edhec study_alm decisions in private banking
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Asset-Liability ManagementDecisions in Private Banking
February 2007
An EDHEC Risk and Asset Management Research Centre Publication
Sponsored by
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Published in France, March 2007. Copyright EDHEC 2007The ideas and opinions expressed in this paper are the sole responsibility of the authors.
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About the Authors ................................................................................................................................................4
Foreword..................................................................................................................................................................5
Executive Summary.....................................................................................................................................8
Rsum.........................................................................................................................................................111. Introduction .....................................................................................................................................................16
2. Asset-Liability Management as a Truly Client-Driven Approach to Private Banking ..................18 2.1. Sources of Added-Value in Wealth Management ............................................................................................................18
2.2. A Typology of Clients Profiles ..................................................................................................................................................18
3. A Brief History of ALM Techniques ...........................................................................................................203.1. Cash-Flow Matching and Immunization .............................................................................................................................20
3.2. Surplus Optimization ....................................................................................................................................................................21
3.3. LDI Solutions ....................................................................................................................................................................................22
3.3.1.StaticLDISolutions................................................................................................................................................................................................................23
3.3.2.DynamicLDISolutions.........................................................................................................................................................................................................23
3.4. Overview ............................................................................................................................................................................................24
4. Illustrations of the Usefulness of an ALM Approach to PWM ...........................................................254.1. Pension-Related Objective .........................................................................................................................................................26
4.1.1.Cash-FlowMatchingStrategy..........................................................................................................................................................................................26
4.1.2.SurplusOptimizationStrategies.......................................................................................................................................................................................26 4.1.3.DynamicLDIStrategies........................................................................................................................................................................................................28
4.1.4.AVariant.....................................................................................................................................................................................................................................30
4.2. Expenditure-Related Objective: the Case of Real Estate ..............................................................................................32
4.3. Bequest-Related Objective .........................................................................................................................................................33 4.3.1.TheBaseCase........................... ............................ ............................ ............................ ............................ ............................ ............................. ....................... 33
4.3.2.IntroducingConstraints.......................................................................................................................................................................................................34
4.3.3.AVariantwithSignificantLump-SumPaymentsExpected.................................................................................................................................34
5. Conclusion........................................................................................................................................................37
6. Mathematical Appendix ...............................................................................................................................38
6.1. Stochastic Model for the Value of Asset and Liabilities ................................................................................................386.2. Objective and Investment Policy .............................................................................................................................................39
6.3. Solution using the Dynamic Programming Approach ...................................................................................................40 6.3.1.GeneralSolution.....................................................................................................................................................................................................................40
6.4. From Static to Dynamic Portfolio Management ...............................................................................................................41
References ............................................................................................................................................................43
About the EDHEC Risk and Asset Management Research Centre ..........................................................45
About Pictet & Cie ..............................................................................................................................................47
Table of Contents
Asset-Liability Management Decisions in Private Banking 3
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Nol Amenc PhD isProfessorofFinanceandDirectorofResearchandDevelopmentat
theEDHECGraduateSchoolofBusiness,whereheheadstheRiskandAssetManagementResearchCentre.HehasaMastersinEconomicsandaPhDinFinanceandhasconductedactiveresearchinthefieldsofquantitativeequitymanagement,portfolioperformanceanalysis andactive asset allocation, resulting in numerous academicandpractitionerarticlesandbooks.HeisanAssociateEditoroftheJournal of Alternative InvestmentsandamemberofthescientificadvisorycounciloftheAMF(Frenchfinancialregulatoryauthority).
Lionel Martellini PhD isa Professor ofFinanceat the EDHECGraduateSchool ofBusinessandtheScientificDirectoroftheEDHECRiskandAssetManagementResearch
Centre.HeholdsgraduatedegreesinEconomics,StatisticsandMathematics,aswellasaPhDinFinancefromtheUniversityofCaliforniaatBerkeley.Lionelisamemberoftheeditorialboardofthe Journal of Portfolio ManagementandtheJournal ofAlternative Investments.Anexpertinquantitativeassetmanagementandderivativesvaluation,Lionelhaspublishedwidelyinacademicandpractitionerjournals,andhasco-authored reference textbooks on Alternative Investment Strategiesand Fixed-IncomeSecurities.
Volker Ziemann isaResearchEngineerattheEDHECRiskandAssetManagementResearchCentre.HeholdsaMastersDegreeinEconomicsfromHumboldt-UniversityinBerlinanda
MastersDegreeinStatisticsfromENSAEinParis,andiscurrentlyaPhDstudentinfinanceattheUniversityofAix-en-Provence.
4 EDHEC RISK AND ASSET MANAGEMENT RESEARCH CENTRE
About the Authors
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High net worth individuals (HNWIs) have
numerous characteristics, in terms of assetsunder management and the sophistication
of their requirements, that they share with
institutionalinvestors.Thisisafactthathaslong
beenrecognised bythe marketing departments
of asset management companies and private
banks,whotypicallyhavespecialconsideration
for these profiles in their marketing and sales
segmentation. We can therefore consider, with
strong justification, that a similar approach
would be appropriate for the investment
management techniques employed for HNWIs
andinstitutionalinvestors.Thisisthelogicthat
wehaveappliedinthepresentresearchpaper,
which is drawn from EDHECs ALM and Asset
Managementresearchprogramme.
This programme aims to apply recent research
in asset-liability management for institutional
investors and to improve asset management
techniques,andinparticularstrategicallocation
tools, to positively impact the performance ofALM programmes. Recent EDHEC publications
in this field include Assessing the Impacts of
IFRS and Solvency II Rules on the Financial
ManagementofEuropeanInsuranceCompanies,
a major study which was jointly produced by
the EDHEC Financial Analysis and Accounting
ResearchCentreandtheEDHECRiskandAsset
Management Research Centre; an academic
analysis of Liability-Driven Investing by Lionel
Martellini,TheTheoryofLDI,whichwaspublished
intheMay2006issueofLife and Pensions;andapaperentitledTheBenefitsofHedgeFundsin
AssetLiabilityManagement,byLionelMartellini
and Volker Ziemann, which appeared in the
Alternative Investment Quarterlyin2005.
The current paper discusses the sources of
added-value in private wealth management,and argues through a series of illustrations
that asset-liability management is the natural
approach for the design of truly client-driven
servicesinprivatebanking.
Wewouldliketoextendoursincerethankstoour
partnersatPictet&Cie,wholentconsiderable
supporttothisproject.Wehopeyouwillfindthe
studybothinterestingandinformative.
NolAmenc,PhD,
Director of the EDHEC Riskand Asset Management Research Centre
Foreword
Asset-Liability Management Decisions in Private Banking
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Executive Summary
Asset-Liability Management Decisions in Private Banking 7
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The private wealth management industry has
nowbecomeaverysignificantindustryduetocontinuing strong economicgrowth in specific
regions of theworld. This increase is currently
driving a larger wealth management market
creating greater opportunities for wealth
advisorstoleveragenewtechnologywithaview
to acquiring new clients and boosting profits.
Asaresult,competitionamongwealthadvisory
firms is increasing to find ways to improve
existing client relationships and provide new
tools to improve advisor efficiency. Current
privatebankingtoolsaretypicallytaxandestate
planning geared towards one specific country
and financial simulation software, relying on
single period mean-variance optimization of
the asset portfolio. These tools suffer from
significant limitations and cannot satisfy the
needsofasophisticatedclientele.
While some industry players have recently
developed planning tools that model assets in
a multi-period stochastic framework, asset-liabilitymatchingforindividualsremainsanarea
forexploration.ThispaperadaptsAsset-Liability
Management (ALM) techniques developed for
institutionalinvestorstothe contextofprivate
bankingcustomers.Asset-LiabilityManagement
(ALM) denotes the adaptation of the portfolio
management process in order to handle the
presence of various constraints relating to the
commitments of an investors liabilities. We
argue that portfolio optimization techniques
used by institutional investors, e.g., pensionfunds, could usefully be transposed to the
contextofprivatewealthmanagementbecause
they have been engineered precisely to allow
for the incorporation of an investors specific
constraints, objectives and horizon in the
portfolioconstructionprocess.Takinginvestors
liabilityconstraints andspecific objectives into
accountactuallyhasadramaticimpactonasset
allocation decisions. For example, clients who
wish tomaintain a givenlevel ofexpenses for
theirretirementyearswillexpecttheinvestment
processperformedontheircurrentwealthtobe
ableto generate cash-flows sufficient to meet
theirconsumptionneeds,whichjustifiesafocus
oninflationhedgingthatisnottypicallyinvolved
inastandardassetmanagementsolution.
Asanillustration,weconsiderthesituationof
an investor who wishes toinvest fixed annual
contributions(x)forafutureexpenditure,e.g.,
the purchase of a house in 5 years, for which
the current value is normalized at100. We
introduceanexplicitmodelforthedynamicsof
real estate prices andtheexhibit below shows
the impact of real estate price uncertainty on
the value of the100 payment scheduled to
bepaidin5yearsfromnow.Aswecansee,real
estate price risk is significant, with a nominal
amount to be secured equal to 156.59 on
averageanda27.18standarddeviation.
In practical terms, the goal is to generate alump sum payment at horizon date (5 years).
