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Risks,Returns,andOptimalHoldingsofPrivateEquity:A
SurveyofExistingApproaches
AndrewAng
MortenSorensen
June2012
2
PolicyRecommendations
Privateequity(PE)investmentsareinvestmentsinprivately‐heldcompanies,
tradingdirectlybetweeninvestorsandnotonorganizedexchanges.Wesummarize
ourfindingsandrecommendationsforinvestmentsinPEasfollows:
1. Standardempiricalapproachesusedtoestimatetheriskandreturnof
standardpublicly‐tradedsecuritiesaredifficulttoapplytoPEinvestment.
ComplicatingfeaturesofPEinvestmentsincludedatalimitations,the
irregularnatureofPEinvestments,andthesampleselectionproblemsthat
typicallyariseinreportedPEdata.Correctingforthesedifficultiesrequires
sophisticatedeconometrictechniques.Naïveanalyses,withoutappropriate
adjustment,maysubstantiallyunderstatePEriskandvolatility,and
exaggerateperformanceestimates.
Recommendation:ReportedestimatesofPEriskandreturnshouldbeinterpreted
withskepticism.Estimatesbasedonsimplestandardmethodologiesfailtomake
correctionsthatarerequiredduetothespecificfeaturesofPEinvestments.Studies
thatdevelopmethodologiestoperformthesecorrectionsarepreliminary,anda
consensusontheappropriateadjustmentshasyettoemerge,butnaïveanalysis
withoutaccountingforbiasesoverstatesPEreturnsandunderstatesPErisk.
2. Commonlyusedfund‐performancemeasure,suchastheIRR,TVPImultiple,
andPME,areproblematic.Thereissubstantialvariationinestimatesofthese
measuresacrossstudiesanddatasources.Themeasurescan,tosomeextent,
bemanipulatedbythetimingandmagnitudesoftheindividualinvestments.
Thesefund‐performancemeasuresuseonlycoarseadjustments,ifany,for
theriskoftheinvestments.Finally,thesemeasuresarenotderivedfrom
underlyingfinancialtheoriesofriskandreturn,makingthemdifficultto
interpretconsistently.
3
Recommendation:Commonlyreportedperformancemeasuresshouldbe
interpretedwithcaution.Theyarenotreturnmeasures.
3. Modelsofassetallocationthattakeintoaccounttransactionscosts,whichare
largeforPE,andilliquidityrisk,whichissubstantialforPE,recommend
modestholdingsofPE.Inthesemodels,rebalancingwillbeinfrequent,so
wideswingsintheholdingsofPEshouldbeexpected,andtheholdingsof
illiquidPEwillbemuchlowerthanpredictedbyassetallocationmodels
assumingthatallassetscanberebalancedwhendesired.
Recommendation:WhendeterminingoptimalPEallocations,assetallocation
modelsmusttakeintoaccounttheinabilitytorebalancePEpositions.Thereshould
begenerallymodestallocationstoilliquidPEinvestments.
4. CurrentPEvehicleshavesubstantialagencyissueswhichpublicequity
vehiclesdonot.WhilethereisheterogeneityinPEcontracts,PEfeesare
largeandconsumeatleastone‐fifthofgrossPEreturns.Incentivefees
accountforlessthanone‐thirdofgeneralpartner(agent)compensation.
Recommendation:Ifanyofthefeespaidtoexternally‐managedPEfundswithGPs
canbebroughtbackin‐housetoinstitutionalassetowners,andifthequalityofthe
PEinvestmentscanbemaintained,therewillbesubstantialsavingstotheasset
owners.
4
Abstract
WesurveytheacademicliteratureabouttherisksandreturnsofPEinvestingand
optimalPEallocations.Empirically,theirregularnatureofPEinvestments
complicatestheestimationandinterpretationofstandardriskandreturnmeasures.
Whilethesecomplicationshaveleadtosubstantialdisparityinperformance
estimatesreportedacrossstudies,naïveanalysisnotaccountingforbiases
overstatesPEmeanreturnsandunderestimatesrisk.AllocationstoPEmusttake
intoaccountsubstantialilliquidityandtransactioncostsandsuggestmodest
optimalholdingsoftheseassets.WhilecurrentcontractsinPEaddressbothmoral
hazardandinformationfrictions,therearesubstantialmanagementand
performancefeesearnedbythePEfirms.
5
I.Introduction
Privateequity(PE)investmentsareinvestmentsinprivately‐heldcompanies,
tradingdirectlybetweeninvestors,notonorganizedexchanges.Theinvestments
aretypicallymadethroughaPEfundorganizedasalimitedpartnershipwiththe
investorasalimitedpartner(LP)andthePEfirmasthegeneralpartner(GP),
overseeingandmanagingtheinvestmentsintheindividualcompanies.Depending
onthetypeofcompaniestheyinvestin,PEfundsaretypicallyclassifiedasbuyout
(BO),venturecapital(VC),orsomeothertypeoffundspecializinginotherilliquid
non‐listedinvestments.BOfundsinvestinmatureestablishedcompanies,using
substantialamountsofleveragetofinancethetransactions.VCfundsinvestinhigh‐
growthstart‐ups,usinglittleornoleverage.Finally,itisnotuncommonforLPsto
alsoinvestdirectlyintoindividualcompanies.Theseinvestmentsareoften
structuredasco‐investmentsintotheportfoliocompaniesalongsidethe
investmentsmadethroughthePEfund.
PEisoftenconsideredadistinctassetclass,anditdiffersfrominvestmentsinpublic
equityinfundamentalways:ThereisnoactivemarketforPEpositions,making
theseinvestmentsilliquidanddifficulttovalue.Theinvestmentsarelong‐term
investments.PEfundstypicallyhavehorizonsoftentothirteenyearsduringwhich
theinvestedcapitalcannotberedeemed.Moreover,partnershipagreements
specifyingthefunds’governancearecomplexdocuments,specifyingtheGPs
compensationasacombinationofongoingfees(managementfees),aprofitshare
(carriedinterest),transactionfees,andotherfees.
ThisarticlesurveystheacademicresearchabouttherisksandreturnsofPE
investingandtheoptimalholdingsofPEinaninvestor’sportfolioalongwitha
reviewofPEcontracts.Researchershavehadlimitedaccesstoinformationabout
thenatureandperformanceofPEinvestments,soresearchinthisareais
preliminaryandofteninconclusive.Researchintomanyimportantaspectsofthese
investments,suchastheperformanceofPEintherecession,thesecondarymarket
6
forLPpositions,andLPs’co‐investments,hasonlyrecentlybegun.Oursurveyonly
coversstudiesofPEdefinedascompaniesownedbyPEfunds.Wedonotconsider
thesubstantialnumberofprivately‐heldandindependentlyownedcompanies,
rangingfromindependentgrocerystoresanddrycleanerstolargefamily‐owned
businesses(seeMoskowitzandVissing‐Jorgensen(2002),Kartashova(2011)and
Faccio,Marchica,McConnell,andMura(2012)).
SectionIIintroducestwoproblemsthatresearchhasencounteredinmeasuringPE
riskandreturns.ThefirstproblemisthestatisticalproblemthatarisesbecausePE
returnsareonlyobservedinfrequently,typicallywithwell‐performingfundsbeing
overrepresentedinthedata.Thismakesitdifficulttoestimatestandardmeasuresof
riskandreturn,suchasCAPMalphasandbetas.Afteraddressingthisproblem,a
secondproblemishowtointerprettheresultingestimates.Standardasset‐pricing
modelsarederivedunderassumptionsthatareappropriatefortraditionalfinancial
markets–withtransparent,liquid,andlow‐frictiontransactions.These
assumptionsareproblematicforPEinvestments,andtheestimatedalphasand
betasneedtobeadjustedtoprovidemeaningfulmeasuresofriskandreturninthe
PEcontext.OnewayofinterpretingtherisksandreturnsofPEinvestments,
especiallyforilliquidityrisk,isforaninvestortoconsiderPEfromaninvestor‐
specificassetallocationcontext.
