IMF -美国外国投资组合超额回报的新证据 New Evidence on the US Excess Return on Foreign Portfolios

NewEvidenceontheUSExcessReturnonForeignPortfolios

CarolC.Bertaut,StephanieE.Curcuru,EsterFaia,andPierre-OlivierGourinchas

WP/24/241

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2024

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ResearchDepartment

NewEvidenceontheUSExcessReturnonForeignPortfolios

PreparedbyCarolC.Bertaut,StephanieE.Curcuru,EsterFaia,andPierre-OlivierGourinchas*

AuthorizedfordistributionbyPierre-OlivierGourinchasNovember2024

IMFWorkingPapersdescriberesearchinprogressbytheauthor(s)andarepublishedtoelicit

commentsandtoencouragedebate.TheviewsexpressedinIMFWorkingPapersarethoseofthe

author(s)anddonotnecessarilyrepresenttheviewsoftheIMF,itsExecutiveBoard,orIMFmanagement.

ABSTRACT:WeprovidenewestimatesofthereturnonUSexternalclaimsandliabilitiesusingconfidential,

high-quality,security-leveldata.Theexcessreturnispositiveonaverage,sinceclaimsaretiltedtowardhigher-returnequities.Theexcessreturnislargeandpositiveinnormaltimesbutlargeandnegativeduringglobal

crises,reflectingtheglobalinsuranceroleoftheUSexternalbalancesheet.Controllingforissuer’snationality,wefindthatUSinvestorshavealargerexposuretoequityissuedbyAsia-headquarteredcorporationsthan

reportedintheaggregatestatistics.Finally,equityportfoliosareconcentratedin’superstar’firms,butforUSliabilitiesforeignholdingsarelessconcentratedthantheoverallmarket.

RECOMMENDEDCITATION:NewEvidenceontheUSExcessReturnonForeignPortfolios,Bertaut,Curcuru,FaiaandGourinchas

JELClassificationNumbers:

F3,F6,G1

Keywords:

Exorbitantprivilege;excessreturn;portfoliocomposition;crises;offshorecenters;superstarfirms

Author’sE-MailAddress:

faia@wiwi.uni-frankfurt.de,

carol.bertaut@,

stephanie.e.curcuru@,

pgourinchas@

2

1.Introduction

Portfolioreturnsplayanimportantroleinglobalwealthdynamics.Akeystylizedfact,firstestablishedby

GourinchasandRey

(2007a),isthatthereturnonUSexternalclaimsconsistently

exceedsthatonUSexternalliabilities,theso-called‘exorbitantprivilege.’1ApositiveexcessreturnhelpstostabilizetheUSexternalassetpositionandmakesUScurrentaccountdeficitsmoresustainable.Itisoftenmentionedinconnectionwithadominantroleofthedollarinthe

internationalmonetarysystem(Caballeroetal.

(2008),

GoldbergandTille

(2009),

Gourinchaset

al.

(2019),

Ilzetzkietal.

(2019),

GopinathandStein

(2021),

Bianchietal.

(2021),

Chahrourand

Valchev

(2022),

Sauzet

(2023)or

KekreandLenel

(2024)arefewrecentcontributions)

.

Intheabsenceofsecurity-by-securitydata,previousestimatesusedtop-downapproachesbasedonhighly-aggregateddata,eitherexploitingbalanceofpaymentaccountingrelationshipsorapprox-imatingreturnswithmarketindexes.2Weimproveonearlierestimatesofcross-borderportfolioreturnsbyusingabottom-upapproach.Specifically,weuseaconfidential,security-leveldatasetofportfolioholdings(equityandbonds)fromtheofficialfilingsofcustodiansandinvestorsthroughtheTreasuryInternationalCapital(TIC)systemavailablefrom2005to2022.Thesesecurity-leveldatahaveneverbeenusedinthistypeofstudy.Ourdetaileddataallowustoexaminethereturnsacrosstimesamples,regions,typeofassets,returncomponents(e.g.,capitalgainsversusdividends),issuertype,andnationalityofparentfirm.3ComparingourexcessreturnscomputedusingTICsecuritiestothetop-downapproachesfromtheliterature,weconfirmsomeofthepreviousfindingsandshednewlightonthestructureofUSexcessreturns.