It is not possible in general to find a perfect
liability-matching portfolio. The existence of a
perfect liability-matching portfolio is actually
onlyensuredon the followingtwo conditions:
the investor must be able to borrow against
future income and invest the presentvalue of
thefuturecontributionsattheinitialdate;and
theremustbeaninvestmentvehicle(e.g.,REITS)
with a payoff which is directly related to real
estate priceuncertainty. Wetesttwo different
situations:anopportunitysetcontainingstocks,
bondsandTIPSandanopportunitysetcontaining
stocks,bonds,TIPSandrealestate(modelledas
Distribution of house prices at final date; mean value = 156.59;standarddeviation=27.18.
Executive Summary
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an investment that will pay the compounded
returnon real estate). To generate comparableportfolios, we looked at the improvement in
surplus volatility for a given level of expected
surplus.
Thegraphshowstheefficientfrontierinboth
cases, while risk-return indicators are reported
in the table. As expected, the presence of
assets allowing investors to span real estate
priceuncertaintyprovestobea keyelementin
improvingtheefficientfrontiersobtainedfrom
an ALM perspective. Looking for example at
portfolioDandDinthetable,weseethatfor
thesamelevelofexpectedsurplus(12.60inboth
cases),thesurplusvolatilityattheoptimallevel
reaches 21.95 when the opportunity set doesnotcontainarealestateasset,whileitmerely
amounts to 4.25, a dramatic risk reduction,
whentherealestateassetisincluded.Againthis
signals the relevance of an ALM approach to
privatewealthmanagement:itisonlybytrying
to fit the client liability constraints that truly
optimalsolutionscanbeproposed.
Inthesamevein,wealsoconsideranumberof
other illustrations that are typical of standard
privatewealthmanagementproblemsandshow
thatoptimalsolutionsarestronglyaffectedby
thepresenceofliabilityconstraints.Inparticular,
we focus on various pension-related objectives
andconsideranindividualwhoiseitheralready
retiredorstillemployed,andwhoseekstoensure
astreamofinflation-protectedfixedpayments,
based either on a lump-sum contribution or a
seriesofannualcontributions.Wealsointroduce
avarietyofbequest-relatedobjectives.
In conclusion, we argue that it is not the
performanceofaparticularfundnorthatofa
givenassetclass(includingcommoditiesorhedge
funds)thatwillbethedeterminingfactorinthe
ability of private wealth management to meet
Executive Summary
ALMEfficientFrontierswithoutRealEstate(A,B,C,D,E,F)andwithRealEstate(A,B,C,D,E,F)
Portfolio
Weights
StocksBondsTIPSRealEstate
Expected
surplus
Volatility
ofsurplus
Prob(S
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investorsexpectations.Whatwillprovetobethe
decisivefactoristheprivatewealthmanagersability to design an asset allocation solution
thatisafunctionofthekindsofparticularrisks
to which the investor is exposed, as opposed
to the market as a whole. Hence, an absolute
returnfund,oftenperceivedasanaturalchoice
in the context of private wealth management,
would not be a satisfactory response to the
needsofaclientfacinglong-terminflationrisk,
where the concern is capital preservation in
real,asopposedtonominal,terms.Similarly,a
clientwhoseobjectivewouldberelatedtothe
acquisitionofapropertywouldacceptlowand
even negative returns in situations when real
estatepricessignificantlydecrease,butwillnot
satisfy himself or herself with relatively high
returnsifsuchhighreturnsarenotsufficientto
meet a dramatic increase in real estate prices.
In such circumstances, a long-term investment
instocksandbondswithaperformanceweakly
correlatedwithrealestatepriceswouldnotbe
therightinvestmentsolution.
In other words, the success or failure of the
satisfactionof theclients long-term objectives
isfundamentallydependentonanALMexercise
that aims to determine the proper strategic
inter-classes allocation as a function of the
clients specific objectives and constraints.
Assetmanagementshouldonlycomenextasa
response to the implementation constraints of
theALMdecisions.Ontheonehand,itismeant
todeliver/enhancetheriskandreturnparameterssupportingtheALManalysisforeachassetclass.
On the other hand, it can also allow for the
managementofshort-termconstraints,suchas
capitalpreservationatagivenconfidencelevel,
whicharenotnecessarilytakenintoaccountby
anALMoptimizationexercise,whichbynature
focusesonlong-termobjectives.
Executive Summary
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Rsum
Asset-Liability Management Decisions in Private Banking 11
Grce une croissance conomique soutenue
dans plusieurs rgions du monde, lindustriede la gestion prive sest octroye une place
considrabledanslepaysagefinanciermondial.
Cetteacclrationsertactuellementdemoteur
dans un march croissant de gestion de
patrimoine, crant ainsi la possibilit pour les
conseillersdecedomainedattirerdenouveaux
clients et daugmenter leurs bnfices. En
consquence, la concurrence entre les socits
de conseil en gestion de patrimoine est en
constante progression dans le but de trouver
des moyens damliorer les relations clients
existantesetdeseprocurerdenouveauxoutils
afin damliorer lefficacit de leurs conseils.
Les expertises actuelles en gestion prive sont
typiquementcellesdelafiscalitetdelagestion
deshritagespropresunpaysparticulier,ainsi
que des progiciels de simulation financire,
souvent bass sur une optimisation moyenne-
variancedunportefeuilledactifsdansuncadre
statique. Ces outils souffrent de limitations
importantesetnepeuventrpondreauxbesoinsduneclientlesophistique.
Siquelquesacteursdelindustrieontrcemment
dveloppdesoutilsprvisionnelsquimodlisent
les actifs dans un cadre stochastique multi-
priodes, la gestion actif-passif pour les
particuliers reste un domaine explorer. Ce
documentadaptelestechniquesdegestionactif-
passif (GAP ou ALM en anglais), dveloppes
pourlesinvestisseursinstitutionnels,aucontexte
desclientsprivs.LAsset-LiabilityManagement(ALM) dsigne ladaptation du processus de
gestion de portefeuille afin de prendre en
comptelaprsencedediversescontrainteslies
auxengagementsquereprsentelepassifdun
investisseur. Nous pensons quil est intressant
de transfrer les techniques doptimisation
de portefeuille utilises par les investisseurs
institutionnels,parexemplelesfondsdepension,
aucontextedelagestionprive,parcequecelles-
ciontprcismenttconuesafindepermettre
lintgrationdescontraintes,desobjectifsetdes
horizons de linvestisseur dans le processus de
constructiondeportefeuille.Enfait,lapriseen
comptedescontraintesdepassifetdesobjectifs
prcisdelinvestisseuraprioriimpactedefaon
significative les dcisions dallocation dactifs.Parexemple,lesclientsquisouhaitentgarderun
niveaudonndedpensesdurantleursannes
de retraite sattendront ce que le processus
dinvestissement appliqu leur patrimoine
actuel puisse gnrer des flux de trsorerie
suffisants pour satisfaire leurs besoins de
consommation,cequijustifielintgrationdune
couvertureparrapportlinflation,quinefait
pastypiquementpartiedunesolutiondegestion
dactifsstandard.
Afin dillustrer ce concept, nous examinons la
situation duninvestisseur qui souhaite allouer
des contributions annuelles fixes (x) pour
une dpense future,par exemple lachat dune
maisondans5ans,lavaleuractuelledecelle-ci
tantnormalise100.Nousintroduisonsun
modleexplicitepourladynamiquedesprixde
limmobilier et le graphique ci-dessous montre
limpactdelincertitudedesprixdelimmobilier
surlavaleurduversementde100
prvupourdans5ans.Commenouspouvonsleconstater,le
risquedeprixdelimmobilierestimportant,avec
unevaleurnominalede156,59enmoyenne
obteniretuncarttypede27,18.
En termes pratiques, le but est de gnrer le
versementdunesommeforfaitaireindexeaux
prixdelimmobilierladatedhorizon(5ans).
Il nest pas toujours possible de trouver un
portefeuille parfaitement adoss au passif.
Distributiondesprixdemaisonladatefinale;valeurmoyenne=156,59;carttype=27,18.
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En effet, dans cet exemple lexistence dun
portefeuille parfaitement adoss au passifdpendrait des deux conditions suivantes :
linvestisseurpeutempruntersurlabasedesses
revenusfutursetpeutinvestirlavaleuractuelle
desesfuturescontributionsladateinitiale;
et il existe un support dinvestissement (par
exempleREITS)avecunrendementdirectement
lilincertitudeduprixdelimmobilier.Nous
testonsdeuxsituationsdiffrentes,unexercice
dallocation avec un menu de classes dactifs
contenant des actions, des obligations et des
obligationsdEtatindexessurlinflation(TIPS),et
unexercicedallocationavecunmenudeclasses
dactifs contenant des actions, des obligations,
des TIPS et de limmobilier (modlis comme
un investissement qui ralisera le rendement
compos de limmobilier). Afin de gnrer des
portefeuilles comparables, nous avons regard
lamliorationdelavolatilitdelexcdentpour
unniveaudonndexcdentescompt.
Le graphique montre la frontire efficiente
danslesdeuxcas,etlesindicateursderisqueet
de rendement sont renseigns dans le tableau
ci-contre.Commeonauraitpusyattendre,la
prsencedactifspermettantauxinvestisseursde
couvrirlincertitudedesprixdelimmobilierest
unlmentcldanslamliorationdesfrontires
efficientesobtenuesdansuneoptiqueALM.En
regardantparexemplelesportefeuillesDetD
dans le tableau, nous constatons que pour un
mmeniveaudexcdentescompt(12,60dans
lesdeuxcas),lavolatilitdelexcdentauniveau
optimalatteint21,95quandlimmobiliernefaitpas partie du menu des classes dactifs, alors
quelleatteint4,25,unerductionderisquetrs
importante,quandlactifimmobilierestcompris.