SectionIIIsummarizestheexistingliteratureontheoptimalallocationofPEin
portfoliosconsistingofpublicliquidpublicequityandilliquidPE.Anewgeneration
ofassetallocationmodelsconsiderstheseissues;thefirstgenerationofasset
allocationapproachesassumedthatassetscanberebalancedwithoutcostatany
time.Theliteraturesonassetallocationincorporatingtransactionscosts,whichare
veryhighforPEinvestment,andsearchfrictions,sincecounterpartiesareoften
hardtofindfortransferringPEinvestments,leadtostrongrecommendationson
optimalholdingsofilliquidPEassets.
InSectionIV,wesurveytheliteratureonPEcontractswithaspecialemphasison
feesandopaqueness.MostPEinvestmentsaremadethroughintermediaries.
7
CurrentPEinvestmentvehiclescannotdisentanglefactorreturnsuniquetothePE
assetclassfrommanagerskill.Furthermore,commonlyusedcontractsmay
exacerbate,ratherthanalleviateagencyissues.
II.EstimatingPrivateEquityRiskandReturn
IIA.DefiningRiskandReturns
Tofixnotationandterminology,itisusefultostartfromthestandardmodelofrisk
andreturn.Fortradedfinancialassets,riskandreturnareusuallymeasuredinthe
contextofthecapitalassetpricingmodel(CAPM)asthe and coefficients
estimatedintheone‐factorlinearregression(theexpectedreturnregression),1
.
Inthisequation, isthereturnearnedbytheinvestorfromperiodt‐1toperiod
t, istherisk‐freerateovertheperiodfromt‐1tot,and isthereturnon
themarketportfolio.Thedefinitionofthereturnearnedonafinancialassetfrom
timet‐1totis
11,
whereCF(t)isthecashflowpaidoutattimet,andP(t)isthemarketpricequotedat
timet,immediatelyafterthepaymentofthecashflow.Fortradedassets,the
expectedreturnregressionisstraightforwardtoestimatebyregressingtheasset’s
observedreturns,sayweekly,onthecorrespondingmarketreturnsoverthesame
periods.
1Thisspecificationassumesthatalphaandbetaareconstantoverthedurationofthedeal.Whileitwouldbeinterestingtoinvestigatethetermstructureoftheriskandreturn,thedatalimitationsandothercomplicationsdescribedherehavepreventedempiricalstudiesofthesedynamics.ThereissubstantialevidencethatalphasandbetasvaryovertimeforlistedequityasAngandKristensen(2012)show.
8
Underappropriateassumptionsaboutinvestors’preferences,suchasconstant
relativeriskaversion(CRRA)ormean‐varianceutility,alongwithassumptions
aboutthemarketenvironment,suchastheabsenceoftransactioncosts,short‐sales
constraints,andtheabilityofinvestorstocontinuouslytradeandrebalancetheir
portfolios,theCAPMmodelspecifiesthateachasset’sexpectedreturnisgivenby
theexpectedreturnregressionwithanalphaequaltozero.Thisimportantresult
hasseveralimplications:Itimpliesthattheappropriatemeasureofriskis ,which
measuresthecorrelationbetweenthereturnontheassetandthereturnonthe
overallmarket(systematicrisk).IntheCAPM,systematicriskistheonlyriskthatis
priced.Idiosyncraticriskisnotpricedbecauseitcanbediversified.Theexpected
returnregressionalsoimpliesthatanasset’sexpectedreturnincreaseslinearlyin .
Finally,itimpliesthatinequilibrium, shouldbezero.Apositive canbe
interpretedasanabnormalpositivereturn.
Followingthislogic,thestandardapproachtoevaluatingrisksandreturnsof
financialassetsproceedsintwosteps:First, and areestimatedusingthe
expectedreturnregression.Second,invokingtheCAPM,theestimated is
interpretedasanabnormalrisk‐adjustedreturn,andthe isinterpretedasthe
systematicrisk.
ForPEinvestments,problemsariseatbothsteps:Atthefirststep,privatelyheld
companiesdonothaveregularlyobservedmarketvalues,bydefinition,andthe
returnsearnedfrominvestinginthesecompaniesareonlyobservedatexit.Hence,
period‐by‐periodreturnsareunavailable,makingitdifficulttoestimatethe
expectedreturnregressiondirectly.Betterperformingprivatelyheldcompanies
mayalsobeoverrepresentedinthedata,creatingsampleselectionproblemsthat
wouldleadthe coefficienttobeoverestimatedandthe coefficienttobe
underestimated.Atthesecondstep,afterestimating and ,itisnotobviousthat
thesecoefficientsappropriatelymeasureexcessreturnsandrisk,respectively.The
assumptionsofliquidandtransparentmarketsunderlyingtheCAPMarefarfrom
therealitiesofPEinvesting.ToreflectactualrisksandreturnsfacingLPinvestors,
9
theestimatedparametersmayrequirevariousadjustmentstoaccountforthecost
ofilliquidity,idiosyncraticrisk,persistence,fundingrisk,etc.
Thelackofregularlyquotedmarketpricesandreturnspresentsafundamental
challengeforempiricalstudiesoftheriskandreturnofPEinvestments.Several
alternativeapproacheshavebeendevelopedusingcompany‐leveldatawith
individualperformanceandvaluationmeasuresandfund‐leveldatawithentire
cash‐flowstreamsbetweenLPsandGPs.Thebenefitsandlimitationsofthese
approachesarediscussednext.
IIB.EstimatesUsingCompany‐levelData
Company‐leveldatacontaininformationaboutinvestmentsbyBOorVCfundsin
individualcompanies.Foreachinvestment,thedatatypicallycontainthenameof
thecompany,theinvestedamount,investmentdate,andtheexitdateandamount.
Suchdataareconfidentialandproprietary,andexistingstudieshaveobtaineddata
throughdirectcontactswithLPsandprofessionaldataproviders.
Franzoni,Nowak,andPhalippou(2012)analyzecompany‐leveldataforBO
investments.Cochrane(2005)andKortewegandSorensen(2010)usecompany‐
leveldataforindividualinvestmentsbyVCsinstart‐ups.TheapplicationtoVC
investingismorechallenging,becausethesampleselectionproblemisparticularly
severefortheseinvestments.
Comparedtofund‐leveldata,company‐leveldatapresenttwoadvantages:First,
therearemanymorecompaniesthanfunds,whichimprovesthestatisticalpowerof
theanalysis.Companiescanbeclassifiedintermsofindustriesandtypes,allowing
foramorenuanceddifferentiationoftherisksandreturnsacrossindustriesand
types,andovertime.Second,investmentsinindividualcompanieshavewell‐
definedreturns.Absentintermediatecashflows,thereturn,asdefinedabove,canbe
calculateddirectlyfromtheinitialinvestmentandthedistributionoftheproceeds
atexit.Aslongasintermediatecashflowsarefewandsmall,asforBOinvestments,
10
thiscalculationprovidesareasonablereturnmeasure.Withmoreintermediatecash
flows,suchasforVCinvestments,thecalculationmaybeperformedseparatelyfor
eachinvestmentround.
Onedisadvantageofcompany‐leveldataisthatthereturnfigurestypicallydonot
subtractmanagementfeesandcarriedinterestpaidbytheLPstotheGPs,andthe
estimatedrisksandreturnsreflectthetotal(grossoffees)risksandreturnsofthe
investments,notthoseearnedbyanLP(netoffees).Translatingbetweennet‐of‐fee
andgross‐of‐feereturnstypicallyrequiresadditionalassumptionsandnumerical
simulations(seeMetrickandYasuda(2010)andFranzoni,Nowak,andPhalippou
(2012)fortwoapproaches).
Continuous‐TimeSpecificationsAtechnicaldisadvantageofcompany‐leveldata
isthatthereturnsaremeasuredoverperiodsofdifferentlengths.Returnsare
measuredfromthetimeoftheinitialinvestmenttothetimeoftheexit,andthe
durationvariessubstantiallyacrossinvestments.Thestandard(discrete‐time)
CAPMmodelisaone‐periodmodel,wheretheperiodmaylastfor,say,aday,a
month,oraquarter.Itdoesnotcompound,however,andallreturnsmustbe
calculatedoverperiodsofthesameduration.