Weestablishfiveresults.First,theUSexcessportfolioreturn–thedifferencebetweenthereturnonclaimsandthatonliabilitiesaveragesamodest0.5%peryearoverthefullsample.Itissignificantlyhigher,averaging1.7%peryear,whenweexcludethepandemicyears(2020-22).

1OftenattributedtoFrenchpresidentdeGaulle,thetermexorbitantprivilegewasinfactcoinedbyhisfinanceministerGiscardd’Estaingin1965whenheexpressedhisunhappinessabouttheabilityoftheUStorunlargedirectinvestmentsurplusesfinancedbyholdingsofdollarreservesattheBanquedeFrance.

2See

GourinchasandRey

(2007a,

2014)forexamplesoftheformer,and

Curcuruetal.

(2008

)foranexampleofthelatter.

3OuranalysisislimitedforportfolioreturnssinceTICportfoliosecuritiesdonotincludedirectinvestmentorothercrossborderfinancialtransactions.

Theseestimatesaresimilartothoseobtainedbytop-downapproachesoverthesameperiods.Oursecurity-leveldataallowustodelveintothecomponentsofreturns(e.g.,pricechanges,dividends,exchangerates).Overthesampleperiod,dollarappreciationsubtracted0.7%peryearfromclaimsreturnsonaverage.

Second,weshowthatthepositiveUSexcessreturnariseslargelybecauseoftheasymmetryinthecompositionofclaimsversusliabilities,withclaimsmoretiltedtowardequitythanliabilities.Theshareofequityinthetotalequityandbondclaimsportfoliowasstablethroughoutoursampleataround75%,whiletheequityshareinliabilitiesincreasedfrom36%in2005to51%in2022asAsianandEuropeaninvestorsincreasedtheirholdingsofUSequities.Thereturnonequitiesisonaverage5.3percentagepointshigherthanthereturnonbondsoveroursample,andthusthehigherequityshareinclaimsisanimportantdriverofthepositiveUSexcessreturn.Decomposingtheexcessreturnintoacompositioneffect–reflectingtheasymmetryinportfolioshares–andareturneffect–reflectingthedifferenceinreturnswithinassetclasses–wefindthatthecompositioneffectcontributed1.9percenttotheexcessreturn,whilethereturneffectcontributed-1.4percent,largelybecauseofalowerreturnonequityclaimsrelativetoequityliabilitiessince2010.4.

Third,wedocumentthattheUSexcessreturnbecomeslargeandnegative,equalto-3.1percent,duringglobalcrises,suchastheglobalfinancialcrisisof2008-09,theEuropeansovereigndebtcrisisof2010-12,andtheglobalpandemicof2020-22.Outsideofglobalcrises,theexcessreturnislargeandpositive,equalto3.3percent.ThisisconsistentwiththeorieshighlightingtheglobalinsuranceroleoftheUSexternalbalancesheet(see

GourinchasandRey

(2022),

Faia

(2007)and

Valchev

(2020))

.Duringglobalcrisesboththecompositioneffectandthereturneffectdeclineorturnnegative,theformerasequitiesunder-performbonds(asintheglobalfinancialcrisis),thelatterasclaimsunder-performliabilities(asintheEuropeandebtcrisisorthepandemic).Externalportfoliosreflectthebalancebetweencross-borderassetdemandsandrelativeassetsupplies.OurfindingsconfirmalargernetdemandforriskyassetsfromUSinvestorsrelativetoforeignones.The‘exorbitantprivilege’ingoodtimesismatchedwithan‘exorbitantduty’incrisestimes(

Gourinchas

4ThisfactisconsistentwiththedeteriorationofNFAdocumentedbyMilesi-Ferretti(2021)andAtkesonetal.

(2022).

3

4

andRey

(2022))

.Dollarmovementsdonotcontributetothisshift,whichcouldinsteadreflecttheincreasedavailabilityofdollarliquidityprovidedbytheUSFederalReserveduringglobalcrises.Inturntheincreasedfrequencyofglobalcriseshascontributedtoreducetheex-postexcessreturnintherecentperiod.

