestori’sequilibriumprobabilityofmonitoring,∗∗+,islessthaninvestorj’s,+. ijAtanintuitivelevel,Lemma5holdsfortworeasons:(1)inequilibriummonitoringmustberandomand(2),counterfactually,thattwoinvestors,one“big”andone“small,”-tion(7)tobesatisfied,thesmallinvestor’,thenbecauseofthebiginvestor’slargerendowments,,inthiscase,-pationwouldleadtoarevisionofthemarket-maker’squotes,,thebiginvestor’-torthat(a)variesbetweentheinvestors,(b)isdeterminedinequilibrium,and(c),toattenuatemonitoringincentivesforthebiginvestor,thevalueofthefirmwithoutthemonitoringofthebiginvestor306
,,,itwillbeshownthat,eveninthiscase,,weassumethatallofthestrategicinvestorshavethesameliquidassetbalance,B/N,,B,uniformedinvestordemand,L,Bmonitoringcosts,c,andthedispersionofmonitorwealth,N,,thereisauniquesymmetricequilibriumwitheachchoiceofexogenousmodelparameters:liquiditytraderdemand,strate-gicinvestorwealthendowments,monitoringcosts,’-askspreadissimplythedifferencebetweentheaskpriceandtheexpectedvalueofthefirm’sshares,p−,wedefinethefollowingfunctions:()LdefNBf v =1− 1−v AB+ v N +LB√defN+ v N =1−1−v -acterizedasfollows:(a)Theequilibriumprobabilitythatastrategicinvestorwillmonitorand∗investallherwealthinthefirm’sstockisgivenby+ v N ,where307
TheReviewofFinancialStudies/v15n12002∗Nvistheuniquesolutiontotheequationf v =B/ B+NC ;theAequilibriumprobabilitythatastrategicinvestorwillnottradeand∗willnotmonitoris1−+ v N .∗N∗(b)Theequilibriumaskprice,p,equalsf v ;theequilibriumbidAA∗∗price,p,,thefollowingcomparativestaticsholdfortheunique,symmetricNashequilibrium:(a)Increasingliquidityinvestorbuy-sidedemand,L,alwaysincreasesB∗∗∗firmvalue,v,andreducesbid-askspreads,p−(b)Increasingaggregatestrategicwealth,B,alwaysincreasesfirmvalue,∗∗∗v,andincreasesbid-askspreads,p−∗(c)Increasingmonitoringcosts,c,alwayslowersfirmvalue,v,andhasanindeterminateeffectonthebid-askspread.(d)Increasingthedispersionofstrategicshareholdings,N,lowersfirm∗∗∗value,-askspreads,p−v,,dispersionincreasesbid-askspreads,,someofthecomparativestaticsobtainedinLemma6arenotsurprising,,itisworthnotingthatincreaseddispersionofstrategicinvestorwealth,whichmightbeexpectedtolowerspreadsbyengenderingcompetitionbetweeninformedinvestors[.,HoldenandSubrahmanyam(1994)],,,-sidertheoppositecase,whenthewealthofstrategicinvestorsconsistsentirelyofaninitialendowmentofthefirm’-vatedbyadesiretoprotecttheinvestor’,assumethateachstrategicinvestorisendowedwith308
InvestorActivismandFinancialMarketStructure /Nsharesofthefirm’,theanalysiswilldelin-eatehowvariationinkeyexogenousparameters—aggregatestrategicinvestorownership, ,uninformedinvestordemand,andthedispersionofstrategicownership—-cussionandproofsoftheseresults,-ticalinthecurrentscenariotothoseobtainedinthepreviousscenario,inthissectionweconsideronlythecaseofnonstrategicinvestorswhosubmitfixeddemands:() +ldefNSf v =1− 1−v B 1−+ v N +lS√defN+ v N =1−1−v -izedasfollows:(a)Theequilibriumprobabilitythatastrategicinvestorwillretainher∗∗holdingsandmonitoris+ v N ,wherevistheuniquesolutiontoNtheequationf v = −NC / ;theequilibriumprobabilitythatB∗astrategicinvestorwillselloutandnotmonitoris1−+ v N .∗N∗(b)Theequilibriumbidprice,p,equalsf v ;theequilibriumaskBB∗∗price,p,,thefollowingcomparativestaticsholdfortheuniquesymmetricNashequilibrium.(a)Increasingliquidityinvestorsell-sidedemand,l,alwayslowersfirmS∗∗∗value,v,andreducesbid-askspreads,p−(b)Increasingstrategicinvestorendowments, ,alwaysincreasesfirm∗value,v,andhasanindeterminateeffectonthebid-askspread.∗(c)Increasingmonitoringcosts,c,-askspreadisindeterminate.∗(d)Increasingthedispersionofstrategicshareholdings,N,,dispersionincreasesbid-askspreads,
