Liquid Assets in Banks: Theory and Practice Guillermo ...

1 LiquidAssetsinBanks:TheoryandPracticeGui llermoAlgerandIngelaAlger November1999 AbstractThispapersummarizestheoretical ndingsaresummarizedinaseriesofprediction s, ,we ndthatbankswithrelativelymoredemanddepos itshaverelativelylessliquidassets, :aretherebanksthatrelymorethanothersonli quidassetstomeettheirliquidityneeds?We cation:G21;G28 Keywords:LiquidAssets;Banks;LiquiditySho cks o,XavierFreixas,DenisGromb, onNacionalBancariaydeValores(M exico)forthedataset, , ,andwewouldliketothankthemfortheirhospit ality, ,byreviewingexistingtheoryandempirical ndings,andbyprovidingsometestsoftheoreti calpredictions, , (typicallylong-term)loans.

2 Indeed,itmaykeepsomeofthefundsincash(orr eservesatthecentralbank) , 'balancesheets1revealsthatasubstantialpa rtofavailablefundsareindeedinvestedinliq uidassets:addingupsecurities,duesfromdep ositoryinstitutions,andcash, ,thequestionis:whydobanksholdliquidasset s?Ouranalysisofthisquestionbeginswithare viewofexistingtheories,includingthosewhi chdonotfocusdirectlyonhowbanksdeterminet heirlevelofliquidassets, rstone,theportfoliomanagementtheorydevel opedinthe50'sand60's, , ,viewingliquidassetsastheresidualbetween ,ontheonehand,thebank'sequityandliabilit ies,andontheotherhand, rstcategoriesoftheoriesdonotexplicitlyta keintoaccountoneofthespeci citiesofbanks,namely,thattheyfacepotenti allylarge,randomliquidityshocks(duetounp redictabledepositwithdrawals,andorunpaid credits).

3 Presumably, ,banksmaywanttokeepliquidassetsinorderto beableto1 Seetheappendixforabriefintroductiontothe itemsonabank' ,thereadermayconsultGarberandWeisbrod(19 92)orHempel,SimonsonandColeman(1994), ,assuggestedbythe\liquidassetsasabu er" :towhatextentmaybanksrelyonincreasedliab ilitiestoraiseliquidityonshortnotice( ,bysellingCDsorborrowingfromotherbanks)? Indeed,thesetheoriesassumeanexogenouslyg ivenpenaltyrateifthebankisnotabletomeeta liquidityneed,withoutmodelingtheliabilit ysideofthebank' ,sinceincreasedliabilitiesat rstsightdoappearasacheapsubstituteforliq uidassets:indeed,byrelyingonliabilities, ' ' ,banksfaceliquidityshockseveryday,togeth erwiththedecisionofhowtoinvestinliquidas setsforfutureneeds,thenete ,introducednext,weexploitthefactthatourd atacoversaperiodwithadramaticliquiditysh ocktoshedsomelightonthequestion.

4 Canwedistinguishbanksthatrelymoreonliqui dassetstomeettheirliquidityneedsthanothe rs?Theempiricalanalysis , (tighteningofmonetarypolicy,politicalunc ertaintyrelatedtothebankingsystem,andast rainontheMexicaneconomyduetoasharpdecrea seintheoilpricesandtheworldwide nancialcrisisin1998),andcomfortedbyecono metrictests,weareabletodistinguishtwoper iods:onecharacterizedby\normal"condition s(January1997-Fabruary1998),andthesecond onecharacterizedbyanaggregate,prolongedl iquidityshockontheMexicanbankingsystem(M arch1998-March1999).Asaresult,weusethe rstperiodtotestthepredictionsconcerningb u er-building,andthesecondonetoshedsomelig htontheabovementionedquestion, , ,itisnecessarytoprovideamoreprecisede , ,wewilladopttheconventionalwisdomfoundin thebankmanagementliterature,3anassetisli quidifitiswidelyknowntohavelowrisk(sucha sgovernmentdebt)andifithasashortmaturity (ashortmaturityimpliesthattheasset'spric eislesssensitivetointerestratemovements, makinglargecapitallossesunlikely).

5 Thetypicalbankassetswhichareliquidaccord ingtothatde nitionincludecash,reservesrep-resentinga nexcedentascomparedtoreservesrequiredbyl aw4,securities( ,governmentdebt,commercialpaper),andinte rbankloanswithveryshortmaturity(onetothr eedays). (1971)andHartandJa ee(1974),abank' , ,itispossibletoapplytheportfoliotheoryde velopedinthe50'sand60' ,adaptedfromFreixasandRochet(1997, ) nancialsecurity(whichmaybein-terpretedas loans),andonerisk-freesecurity(theliquid asset ),withreturns~rLandr, +D(equityanddeposits,takenasanexoge-nous lygivenamounthere),thebankmanagerdetermi nestheamountsxLtoinvestintheriskysecurit y,therestbeinginvestedintherisk-free, (1985),andalsoO'Hara(1995) (1992)andHempeletal.