Fourth,oursecurity-leveldataallowsustoidentifytheissuerofeachsecurity,andthustoremapthesecuritiestothecountryoftheparentoftheissuingfirm.ThisremappingisimportantasalargeandgrowingshareofsecuritiesheldbyUSinvestorsareissuedinoffshorefinancialcenters,attimesbyfirmswithUSparents(seealso

Zucman

(2013)and

Coppolaetal.

(2021))

.Growthinglobalprofits,aswellasofpotentialforprofitshiftingbyUSfirms,isexploredin

Chodorow-Reich

etal.

(2024)usinganovelfirmleveltaxreturnsdataset

.Inourdata,theremappingrevealsthatUSinvestorsholdalargershareofsecuritiesissuedbyfirmsinemergingAsiathanreportedintheresidence-basedaggregatestatistics.TheeffectofthisremappingontheUSexcessreturnissmall,however.

Finally,wedocumentthatequityholdingsareconcentratedinsuperstartechnologyandpharma-ceuticalfirms.Thisconcentrationismuchlargerinequityliabilities,wherethelargetech-relatedUSfirmsknownastheMagnificent7comprise16.2%ofequityliabilitiesholdingsin2022.5Theconcentrationinequityclaimsholdingsislessextreme,with7.4%ofholdingsinvestedEuropeanGRANOLASfirmsplustheTaiwanfirmTSMC.6Relativetothesharesoftotalmarketcapitalization,USequityinvestmentabroadismorehighlyconcentratedinsuperstarfirmsthantheoverallmarket,whileforeigninvestmentintheUSislessconcentrated.

Ourpaperaddstothelong-standingdebateonthesizeoftheUSexcessreturnandtheimplicationforglobalimbalances.EarlypapersnotedtheevidenceofapositiveexcessreturnaccruingtoUSinvestorsontheirexternalassetholdings,including

LaneandMilesi-Ferretti

(

2004

),

Obstfeld

andRogoff

(2005),

MeissnerandTaylor

(2006),

GourinchasandRey

(2007b),

Eichengreen

(2011),

GourinchasandRey

(2014)or

Gourinchasetal.

(2019)

.

5ThetermwascoinedinMay2023byMichaelHartnett,theChiefInvestmentStrategistandManagingDirectoratBankofAmericaGlobalResearch.ItincludesAlphabet,Amazon,Apple,Meta,Microsoft,NvidiaandTesla.

6Thetermwascoinedin2020byGoldmanSachstorefertoagroupof11Europeancompanieswithstrongearningsgrowth,lowvolatility,andstableprofitmargins.ItincludesGSK,Roche,ASML,Nestle,Novartis,NovoNordisc,L’Oreal,LVMH,Aztrazeneca,SAP,Sanofi.

5

ThesepapersinfertheaggregatereturnsandtheirdifferentialsfromthechangesinnetforeignassetpositionsandtransactionsreportedintheUSInternationalInvestmentPosition(IIP).WerefertothisprocedureastheBureauofEconomicAnalysisor‘BEA’method.ValuationchangesareakeycomponentoftheUSexcessreturn,butintheBEAmethodtheyareimputedbysubtractingBalance-of-Paymentcapitalflowsfromchangesinreportedholdings.Becausethecapitalflowsarecollectedfromdifferentreportingagenciesandatadifferentfrequencythanthesurveysusedtocollecttheholdingsinformation,theBEAmethodofestimatingvaluationchangesisquiteimprecise.7Worksby

Curcuruetal.

(2008)and

Curcuruetal.

(

2013

)computedreturnsusingmarketindexesandhighlightedtheimportanceofassetcompositioninexplainingthereturndifferential.8However,thismethodisalsoimpreciseasthecommercialindexeswillhaveadifferentcompositionthanactualassetholdings.