Astandardsolutionistousethecontinuous‐timeversionoftheCAPM,whichdoes
compoundandwhichallowsforacomparisonofrisksandreturnsofinvestmentsof
differentdurations.Campbell,Lo,MacKinlay(1997)provideanextensivediscussion
oftheunderpinningsofthismodel.Inthecontinuous‐timeCAPM,theexpected‐
returnregressionisrestatedinlog‐returns(continuously‐compoundedreturns)as
ln 1 ln 1 ln 1 ln 1 .
Onecomplicationisthattheestimatedinterceptinversionoftheexpectedreturn
equationcannotbeinterpretedasanabnormalreturn,asinthestandarddiscrete‐
timeCAPM.Underspecificassumptionsaboutthewayvolatilityincreaseswiththe
11
durationoftheinvestments,theabnormalreturnscanbecalculatedusingan
adjustmentthataddsthevolatilityasfollows
.
Thisnon‐linearadjustmentleadstohighalphaswhenthevolatilityofindividual
dealsishigh(seeCochrane(2005)andKortwegandSorensen(2011)fordetails
aboutthederivationandimplementationoftheadjustment).Forexample,Cochrane
(2005)reportsanannualvolatilityaround90%,resultinginanestimatedalphaof
32%annually,whichappearsunreasonablyhighcomparedtostudiesusingfund‐
leveldata,raisingdoubtsabouttheappropriatenessoftheassumptionsaboutthe
growthofvolatilitywiththedurationoftheinvestments.
Franzoni,Nowak,andPhalippou(2012)sidestepsthisproblembyestimatingthe
modelafterformingportfoliosofdeals,ratherthanindividualones.This
substantiallylowersthevolatilitiesandreducesthemagnitudeofthisadjustment.It
does,however,reducetheotheradvantagesofusingindividualdeals:inparticular,
itreducesstatisticalpowerandrequiresthemtouseamodifiedIRR(MIRR)
approximationofreturns.
SelectionBiasAnotherprobleminusingcompany‐leveldataissampleselection.
Toillustrate,VCinvestmentsarestructuredovermultiplefinancingrounds,and
better‐performingcompaniestendtoraisemoresuchrounds.Hence,datasetswith
valuationsofindividualVCroundsaredominatedbythesebetter‐performing
companies.Moreover,distressedcompaniesareusuallynotformallyliquidated,and
areoftenleftasshellcompanieswithouteconomicvalue(“zombies”).This
introducesanotherselectionproblemfortheempiricalanalysis.Whenobserving
oldcompanieswithoutnewfinancingroundsorexits,thesecompaniesmaybealive
andwellortheymaybezombies,inwhichcaseitisunclearwhenthewrite‐offof
thecompany’svalueshouldberecorded.ThislatterproblemislesssevereforBO
investments,becausethesemostlyresultinawell‐definedexit(acquisitionorIPO)
orawell‐definedliquidation.
12
TheselectionproblemisillustratedinFigure1(fromKortewegandSorensen
(2010)).Theuniverseofreturnsisillustratedbyallthedots.Thedata,however,
onlycontaintheobservedgoodreturnsabovethex‐axis(inblack).Worsereturns
(shadedgray)areunobserved.Sinceonlytheblackdotsareobserved,asimple
estimationoftheexpectedreturnregressiongivesanestimateofalphathatis
biasedupwards,anestimateofbetathatisbiaseddownwards,andatotalvolatility
thatistoolow.Hence,ananalysisthatdoesnotcorrectforthesebiaseswillpaintan
overlyoptimisticpictureoftheriskandreturnperformanceoftheseinvestments.
Figure1:Illustrationofselectionbias
Thestatisticalmethodologyforaddressingsuchselectionbiaseswasfirst
introducedbyHeckman(1979).Cochrane(2005)estimatesthefirstdynamic
selectionmodelonVCdataandfindsthattheeffectofselectionbiasisindeedlarge.
Theselectioncorrectionreducestheinterceptofthelog‐marketmodel,denoted
above,from92%to‐7.1%.Cochranealsohighlightsthedifficultoftranslatingthis
interceptintoanabnormalreturn.KortewegandSorensen(2010)estimatean
extendedversion.Theyalsofindthatselectionover‐statestheriskandreturntrade‐
offofVCinvestments.Withoutselection,theestimateoftheintercept, ,is‐19%
annuallywhiletakingintoaccounttheselectionbiasreducesthisestimateto‐68%
(noteagain,theseinterceptscannotbeinterpretedasreturns).
13
Inthecontinuous‐timemodel,theestimated coefficientcanbeinterpretedasthe
CAPMsystematicrisk,withoutadjustments.Cochranefindsaslopeof0.6‐1.9forthe
systematicrisk.Thisfigureseemslow,however.Itincludesestimatesatthe
individualindustrylevelsof,forexample,‐0.1forretailinvestments.
KortewegandSorensen(2010)reportsubstantiallyhigherbetaestimatesof2.6‐2.8,
whichmaybemorereasonableforyoungstartupsfundedbyVCinvestors.They
alsofindsubstantialtimevariationasVCinvestinghasmatured.Theyestimate
alphasovertheperiods1987‐93,1994‐2000,and2001‐2005,andfindthatthe
alphasintheearlyperiodwerepositivebutmodest,thealphasinthelate1990s
wereveryhigh,butthealphasinthe2000shavebeennegative,consistentwith
patternsfoundbystudiesusingfund‐leveldata.
IIC.EstimatesUsingFund‐levelData
Fund‐leveldataaretypicallyobtainedfromLPswithinvestmentsacrossmanyPE
funds.Eachobservationrepresentstheperformanceofanentireportfolioof
investments.Inadditiontoinformationaboutthefund,suchasitstypeandvintage
year,thesedatamaycontainthecashflowstreambetweentheLPandthefundora
performancemeasurecalculatedfromthiscashflowstream(suchastheIRR,TVPI
andPME,asdiscussedbelow).Whenindividualcashflowsareavailable,however,
theyaretypicallynottiedtoindividualportfoliocompanies.
Thereareseveraladvantagestofund‐leveldata:First,fund‐leveldatareflectactual
LPreturns,netoffees,resultinginestimatesoftherisksandreturnsactually
realizedbytheLPs.Thesampleselectionproblemissmaller,sincetheperformance
ofcompaniesthatultimatelyneverproduceanyreturnsfortheinvestingfunds
(zombies)iseventuallyreflectedinthefund‐levelcashflows.Othersampleselection
problemsmayarise,however.Fund‐levelperformanceistypicallyself‐reported,and
betterperformingfundsmaybemorelikelytoreporttheirperformance(as
suggestedbyPhalippouandGottschalg(2009),althoughStucke(2011)arguesthat
14
returnsreportedbyVentureEconomicsunderstateactualperformance).2Still,
theseselectionproblemsarelikelysmallerthantheproblemsthatarisewith
company‐leveldata.Finally,sincefundshavesimilarlifetimes(typicallytenyears),
theexpectedreturnequationcanbeestimateddirectly,avoidingtheproblemswith
thecontinuous‐timelog‐returnspecificationusedforcompany‐leveldata.
Fund‐levelPerformanceMeasuresThemaindisadvantageoffund‐leveldatais
thatitisunclearhowtomeasurethe“return.”Calculatingperiod‐by‐periodreturns,
aspreviouslydefined,requiresassessingthemarketvaluesofthePEinvestment
(P(t)inthereturncalculation)atintermediateperiods.Absentquotedmarket
values,however,thiscalculationisinfeasible.Unfortunately,marketvaluesare
typicallyunavailable,andreportedNAVsarenoisysubstitutesforthesevalues(for
example,ithasbeencustomarytovalueinvestmentsinindividualcompaniesatcost
untilthecompanyexperiencedamaterialchangeinthecircumstances,whichdoes
notcapturesmallerongoingchangesintheprospectsandmarketvaluesofthese
companies).Giventheabsenceofregularlyquotedreturns,severalalternative
measureshavebeenproposed.However,noneofthesemeasuresdefineareturn,as
previouslydefined,andtheirrelationshipstoassetpricingmodelsaresomewhat
tenuous.
