Lecture 5.ppt

lecture7 liquidity liquidity concepts liquidityislikepornography easytoidentifywhenseen butitisdifficulttodefine but clmdefinesliquidityas abilitytobuyorsellsignificantquantitiesofasecurityquickly anonymously andwithminimalornopriceimpact market makers provideliquiditybytakingtheoppositesideofatransaction ifaninvestorwantstobuy themarket makersellsandviceversa inexchangeforthisservice market makersbuyatalowbidpricepbandsellatahigheraskpricepa thisabilityinsuresthatthemarket makersmakesprofits thedifferencepa pbiscalledthebid askspread atradingcost weassociatelowerbid askspreadswithmoreliquidsecurities hightradingcosts commissions fees opportunitycosts bid askspreads etc arelinkedtolessliquidsecurities relatedconcepts depth thequantityavailableforsaleorpurchaseawayfromthecurrentmarketprice breadth themarkethasmanyparticipants resilience priceimpactscausedbythetradingaresmallandquicklydieout overallliquidityfindings oldpapers demsetz 1968 determinantsofliquidity tradingvolumeandnumberoftrades volatility firmsizeandprice tinic 1972 andbenstonandhagerman 1974 findapositiverelationbetweentradingactivityandliquidityandanegativerelationbetweentradingactivityandvolatility newpapers firstaskedthequestion doassetswithhighspreadsand orpriceimpacthavehighaveragereturns cross sectionalanswer findings positiverelationshipbetweenexpectedstockreturnsandalternativeproxiesforindividualilliquiditylevels amihudandmendelson 1986 bid askspreads brennanandsubrahmanyan 1996 priceimpacts dataretal 1998 bid asksspreads easleyetal eho 2002 pins second papersstudythetimeseriespropertiesofaggregateliquiditymeasures findings existenceofpredictabilityandcommonalityinliquidity chordia rollandsubrahmanyam 2001 hasbrouckandseppi 2001 amihud 2002 jones 2002 hubermanandhalka 2001 recently paperslookedatthesystematiccomponentofliquidityasasourceofpricedrisk theliteratureisstillmostlyempirical withtheintuitionthatinvestorspreferastockwithhigherreturnswhenmarketwideliquiditydrops seelustig 2001 findings liquidityriskisapricedsourceofriskwhenthemodelisfittedtou s equitydata pastorandstambaugh 2003 acharyaandpedersen 2005 sadka 2005 themagnitudeofthepremiumvariesamongthestudiesandproxiesformarketwideliquidity pastorandstambaugh 2003 reportaveryhigh7 5 annualpremium acharyaandpedersonreport1 1 annualpremium note piqueira 2005 doesnotfindaliquidityriskpremium mainproblem liquidityisunobservable unobservablevariablescreatemeasurementerror theproblemwithmeasurementerrorwasinthex s notwiththey s basicmeasurementerrorframework weareinterestedinestimatingtheeffectoftheunobservable x liquidity onadependentvariable y returns y x letxbeobservable witharelationtox givenby x x ifweregressyonx plimb var x var x 2 inconsistent andbiased note as 2 increases theolsestimatesbecomesmoreunreliable usualsolutiontomeasurementerror ivestimation structuralmodels iverequires findz uncorrelatedwith butcorrelatedwithx difficulttofindsuchaz commonsolution ignoreproblem proxies areusedwhenthereisnoobservablecounterpart proxiesareusedtoavoidomittedvariablebias supposewehaveamultipleregressionwithz observable andx weuseaproxyforx y z x substitutex x intoequation y z x wecanestimate withols butnot omittedvariablebiassolved butmeasurementerrorisintroduced aproxyshouldbecorrelatedwithx theoryshouldhelpinselectingproxies alwaysaproblem wehavenodataonx q howgoodisthecorrelationwithx istherelationlinearwithx aproxyisnotaninstrumentalvariable thesolutiontothemeasurementerrorintroducedbytheproxyisive weneedtofindanotherproxyforx sayw andtreatitasaninstrumentforx wshouldbecorrelatedwithx butw serrorsshouldbeuncorrelatedwith and wheredowefindw simpleliquiditymeasures proxies inpractice amarketwithverylowtransactioncostsischaracterizedasliquidwhileonewithhighcostsisilliquid itisdifficulttomeasurethesecosts theydependonmanyfactorssuchasthesizeofatrade itstiming thetradingvenue andthecounterparties moreover theinformationneededtocalculatetransactioncostsisoftenunavailable thus awiderangeofmeasuresareusedtoevaluateliquidity tradingvolume scaledorunscaled indirectbutwidelyusedmeasure itissimpleandavailable fact moreactivemarketstendtobemoreliquid but tradingvolumeiscorrelatedtovolatility whichcanimpedemarketliquidity tradingfrequency numberoftradesexecutedwithinaspecifiedinterval