Insum,ouruseofsecurity-leveldatamovestheliteratureforwardinanumberofways.First,itimprovesaccuracyovertop-downapproacheswhichhavetomakeanumberofassumptionsabouttheunderlyingholdings.Second,thedis-aggregatednatureincludesdividendsandcouponssowecancalculateincomedirectlyratherthanestimatingit,andallowsustodecomposetheportfolioreturnsacrossassetclasses,issuers,andthevariousreturncomponents(capitalgainsversusexchangerates),andtoassessthedegreeofconcentrationinholdings.9Third,becauseweknowtheidentityoftheissuerofeachsecuritywecandeterminetheissuer’snationalityusingthemethodologydevelopedby

Bertautetal.

(

2019

).Theimportanceofcorrectlyimputingthenationalityoftheparentholdingfortheallocationofglobalwealthandprofitshasbeenhighlightedin

HinesandRice

(1994),

Bernardetal.

(2006),

Zucman

(2013)or

Coppolaetal.

(2021)

.Thecomparisonoftheportfolioweightsbyresidenceandnationalityallowsustocaptureanychangein

7AnadditionalsourceofmeasurementerrorintheBEAmethodisthatliabilitiessurveydataiscollectedasofeachend-June,whiletheBEApublishesestimatedpositionsasofend-December,usingmarketindexestoestimatethevaluationchangesbetweenJuneandDecember.

8InthatcontexttheauthorsdiscussotherpotentialmeasurementissuesoftheBEApositions.Theyreferinparticulartotheasymmetricadjustmentbetweentheflowandthestockpositionswhichcreatesadifferencebetweenthevaluationchannelmeasuredthroughaggregatenetforeignassetpositionsandthereturns’differentialsmeasuredthroughmoregranulardata.

9Fortheperiodunderconsideration,pricereturnsanddividendsarebasedonthevaluesreportedbythesurveyrespondents.AsdetailedinAppendix

A

,thosereturnsarealsofrequentlybenchmarkedtothosefromexternalsources.

6

theportfoliocompositionattributabletoissuanceinoffshorefinancialcenterstogetamoreaccuratepictureofthegeographicalexposureofinvestorsandtheeffectofoffshoreissuanceontheexcessreturn.

2.PortfolioReturnsandTheirDecomposition

Auniquefeatureofourdataisthatweareabletocomputecross-borderreturnsfromtheunderlyingsecuritiescollectedbythehighlyconfidentialandlegally-mandated,hencehighlyreliable,TreasuryInternationalCapital(TIC)surveys.10Wereportaveragesfortheentireperiod,2005-2022,aswellasreturnsacrosssub-periods.Westudytheassetandgeographiccompositionoftheunderlyingclaimsandliabilitiesportfoliosandtheirroleindrivingthereturns.Wefurtherdecomposebondreturnsbybondtype(i.e,high-gradesovereignsversuscorporate),anddecomposeequityreturnsintoitscomponents(i.e.,capitalgains,exchangerates,anddividends).

2.1.Methodology

Portfolioreturnsarecomputedwiththeusualformula,weightingthereturnofeachsecurityinthe

portfoliobyitsshare.Forinstancethereturnronportfoliop(e.g.,USequitiesheldbyforeign

investorslocatedinaspecificregion)isthesumoftheproductsoflaggedassetweightsandcurrentreturnsacrosstheJindividualassetsjinportfoliop,whilethemeanreturnE[rp]isestimatedasthesimpletime-averageofthesereturnsoverTperiods:

J

;

(1)

10Securitiescustodiansarelegally-mandatedtocompletetheTICsurveybothforforeignsecuritiesownedbyUSinvestorsandUSsecuritiesheldbyforeigninvestors.Theassetvaluesandothersurveyinformationareregularlycross-checkedwithcommercialdatasourcestoverifytheiraccuracy.MoredetailsonthedataareprovidedinAppendix

A.

7

wherewj,t−1istheweightofassetjinportfoliopattheendofperiodt−1,andrj,tistheUSdollarreturnonassetjbetweent−1andt.Thisreturnconsistsofacapitalgainandayield(dividendorcoupon):

wherepj,tdenotestheUSdollarpriceofsecurityjattimetanddivj,tdenotesthedollardividendorcoupon.Ourdatasetcontainssecurity-levelinformationonholdings,prices,anddividendsor

coupons(seeAppendix

A

)fromwhichwecanconstructrj,t,r,andrp.Themainobjectofinterest

isthemeanreturnonclaims,E[rA],andthatonliabilities,E[rL].