6 (1994) ,reserves( ,fundsheldintheaccountatthecentralbank) ,thebankmanagerisassumedtoactfullyinline withthebankownersobjectives, , , ,therandompayo isequalto:6~ =r(E+D)+(~rL r)xL:Thebankmanagerisriskaverse,andassum edtohavemean-variancepreferences:U(E(~ );var(~ )),withUincreasingintheexpectedpro t, ,thefollowingresultobtains:iftheexpected returnsareorderedinthefollowingway, rL>r>0thenxL> ,E+D xL,themostimportantdeterminantisrisk, ,boththelevelofriskaversion, ,E+D xLisincreasinginthedegreeofriskaversiono fthemanager(forlowdegreesofriskaversion, itmaybenegative).

7 Hence, ,foragivenfunctionU,andforgivenexcessret urns( rL r),theamountinvestedinliquidassetsisincr easinginvar(~rL),keeping ,whenthevolatilityofinterestratesincreas es,banksshoulddecreasetheamountofloans, ,ifdepositsandequityarealsoin-terpreteda ssecurities( ,ifEandDareendogenized), ,anymultipleoftheportfoliowhichisoptimal foragivenlevelofequityanddeposits, ,sizeshouldbearandomvariable, , , ,thefocusbeingonthee ectofriskaversiononthebank' ,forbanksownedbyshareholderswhohavewell- diversi edstockportfolios, , , erencebetweenequityplusdepositsandcredit s,andapplyaclassicalmicroeconomicanalysi softhedeterminantsofdepositsandcreditsin termsofsupplyanddemand(takingequityasgiv en).

8 ,bankssellcredit, , , , ,di erencesinbalancesheetcompositionscouldbe tracedtodi 'scostfunctionsarenotobservablebyoutside rs,itishoweverdi erentdeterminantofcreditsupplyisintroduc edwhenconsideringbor-rowers' ,asshownbyStiglitzandWeiss(1981)andBeste randHellwig(1987),7adverseselectionormor alhazardmayleadtocreditrationing,inthese nsethattheredoesnotexistaninterestratefo rwhichthe(competitive) ,intheadverseselectioncase,anincreaseint hecreditinterestrateleadstoariskierpopu- lationofborrowers, , ,creditsupplyissmaller,andceterisparibus ,theinvestmentin7 Althoughthemodelsinthesepapersdonotinclu debanks'decisionstoinvestinliquidassets, webelievetheideasexposedinthemcanbeusedt o(partially)

9 Explainwhyabank,foragivenamountofdeposit s,wouldlimititscredits, ,givenalevelofdeposits,theliquidassetshe ldbybanksshouldincreaseifthepopulationof borrowersisbelievedtohavebecomemorerisky , erAlltheabovementionedmodelsmakeanimport antsimpli cation:theydonottakeintoaccounttheunpred ictabilityofdepositwithdrawals,orotherfa ctorsa ectingtheuncer-taintyof owsinandoutofthebank,andthee ,anumberofresearchershavesoughttomodelth ee , (1888),andwasfurtherdevelopedduringthe19 60's(see, ,Porter(1961),andKaneandMalkiel(1965)).A simplemodel,takenfromFreixasandRochet(19 97, ), ,xD+E, :rL>r> ,somedepositsarewithdrawnandnewdepositsa rrive;thenetresultistherealizationwofthe randomvariable~w(thisistheonlyuncertaint yinthemodel).

10 Ifwexceedsthereservesx,thebanksu ersaliquidityshortage;itmustthenpayapena ltyrP(w x)(wewillcommentfurtherontheinterpretati onofrPbelow),whererP> ,theobjectiveofthebankistomaximizetheexp ectedpro t: (x)=rL(xD+E x)+rx rPE[max(0;~w x)]:The rst-orderconditionis: 0(x)= (rL r)+rPProb[~w x]:6 Thisexpressiondeterminestheoptimalamount ofliquidassetsx asfollows:8 Prob[~w x ]=rL ,theamountinvestedinliquidassetsdecrease swiththeopportunitycostofinvestinginliqu idassets,rL ,itincreaseswhenhighvaluesof~wbecomemore likelyinthesenseof ~wbecomesmoreriskyinthesenseofsecond-ord erstochasticdominance,thee ectonx isnotclear.