withoutregardtotradesize hightradingfrequencymayalsoindicateamoreliquidmarket butittoocanbeassociatedwithvolatilityandhencelowerliquidity thebid askspread levelor itmeasuresthecostofexecutingasmalltrade usuallycalculatedasthedifferencebetweenthebidorofferpriceandthebid askmidpoint itcanbecalculatedquickly withdatawidelyavailableinrealtime but bidandofferquotesaregoodonlyforlimitedquantitiesandtimeperiods thespreadjustmeasuresthecostofexecutingasingletradeofacertainsize quotesize quantityofsecuritiestradableatthebidandofferprices itaccountsformarketdepthandcomplementsthebid askspread marketmakersoftendonotrevealthefullquantitiestheywilltransactatagivenprice sothemeasureddepthunderestimatesthetruedepth tradesize quantityofsecuritiestradedatthebidandofferprices reflectinganynegotiationoverquantity alternativedepthmeasure tradesizealsounderestimatesmarketdepth becausethequantitytradedisoftenlessthanthequantitythatcouldhavebeentradedatagivenprice priceimpactcoefficient temporaryorpermanent itconsiderstherise fall inpricethattypicallyoccurswithabuyer initiated seller initiated trade usefulforlargetradesoraseriesoftrades togetherwiththebid askspreadanddepthmeasuresprovidesagoodpictureofliquidity adrawbackisthedifficultyofobtainingthedatarequiredforestimation particularlyonareal timebasis bid askspreadofust notes priceimpactofust nots 3 montht billand10 yeart notevolatility figuresfromfleming 2001 measuringtreasurymarketliquidity figuresfromjones 2002 acenturyofstockmarketliquidityandtradingcosts amp 2006 workwithilliquidity manymeanings 1 marketimpactcostkyle 1985 pt lt lt tradesize f informationvariance noisevariance breen hodrick korajczyk 2002 pt pt lt lt turnover 2 bid askspreadstoll 1978 risk amihud mendelson 1980 inventory bagehot 1977 glosten milgrom 1985 information amihud mendelson pedersen s 2006 survey illiquidity 3 searchanddelaycosts priceandexecutionrisk 4 commissions fees costoftime etc liquiditylevelspremium cross section amihudandmendelson 1986 microstructureequilibriummodel negativerelationbetweentransactioncosts s andstockprices inequilibrium 1 investorschooseassetsdependingonthe sj ifaninvestoriswillingtoholdstocksforalongperiod theinvestoriswillingtobuyhighsjstocks liquidityclientele 2 modellinks i expectedreturnandspread ii expectedreturnandturnover reflectingholdingperioddifferences findings using49stockportfolios sortedby ands updatingthegroupingeveryyearandlookingatreturnsoneyearahead example ri 0 0065 0 01 i 0 0021 log si eleswarapu 1997 effectsof bid askspreadandsizeinnasdaq 1976 90 spreadportfoliosareupdatedatthebeginningoftheyear findings resultsarestrongerthanforthenyse wheremanytransactionstakeplacewithinthespread onnasdaq transactionsaremorelikelyatthequotes datar naikandradcliffe 1998 liquidityismeasuredbyturnover volume numberofshares turnoverproxiesfor inamihud mendelson 1986 1 holdingperiod higher lower1 iscorrelatedwithgreaterliquidity unobserved resultspersistoversubperiods findings liquidity higherturnover isassociatedwithlowerexpectedreturns brennanandsubrahmanyam 1996 illiquidityisestimatedfromakyle inspiredmodel seeglostenandharris 1988 pt xt qt qt 1 ut x signedtradesizeq theask bidindicator proportionalcostcomponents x p variablecost and p fixedcost model pooledtimeseries crosssection 25portfolios bysizeand reit k k lik i rmt i smbt ihmlt eit lik f x p p theirsquaredterms 1 p size findings returnisincreasingandconcaveinboth x pand p amihud s 2002 measure amihudproposesaproxyofilliquidity ai t illiqorilliquidityratio easilyobtainedfromdailydata realizedscaledvolatility ri j dailyreturndvoli t dollarvolumeintuition ai tproxiesmarketimpact whatistheeffectonreturnofagiventradingvolume signedvolumeisunavailable strongpositiverelationwith x pand p hasbrouck 2003 spearman pearson correlationofai twith modified is0 74 0 47 forportfolios correlationis90 theeffectofilliqonmonthlystockexpectedreturn constantomitted 1964 1997 lesmond ogden andtrzcinka s 1999 lot measurelotuseamodel basedmeasureusingatobin 1958 limiteddependentvariable ldv procedure onlythetimeseriesofdailysecurityreturnsisneededtoestimatetheeffectivetransactioncostsforastock intuition arbitrageurstradeonlyifthevalueofaccumulatedinformationexceedsthemarginalcostoftrading iftradingcostsaresizable