InternalRateofReturn(IRR)Anaturalstartingpointistointerprettheinternal
rateofreturn(IRR)ofthecashflowsbetweentheLPandGPasareturnearnedover
thelifeofthefund.DenotingthecashflowattimetasCF(t),andseparatingthose
intothecapitalcallspaidbytheLPtotheGP,denotedCall(t),andthedistributions
ofcapitalfromtheGPbacktotheLP,denotedDist(t),theIRRisdefinedasthe
solutiontotheequation:
1 10,
2AnecdotalevidencefromHarris,Jenkinson,andKaplan(2011)suggeststhatthisbiasmadeVentureEconomicsmoreattractiveforbenchmarkingGPperformance.
15
⇒∑
1
∑1
1.
LjungqvistandRichardson(2003)investigatecash‐flowdatafromalargeLP
investinginfundsraisedin1981‐1993(19VCfundsand54BOfunds).Theyreport
averagefundIRRs(netoffees),combiningPEandVCinvestments,for1981‐1993,
of19.81%,whiletheaverageS&P/500returnis14.1%,suggestingthatPE
investmentsoutperformthemarket.
KaplanandSchoar(2005)usefund‐levelquarterlyperformancemeasuresfrom
VentureEconomicscoveringfor1,090VCandBOfunds,ofwhich746fundswere
fullyormostlyliquidatedatthetimeofthestudy.KaplanandSchoarfindVCandBO
returnsslightlybelowthoseoftheS&P/500indexonanequal‐weightedbasis
(value‐weightedVCfundsperformslightlybetterthantheindex)usingtheirsample
offullyliquidatedfunds.Thevalue‐weightedIRRequals13%.3Extendingthe
sampletomature,butnotliquidatedfunds,raisestheIRRforVCto30%butleaves
itunchangedat13%forBOs,resultinginanoverallaverageIRRof18%.4
FocusingonVCinvestments,BygraveandTimmons(1992)findanaverageIRRof
13.5%over1974‐1989.GompersandLerner(1997),usinginvestmentsofasingle
VCfirm,reportanIRRof30.5%over1972‐1997.
ArecentsurveybyHarris,Jenkinson,andKaplan(2011)summarizestheacademic
studiesusingfund‐leveldatafromvariousdataproviders.5ForBOfunds,they
3AspointedoutbyPhalippouandGottschalg(2009),itisnotobvioushowtovalue‐weightPEfunds.Onepossibilityistoweightbytotalcommittedcapital,butfundsvaryintheirinvestmentspeed,andworseperformingfundsmayinvestmoreslowly,introducingadownwardbiasinvalue‐weightedperformanceestimates.4ThefinalreportedNAVoffundsthatarenotfullyliquidatedistreatedasafinalcashflowinthecalculation.PhalippouandGottschalg(2009)arguethatinterimNAVsmayexaggeratetheactualvalues,leadingtoupward‐biasedperformanceestimates.Incontrast,Stucke(2011)arguesthattheNAVsaresubstantiallybelowactualeconomicvalue,usingVentureEconomicsdata.KaplanandSchoar(2005)andHarris,Jenkinson,andKaplan(2011)usereportedNAVsasstated.5ThesestudiesincludeLjungqvistandRichardson(2003),KaplanandSchoar(2005),PhalippouandGottschalg(2008),andRobinsonandSensoy(2011b).
16
reportweightedaverageIRRsof12.3‐16.9%.ForVCfunds,theweightedaverage
IRRsare11.7‐19.3%.Acrosstimeperiods,BOfundshavehadmorestable
performance,withweightedaverageIRRsof15.1‐22.0%inthe1980s,11.8‐19.3%
inthe1990s,and5.8‐12.8%inthe2000s.VCfundperformancehasmorevolatile
overtime,withweightedaverageIRRsrangingfrom8.6to18.7%inthe1980s,22.9
to38.6%inthe1990s,and‐4.9to1.6%inthe2000s.
OverallthesefiguresrevealsubstantialvariationinIRRsacrossstudiesanddata
sources.Moreover,theIRRisaproblematicmeasureofeconomicperformance.The
IRRisanabsoluteperformancemeasurethatdoesnotcalculateperformance
relativetoabenchmarkormarketreturn.Moreover,theIRRcalculationimplicitly
assumesthatinvestedandreturnedcapitalcanbereinvestedattheIRRrate.Ifa
fundmakesanearlysmallinvestmentwithalargequickreturn,thissingle
investmentcanlargelydefinetheIRRfortheentirefund,regardlessofthe
performanceofsubsequentinvestments.Indeed,Phalippou(2011)suggeststhat
GPsmayactivelymanagetheirinvestmentstoinflatefundIRRs.
TotalValuetoPaid‐inCapitalMultiple(TVPI)Analternativeperformance
measurethatislesssusceptibletomanipulationthantheIRRisthetotal‐value‐to‐
paid‐incapital(TVPI)multiple.Thismultipleiscalculatedasthetotalamountof
capitalreturnedtotheLPinvestors(netoffees)dividedbythetotalamount
invested(includingfees).Formally,theTVPIisdefinedas
∑∑
.
Thiscalculationisperformedwithoutadjustingforthetimevalueofmoney.
WhereastheIRRiscalculatedundertheimplicitassumptionthatcapitalcanbe
reinvestedattheIRRrate,theTVPIiscalculatedundertheimplicitassumptionthat
thecapitalcanbereinvestedatazerorate.Harris,Jenkinson,andKaplan(2011)
reportweightedaverageTVPIsof1.76‐2.30forBOinvestors,and2.19‐2.46forVCs.
Thismultiplevariessubstantiallyovertime,though.ForBOfunds,thereported
17
multiplewas2.72‐4.05inthe1980s,1.61‐2.07inthe1990s,and1.29‐1.51inthe
2000s.ForVCfunds,thereportedmultiplewas2.31‐2.58inthe1980s,3.13‐3.38in
the1990s,and1.06‐1.09inthe2000s.
PublicMarketEquivalent(PME)BoththeIRRandTVPImeasuresareabsolute
performancemeasures.Toevaluateperformancerelativetothemarket,thepublic
marketequivalent(PME)isused.Itiscalculatedastheratioofthediscountedvalue
oftheLP’sinflowsdividedbythediscountedvalueofoutflows,withthediscounting
performedusingrealizedmarketreturns,
∑∏ 1
∑∏ 1
.
KaplanandSchoar(2005)arguethatwhenPEinvestmentshavethesameriskas
thegeneralmarket(abetaequaltoone),aPMEgreaterthanoneisequivalenttoa
positiveeconomicreturnfortheLPs.Thisinterpretationmaybemisleadingwhen
theriskofdistributions(thenumeratorinthePME)isgreaterthantheriskof
capitalcalls(includingmanagementfees,whicharelargelyarisk‐freeliability).
Usingalowerdiscountrateforcapitalcallswouldinflatethedenominatorand
reducethePME.Hence,morecarefullyaccountingfordifferentriskswouldsuggest
thatthePMEmayhavetoexceedonebysomemarginbeforeLPsearnapositive
economicreturn.6
KaplanandSchoar(2005)findaverageequal‐weightedPMEsof0.96.Value‐
weighted,thePMEforVCis1.21andthePMEforBOis0.93.Phalippouand
Gottschalg(2009)usedatafor852fundstocalculateaPMEof1.01(theycallthis
measuretheprofitabilityindexorPI).Thefiguredecreasesto0.88aftervarious
adjustments.
6Additionally,asatechnicalpoint,theCAPMmodelprescribesthatthediscountingshouldbeperformedusingexpectedreturns,notrealizedreturnsasinthePME.Usingtherealizedreturnsdistortsthecalculation(accordingtoJensen'sinequality).
18
Comparingdifferentstudiesanddatasources,Harris,JenkinsonandKaplan(2011)
reportweightedaveragePMEsof1.16‐1.27forBOfunds,and1.02‐1.45forVC
funds.PMEsforBOhavevariedfrom1.03‐1.11inthe1980s,to1.17‐1.34inthe
1990s,and1.25‐1.29inthe2000s.ForVC,thereportedPMEsare0.90‐1.08inthe
1980s,to1.99‐2.12inthe1990s,and0.84‐0.95inthe2000s.The1990swastheVC
decade,andthe2000shasbeentheBOdecade.
RiskMeasuresFund‐leveldataarepoorlysuitedforestimatingtheriskofPE
investing.Few,ifany,academicstudiesattempttousefund‐leveldatatodoso.