Toillustratetheimportanceofusingsecurity-leveldatawealsoprovideestimatesofthereturnscalculatedbythetop-downmethodsusedinpreviousliterature.Werefertoestimatesusingthemethoddescribedaboveasthe‘security-level’results.Inthesecond‘index’method,wefirstaggregatetheequitiesorbondsatthecountrylevelandthenusecommerciallyavailablecountry-levelequityandbondindexesweightedbytheshareinvestedineachcountry.Thisisthemethodfollowedby

Curcuruetal.

(2008)

.Thethirdapproach,the‘BEA’method,infersreturnsfromthewealthandincomecomponentsoftheUSIIPpublishedbytheBEA.Moredetailsonthecomputationofthereturnsineachmethod,andthemappingbetweenwealthandreturnsundertheBEAmethod,arereportedinAppendix

B.

2.2.ReturnsandtheirComponents

Table

1

reportsthereturnsusingeachofthethreemethodsdescribedabove,separatingequityandbondportfolios,andacrossdifferenttimesamples.TheaverageUSexcessreturnoverthefullsample,2005-2022,is0.5%peryearbutthisresultisheavilyimpactedbythepandemicyears2020-2022.Excludingtheseyears,theexcessreturnissignificantlyhigher,averaging1.7%peryear. Theresultsaresimilaracrossthedifferentmethods,withslightlyhigheraverageexcessreturnsusingtheBEAmethod.TheindexandBEAbondreturnestimatesarenoticeablydifferentthanthesecurity-levelestimatesinsomeperiods.ForbondclaimsthisislikelybecauseUSinvestorsholdamaterialamountofdollar-denominatedandfloating-ratebondsissuedbyforeignentitiesandthese

8

aretypicallyexcludedfromcountryreturnindexes;thusreturnestimatesbasedonindexeswillhavealargereffectofexchangeratesandlowerinterestratevolatility.Similarly,ontheliabilitiesside,foreigninvestorsholdfloating-rateUSbondsandasubstantialamountsofasset-backedsecurities,especiallybeforethefinancialcrisis.AsexplainedmoreindetailinAppendix

B

thedifferencebetweenthesecurity-levelandtheBEAreturnsisalsoduetothetimingofthedatacollectionmentionedearlierandtothe‘othercomponents’categoryoftheIIPwhichincludeschangesincoverageandotheritems.

Asexpected,equityreturnsarelargerthanbondreturns,withthedifferenceaveraging5.3%peryear,areasonableestimateoftheequitypremium.Before2010thedollarreturnonequityclaimswashigherthanthatonequityliabilities,butsince2010equityliabilitieshavesubstantiallyoutperformedequityclaims.Thisfactisconsistentwiththedeteriorationofthenetforeignassetpositiondocumentedin

Atkesonetal.

(

2022

).Bondclaimsoutperformedbondliabilitiesinallpre-pandemicsamples,possiblyreflectingtheconvenienceyieldassociatedwithUSTreasurybonds.Lookingacrosssampleperiods,bondclaimsandliabilitiesreturnsbothpeakedinthe2010-12periodandhavebeenmuchsmallersince.

Partofthedifferenceinreturnscanbeattributedtoexchangeratemoves.Table

2

providesabreakdownofreturnsintothecontributionsof(localcurrency)pricechanges,dividends/coupons,andexchangerates.Before2008,exchangeratemoveshelpedboostthereturnonequityclaimsandbondreturnsbecauseofdollardepreciation,butinthesubsequentsampleperiodsthecontributionofexchangerateshasbeensmallornegative.