Ceci tmoigne nouveau de la pertinence
duneapprocheALMdanslagestionprive:ce
nest quen essayant de garantir ladquation
des contraintes de passif du client que des
solutionsvritablement optimalespeuventtre
proposes.
Dans la mme ligne, nous dvelopponsplusieurs autres expriences qui sont typiques
des problmatiques de gestion prive et nous
montrons que les solutions optimales sont
fortement impactes par la prsence des
contraintes de passif. Nous nous concentrons
notamment sur diffrents objectifs lis la
retraite,etnousconsidronslecasdunindividu
quiestdjretraitoubientoujourssalari,et
qui cherche garantir un flux de versements
fixes protgs contre linflation, partir soitdune contribution forfaitaire soit dune srie
de contributions annuelles. Nous introduisons
galementdiversobjectifsrelatifsdeslegs.
En conclusion, nous avanons lide quil
nest pas tant la performance dun fonds en
particuliernimmeduneclassedactifsdonne
(ycomprislesmatirespremiresouleshedge
funds) qui sera le facteur dterminant dans la
capacit de la gestion prive rpondre aux
attentes des investisseurs. Ce qui sera dcisifestlacapacitdugrantprivconcevoirune
solution dallocation dactifs en fonction des
risquesprcisauxquelslinvestisseur,pluttque
lemarchdanssonensemble,estexpos.Ainsi,
un fonds de rendement absolu, souvent peru
comme un choix naturel dans le contexte de
la gestion prive, ne fournira pas une rponse
satisfaisante aux besoins dun client qui doit
faire face un risque dinflation sur le long
terme, auquel cas le souci sera la prservation
ducapitalentermesrelspluttquenominaux.
De mme, un client dont lobjectif est li
lacquisition dune proprit accepterait des
rendements bas ou mme ngatifs dans des
Rsum
Frontires efficientesALMsansimmobilier(A, B,C,D, E,F) etavecimmobilier(A,B,C,D,E,F)
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situations o les prix de limmobilier sont en
nettediminution,maisnesecontenterapasde
rendements relativement levs si ceux-ci ne
lui permettent pas de faire face des hausses
sensiblesdeprixdelimmobilier.Dansdetelles
circonstances, un investissement sur le long
termedansdesactionsetdesobligationsavec
une performance faiblement corrle avec les
prix de limmobilier ne serait pas la bonne
solutiondinvestissement.
En dautres termes, la capacit de rpondre
aux objectifs long terme du client dpend
fondamentalementdelexercicedALMquivise
dterminerlabonneallocationstratgiqueentrelesclassesenfonctiondesobjectifsetcontraintes
spcifiques du client. La gestion dactifs doit
seulementsuivreenrponseauxcontraintesde
miseenuvredesdcisionsdALM.Dunepart,
celadoitpermettre damliorer des paramtres
de risque et de rendement soutenant lanalyse
ALMpourchaqueclassedactifs.Dautrepart,le
processusdegestiondactifspeutpermettrela
gestiondecontraintescourtterme,tellequela
prservationducapitalunseuildeconfiance
donn, qui ne sont pas forcment prises encompteparunexercicedoptimisationdALM,ce
derniersefocalisantparnaturesurlesobjectifs
longterme.
Rsum
Portefeuille
Allocation
Obligationsdtat indexes
sur linflation
Actions Obligations (TIPS) Immobilier
Excdent
escompt
Volatilit de
lexcdentProb(S
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15/52Asset-Liability Management Decisions in Private Banking 1
Asset-LiabilityManagement Decisionsin Private Banking
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The private wealth management industry has
now become a very significant industry due tocontinuing strong economic growth in specific
regionsoftheworld.Accordingtoarecentsurvey,
thewealthofhighnetworthindividuals(HNWIs),
peoplewithnetfinancialassetsofatleastUS$1
million excluding their primary residence and
consumables,climbedtoUS$33.3trillionin2005,
whichrepresentsanannualrateof8.0%overthe
lastdecade1. According tothe same survey, the
numberofHNWIsgrewby6.5percentover2004,
to 8.7million, and the number of Ultra-HNWIs
thosewhohavefinancialassetsofmorethan
US$30 million grew by 10.2%, to 85,400 in
2005.
This increase is currently driving a larger
wealth management market creating greater
opportunitiesforwealthadvisorstoleveragenew
technology to acquire new clients and increase
profits. As a result, competition among wealth
advisoryfirmsisincreasingtofindwaystoimprove
existingclientrelationshipsandprovidenewtoolstoimproveadvisoreffectiveness.Currentprivate
bankingtoolsaretypicallytaxandestateplanning
gearedtowardsonespecificcountryandfinancial
simulation software, relying on single period
mean-varianceoptimizationofanassetportfolio.
These tools suffer from significant limitations
and cannot satisfy the needsofa sophisticated
clientele.
Firstly,singlecountrytaxplanningtoolsareoflittle
relevancetohighnetworthindividualsoperatingoffshore or across multiple tax jurisdictions.
Secondly, financial simulation software relying
on single period mean-variance optimization of
asset portfolios cannot yield a proper strategic
allocation for at least two reasons.On the one
hand,optimizationparameters(especiallyexpected
returns)aredefinedasconstants,apracticewhich
iscontradictedbyempiricalobservationanddoes
notallowforthelengthoftheinvestmenthorizon.
Ontheotherhand,andmostimportantlyperhaps,
liabilityconstraintsandriskfactorsaffectingthem,
such as inflation-risk on targeted spending, are
neithermodelednorexplicitlytakenintoaccount
intheportfolioconstructionprocess.
The process involved in dealing with a private
client typically leads to a detailed analysis ofthe clients objectives, constraints, as well as
risk-aversion parameters (sometimes on the
basisofrathersophisticatedapproaches).Yet it
itsstrikingthatoncethisinformationhasbeen
collected,andsometimesformalized,verylittleis
doneintermsofcustomizingaportfoliosolution
tothebenefitofthespecificneedsoftheclient.
Typically, the approach consists in providing
several profiles expressed in terms of volatility
or drawdown levels, with in some instances a
distinctioninhowthecapitalwilleventuallybe
accessed(annuitiesorlumpsumpayment),but
theclientsobjectives,constraintsandassociated
specific risk factors are simply not taken into
accountinthedesignoftheoptimalallocation.
While some industry players have recently
developed planning tools that model assets in
a multi-period stochastic framework, asset-
liability matching for individuals remains an
areaforexploration.Theobjectiveofthispaperis to adapt Asset-Liability Management (ALM)
techniquesdevelopedforinstitutionalinvestors
to the context of private banking customers.
Asset-Liability Management denotes the
adaptationoftheportfoliomanagementprocess
in order to handle the presence of various
constraints relating to the commitments that
representtheliabilitiesofaninvestor.Itshould
beemphasizedatthisstagethatthedefinitionof
liabilitiesweuseinwhatfollowsisratherbroad
and encompasses any commitment, whetherexternalorself-imposed,thataprivateinvestor
is facing. For example, an investor committed
to a real estate acquisition will perceive such
anexpenseasafuturecommitmentforwhich
moneyshallbeavailablewhenneeded.Similarly,
clientswhodesiretomaintainagivenlevelof
expenses for their retirement years will expect
the investment process performed on their
currentwealthtobeabletogeneratesufficient
cash-flowstomeettheirneeds.Inwhatfollows,
wearguethatportfoliooptimizationtechniques
used by institutional investors, e.g., pension
funds, could usefully be transposed to the
contextofprivatewealthmanagementbecause
1. Introduction
16 EDHEC RISK AND ASSET MANAGEMENT RESEARCH CENTRE
1-MerrillLynch&CapgeminiWorldWealthReport2006availableatwww.us.capgemini.com/worldwealthreport06
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they have been engineered precisely to allow
for the incorporation of an investors specificconstraints,objectivesandhorizon(allofwhich
canbebroadlysummarizedintermsofliability
constraints) in the portfolio construction
process.
The rest of the paper is organized as follows.
Insection2, wediscussthe sourcesof added-
valueinprivatewealthmanagement,andargue
that asset-liability management is the natural
approach for the design of truly client-driven
services in private banking. In section 3, we
provideabriefhistoryofALMtechniques,witha
specificemphasisonthebenefitsandweaknesses
ofcompetingapproaches,bothfromapractical
and a conceptual standpoint. In section 4, we
presentaseriesofillustrationsoftheusefulness
of asset-liability management techniques in a
private banking context. A conclusion can be
found in section 5, while technical details are
relegatedtoadedicatedappendix.
1. Introduction
Asset-Liability Management Decisions in Private Banking 17
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2.1. Sources of Added-Value in
Wealth ManagementIt has often been argued that the proximity
toclientsisthemainraisondtreandakey
source of competitive advantage for private
wealthmanagement.Buildingonthisproximity,
private bankers should be ideally placed to
betteraccountfortheirclientsspecificliability
constraints when engineering an investment
solutionforthem.Inotherwords,asset-liability
managementisthetruesourceofadded-valuein
privatewealthmanagement.
Mostprivatebankersactuallyimplicitlypromote
an ALM approach to wealth management.