Instead,LjungqvistandRichardson(2003)estimateriskbyassigningeachportfolio
companytooneof48broadindustrygroupsandusethecorrespondingaverage
betaforpubliclytradedcompaniesinthesameindustry.Theyreportthatthe
correspondingbetaforpubliclytradedcompaniesis1.08forBOand1.12forVC
investments.NotethatthesebetasdonotadjustforthehigherleverageusedinBO
investmentsrelativetoVCinvestments.Assigningbetas,theyfinda5‐6%premium,
whichtheyinterpretastheilliquiditypremiumofVCinvestments.
KaplanandSchoarstatethatthey“believeitispossiblethatthesystematicriskof
LBOfundsexceeds1becausethesefundsinvestinhighlyleveredcompanies.”They
regressIRRsonS&P/500returns,andfindacoefficientof1.23forVCfundsand
0.41forBOfunds.Aleveredbetaof0.41seemsunreasonablylow.
PersistenceandPredictabilityKaplanandSchoar(2005),Phalippouand
Gottschlag(2009),Hochberg,Ljungqvist,andVissing‐Jorgensen(2010),alongwith
otherstudiesfindevidenceofperformancepersistenceforPEfunds.The
performanceofanearlyfundpredictstheperformanceofsubsequentfunds
managedbythesameGP.ThispersistenceisinterpretedasevidencethatGPsvary
intheirskillsandabilitiestopickinvestmentsandmanagetheportfoliocompanies.
Estimatessuggestthataperformanceincreaseof1.0%forafundisassociatedwith
around0.5%greaterperformancefortheGP’snextfund,measuredeitherinterms
ofPMEorIRR.Formoredistantfunds,persistencedeclines.
19
Duetodatalimitations,studiesthatdocumentpredictabilityinPEreturnsconduct
statisticalanalysisonin‐samplebasis,ratherthanonanout‐of‐samplebasis.In
KaplanandSchoar,forexample,PEfundsinthe“topquartile”dowell,butthese
fundsareidentifiedexpost.Withinafundfamily,fundsoftenhavelifetimesof10
yearsbutoverlaptosomeextent.In‐sampleanalysisusestheultimateperformance
ofapreviousfundtopredicttheperformanceofasubsequentfund,evenifthis
subsequentfundisraisedbeforetheultimateperformanceofthepreviousfundsis
fullyrealized.Thestudiesemployvariousrobustnesschecks,suchasusing
intermediateNAVsinsteadofultimateperformanceorusingtheperformanceof
fundsseveralgenerationsagotopredictfutureperformancetomitigatethis
concern.Still,somerecentresearch,suchasHochberg,LjungvistandVissing‐
Jorgensen(2010)findweakerevidenceofpersistenceusingonlyinformation
availablewhenthenewfundisraised.
IID.SummaryofEmpiricalEvidence
Basedontheexistingevidencefromstudiesusingfund‐leveldata,itseemsearlyfor
apreciseassessmentofhowtheriskofPEinvestingcomparestotheriskof
investinginpubliclytradedequitiesevenintermsofthesemostbasicmetrics.
MeasuringPEriskandreturnsisdifficultbecauseoftheinfrequentobservationsof
fundorcompanyvaluesandselectionbias.Studiesusingcompany‐leveldatathat
accountforselectionbiasfindhighalphasforPEinvestmentsonlyduringthelate
1990s,butnegativealphaspost‐2000.Thepositivealphaestimatesarehardto
interpretintermsofarithmeticreturns,however,becauseoftheveryhighvolatility.
Estimatesofbetasvarysubstantially,rangingashighas3.6forVCinvestments,but
generallyPEbetasarewellaboveone.Studiesusingfund‐leveldatahavefewer
selectionproblems,butstillsufferfromthefactthatnodirectPEreturnsare
observed.Unlikestandardreturnmeasures,fund‐levelIRRs,TVPI,andPME
measurescanbemisleadingandshouldbeinterpretedwithcautiontoinferPE
performance.Intermsofrawperformance,inthewordsofHarris,Jenkinson,and
Kaplan(2011)"itseemslikelythatbuyoutfundshaveoutperformedpublicmarkets
20
inthe1980s,1990s,and2000s."However,duetotheuncertaintyabouttheriskof
privateequityinvestments,itisnotyetpossibletosaywhetherthisoutperformance
issufficienttocompensateinvestorsfortheriskoftheseinvestmentsandwhether
theinvestmentsoutperformonarisk‐adjustedbasis.Finally,thereisevidenceof
persistenceofPEfundreturnsandsome,albeitweakerandlessconsistent,evidence
thatcharacteristicslikefundsizeandpastcapitalraisingspredictPEfundreturns.
III.AssetAllocationstoPrivateEquity
HavingdiscussedthemeasurementofPEreturns,wenowconsideroptimal
allocationstoPE.Thisrequires,ofcourse,asuitablerisk‐returntrade‐offforPE
investmentsaswellascorrelationsofPEreturnswithotherassetsintheinvestor’s
opportunityset.AsSectionIIpointsout,measuringtheseinputsforPEforuseinan
optimizationproblemrequiresspecialconsiderations.Wenowtakeasgiventhese
inputsandfocusonthedimensionofilliquidityriskofPEandhowtoincorporate
illiquidityPEriskintoanoptimalassetallocationframework.Therehavebeen
severalapproachestohandlingilliquidityriskinassetallocation,allofwhichhave
relevanceindealingwithPEallocation.Toputintocontextthesecontributions,we
startwiththecaseofassetallocationwithoutfrictions.
IIIA.FrictionlessAssetAllocation
TheseminalcontributionsofMerton(1969,1971)characterizetheoptimalasset
allocationofaninvestorwithConstantRelativeRiskAversion(CRRA)utility
investinginarisk‐freeasset(withconstantrisk‐freerate)andasetofriskyassets.
TheCRRAutilityfunctionwithriskaversionisgivenby
1
( ) .1
WU W
21
CRRAutilityishomogeneousofdegreeone,whichmeansthatexactlythesame
portfolioweightsarisewhether$10millionofwealthisbeingmanagedor$1billion.
Thismakestheutilityfunctionidealforinstitutionalassetmanagement.
Assumetheriskyassetsarejointlylog‐normallydistributed.Underthecaseofiid
returns,thevectorofoptimalholdings,w,oftheriskyassetsaregivenby
whereisthecovariancematrixoftheriskyassetreturns,isthevectorof
expectedreturnsoftheriskyassets,andrfistherisk‐freerate.Thisisalsothe
portfolioheldbyaninvestorwithmean‐varianceutilityoptimizingoveradiscrete,
one‐periodhorizon.
Therearetwokeyfeaturesofthissolutionthatbearfurthercomment.First,the
Mertonsolutionisadynamicsolutionthatinvolvescontinuousrebalancing.Thatis,
althoughtheportfolioweights,w,areconstant,theinvestor’spolicyisalwaysto
continuouslysellassetsthathaveriseninvalueandtobuyassetsthathavefallenin
valueinsuchawayastomaintainconstantweights.Clearly,thediscretenatureof
PEinvestmentandtheinabilitytotradeitfrequentlymeanthatallocationstoPE
shouldnotbedonewiththestandardMertonmodel.
Second,thecostofemployinganon‐optimalstrategy,forexample,notholdinga
particularassetwhichshouldbeheldinanoptimalportfolio,canbecomparedto
theoptimalstrategyandthecostofholdingthenon‐optimalportfoliodependson
theinvestor’sriskaversion.Thatis,thecostofbearingnon‐optimalweightsis
dependentontheinvestor’sriskpreferences.Thecostsarecomputedusingutility
certaintyequivalents:thecertaintyequivalentcostishowmuchaninvestormustbe
compensatedindollarsperinitialwealthtotakeanon‐optimalstrategybuthave
thesameutilityastheoptimalstrategy.Arelevantcost,whichthesubsequent
literatureexplores,ishowmuchaninvestorshouldbecompensatedfortheinability
11( ),fw r
22
totradeassetslikePEforcertainperiodsoftimeortobecompensatedforbeing
forcedtopayacostwheneveranassetistraded.