Table1:Averageportfolioreturnsoverdifferentperiodsinpercentperannum.Security-LevelreturnsarecalculatedfrompositionsandreturnsreportedinTICsurveys.IndexreturnsarecalculatedfrompositionsreportedinTICsurveysaggregatedatthecountrylevelswiththerelevantreturnindicesobtainedfromBloomberg;forequities,thecountry-levelMSCIequitytotalUSDreturnindexes;forforeignbonds,country-levelBloombergbondtotalUSDreturnindexes;forUSbonds,theBloombergUSTreasury1-5YearTotalReturnIndex,BloombergUSCorporateTotalReturnIndex,BloombergUSAgencyIndex.BEAreturnscalculatedfromtheBEA’sInternationalInvestmentPosition(IIP)andbalanceofpayments.ThereturncombinesthevaluationadjustmentsfromBEAIIPtable1.3plustheincomefromBEAtransactionstable4.1.Security-levelandindexliabilitiesreturnsareasofendofJuneeachyearbecausetheyusetheholdingsfromtheendofJuneliabilitiessurvey,whileclaimsareasofend-December.Theexcessreturniscalculatedusingtheaverageofcurrentandfollowingyearliabilitiesreturnsbecauseofthistimingdifference.TheBEAreturnsareonacalendarbasis.Additionaldetailsin

Appendix

B.

Security-Level

2005-20072008-20092010-20122013-20192020-20222005-20222005-2019

Equityclaims

EquityliabilitiesBondclaims

Bondliabilities

Totalclaims

Totalliabilities

9

Totaldifferential

20.3

-4.0

5.7

9.0

0.2

7.4

11.6

-15.7

15.1

13.8

13.0

10.3

5.2

5.6

7.8

3.4

-1.2

3.9

4.3

3.5

6.6

2.6

-0.3

3.2

16.6

-2.6

6.2

7.4

-0.1

6.4

6.8

-2.8

8.9

6.9

5.4

5.9

9.8

0.2

-2.8

0.6

-5.5

0.5

8.99.74.93.87.76.01.7

Index

2005-20072008-20092010-20122013-20192020-20222005-20222005-2019

Equityclaims

EquityliabilitiesBondclaims

Bondliabilities

Totalclaims

Totalliabilities

Totaldifferential

20.9

-1.3

5.6

7.9

3.0

7.8

12.1

-19.4

17.0

14.2

12.7

10.3

6.2

4.8

7.8

1.5

-4.8

2.6

3.6

5.6

5.9

2.4

-0.2

3.1

17.2

-1.0

6.0

6.1

1.2

6.4

6.5

-2.5

9.0

6.8

5.4

5.9

10.7

1.5

-3.0

-0.7

-4.1

0.5

8.89.84.13.77.46.01.4

BEA

2005-20072008-20092010-20122013-20192020-20222005-20222005-2019

Equityclaims

EquityliabilitiesBondclaims

Bondliabilities

Totalclaims

Totalliabilities

Totaldifferential

20.7

-9.8

7.4

8.2

2.4

7.2

9.4

-13.8

11.3

11.5

15.0

8.9

5.1

5.4

8.1

4.9

-2.4

4.3

3.9

4.5

5.6

1.9

1.3

3.1

16.9

-6.1

7.6

7.3

1.3

6.5

5.8

-1.1

7.3

5.7

8.0

5.6

11.1

-5.0

0.3

1.6

-6.7

0.9

8.17.75.63.47.55.12.4

10

Table2:SubcomponentsofEquityReturns.Averagecontributionsofpricechanges,dividends,andexchangeratestototalequityreturnsconstructedfromsecurity-levelTICsurveydata.