In particular, they claim to account for the
clients goals and constraints. The technical
toolsinvolved,however,areoftennon-existent
or ill-adapted. As a result, current practice in
addressingclientsneedsismostlyafailure,with
onlya very limited fraction of private bankers
actuallydesigningportfoliosconsistentwiththe
clientsneeds.Whiletheclientisroutinelyasked
allkindsofquestionsregardingcurrentsituation,
goals,preferences,constraints,etc.,theresulting
service and product offeringmostly boil down
toa ratherbasicclassification interms ofrisk
profiles.
In principle, several situations exist,
correspondingtovaryinglevelsofsophistication
andconsiderationofclientsneeds.
Thefirstcaseiswhenprivatebankerssimplydo
not use any portfolio construction tool. Since
the solutions theythen offerdo not take into
account clients objectives, risk-aversion or
constraints, this is simply not acceptable. A
slightlymoresatisfyingsituationinvolvesprivate
wealthmanagementperceivedasapureasset-
management exercise. The solution consists of
theoptimaldesignofdifferentportfolioswith
different risk profiles, where the clients goals
and constraints are not taken into account. Athirdsituationinvolvestestingfortheimpactof
assetallocationdecisionsintermsofcompliance
withrespecttotheclientsliabilityconstraints.
Forexample,someprivatebankersuseamodel
totestprobabilityofa shortfallathorizon.Theoptimal asset portfolio, however, is designed
independently of clients needs. Finally, the
last, fully satisfactory situation, involves the
incorporation of the clients full profile in
portfolio construction. Only this can ensure
thatclientsneedsareproperlyaddressed.This
requires the development of proper portfolio
construction tools similar to the ones used in
institutionalmoneymanagement.Explaininghow
asset-liability management techniques used in
thecontextofinstitutionalmoneymanagementcan/should be transposed to private wealth
managementispreciselythefocusofthispaper.
2.2. A Typology of Clients Profiles
Broadly speaking, there are at least four
dimensionsinaclientprofile.
Objectiveprofile
Time-horizonprofile
Constraintsandrisk-aversionprofiles
Contributionprofile
Each of these dimensions is related to the
definition of a clients liabilities. The first
dimension, the objective profile, is related
to the particular type of liability a client is
facing.Examplesarepensionneeds,realestate
acquisition,payingforchildrenseducation,etc.
Theseconddimension,thetime-horizonprofile,is of significance since it can be shown that,
unlessunderveryspecificassumptions,optimal
portfolioallocationsdependontherisk-horizon
(see Merton (1971) for a general theory of
dynamicassetallocationdecisions).Itisoftenthe
casethattheactualhorizonislong,sometimes
with intermediate, short-term constraints or
goals.Thethirddimension,theconstraintsand
risk-aversionprofiles,correspondstoanecessary
enlargement of typical clientele segmentation,
whichoftenboilsdowntosubjectiveclassificationintermsofrisktolerance.Abetterunderstanding
canbeobtainedfromtheperspectiveinterms
of risk constraints. The fourth dimension, the
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18 EDHEC RISK AND ASSET MANAGEMENT RESEARCH CENTRE
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Recentdifficultieshavedrawnattentiontotherisk
managementpracticesofinstitutionalinvestorsin general and defined benefit pension plans
inparticular.Whathasbeenlabeledaperfect
stormofadversemarketconditionsattheturn
ofthemillenniumhasdevastatedmanycorporate
defined benefit pension plans. Negative equity
marketreturnshaveerodedplanassetsatthesame
time as declining interest rates have increased
mark-to-market value of benefit obligations
andcontributions.Inextremecases,thishasleft
corporate pension plans with funding gaps as
largeasorlargerthanthemarketcapitalization
oftheplansponsor.Thatinstitutionalinvestors
ingeneralandpensionfundsinparticularhave
beensodramaticallyaffectedbyrecentmarket
downturns has emphasized the weakness of
riskmanagementpractices.Inparticular,ithas
been argued thatthe kinds ofasset allocation
strategies implemented in practice, which used
to be heavily skewed towards equities in the
absenceofanyprotectionwithrespecttotheir
downsiderisk,werenotconsistentwithasoundliabilityriskmanagementprocess.
In this context, a renewed interest in asset-
liability management techniques has surfaced
in institutional money management. New
approaches that are referred to as liability
driven investment (LDI) solutions have also
been introduced following recent changes in
accounting standards and regulations that
have led toan increased focuson liability risk
management. In what follows, we will providea brief review of standard asset allocation
techniquesusedinALM,whichcanbeclassified
intoseveralcategories.
3.1. Cash-Flow Matching andImmunization
A first approach called cash-flow matching
involvesensuringaperfectstaticmatchbetween
the cash flows from the portfolio of assetsand the commitments in the liabilities. Let us
assumeforexamplethatapensionfundhasa
commitment topay out a monthly pension to
a retired person. Leaving aside the complexity
relatingtotheuncertainlifeexpectancyoftheretiree,thestructureoftheliabilitiesisdefined
simplyasaseriesofcashoutflowstobepaid,
therealvalueofwhichisknowntoday,butfor
which the nominal value is typically matched
withaninflationindex.Itispossibleintheory
toconstructaportfolioofassetswhosefuture
cashflowswillbeidenticaltothisstructureof
commitments.Todoso,assumingthatsecurities
ofthatkindexistonthemarket,wouldinvolve
purchasing inflation-linked zero-coupon bonds
withamaturitycorrespondingtothedateson
whichthemonthlypensioninstallmentsarepaid
out,withamountsthatareproportionaltothe
amountofrealcommitments.Thetechniquecan
also be implemented in a synthetic way using
interestratesandinflationswaps.
Thistechnique,whichprovidestheadvantageof
simplicityandallows,intheory,forperfectrisk
management, nevertheless presents a number
of limitations. First of all, it will generally beimpossible to find inflation-linked securities
whose maturity corresponds exactly to the
liabilitycommitments.Moreover,mostofthose
securitiespayoutcoupons,whichleadstothe
problemofreinvestingthecoupons.Totheextent
thatperfectmatchingisnotpossible,thereisa
techniquecalledimmunization,whichallowsthe
residualinterestrateriskcreatedbytheimperfect
match between the assets and liabilities to be
managedinadynamicway.Thisinterestraterisk
managementtechniquecanbeextendedbeyond
a simple duration-based approach to fairly
generalcontexts,includingforexamplehedging
larger changes in interest rates (through the
introductionofaconvexityadjustment),hedging
non-parallel shifts in the yield curve (see for
exampleFabozzi,MartelliniandPriaulet(2005)),
or simultaneous management of interest rate
riskandinflationrisk(SiegelandWaring(2004)).
Itshouldbenoted,however,thatthistechnique
isdifficulttoadapttohedgingnon-linearrisksrelated to the presence of options hidden in
theliabilitystructures,and/ortohedgingnon-
interestraterelatedrisksinliabilitystructures.
3. A Brief History of ALM Techniques
20 EDHEC RISK AND ASSET MANAGEMENT RESEARCH CENTRE
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Another,probablymoreimportant,disadvantage
ofthecash-flowmatchingtechnique(oroftheapproximate matching version represented by
theimmunizationapproach)isthatitrepresents
apositioningthatisextremeandnotnecessarily
optimalfortheinvestorintherisk/returnspace.
Infactitcanbesaidthatthecash-flowmatching
approach in asset-liability management is the
equivalent of investing in the risk-free asset
inan asset management context. Itallows for
perfect management of the risks, namely a
capital guarantee in the passive management
framework, and a guarantee that the liability
constraintsarerespectedintheALMframework.
However, the lack of return, related to the
absenceofriskpremia,makesthisapproachvery
costly, which leads to an unattractive level of
contributiontotheassets.
3.2. Surplus Optimization
In a concern to improve the profitability of
the assets, and therefore reduce the level ofcontributions,itisnecessarytointroduceasset
classes(stocks,governmentbondsandcorporate
bonds) that are not perfectly correlated with
the liabilities into the strategic allocation.
It will then involve finding the best possible
compromise between the risk (relative to the
liability constraints) thereby taken on, and the
excessreturnthattheinvestorcanhopetoobtain
throughtheexposuretorewardedriskfactors.
Differenttechniquesarethenusedtooptimize
the surplus, i.e., the excess valueof the assets
comparedtotheliabilities,inarisk/returnspace.
In particular, it is useful to turn to stochastic
models that allow for a representation of the
uncertaintyrelatingtoasetofriskfactorsthat
impactupontheliabilities.Thesecanbefinancial
risks (inflation, interest rate, stocks) or non-
financialrisks(demographiconesinparticular).
Twokeystepsareinvolvedinsurplusoptimization.Thefirst step consists in using a mathematical
model for generating stochastic scenarios for
all risk factors affecting assets and liabilities
(typically, interest rates, inflation, stock prices,
real estate, etc.). Models are chosen so as torepresent actual as well as possible behaviors
andparametersarechosensoastobeconsistent
withlong-termestimates.Thenextstepinvolves
usinganoptimizationtechniquetofindtheset
ofoptimalportfolios.