newinformationmustaccumulatelongerbeforeinvestorsengageintrading therefore frequencyofthezero returndayscanbeaproxyforthelengthofinformationaccumulation ldvmodel r jt jrmt jt wherer jtismeasuredreturns andrjtisrealizedreturn and r jt jrmt 1jifr jt 2j 1j seller sidetradingcost 2j purchasesidecostforasseti assumingthedistributionofreturnsisnormal wecanestimatetheparametersofthemodelusingmle r1 non zeronegativereturnregion r2 non zeropositivereturnregion rm t marketreturnindex i marketbeta i2 varianceofthenon zeroobservedreturns r0denotesthezero returnregion 2j 1j impliedroundtriptransactioncosts i e lotmeasure lotmeasureismoreconservativethanusingthesumofspreadandcommissions 30 lower accordingtolot 1999 lesmond 2005 usingemergingmarketsfirm levelquotedbid askspreads findsthatprice basedliquiditymeasuresoflot 1999 androll 1984 dobetteratrepresentingcross countryliquidityeffectsthandovolumebasedliquiditymeasures within countryliquidityisbestmeasuredwiththeliquidityestimatesofeitherlotor toalesserextent amihud 2002 bigdrawbackoflotmeasure itisbasedonanormaldistributionforreturns notarealisticassumption q whathappenstolotifreturnsarefat tailed othermeasures stollandwhaley 1983 spread commission directandobservabledata roll s 1984 c glostenandharris s 1988 and hasbrouk s 2005 cgibbs rabinovitchetal 2003 estimateno arbitragespreads percentageofzeroreturns similarideatolog 1999 usedinchen lesmondandwei 2007 percentageofnon tradingdays usedinrabinovitchetal 2003 piqueira 2004 othermodelsoftheeffectofliquidity constantinides 1986 equilibriummodelwith2assets riskyandriskless theinvestorwantstomaintainaconstantratiooftheassets whichrequirescontinuoustrading costly solution ano tradezonearoundtheoptimalratio greatervolatility highertradingcosts widerno tradezone costofilliquidity themonetaryequivalenceofthelossinexpectedutilityofdeviatingfromtheoptimalratio secondordereffect huang 2003 equilibriummodelwithtwoassetsandrandomliquidityshocks oneliquid oneilliquid thenet of transaction costsreturnoftheilliquidassetisrisky optimalpolicy investinacombinationofthetwoassetsforsomerangeofliquiditypremium widerrangeforhigherriskaversion tradingcostsandprob ofshockarrival noborrowingconstraint liquiditypremiumequalsthepvoftradingcosts asinthecaseoffixedhorizon equatingnetreturns borrowingconstraint higherliquiditypremium reflectingtherisk olderinvestorsaremorelikelytoholdtheilliquidasset liquiditypremiumishigherforsmallerrelativesupplyofliquidasset liquidityrisk pastorandstambaugh 2003 fama macbethapproachgreaterexposuretoliquidityrisk higherexpectedreturn liquiditymeasure i t estimateforeachmonthtusingthedailymodelrei d i i ri d 1 i sign rei d 1 vi d 1 ei d rei d excessreturnoverrm d v volumeinusd i 0 reflectsreturnreversalaftertrading theliquidity cost intermsofreturnreversal thelargerthevolume thelargerthereturnreversal thelargerthecost ismorenegativeformoreilliquidstocks themodelisestimatedeachmonthforeachstock dailydata marketliquidity gt istheaverageacrossstocksineachmonth gtisautocorrelated pastorandstambaugh 2003 usea2 stepfilter 1 gt mt m1962 i gi t gi t 1 nt mt total valueattheendofmontht 1ofstocksincludedinmontht nt numberofstocksinmontht 2 gt a b gt 1 c mt m1962 g t 1 lt lt liquidity innovationthestock sexposuretomarketliquidityismeasuredby li ri t 0i li lt mi rmt s smbt hi hmlt ei t liispositivelycorrelatedwithsize negativelywith m sand h weakforall stocksaresortedinto10portfoliosbytheir li findings sfrommarketorffmodelsarestronglyincreasingin li acharyaandpedersen 2004 liquidity adjustedcapmsignofcovcov rit cit rmt cmt cov rit rmt standardcapm cov cit cmt cov rit cmt relatedtop s s li cov cit rmt cit amihud 2002 illiquiditymeasure dividingbyvar rmt cmt yields4 s traditional 3liquidity s pricingmodel et 1 rit rft et 1 ci t 1 1 2 3 4 where t 1 et 1 rmt cmt rf time varyingriskpremium findings modelisbetterthanstandardcapm stockreturnsareincreasingsignificantlyinthesumof s t 1 0 thecross sectionliquidity sallhavethepredictedsigns estimatedannualizedpremium 1 1 0 82 correspondstothemarketilliquidity korajczykandsadka 2007 commoncomponentinliquiditymeasures useprincipalcomponentstoextractacommoncomponentfromdifferentmeasuresofliquidity i e differentproxies amihud 2002 illiquidmeasure turnoverratio quotedspread foreachtrade averagedthrou