TheReviewofFinancialStudies/,,notably,KahnandWinton(1998)andMaug(1998),,inasomewhatdifferentcontextfeaturingexogenousprivateinformation,KhannaandSonti(1999),therelationshipisnot,ingen-eral,,,asstrategicownershipendow-mentsincrease,thepotentialprofitsofinformedtradedecrease,**p–ΦoO246810Figure1Increasinginformedstrategicdemandreducesbid-askspreadsThefixedparametersforthisexampleareasfollows:N=7,l=8 00,C=0 ( ),plottedonthehorizontalaxis,varyfrom0 -ask∗∗spreadp−
(informed)ownershipincreases,:modeloforderflowOurmodeloffinancialmarketstructurefollowsasimplifiedversionoftheAdmatiandPfleiderer(1989)andEasleyandO’Hara(1992)-laslinkingtradeintensitytoshareendowmentsandinvestoractivism[.,Equation(12)].MicrostructuremodelssuchasKyle(1985)andGlostenandMilgrom(1985),,themarket-maker’-mulasmustbedevelopedforupdatingthemarket-maker’,threeconditionsareessentialfordevelopingthisupdatingrule:normallydistributeddemandvectorsfornoisetraders,exogenoussignalsthatarenormallydistributed,-ever,,optimalstrategieswillneverplaceanyweightonmonitoringconjoinedwithsmallbuyorders(suchorderscan-notrecoverthecostsofmonitoring).Becausealluncertaintyisgeneratedendogenouslyinourmodel,thisimpliesthattheconditionaldistributionoftradeconditionedonmonitoringwillhavelimitedandasymmetricsupport,,linear,updatingrulescannotbedevelopedtomodelthemarket-maker’,,thatmonitoringisnot,ingen-eral,monopolizedbythelargesttraders(theinvestorsholdingthemostsharesofthefirm’sstock),:Inourfixed-quoteanalysis,iftheprob-abilityofmonitoringforthesmallinvestorislessthanthatforthelargeinvestor,,predictability311
TheReviewofFinancialStudies/,thiscontradictstheexistenceofequilibriainwhichmonitoringactivitywassharedbetweeninvestors,,aneweffectisintroduced:,:twoinvestors,,insteadofselling,shedecidestobuy,,withconditionalquotes,-intensitymonitoringinvestorsalsohavelargerholdings,thentheyalsohavemoretogain,intermsoftheintrinsicvalueoftheirholdings,,,conditionalquotesstrengthen,ratherthanattenuate,:(liquidity)orriskaver-sion(hedging);see,forexample,DowandGorton(1995).,withendogenousdemand,incontrasttotheexogenousnonstrategictraderbehaviormodeledherein,,“marketbreakdown”
-ketbreakdown,,,,,,,-agement’,thatis,,changesinmarket-structureparameterswouldinducestrategicmanagerstochangeperkconsumptionbehaviortocompensateforshiftsinthecost/,,tosomeextent,,withaninternalgovernancesystem,:,
TheReviewofFinancialStudies/-ever,(1973)hasshown,,+4˜.Strategicinvestoriwillmonitorwhenishehasarelativelylowdrawof4andnotmonitor(eithersellingornotitradingatall)˜,≈0forallstrategicinvestors,thestrategiesinithisperturbedgameapproximate,toanarbitrarydegreeofaccuracy,:portfolioallocationInthisarticleweallowformanyactivistinvestors,;however,,,theseinvestorsadoptapassive,,suchstrategicinvestorsmightbeattractedtofirmswithlessstrategicinvestorinterestand/,internalcontrol,,
,theinitialpre-monitoringwealthandshareholdingsofstrategicinvestors,:ProofsofSelectedPropositions˜˜ X I =−P I=0 E X−EX I=0 ()˜,let5=P I=1 .Thepropertiesofconditionalexpectationsimplythat˜˜˜˜˜˜˜˜˜˜˜˜cov X I =E I−EI X−EX I=0 1−5 +E I−EI X−EX I=1 5˜˜˜˜˜˜=−5 1−5 E X−EX I=0 +5 1−5 E X−EX I=1 ˜˜˜˜˜˜=5 1−5 E X−EX I=1 −E X−EX I=0 ()Now,˜˜˜˜˜˜˜˜0=E X−EX =5E X−EX I=1 + 1−5 E X−EX I=0 ()Thus 1−5 ˜˜˜˜˜˜E X−EX I=1 =−E X−EX I=0 ()5CombiningEquations()and()yieldsthedesiredresult. ,,+ · ,+representstheprobabilitythatastrategicinvestorwillmonitoranduseallherwealthtobuyclaims,and1−++˜˜˜cov D I = 1−v E D ()AMAThus,˜˜cov D I = 1−v B+ ()AM315