Intermsofstochasticscenariosimulation,one
typically distinguishes between three main
riskfactors affecting asset and liability values:
interest rate risk (or, more accurately, interest
raterisks,sincethereismorethanoneriskfactoraffecting changes in the shape of the yield
curve),inflationrisk,andstockpricerisk.When
realestateisusedasanALMassetclass,thenan
additionalmodelforthedynamicsofrealestate
pricesshouldbeadded.Intheillustrationsthat
followinalatersection,wehaveusedasetof
standardstochasticmodelsfortheseriskfactors,
including as key features a two-factor mean-
revertingprocessforrealinterestrates,aone-
factormean-revertingprocessforinflationratesandaMarkovregimeswitchingmodelforexcess
returnon equity (excess return)2.Ourmodelis
borrowed from Ahlgrim, DArcy and Gorvett
(2004)andcanbewrittenas3:
( )
( )
( )
( ) xts
x
s
xtttt
ttt
l
tltllt
r
trttrt
dWdtbdtrSdS
dWdtbad
dWdtlbadl
dWdtrladr
+++=
+=
+=
+=
Here rt (respectively, t) is the real short-term
rate (respectively, inflation rate) at date t, ar
(respectively,a)isthespeedofmeanreversionof
theshort-termrate(respectively,inflationrate),
lt(respectively,b)isthelong-termmeanvalue
of the short-term rate (respectively, inflation
rate),andr(respectively,)isthevolatilityof
theshort-rate(respectively, inflation rate).This
model assumes a particular two-factor process
fortherealratesoastoaccountforthenon-
perfectcorrelation betweenbonds of differentmaturities. In particular, it assumes that the
long-termmeanvalueltoftheshort-termrateis
alsostochasticallytime-varying,withaspeedof
3. A Brief History of ALM Techniques
Asset-Liability Management Decisions in Private Banking 21
2-Amean-revertingmodelforrealestatepriceshasalsobeenusedfortheillustrationswhererealestatewasintroduced.
3-OthercompetingmodelscanofcoursebeusedinALMsimulationsandoptimization,buttheyaremostlyconsistentinspiritwiththisparticularmodel,whichwehavechosenbecauseitrepresentsastandardexampleofastate-of-the-artALMmodelwhichismadeavailableforpublicusebytheCasualtyActuarialSociety(CAS)andtheSocietyofActuaries(SOA)(seereferencelistforexactreferencesofthepaperandawebsitewherethepapercanbedownloaded).
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meanreversiondenotedby al,along-termmean
valuedenotedbyblandavolatilitydenotedbyl. By contrast the long-term mean value of
theinflationrateisassumedtobeaconstant.
HererW ,
lW and
W arethree(correlated)
standard Brownian motions representing
uncertainty driving the three risk-factors.
Besides, a Markov-regime switching model is
assumedforequityreturns,withbxasthe(state-
dependent) excess expected return (over the
nominal rate ( )tt
r + )and xasthe(state-dependent)stockvolatility.Here
sW isastandard
Brownian motion representing uncertainty
drivingstockreturns,andis correlatedtorW ,
lW and
W . The introduction of a Markov
regime-switching model is motivated by the
desire tofitimportant empiricalcharacteristics
ofequityreturns,suchasthepresenceoffat-
tails and stochastic volatility with volatility
clusteringeffects.Thebasicideaisthatreturns
arenotdrawnfromasinglenormaldistribution;
rather there are two distributions at work
generating the returns observed. The equityreturnsdistributionisassumedtojumpbetween
twopossiblestates,usuallyreferredtoasregimes,
denoted by x=1 and x=2 and interpreted as a
low and a high volatility regimes. A transition
matrix controls the probability of moving
betweenstates.
In terms ofoptimization, the objective can be
tominimizethevolatilityofthesurplus/deficit;
itcanalsoinvolveotherriskmeasuressuchas
theexpectedshortfall(averagevalueofadeficitconditionalonadeficit),ortheprobabilityofan
(extreme)deficit.Theperformance,ontheother
hand,istypicallymeasuredintermsofexpected
surplus, or necessary contributions. Different
choicesintermsofoptimizationmodelarealso
available,withpossibleoptionsinvolvingsimple
static optimization or dynamic optimization
with time- and state-dependent solutions (see
for example Ziemba and Mulvey (1998), as
well as references therein for more details on
optimizationmodelsusedinALM).
3.3. LDI Solutions
Surplus optimization typically allows for
higher returns (on average), and hence lower
contributions(onaverage),sinceitleadstothe
introductionofriskyassetclasses,withtheaccess
to associated risk premia. On the other hand,
it introduces a significant source of risk since
assetclassespoorlycorrelatedwithliabilitiesare
introduced.
Inanattempttomitigatetheserisks,andenhance
liability risk management, a new approach(known as liability-driven investment, or LDI)
has recently been proposed; itis basedon the
introductionofaliability-matching(orliability-
hedging)portfoliointhemenuofassetclasses.It
thusbuildsonthetraditionalapproachofcash-
flow matching and immunization, focused on
riskmanagement,towhichitaddsacomponent
dedicatedtoperformance.
It should be noted that when the liability
matching portfolio is available in the menu
of asset classes, the minimum risk solution of
surplus optimization corresponds to the cash-
flowmatchingstrategy,whichisthusrecovered
asaspecificcase.Inprinciple,oneshouldagain
distinguishbetween:
Cash-flow matching: a perfect match is
possiblebetweenassetandliabilitycash-flows,
usingcashinstruments(nominalandrealbonds)
andpossiblydedicatedderivatives(interestrate
andinflationswaps)(seeExhibit1).
3. A Brief History of ALM Techniques
22 EDHEC RISK AND ASSET MANAGEMENT RESEARCH CENTRE
Exhibit1:Surplusoptimizationwithoutaliability-matchingportfolio
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Cash-flowhedging(immunization):aperfect
matchisnotpossibleandduration(orextendedduration) hedging techniques are implemented
soastominimizemismatchrisk(seeExhibit2).
Fromthepreviouscomments,itmightseemthat
so-calledLDIsolutionsaremerelyaspecificcase
ofsurplusoptimizationtechniques,inacontext
wherealiability-matching(orliability-hedging)portfolioisavailableinthemenuofassetclasses.
Thereisasomewhatsubtledifference,though,
betweenLDIsolutionsandsurplusoptimization
withaliability-matchingportfolio.LDIsolutions
advocateanapproachtoALMthatisexpressedin
termsofallocationtothreebuildingblocks(cash,
liability-matching portfolio, and performance
portfolio),asopposedtoallocationtostandard
assetclasses,asdoneinthecontextofsurplus
optimizationtechniques.Assuch,itisconsistent
withanextendedversionofthestandardfundseparationtheoremthatiswell-knowninasset
management(seenextsectionandtheappendix,
orMartellini(2006ab)).
3.3.1. Static LDI Solutions
This is the standard approach that has rapidly
gained interest from pension funds, insurance
companies,andinvestmentconsultantsalike.As
recalledbefore,whiletheycanvarysignificantly
across providers, LDI solutions typically involve
a hedge of the duration and convexity risks
via several standard building blocks, while
keepingsomeassetsfreeforinvestinginhigher
yielding asset classes. These solutions may or
may not involve leverage, depending on the
institutional investors risk aversion. Whenno leverage is used, a fraction of the assets
(known as the liability-matching portfolio) is
allocated to risk management, while another
fractionoftheassetsisallocatedtoperformance
generation.Onemayactuallyviewthisapproach
as a combination of two strategies, involving
investing in immunization strategies (for risk
management) as well as investing in standard
asset management solutions (for performance
generation). As explained above, this approach
stands in contrast to more traditional surplus
optimization methods (in particular when a
dedicated liability-matching portfolio is not
introduced),wherebothobjectives(liabilityrisk
management and performance generation) are
pursuedsimultaneouslyinanattempttoachieve
theportfoliowiththehighestpossiblerelative
risk/relativereturnratio.
3.3.2. Dynamic LDI Solutions
The implementation of LDI solutions cruciallydependsontheinvestorsriskaversion.Highrisk
aversionleadsto a predominant investment in
theliability-hedgingportfolio,whichimplieslow
extremefundingrisk(zeroriskincompletemarket
case)aswellaslowperformance(andtherefore
high necessary contributions), while low risk
aversionleadstopredominantinvestmentinthe
performance-seeking portfolio, which implies
high funding risk as well as higher expected
performance,andhencelowercontributions.
Another way to approach the trade-off
betweenriskmanagementontheonehandand
performance generation on the other consists
in implementing a dynamic, as opposed to
static,allocationbetweentheliability-matching
portfolioandtheperformance-seekingportfolio.
Suchdynamicallocationmethods,whichattempt
todeliverthebestofbothworlds(downsiderisk
protection and access to upside potential), are
inspired by the portfolio insurance techniques,
whichareextendedtoanALMframework(see
inparticularLeibowitzandWeinberger(1982ab)
for the contingent optimisation technique, as
wellasAmenc,MalaiseandMartellini(2004)or
3. A Brief History of ALM Techniques
Asset-Liability Management Decisions in Private Banking 23
Exhibit2:Surplusoptimizationwithaliability-matchingportfolio
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4. Illustrations of the Usefulness of anALM Approach to PWM
Asset-Liability Management Decisions in Private Banking 2
Inwhatfollows,wepresentasetofexamplesofthe
useofasset-liability managementtechniques inprivatebanking.Ourexamplesaredrawnfromthe
simplifiedtypologyofclientprofilesdocumented
insection2.Weusethestandardmodelintroduced
insection3forgeneratingstochasticscenariosfor
riskfactorsaffectingassetandliabilityvalues;and
wegenerateasetof1,000scenariosforinterest
rates,inflationrateandequityprices,aswellas
realestateprices,whenneeded.