IIIB.AssetAllocationwithTransactionsCosts
InvestinginPEincurslargetransactionscostsininitiallyfindinganappropriatePE
managerandconductingappropriateduediligence.Then,therearepotentially
largediscountstotherecordedassetvaluesthatmaybetakenintransferring
ownershipofaPEstakeinilliquidsecondarymarkets.SinceConstantinides(1986),
alargeliteraturehasextendedtheMertonsetuptoincorporatetransactionscosts.
Constantinidesconsidersthecaseofonerisk‐freeandoneriskyasset.Whenthere
areproportionaltransactionscosts,sothatwhenevertheholdingsoftheriskyasset
increase(ordecrease)byv,theholdingoftherisklessassetdecreasesby(1+k)v.
Whentherearetradingcosts,theinvestornowtradesinfrequently.Constantinides
showsthattheoptimaltradingstrategyistotradewhenevertheriskyassetposition
hitsupperandlowerbounds, and ,respectively.Theseboundsstraddlethe
optimalMertonsolutionwheretherearenofrictions.Theholdingsofriskytorisk‐
freeassets,y/x,satisfy
sothatwheny/xlieswithintheinterval thereisnotradeandwheny/xhits
theboundariesoneitherside,theinvestorbuysandsellsappropriateamountsof
theriskyassettobringtheportfoliobacktotheMertonsolution.
Theno‐tradeinterval, ,increaseswiththetransactionscosts,k,andthe
volatilityoftheriskyasset.TransactionscoststosellPEportfoliosinsecondary
marketscanbeextremelysteep.WhenHarvardendowmenttriedtosellitsPE
investmentsin2008,potentialbuyerswererequiringdiscountstobookvalueof
w w
,y
w wx
[ , ]w w
w w
23
morethan50%.7Evenfortransactionscostsof10%,Constantinidescomputesno‐
tradeintervalsgreaterthan0.25aroundanoptimalholdingof0.26forariskyasset
withavolatilityof35%perannum.Thus,PEinvestorsshouldexpecttorebalance
PEholdingsveryinfrequently.
Thecertaintyequivalentcosttoholdingariskyassetwithlargetransactionscostsis
smallformodesttransactionscosts,atapproximately0.2%forproportional
transactionscostsof1%,butcanbesubstantialforlargetransactionscosts—which
isthemorerelevantrangeoftransactionscostsforPEinvestments.For
transactionscostsof15%ormore,therequiredpremiumtobringtheinvestorto
thesamelevelofutilityasthefrictionlessMertoncaseismorethan5%perannum.
Theliteraturehasextendedthisframeworktomultipleassets(see,forexample,Liu
(2004))anddifferenttypesofrebalancingbands.Leland(1996)andDonohueand
Yip(2003)suggestrebalancingtotheedgeofabandratherthantoatargetwithina
band.Others,likePliskaandSuzuki(2004)andBrown,Ozik,andScholtz(2007)
advocateextensionstotwosetsofbands,wheredifferentformsoftradingaredone
attheinnerbandwithmoredrasticrebalancingdoneattheouterband.Inallthese
extensions,theintuitionisthesame:PEinvestmentsshouldbeexpectedtobe
rebalancedveryinfrequently,andtherebalancingbandswillbeverywide.Thecase
oftransactionscostswhenreturnsarepredictableisconsideredbyGarleanuand
Pedersen(2010).ArelatedstudyisLongstaff(2001),whoallowsinvestorstotrade
continuously,butonlywithboundedvariationsothereareupperandlowerbounds
onthenumberofshareswhichcanbetradedeveryperiod.ThismakesLongstaff’s
modelsimilartoatime‐varyingtransactionscost.
Amajorshortcomingofthisliteratureisthatitassumesthattradeinassetsis
alwayspossible,albeitatacost.ThisisnottrueforPE—overashorthorizon,there
maybenoopportunitytofindabuyerandevenifabuyerisfound,thereisnot
enoughtime,relativetotheinvestor’sdesiredshorthorizontoraisecapital,togo
7See“LiquidatingHarvard”ColumbiaCaseWorksID#100312,2010.
24
throughlegalandaccountingprocedurestotransferownership.Animportant
frictionforPEinvestorsinsecondarymarketsisthesearchprocessinfindingan
appropriatebuyer.Theremaybenoopportunitytotrade,evenifdesired,at
considerablediscounts.Thiscaseiswhatthenextliteratureconsiders.
IIIC.AssetAllocationwithSearchFrictions
AsPEinvestmentsdonottradeonacentralizedexchange,animportantpartof
rebalancingaPEportfolioisfindingacounterpartyinover‐the‐countermarkets.
Or,ifmoneyisspunofffromexistingPEinvestments,neworexistingPEfundsmust
befoundtoinvestin.Thisentailsasearchprocess,incurringopportunityandsearch
costs,aswellasabargainingprocess,whichreflectsinvestors’needsforimmediate
trade.Thelatteriscapturedbyatransactionscost,asmodeledintheprevious
section.Theformerrequiresatradingprocessthatcapturesthediscretenatureof
tradingopportunities.
SinceDiamond(1982),search‐basedfrictionshavebeenmodeledbyPoissonarrival
processes.Agentsfindcounterpartieswithanintensity,andconditionalonthe
arrivalofthePoissonprocess,agentscantradeandrebalance.Thisproduces
intervalswherenorebalancingispossibleforilliquidassetsandthetimeswhen
rebalancingarepossiblearestochastic.Thisnotionofilliquidityisthatthereare
timeswhereitisnotpossibletotrade,atanyprice,anilliquidasset.These
particulartypesofstochasticrebalancingopportunitiesareattractiveformodeling
PEinanotherway:theexitinPEvehiclesisoftenuncertain.AlthoughaPEvehicle
mayhaveastatedhorizon,sayof10years,thereturnofcashfromtheunderlying
dealsmaycauselargeamountsofcapitaltobereturnedbeforethestatedhorizon,
orinmanycasesthehorizonisextendedtomaximizeprofitabilityoftheunderlying
investments(ortomaximizethecollectionoffeesbyGPs).
Anumberofauthorshaveusedthissearchtechnologytoconsidertheimpactof
illiquidity(search)frictionsinvariousover‐the‐countermarkets,suchasDuffie,
GarleanuandPedersen(2005,2007).Whiletheseareimportantadvancesfor
25
showingtheeffectofilliquidityriskonassetprices,theyarelessusefulforderiving
assetallocationadviceonoptimalPEholdings.Duffie,GarleanuandPedersen
(2005,2007)consideronlyrisk‐neutralandCARAutilitycasesandrestrictasset
holdingstobe0or1.Garleanu(2009)andLagosandRocheteau(2009)allowfor
unrestrictedportfoliochoice,butGarleanuconsidersonlyCARAutilityandLagos
andRocheteaufocusonshowingtheexistenceofequilibriumwithsearchfrictions
ratherthanonanypracticalcalibrations.Neitherstudyconsidersassetallocation
withbothliquidandilliquidassets.
IIID.AssetAllocationwithStochasticNon‐TradedPeriods
Ang,Papanikolaou,andWesterfield(2011)[APW]solveanassetallocationproblem
withliquidsecurities,correspondingtotradedequitymarketswhichcanbetraded
atanytime,andilliquidsecurities,whichcanbeinterpretedasaPEportfolio.The
investorhasCRRAutilitywithaninfinitehorizonandcanonlytradetheilliquid
securitywhenaliquidityeventoccurs,whichisthearrivalofaPoissonprocesswith
intensity.Inthisframework,thespecialcaseofMertonwithcontinuous
rebalancingisgivenby .Asdecreasestozero,theopportunitiesto
rebalancetheilliquidassetbecomemoreandmoreinfrequent.Themeantime
betweenrebalancingopportunitiesis1/.Thus,indexesarangeofilliquidity
outcomes.
Theinabilitytotradeforstochasticperiodsintroducesanewsourceofriskthatthe
investorcannothedge.Thisilliquidityriskinduceslargeeffectsonoptimal
allocationrelativetotheMertoncase.APWshowthatilliquidityriskaffectsthemix
ofliquidandilliquidsecuritiesevenwhentheliquidandilliquidreturnsare
uncorrelatedandtheinvestorhaslogutility.