2005-20072008-20092010-20122013-20192020-20222005-2022

Totalequityclaims

20.3

-4.0

5.7

9.0

0.2

7.4

Price

15.0

-6.4

2.3

8.5

-0.1

5.4

Dividend

3.0

3.2

3.0

2.8

2.0

2.8

Exchangerate

2.3

-0.7

0.4

-2.3

-1.6

-0.8

Totalequityliabilities

11.6

-15.7

15.1

13.8

13.0

10.3

Price

10.0

-17.6

13.0

11.9

11.6

8.4

Dividend

1.7

1.9

2.1

1.9

1.4

1.8

Totalbondclaims

5.2

5.6

7.8

3.4

-1.2

3.9

Price

-1.1

1.0

2.9

0.0

-4.5

-0.4

Coupon

5.9

4.8

5.0

4.2

3.7

4.6

Exchangerate

0.4

-0.3

-0.1

-0.7

-0.5

-0.3

Totalbondliabilities

4.2

3.6

6.5

2.5

-0.3

3.2

Price

-0.5

-1.4

3.0

-0.1

-2.5

-0.2

Coupon

4.4

4.8

3.6

2.7

2.3

3.4

Exchangerate

0.4

0.2

-0.1

-0.1

-0.1

0.0

2.3.TheRoleofAssetComposition.

OnedriverofthepositiveUSexcessreturnistheasymmetryinthecompositionofclaimsandliabilities,withclaimstiltedtowardequitiesandliabilitiestiltedtowardbonds.ThefirstpanelofFigure

1

showstheevolutionoftheequityshareinthecombinedequityandbondsclaimsandliabilitiesportfolios.Thesharesforeachregionisshownintheremainingpanels.Equitysharesinclaimsaremuchhigherthanequitysharesinliabilitiesoverallandinmostregions,withtheimmediateimplicationthatbondsharesarerelativelyhighinliabilities.Thebiasispersistentinclaimsrangingfrom70%to80%andaveraging75%overthefullsample.Theequityshareinliabilitiesincreasedfrom36%to51%overthesampleperiod.Theincreaseiswidespreadgeographically,andinthecaseofAsianinvestorscoincideswiththeslowdowninreserveaccumulation,whichhadbeenlargelyintheformofUSTreasuryandagencysecurities.

11

Tomeasuremorepreciselytheimpactoftheasymmetricportfoliocomposition,weusethefollowingexactdecompositionofthemeanexcessreturnbetweenclaimsE[rA]andliabilitiesE[rL]:

E[rA−rL]=E[E(r−r)]+E[B(r−r)]+E[(E−B)(µ−µ)],(3)

whereµ(resp.µ)denotestheshareofassetclassiinclaims(resp.liabilities),r(resp.r)

denotethereturnonassetclassiinclaims(resp.liabilities),i=(µ+µ)/2istheaverageshare

ofassetclassi,andi=(r+r)/2istheaveragereturn.Thefirsttwotermsineq.

(3)capturethe

returneffect,i.e.thedifferenceinreturnswithinassetclass.Thelasttermcapturesthecompositioneffect,i.e.therelativetiltintheclaimsportfoliostowardsequities.Usingthisdecomposition,table

3

showsthatthecompositioneffectislargeandpositive,at1.9%whilethereturneffectis-1.4%,mostlycomingfromahigherreturnonequityliabilities.Thenegativereturneffectonequitiessince2010,althoughnotsufficienttoeliminatetheoverallexcessreturn,significantlyerodeditinrecentyears.11

2.4.CrisisPeriods.

Thesampleperiodischaracterizedbythreesignificantcrisisperiods:theglobalfinancialcrisis(2008-2010),theEuropeansovereigndebtcrisis(2010-2012)andtheglobalpandemic(2020-2022).InspectingTable

1

weobservethattheUSexcessreturnissmallornegativeineachofthesecrisisperiods.Table

3

averagesthereturnsofeachassetclassoverthesethreecrisisperiodsandseparatelyoverthenon-crisisperiods.Excessreturnsarelargeandnegativeonaverageduringcrisisperiods,at-3.1%,andarelargeandpositiveduringnon-crisisperiods,at3.3%.Equityreturnsarehigherduringnon-crisisperiods,moresoforequityclaims.Thepictureisdifferentforbonds.Weleverageoursecurity-leveldatatosplitbondclaimsinto‘highgrade’debtandotherdebt.Weclassifysovereigndebtwhichreceivesthehighestbondratingfromatleastonemajorcreditratingsfirminagivenyearas‘highgrade’.Thebondclaimsreturnissimilarincrisisandnon-crisisperiods

11Thisresultcomplements

Atkesonetal.

(2022)whodonotcomputetheexcessreturnonclaimsversusliabilities,

butdocumentthedeteriorationof