Inordertoalleviateapossibleconcernoverthe
impact of arbitrary parameter values, we takeparameter values that are identical to those in
Ahlgrim,DArcyandGorvett(2004),whocalibrate
the model with respect to long time-series.
Otherchoicesofparametervaluescanofcourse
beadoptedandtheirimplementationwouldbe
straightforward.
TheparametervaluesaregiveninExhibit4.
Real interest Parameter value
Mean reversion speed for short rate process 1
Volatility of short rate process 0.01
Mean reversion speed for long-term mean value 0.1
Volatility of long-term mean value 0.016
Long-term mean reversion level for long-term mean value 0.028
Correlation between short-rate and long-term mean value 0.
Inflation
Mean reversion speed for inflation process 0.4Volatility of inflation process 0.04
Long-term mean reversion level for inflation 0.048
Correlation between inflation and short-term interest rate -0.3
Equity model Regime switching
(Monthly) mean equity excess return in state 1 0.008
(Monthly) volatility of equity return in state 1 0.039
(Monthly) mean equity excess return in state 2 -0.011
(Monthly) volatility of equity return in state 2 0.113
Equity model - Regime switching probabilities
Probability of staying in state 1 0.989
Probability of switching from state 1 to state 2 0.011
Probability of staying in state 2 0.941
Probability of switching from state 2 to state 1 0.09
Real estate
Real estate yield reversion speed 1.2
Real estate quarterly yield reversion level 0.023
Real estate yield volatility 0.013
Exhibit4:ParametervaluesborrowedfromAhlgrim,DArcyandGorvett(2004)
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For simplicity of exposure, we have chosen
to focus on static allocation strategies. Whileappealingfromaconceptualstandpoint,general
time- and state-dependent portfolio strategies
tend to generate a source of confusion for
privateclients,whomayperceivesuchdynamic
allocation strategies as attempts to implement
tactical asset allocation decisions. In what
follows,wehavetestedfortheimplementation
ofextendedCPPIALMstrategiesasachoiceof
pragmatic,rule-basedtechniquesallowingusto
better understand the benefits of introducing
time-varyingallocations.Forthesakeofbrevity,
theresultsrelatedtothedynamicLDIstrategies
are only reported for a single illustration, the
firstone.Thebenefitstobeexpectedfromsuch
strategies would be qualitatively equivalent in
thecontextoftheotherillustrationsdiscussed
below.
In all cases, we report standard risk-return
indicatorssuchasexpectedsurplus,volatilityof
the surplus, probability of a deficit, as well asexpectedshortfall(expectedvalueofthedeficit
conditionalonhavingadeficit).
4.1. Pension-Related Objective
As a first illustration, we focus on a pension
objectiveandconsidera 65-year-old individual
whoisalreadyretired.His/hergoalistoensure
astreamofinflation-protectedfixedpayments,
whichwenormalizedat100,forthenext20years(i.e.,fromage65toage85)4.Toachieve
thisgoal the individual is prepared toinvesta
fixedamountofmoney.
Wetestthreedifferentstrategies:
Cash-flowmatchingstrategies
Surplusoptimizationstrategies
DynamicLDIstrategies
4.1.1. Cash-Flow Matching Strategy
One natural solution for meeting the clients
objective consists in buying equal amounts
of zero-coupon inflation-protected securities
(TIPS) with maturities ranging from 1 year to
20 years, assumingthey exist (alternatively, an
OTC interest rate and inflation swaps can beused to complement existing cash instruments
soastogenerateaperfectmatchwithliabilities,
here a stream of 20 annual 100 payments).
This equally-weighted portfolio of TIPS is
the practical implementation of the liability
matchingportfolio introduced at a conceptual
levelinsection3.
Usingtheaforementionedstochasticmodeland
associatedparametervalues,wegeneraterandom
pathsforthepriceof20zero-couponTIPSwith
maturities matching expected payment dates.
Wefindthepresent value ofliability-matching
portfolio, denoted as L(0), and we obtain L(0)
= 1777.15. As we can see, the performance is
poor and the burden of contributions is very
high:theamountofmoneyneededtogenerate
20annual100paymentsisnotmuchsmaller
than20x100.Thisisduetothefactthatratesare
typicallyverylow.Theclientneedsaveryhigh
current contribution to sustain his/her futureconsumptionneeds.
On the other hand, one key advantage of
this approach, which represents an extreme
positioningintherisk-returnspace,isthatthe
distribution of surplus at date 20 is trivially
equal to 0. There is no possible deficit (nor
surplus),becausethepresentvalueofthefuture
liabilitypaymentshasbeeninvestedinaperfect
replicatingportfoliostrategy.
In this context, it is reasonable, unless in the
presence of an extremely (infinitely) high
risk aversion, to add risky asset classes to
enhancethereturnanddecreasethepressureon
contributions,atthecostsofintroducingarisk
ofmismatchbetweenassetsandliabilities.This
iswhatweturntonext.
4.1.2. Surplus Optimization Strategies
Wenowgeneratestochasticscenariosfornominal
bonds and stocks also. We thenstart with the
same initial amount L(0), and find the best
fixed-mixstrategythatconsistsofinvestmentin
stocks,bondsandaliability-matchingportfolio
4. Illustrations of the Usefulness of anALM Approach to PWM
26 EDHEC RISK AND ASSET MANAGEMENT RESEARCH CENTRE
4-Wethusassumeawaythecomplexityrelatedtomortalityrisk,whichcanbedealtwiththroughanannuitycontractprovidedforbyaninsurancecompany.
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(regarded as a whole) so as to generate an
efficient frontier in a surplus space based onoptimizing the trade-off between expected
surplusandvarianceofthesurplus(boldlinein
Exhibit5).Ofcourse,ashighlightedinsection3,
theminimumriskportfoliocorrespondsto100%
investment in the liability-matching portfolio
(correspondingtopointAinExhibit5).Formally,
weassumethattheassetportfolioisliquidated
eachyear,aliabilitypaymentismade,andthe
remaining wealth is invested in an optimal
portfolio;in scenariossuch that theremaining
wealth is not sufficient to make the promised
liability payment, we assume that borrowing
attherisk-freerateisperformedsoastomake
upforthedifference.Weestimateprobabilities
ofnotmeetingtheobjectives(probabilityofa
deficit),whicharereportedinExhibit6,andalso
plotthedistributionofthesurplusatdate20for
afewpointsontheefficientfrontier(seeExhibit
7). As can be seen inExhibit6, increasingthe
allocationstostocksandnominalbonds,which
havealong-termperformancehigherthanthatof inflation-protected bonds but are not as
good a match with respect to liabilities, leads
toahighervalueoftheexpectedsurplus,and
therefore to average contribution savings, but
alsotoanincreasedvolatilityofthesurplusand
anincreasedprobabilityofthedeficit.
For comparison purposes, we also perform the
sameexercise anddesign theefficient frontier
when the liability-matching portfolio is not
available inthe menu ofasset classes (see thefinelineinExhibit5).Theimprovementinduced
by the introduction of a liability-matching
portfolio is spectacular, as can be seen by a
simple comparison between point A and A or
BandB.RegardingpointBandBforinstance,
onecanseethatforthesamelevelofexpected
surplus(376.78),thevolatilityofthesurplusis
increasedbymorethan50%whentheliability-
matching portfolio is not available (640.24
versus423.65).Theriskreductionbenefitsare
alsospectacularwhenriskismeasuredinterms
ofprobabilityofa deficitorexpectedshortfall.
Intuitively, such a dramatic improvement in
investors welfare is related tothe fact that it
isonlythroughthecompletionofthemenuof
asset classes that arises from the introductionofa dedicatedliability-matching portfoliothat
theinvestorsspecific objectiveand constraints
aswellasrelatedriskexposuresarefullytaken
intoaccount.
Of course, the difference between optimal
portfoliosinthepresenceandintheabsenceof
aliability-matchingportfoliodecreaseswiththe
investors risk-aversion: risk-seeking investors
do not seek to enjoy the benefits of liability
protectionandmostlyinvestinstocksandbonds
anyway.
This ALM optimization exercise consists in
findingtheportfoliosthatareoptimalfromthestandpoint of protecting investors liabilities. A
pure asset management (AM) exercise, on the
otherhand,focusesondesigningtheportfolios
withtheoptimalrisk-returntrade-off.Ofcourse,
nothingguaranteesthatAMefficientportfolios
willbeefficientfromanALMperspective(and
vice-versa);inparticular,thefocusisonnominal
return from an AM perspective, while it is on
realreturnfromanALMperspective.Totestfor
theALMperformanceofAMefficientportfolios,
we have conducted the following experiment.
Wefirstfindthestandard(Markowitzefficient)
frontier based on horizon returns, i.e., the
portfolios that achieve the lowest level of
4. Illustrations of the Usefulness of anALM Approach to PWM
Asset-Liability Management Decisions in Private Banking 27
Exhibit5:Efficientfrontierinamean-variancesurplusspace
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volatility(acrossscenariosathorizon)foragiven
expected return (across scenarios at horizon).
Wethenplottheseportfolios(fineline)inthe
(expectedsurplus-volatilityofthesurplus)ALM
space(seeExhibit8).
From Exhibit 8, we can see that a portfolio
efficientinanAMsenseisindeednotnecessarily
efficientinanALMsense,andvice-versa.Hence,
not taking into account liability constraintsleads to potentially severe inefficiencies from
theinvestorsstandpoint.