ThemostimportantresultthatAPWderiveisthatthepresenceofilliquidityrisk
inducestime‐varying,endogenousriskaversion.Theintuitionisthattherearetwo
levelsofwealththatarerelevantfortheinvestor:totalwealth,whichisthesame
effectasthestandardMertonproblemwheretheriskisthatiftotalwealthgoesto
26
zerotheagentcannotconsume,andliquidwealth.Theagentcanonlyconsumeout
ofliquidwealth.Thus,withilliquidandliquidassets,theinvestoralsocaresabout
theriskofliquidwealthgoingtozero.Thiscanbeinterpretedasasolvency
condition:anagentcouldbewealthybutifthiswealthistiedupallinilliquidassets,
theagentcannotconsume.AlthoughtheCRRAagenthasconstantrelativerisk
aversion,theeffectiveriskaversion—thelocalcurvatureofhowtheagenttradesoff
liquidandilliquidriskinherportfolio—isaffectedbythesolvencyratiooftheratio
ofliquidtoilliquidwealth.Thissolvencyratioalsobecomesastatevariablethat
determinesoptimalassetallocationandconsumption.Thisilliquidityriskcauses
theoptimalholdingsofeventheliquidassettobelowerthantheoptimalholdingof
liquidassetsinapureMertonsetting.
APWderivefivefindingsthatareimportantconsiderationsforinvestinginPE:
1. Illiquidityriskinducesmarkedreductionsintheoptimalholdingsofassets
comparedtotheMertoncase.UnderAPW’scalibrationsforthesamerisk
aversionasa60%riskyassetholding(and40%risk‐freeholding)inthe
Mertoncase,introducinganaveragerebalancingperiodofonceayear
reducestheriskyassetholdingto37%.Whentheaveragerebalancing
periodisonceeveryfiveyears,theoptimalallocationisjust11%.Thus,PE,
whichishighlyilliquid,shouldbeheldinmodestamountsininvestors’
portfolios.
2. Inthepresenceofinfrequenttrading,thefractionofwealthheldinthe
illiquidassetcanvarysubstantiallyandisveryrightskewed.Thatis,
supposetheoptimalholdingtoilliquidassetsis0.2whenrebalancingcan
takeplace.Thentheinvestorshouldexpecttherangeofilliquidholdingsto
varyfrom0.15to0.35duringnon‐rebalancingtimes.Becauseoftheskew,
theaverageholdingstotheilliquidassetwillbehigherthantheoptimal
rebalancingpoint,atsay0.25.Thus,whenanilliquidPEportfoliois
27
rebalanced,theoptimalrebalancingpointistoaholdingmuchlowerthan
theaverageholding.
3. Theconsumptionpolicy(orpayoutpolicy)withilliquidassetsmustbelower
thantheMertonpayoutpolicywithonlyliquidassets.Intuitively,holding
illiquidassetsmeansthatthereisadditionalsolvencyriskthatliquidwealth
goestozeroandconsumptioncannotbefunded.Thus,payoutsoffunds
holdingilliquidassetsshouldbelowerthanthecasewhentheseassetsallare
fullytraded.Asthefractionofilliquidassetsintheportfolioincreases,
consumptionasafractionoftotalwealthdecreases.
4. Thepresenceofilliquidityriskmeansthataninvestorwillnotfullytake
advantageofopportunitiesthatmightlooklikeclosetoan“arbitrage”,for
example,wherecorrelationstotheliquidandilliquidreturnsarenearlyplus
orminusone.Traditionalmean‐varianceoptimizerswithoutconstraints
wouldproduceweightsclosetoplusorminusinfinityinthesetwoassets.
Thisdoesnothappenwhenoneassetisilliquidbecausetakingadvantageof
thisapparentarbitrageinvolvesastrategythatcausestheinvestor’sliquid
wealthtodroptozerowithpositiveprobability.Thus,near‐arbitrage
conditionswhenthereisilliquidityriskarenotexploitedliketheMerton
setting.
5. Finally,thecertaintyequivalentrewardrequiredforbearingilliquidityriskis
large.APWreportthatwhentheliquidandilliquidreturnsarelowly
correlatedandtheilliquidportfoliocanberebalanced,onaverage,once
everyfiveyears(whichisatypicalturnoverofmanyPEportfolios),the
liquiditypremiumisover4%.Forrebalancingonceayear,onaverage,the
illiquiditypremiumisapproximately1%.Thesenumberscanbeusedas
hurdleratesforinvestorsconsideringinvestinginPE.
AnumberofauthorsincludingDai,Li,andLiu(2008),Longstaff(2009),DeRoon,
Guo,andTerHorst(2009),andAngandBollen(2010)alsoconsiderassetallocation
28
wheretheilliquidassetcannotbetradedovercertainperiods.However,inthese
studies,theperiodofnon‐tradingisdeterministic.Incontrast,theAPWframework
hasstochasticandrecurringperiodsofilliquidity.Deterministicnon‐trading
periodsareprobablymoreappropriateforhedgefundinvestmentswherelock‐ups
haveknownexpirations.PEinvestingismoreopenendedandhasrandom,and
infrequent,opportunitiestorebalance.
APWstillmissanumberofpracticalconsiderationsthatthefutureliteratureshould
address.ThemostimportantoneisthatintheMertonsettingintowhichAPW
introduceilliquidity,therearenocashdistributions;allriskyassetreturns(both
liquidandilliquid)arecapitalgains.PEinvestmentsrequirecashflowmanagement
ofcapitalcallsanddistributions.Somead‐hocsimulationshavebeenconductedby
someindustryanalystsonthisissue,likeSiegel(2008)andLeibowitzandBova
(2009),butwithoutexplicitlysolvingoptimalportfolioswithilliquidityrisk.An
extensionofAPWtoincorporatecashflowstreamscouldaddressthis.
IIIE.Summary
TheinabilitytocontinuouslyrebalancePEpositions,potentiallyevenbypaying
transactionscosts,makesoptimalholdingsofilliquidPEinvestmentsverydifferent
fromthestandardMertonframeworkwhichassumesnoilliquidityrisk.Since
transactionscostsinrebalancingPEportfoliosareverylarge,inbothenteringnew
PEpositionsandsellingexistingPEpositions,PEpositionsshouldbeexpectedtobe
rebalancedveryinfrequentlyandinvestorsshouldsetverywiderebalancingbands.
InassetallocationmodelswhereilliquidassetslikePEcanonlybetradeduponthe
arrivalofa(stochasticallyoccurring)liquidityevent,illiquidityriskmarkedly
reducestheholdingsofilliquidassetscomparedtothestandardMertonmodel.For
example,anassetwhichcouldbetradedcontinuouslyintheMertonsettingthatis
heldwitha60%optimalweightwouldhaveanoptimalholdingoflessthan10%ifit
couldberebalancedonlyonceeverytenyears,onaverage.Thecertaintyequivalent
reward,orequivalentlythehurdlerate,forbearingilliquidityriskislarge.Fora
29
typicalPEinvestmentthatcanbetradedonlyonceintenyears,onaverage,the
illiquiditypremiumiswellabove4%.
IV.IntermediaryIssuesinPrivateEquity
Mostcommonly,assetownersmakePEinvestmentsasanLPinafundwhere
investmentdecisionsaremadebyfundmanagersactingasGPs.Thisarrangement
raisespotentialagencyissues.OnecharacteristicofPEinvestmentisthatthe
investmentdecisionsarisingfromsuchmanagementconsiderationsandtherelated
agencyissuesbecomeintrinsicallyintertwinedwithPEperformance.Inpublic
equitymarkets,factorreturnsandactivemanagementcanbeseparatedduetothe
existenceofinvestableindexstrategies.
IVA.AgencyIssues
WhiletheagencyproblemiscentralforPEinvestments,thereisonlyasmall
literatureonoptimaldelegatedportfoliomanagement(seethegoodsurveysbythe
BIS(2003)andStracca(2006)).Thereis,however,alargeliteratureonagency
issuesinstandardcorporatefinancesettings(see,forexample,thetextbookby
Salanie(1997)andBoltonandDewatripont(2005)).Delegatedportfolio
managementisdifferentfromstandardagencyproblemsbecausethe“action”
chosenisgenerallyobserved(theinvestmentsmadebytheGP),butthesetof
actionsisunknown(thefullsetofdealsavailabletotheGP).Incontrast,instandard
moralhazardproblemsthe“action”isunobservable,butthesetofpotentialactions
isusuallyknown.8Thus,littleisknownabouttheoptimaldelegatedportfolio
contract,andtheliteraturehasfew,ifany,specificconclusionsorprescriptions
aboutwhatformtheoptimalPEcontractbetweenLPsandGPsshouldtake.