TheReviewofFinancialStudies/v15n12002Thedefinitionofthemarket-maker’sbestresponsethenimpliesthattheaskpriceisgivenbyNf · .Forstrategicinvestorstobewillingtorandomize,thepayofffrommonitoring,givenANby B/N /f−C,andthepayofffromnotmonitoring,givenby B/N ,,inanysymmetricequilibrium,itmustbethecasethatf v =B/ B+NC .TheANexistenceofauniquevalueofv∈ 0 1 satisfyingthisconditionfollowsfromthefactthatfANNisincreasingandcontinuousovertheinterval 0 1 ,withf 0 =0andf 1 =1. ,intheuniquesymmetricequilibriumthefollowingrela-tionshipholds:Nf v =B/ B+NC ()AManipulationofthisequationyieldsthefollowingexpression:LB 1−v defBc=6 v"B L = ()NBN Lv+B+ v N BForallvaluesoftheparametersN L,andB 6isacontinuous,strictlydecreasingfunctionBNofvwithlim6= andlim6=→0Nv→1NUsingEquation(),(a).Increasingliquidity,L,uniformlyincreases6,thus,Btomaintainequality,()thenyieldstheassertionsofpart(a)=B/ B+NC ,whichimpliesAthattheequilibriumspread,thedifferencebetweentheaskpriceandexpectedfirmvalue,isgivenby∗B/ B+NC −v ()∗IncreasingLincreasesvandthus,fromEquation(),,considerpart(b).().Forthesamereasonsasthosegivenintheproofof(a),thisestablishestheresultsin(b)[Equation()]increasewhenBincreases,,(c).AnincreaseincrequiresacorrespondingdecreaseinvtomaintainequalityinEquation().(a)and(b),thisargumentestablishestheresultsin(c),,Equation(),decreasewhencincreases,,,consider(d).AsafunctionofN,∗N L 1−z +B+ v N ()√NN Lv+B 1−1−v ()B316
InvestorActivismandFinancialMarketStructureandfromthefollowingfact:foranyconstanty∈ 0 1 ,thefunction√NN→N 1−1−y ()()follows,forinstance,fromtheproofofResult42inHardy,Littlewood,andPólya(1952).′′′′′′∗′Let N c B L and N c B L betwofixedsetsofparameters,N>N,andletvbeBB∗′∗′′∗′′implicitlydefinedbyc=6 v B L .Letvbeimplicitlydefinedbyc=6 v B L .′′NBNBThen,because6isdecreasinginN,∗′∗′6 v >6 v ()′′′NN∗′∗′′Because,bydefinition,c=6 v andc=6 v ,′′′NN∗′∗′′6 v =6 v ()′′′NN∗′′∗′Equations()and()implythat6 v >6 v .Thefactthat6isdecreasing′′′′′′NNN∗′′∗′′thenimpliesthatv<,which∗′′′isgivenbyv,ishigherthantheequilibriumvalueofthefirmassociatedwithN,whichis∗′′givenbyv. ,A.,,1989,“DivideandConquer:ATheoryofIntradayandDay-of-the-WeekMeanEffects,”ReviewofFinancialStudies,2,189–,A.,,,1994,“LargeShareholderActivism,Risk-Sharing,andFinancialMarketEquilibrium,”JournalofPoliticalEconomy,102,1097–,J.,,,1998,“BlockSharePurchasesandCorporatePerformance,”JournalofFinance,52,605–,D.,,1997,“SplittingOrders,”ReviewofFinancialStudies,10,69–,1998,“WhyCorporateGovernanceToday?,”positionpaper,availableat,J.,,1993,“ThreeStudiesSupportRelationshipInvesting,”Pensions&Investments,21,3–,F.,,1999,“RiskArbitrageinTakeovers,”workingpaper,,T.,,1983,“InformationEffectsandtheBid-AskSpread,”JournalofFinance,38,1457–’Mello,R.,,,2000,“InstitutionalOwnershipandthePerformanceofFirmsthatIssueEquity,”workingpaper,,J.,,1995,“ProfitableInformedTradinginaSimpleGeneralEquilibriumModelofAssetPricing,”JournalofEconomicTheory,67,327–,D.,’Hara,1992,“AdverseSelectionandLargeTradeVolume:TheImplicationsforMarketEfficiency,”JournalofFinancialandQuantitativeAnalysis,27,185–,1997,“IntheBoardroom:Kid’sStuff,”Economist,June21,66–
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