Wenowturntodynamicportfoliostrategies.
4.1.3. Dynamic LDI Strategies
In testing the implementation of the dynamic
LDIstrategies,theperformanceportfolioistaken
tobethestock-bondportfoliowiththehighest
Sharpe ratio (with our choice of parameter
values, and a 4%risk-freerate, weobtain the
followingportfolio:28.5%instocksand71.5%
inbonds),whiletheliability-matchingportfolio
istheaforementionedportfolio investedinthe
20zero-couponTIPSwithmaturitiesmatching
expectedpaymentdates.
We consider the extended CPPI strategy
introducedin section3.Weconsider6 variants
of the strategy, with the level of protection
k=90%,ork=95%,andthemultipliervaluem=2,3and4.Theresultsarereportedinexhibits9to
12, where we present the performance of the
variousdynamicstrategiesandcomparethemto
4. Illustrations of the Usefulness of anALM Approach to PWM
28 EDHEC RISK AND ASSET MANAGEMENT RESEARCH CENTRE
Exhibit7:Distributionoffinalsurplus/deficit
Exhibit8:AMandALMefficientfrontiersinamean-variancesurplusspace
WeightsStocksBondsLiab-PF
Expectedsurplus
Volatilityofsurplus
Prob(S
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theperformanceoftheirstaticcounterpart.The
staticcounterpartofa givendynamicportfoliostrategy is defined as the strategy involving
constant(fixed-mix)allocationtotheportfolio
with the highest Sharpe ratio and liability-
matching portfolio that matches the initial
allocationofthecorrespondingdynamicstrategy.
Forexample,whenk=95%andm=4,theinitial
allocation to the liability-matching portfolio
(respectivelythehighestSharperatioportfolio)is
givenby1-(1-k)m=80%(respectively,20%).The
staticcounterpartoftheextendedCPPIstrategy
withparametersk=95%andm=4isthereforea
fixed-mix strategy with a constant 80%-20%
allocation to liability matching portfolio and
performance-seekingportfolio.
As can be seen in Exhibit 9 and Exhibit 10,
mostdynamicstrategies allow forsignificantlylower expected shortfall numbers as well as
higher expected surplus (and hence higher
contribution savings) when compared to their
static counterparts. On the other hand, they
tend to generate higher volatility. Also, the
probability of a deficit is rather large with
dynamicstrategies,whichaimtoavoidalldeficit
beyondtheminimumthreshold(90%or95%),
as opposed to minimizing the probability of
facingsucharelativelylowdeficit.Inessence,
dynamic ALM strategies generate asymmetric
surplusdistributions,asconfirmedbyExhibits11
and12,wherethevarioussurplusdistributions
are presented. We also note, as expected, that
4. Illustrations of the Usefulness of anALM Approach to PWM
Asset-Liability Management Decisions in Private Banking 29
DynamicCPPIExpectedsurplus
Volatilityofsurplus
Prob(S
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increasingtheguaranteedlevelkanddecreasing
themultipliervaluemleadtomoreconservativestrategies, with less potential for surplus
performanceandlowerrisk.
Overall, the results reported in exhibits 7 to
10show the very significant risk management
benefitsthatarisefromdynamicstrategies.
4.1.4. A Variant
Wenowconsideraslightvariantofthepension
relatedobjective,wheretheclientisassumedto
be a 45-year-old individual who is not retired
yetandplanstoretireatage65.Thegoalisto
ensure at age 65 a single lump-sum payment
normalizedat100plusinflationforretirement.
Toachievethisgoaltheindividualispreparedto
contributeanamountx(outofhisyearlysalary)
fortheremaining20yearsofhisworkinglife.
Exhibit 13 shows the impact of inflation risk
on the value of the100 payment scheduled
to be paid in 20 years from now. As we can
see,inflationriskissignificant,withanominalamount to be secured for retirement equal
to247.39 on average and a 94.50 standard
deviation.
The main difference with the previous case is
thattheinvestormaynotbeabletoimplement
aperfectliability-matchingportfoliounlesshe/
sheisallowedtoborrowagainsthis/herfuture
income.
Whereborrowingispossible,thestrategyisas
follows:
Borrow xB(0,1)+xB(0,2)++xB(0,20), where
B(s,t)isthepriceatdate sofaunitfacevalue
pure discount nominal bond that matures at
timet.Investthisamountinazero-couponinflation
protectedbondwitha20-yearmaturity.
The optimal value for x is given by: x =
100P(0,20)/(B(0,1)+B(0,2)++B(0,20)), where
P(s,t)isthepriceatdatesofaunitfacevalue
purediscountrealbondthatmaturesattime t.
Withourchoiceofparametervalues,xturnsout
tobeequalto6.07.Thisistheamountneeded
toallow for a perfect ALM match. Inpractice,
itishowevergenerallynotfeasible/practicalto
borrowagainstfutureincome,anditistherefore
impossibletogenerateaperfectALMmatchdue
to uncertainty over investment conditions for
futurecontributions.
4. Illustrations of the Usefulness of anALM Approach to PWM
30 EDHEC RISK AND ASSET MANAGEMENT RESEARCH CENTRE
Exhibit13:Distributionofliabilitiesatfinaldate;meanvalue=247.39,standarddeviation=94.50.
Exhibit 11: Distribution of final surplus/deficit for extended CPPIstrategiesfora90%guaranteelevel
Exhibit 12: Distribution of final surplus/deficit for extended CPPIstrategiesfora95%guaranteelevel
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Asanattempttoestimatetheoptimalallocation
strategies in this context, we perform thefollowingnumericalexercise.Wefirstgenerate
random paths for stock, bond and TIPS prices
with parameters consistent with long-term
estimates, where bond and TIPS are regarded
asindices(modelledasconstantmaturityzero-
couponsecurities).Wethentakex=100P(0,20)/
(B(0,1)+B(0,2)++B(0,20))= 6.07, as explained
before, and find the set of optimal portfolios
that will minimize the volatility of a deficit/
surplus,definedasassetvalueatdate20minus
liabilityvalueonretirementdate(i.e.,100plus
20yearsworthofinflation),foragivenlevelof
surplusexpectedvalue.Foreachportfolioontheefficientfrontier,wethenfindthevaluex
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Asbefore,wecanseethataportfolioefficient
inanAMsenseisindeednotnecessarilyefficientinanALMsense,andvice-versa(seeexhibit16),
which suggests that omitting to take liability
constraintsintoaccountinthedesignofoptimal
portfolio solutions leads to potentially severe
efficiencylossesfromtheinvestorsstandpoint.
4.2. Expenditure-RelatedObjective: the Case of Real Estate
We now consider an investor who wishes to
investfixedannualcontributions(x)forfuture
expenditure,e.g.,tobuyahousein5years,the
currentvalueofwhichisnormalizedat100(we
mayalternativelyinterpretthisastherequired
downpayment).Forsimplicity,onecouldassume
thathousepricesincreasewithinflationanduse
the stochastic model for inflation to generate
adistributionoffuturehouseprices.Ofcourse,
because real estate prices are only imperfectly
correlated with a broad-based consumer priceindex,itismoreaccuratetointroduceanexplicit
model for the dynamics of real estate prices,
whichiswhatwedohere.
Exhibit17showstheimpactofrealestateprice
uncertaintyonthevalueofthe100payment
scheduledtobepaidin5yearsfromnow.Aswe
cansee,realestatepriceriskissignificant,witha
nominalamounttobesecuredequalto156.59
onaverageanda27.18standarddeviation.
In practical terms, the goal is to generate a
lump sum payment at horizon date (5 years).As in the previous example, it is not possible
in general to find a perfect liability-matching
portfolio. The existence of a perfect liability-
matching portfolio is actually onlyensuredon
thefollowingtwoconditions:
Investors can borrow against future income
and can invest at the initial date the present
valueofthefuturecontributions.
Thereexistsaninvestmentvehicle(e.g.,REITS)
whose payoff is directly related to real estate
priceuncertainty.
In what follows, we test two different
situations:
The opportunity set contains stocks, bonds
andTIPS
The opportunity set contains stocks, bonds,
TIPS,plusrealestate(modelledasaninvestment
that will pay the compounded return on realestate)
To generate comparable portfolios, we have
lookedattheimprovementinsurplusvolatility
foragivenlevelofexpectedsurplus.
4. Illustrations of the Usefulness of anALM Approach to PWM
32 EDHEC RISK AND ASSET MANAGEMENT RESEARCH CENTRE
Exhibit 17:Distributionof housepricesat final date;mean value=156.59,standarddeviation=27.18.
Exhibit18:ALMEfficientFrontierswithoutRealEstate(A,B,C,D,E,F)andwithRealEstate(A,B,C,D,E,F)
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Exhibit 18 shows theefficient frontier in both
cases, while risk-return indicators are reported
in Exhibit 19. As was expected, the presence
ofassetsallowinginvestorstospanrealestate
priceuncertaintyprovestobea keyelementinimprovingtheefficientfrontiersobtainedfrom
an ALM perspective. Looking for example at
portfolioDandDfromExhibit19,weseethat
forthesamelevelofexpectedsurplus(12.60in
bothcases),thesurplusvolatilityattheoptimal
levelreaches21.95whentheopportunitysetdoes
notcontainarealestateasset,whileitmerely
amounts to 4.25, a dramatic risk reduction,
whentherealestateassetisincluded.Againthis
signals the relevance of an ALM approach to
privatewealthmanagement:itisonlybytrying
to fit the client liability constraints that truly
optimalsolutionscanbeproposed.