8Thereareotherreasonsthatmakethedelegatedoptimalportfoliomanagementproblemchallenging.Theagent(fundmanager)cancontrolboththemean,whichistheresponsetothesignalbybuyingagoodstock,andalsothevariance,throughleverage.Inatypicalagencyproblemtheagentcontrolsonlythemean(occasionallythevariance),butnotboth.Incontinuoustime,whichisoftenusedtosolveagencyproblems,diffusiondynamicsareeffectivelyobservableathighenoughfrequencies.
30
PEinvestingisfurthercomplicatedbyhavingtwolevelsofprincipal‐agentrelations
ratherthanjustasingleone:alevelbetweentheLPs(principal)andGPs(agent)
andanotherlevelbetweentheGPsasfundmanagers(principal)anditsunderlying
portfolioofcompanies(agent).Bothlevelsrelyonstrongdirectmonetary
incentives.Apartfromthesemonetaryincentives,however,therelationbetween
LPsandGPsisonewithlimitedinformation,poormonitoring,rigidfeestructures,
andtheinabilitytowithdrawcapital,ordirectlycontrolmanagers.Ononehand,
thesefeaturestendtoheightentensionsbetweentheLPsandGPsandexacerbate,
ratherthanalleviate,agencyissues.Ontheotherhand,thedistancebetweentheLP
andGPmayallowGPstoinvestandmanagecompaniesmorefreely.
Theotherprincipal‐agentrelationbetweenthefundanditsportfoliocompaniesis
onewithstronggovernance,transparentinformationflows,goodincentivesfor
monitoring,andahighalignmentofinterestsbetweenownersandmanagement
(seeJensen(1989)).ThereisstrongevidencethatPEfundsaddsignificantvalue,on
average,tothecompaniesintheirportfolio.ThisliteratureissurveyedbyKaplan
andStromberg(2009).
Theinteractionsbetweenthesetwolayersofprincipal‐agentproblemshavenot
beenfullyexplored.Itisnotinconceivable,though,thatmitigatingtheprincipal‐
agentproblemsattheLP‐GPlevelwouldcomeatthecostofincreasingtheproblems
atthefund‐companylevel.Forexample,greatertransparencyaboutthe
managementofindividualportfoliocompaniesmayinturnleadGPstomanage
thesecompanieswithaneyetowardsmanagingshort‐termearningsexpectations
andsatisfyingpublicexpectationsmorebroadly,aconcernforpubliclytraded
companies,ratherthansimplymanagingcompaniestomaximizetheirtotalvalue.
IVB.PrivateEquityContracts
BecausePEis,byitsnature,private,itisdifficulttoperformsystematiclarge‐sample
studiesofcontractualfeaturesandseehowtheyrelatetoperformance.Gompers
31
andLerner(1999),Litvak(2009),andMetrickandYasuda(2010)examinesmall
samplesofvariousPEcontracts.Severaltentativeconclusionsemerge:
1. PEcontractsarelargelystandardized.Anoften‐quotedfeearrangementisa
managementfeeof2%andacarryof20%.Thereissomevariationinthe
numbers(e.g.,managementfeestendtovarybetween1‐2.5%andcarried
interestvariesbetween20‐35%),butthegeneralstructureiswidelyused.
Additionally,asubstantialpartoftheGPscompensationmaybeintheform
oftransactionfees.PEfeesarehigh.
2. Thereissomevariationinthespecificprovisionsgoverningthecalculation
andtimingofthefeesandcarriedinterest.Forexample,amanagementfee
couldbeflat(oncommittedcapital),decliningoverthelifeofthefund,a
(time‐varyingbutdeterministic)combinationofcommittedandmanaged
capital,orevenanabsoluteamount.
3. Fixedfeeandperformancecomponentsarenotsubstitutesbutcomplements.
Thatis,fundstendtoraiseboththefixedfeeandvariablefeecomponents
(andtheothercompensationcomponents)together.Fundsizetendstobe
positivelycorrelatedwithfees,andKaplanandSchoar(2005),alongwith
othersfindthatsizeisnegativelycorrelatedwithperformance.More
recently,however,RobinsonandSensoy(2011a)investigateanextended
samplewithcontracttermsandperformance,andfindnorelationbetween
net‐of‐feeperformanceandthesizeofthefundorthefees.
4. ThereisadebateabouttheperformancesensitivityofPEcompensation.
MetrickandYasuda(2010)findthatclosetoone‐halfthepresentvalueofGP
compensationarefrommanagementfeesratherthancarriedinterestand
findthistobetrueforbothVCandBOfunds.However,Chungetal.(2011)
pointoutthatasubstantialamountofGPs'performancepayarisesthrough
thecontinuationvalueofraisingfuturefunds,whicharehighlysensitiveto
currentperformance.
5. PEcontractsarecomplexdocuments.Litvak(2009),however,findslittle
relationbetweenopaquenessandtotalcompensation.
32
ThemanagementfeeschargedbyprivateequityandVCfundsarehigh.Accordingto
MetrickandYasuda(2010)suchfeesconsumeatleastone‐fifthofgrossPEreturns.
MetrickandYasudafoundthatoutofevery$100investedwithaVCfund,an
averageof$23ispaidtotheGPsintheformofcarryandmanagementfees.ForBOs,
themeanofthecarryandmanagementfeescomesto$18per$100.
ThehighfeeschargedbyGPspointtothefactthatifaninstitutionalinvestor
wishingtoallocatetoPEcandothisin‐house,thentherearesubstantialsavings
available.Ofcourse,attractingtalentandrunninganin‐housePEshoppresentsa
differentsetofagencyissuesthanout‐sourcingtoPEfundswithGPs.Despitethe
pessimisticviewofreturnsofPEinvestmentstoLPsinSectionII,thehighPEfees
impliesthatifassetownerscancomeclosetocapturinggrossreturns,PEbecomes
muchmoreattractive.
Whileopacitypersedoesnotseemtoberelatedtototalcompensationandreturns,
opacityhasotherimportantknock‐oneffectsforotheraspectsofanassetowner’s
largerportfolio.Complexityandnon‐transparencycanincreaseagencyproblems
andmakeriskmanagementmoredifficult.TheleverageinvolvedinmanyBOfunds
canbemoreexpensive,andisoftenhardertomonitor,thanleveragedonedirectly
bytheassetowner.
IVC.Summary
AgencyissuesarefirstorderproblemsinPEinvestments,unlikeinvestmentsin
publicequity.Indeed,thereisnowaytoseparateactivemanagementfrompassive
managementinPEinvestment.Whilethereislittleliteratureonwhatcontractual
designisoptimalinPEinvestments,existingPEcontractstypicallyassigna
managementfeeof2%andcarryof20%.Thesetranslateintoveryhighfeeswhich
represent20‐25%ofgrossPEreturnsforinvestorspointingtotremendoussavings
forinstitutionalinvestorsifPEinvestmentcanbedoneinhouseassumingthereis
nolossinreturnquality.
33
V.Conclusion
Relativelylittleisknownaboutriskandreturns,assetallocation,andoptimal
contractingforprivateequity(PE)investmentsincontrasttoinvestmentsinlisted,
publicequitymarkets.TheirregularnatureandlimiteddataofPEinvestments
complicatetheestimationandinterpretationofstandardriskandreturnmeasures;
naïvemeasureoverstatePEreturnsandunderstateriskandcommonlyreported
measures(IRR<TVPImultiple,andPME)needtobeinterpretedwithcaution.
Modelsofassetallocationthattakeintoaccounttransactionscostsandilliquidity
risksuggestholdingsofPEshouldbesmallerthantraditionallistedpublicequity.
WhileincentivefeesinPEaddressmoralhazardandinformationagencyproblems,
totalfeesinPEinvestmentsareverylargeandincentivefeesaccountforaminority
oftotalcompensation.
34
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