4.3. Bequest-Related Objective
We now consider a wealthy 65-year-old
individual who is already retired. He/she has
significant wealth (say 100 million euros) andwishestomaintainastandardof living(annual
expenses say at 2 million euros plus inflation)
withanadditionalbequestmotivein20years5.
The analysis aims to find the optimal policy
so as to generate thehighest possible bequest
levelwithagivenprobabilitydenotedby .We
first discuss this situation as a base case, and
subsequentlyturntodifferentvariants.
4.3.1. The Base Case
Exhibit20showstheoptimalallocationstrategy,
as well as related risk-return indicators, for
various values of the confidence level ,
while Exhibit 21 shows the distribution of the
discountedvalueoffinalbequestalsoforthese
differentvalues.
4. Illustrations of the Usefulness of anALM Approach to PWM
Asset-Liability Management Decisions in Private Banking 33
5-Weagainassumeawaythecomplexityrelatedtomortalityrisk,whichcanbedealtwiththroughanannuitycontractprovidedforbyaninsurancecompany.
Portfolio
Weights
StocksBondsTIPSReal
Estate
Expectedsurplus
Volatilityofsurplus
Prob(S
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4.3.2. Introducing Constraints
Wealsoconsidertwovariantsinwhich:Halfoftheclientwealth(100million)isheld
asstockinhis/herownprivatecompany,which
willbesoldin5yearsfromnow;inthiscase,
we impose a 50% lower constraint on equity
allocation)6.
The value of existing property is accounted
for(e.g.,theclienthasa e10millionworthof
propertyvalueinadditiontothee100million).
TheseresultscanbefoundinExhibits22and23.
4. Illustrations of the Usefulness of anALM Approach to PWM
34 EDHEC RISK AND ASSET MANAGEMENT RESEARCH CENTRE
6-Inotherworlds,weassumeawayspecificriskinprivateequityreturnwhenoptimizingtheportfolio,andmodelthe2100millionasifitwasinvestedintheequityindex.
Exhibit23:Distributionofthediscountedvalueoffinalbequestasafunctionoftheconfidencelevel,withadditionale10millioninitiallyheldinrealestate(left)andwithaminimumof50%investedinequity(right)
AswecanseethroughacomparisonwithExhibit
20, the presence of constraints related to the
clients situation will impact upon the optimal
portfoliostrategy.
Exhibit21:Distributionof thediscountedvalueoffinalbequestasafunctionoftheconfidencelevel
Exhibit22:Allocationstrategiesandrisk-returnindicatorsasafunctionoftheconfidencelevel,includingallocationconstraints(realestateorequity)
Target
Percentile
Weights
StocksBondsLMP
Expected
bequest
Volatility
ofbequest
Bequestpercentiles
5 10 20 Median 75 95
Min 0%
in stocks
alpha= % 0% 40% 10% 181.3 142.68 37.23 2.0 73. 142.62 239.44 462.09
alpha=10% 0% 1% 3% 187.21 12.9 3.82 3.11 7.00 147.21 242.09 490.4
alpha=20% 3% 23% 24% 194.20 162.69 34.9 1.10 76.33 149.1 24.2 16.30
Additional 10m
in real estate
property at T0
alpha= % 22% 36% 42% 12.14 9.32 79.21 88.47 103.63 141.31 182.29 260.71
alpha=10% 24% 44% 32% 1.60 62.90 78.76 90.32 104.1 143.97 186.0 277.0
alpha=20% 2% 23% 2% 241.94 179.88 62.03 83.67 111.22 192.13 309.43 94.38
4.3.3. A Variant with Significant Lump-Sum
Payments ExpectedWefinallyconsidera65-year-oldindividualwho
is already retired. He/she has significant wealth
(say e100 million) and wishes to maintain a
standard of living (annual expenses say at 2
millioneurosplusinflation),plustwosignificantexpenses(10millionin5yearsand10millionin
10years),e.g.,tobuyaprivatejetorayacht,with
anadditionalbequestmotivein20years.
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4. Illustrations of the Usefulness of anALM Approach to PWM
Asset-Liability Management Decisions in Private Banking 3
Exhibit24:Distributionofthediscountedvalueoffinalbequestasafunctionoftheconfidencelevel
Exhibit26:Distributionofthediscountedvalueoffinalbequestasafunctionoftheconfidencelevel andexpectedbequestlevel
Exhibit25:Allocationstrategiesandrisk-returnindicatorsasafunctionoftheconfidencelevel
Target
Percentile
Weights
Stocks Bonds LMP
Expected
Bequest
Volatility
of Bequest
Bequest Percentiles
10 20 median 7 9
alpha= % 17% 47% 36% 74.7 31.11 3.30 41.26 48.70 69.2 91.33 133.3
alpha=10% 17% 40% 43% 7.88 32.27 34.43 41.84 49.69 70.01 93.46 13.48
alpha=20% 48% 31% 21% 141.03 118.82 19.73 32.68 4.10 110.9 187.23 363.20
The analysis aims at finding the optimal
policysoasto:
Generate the optimal distribution of
bequestforagivenlevelofannualexpenses
(Exhibits24and25).
Generatetheoptimaldistributionoflevel
of annual expenses for a given level of
bequest(Exhibits26and27).
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4. Illustrations of the Usefulness of anALM Approach to PWM
36 EDHEC RISK AND ASSET MANAGEMENT RESEARCH CENTRE
Bequest
level
Target
percentile
Weights
Stocks Bonds LMP
Expected
annualexpenses
Volatility
of annualexpenses
Annual expenses percentiles
10 20 Median 7 9
7 alpha= % 17% 47% 36% 1.3 1.8 -1.20 -0.60 0.33 1.73 2.64 3.72
alpha=10% 17% 40% 43% 1. 1.62 -1.11 -0.67 0.31 1.76 2.67 3.81
alpha=20% 48% 31% 21% 3.28 3.23 -2.06 -0.63 0.81 3.44 .43 8.01
100 alpha= % 17% 47% 36% 0.26 2.04 -3.62 -2.30 -1.10 0.6 1.70 2.98
alpha=10% 17% 40% 43% 0.30 2.08 -3.63 -2.34 -1.02 0.6 1.74 3.08
alpha=20% 48% 31% 21% 2.1 3.70 -3.98 -2.17 -0.61 2.47 4.66 7.38
10 alpha= % 17% 47% 36% -2.3 3.07 -8.18 -6.26 -4.1 -1.86 -0.18 1.0
alpha=10% 17% 40% 43% -2.31 3.14 -8.29 -6.38 -4.4 -1.78 -0.08 1.9
alpha=20% 48% 31% 21% -0.13 4.80 -8.33 -.63 -3.44 0.37 3.10 6.40
Exhibit27:Allocationstrategiesandrisk-returnindicatorsasafunctionoftheconfidencelevel andexpectedbequestlevel
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This paper has provided ample evidence that
asset-liability management is an essentialimprovement in private wealth management
that allows private bankers to provide their
clients with investment solutions and asset
allocation advice that truly meet their needs.
We have also provided a series of illustrations
thatshowthatsomeofthemostsophisticated
ALM techniques used in institutional money
managementcansatisfactorilybeimplemented
inprivatewealthmanagement.
Ultimately,wearguethatitisnottheperformance
of a particular fund nor that of a given asset
class (including commodities or hedge funds)
thatwillbethedeterminingfactorintheability
ofprivatewealthmanagementtomeetinvestors
expectations.Whatwillprovetobethedecisive
factor is the private wealth managers ability
to design an asset allocation solution that is
a function of the kinds of particular risks to
whichtheinvestorisexposed,asopposedtothe
market as a whole. Hence, an absolute returnfund,oftenperceivedasanaturalchoiceinthe
context of private wealth management, shall
not be a satisfactory response to the needs
of a client facing long-term inflation risk,
where the concern is capital preservation in
real,asopposedtonominal,terms.Similarly,a
clientwhoseobjectivewouldberelatedtothe
acquisitionofa propertywouldacceptlowand
even negative returns in situations when real
estatepricessignificantlydecrease,butwillnot
satisfy himself or herself with relatively highreturnsifsuchhighreturnsarenotsufficientto
meet a dramatic increase in real estate prices.
In such circumstances, a long-term investment
instocksandbondswithaperformanceweakly
correlatedwithrealestatepriceswouldnotbe
therightinvestmentsolution.
In other words, the success or failure of the
satisfactionof theclients long-term objectives
isfundamentallydependentonanALMexercise
that aims to determine the proper strategic
inter-classes allocation as a function of the
clients specific objectives and constraints.
Assetmanagementshouldonlycomenextasa
response to the implementation constraints of
theALMdecisions.Ontheonehand,itismeanttodeliver/enhancetheriskandreturnparameters
supportingtheALManalysisforeachassetclass.
On the other hand, it can also allow for the
managementofshort-termconstraints,suchas
capitalpreservationatagivenconfidencelevel,
whicharenotnecessarilytakenintoaccountby
anALMoptimizationexercise,whichbynature
focusesonlong-termobjectives.
5. Conclusion
Asset-Liability Management Decisions in Private Banking 37
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Inthisappendix,wepresentageneralcontinuous-
timemodelofassetallocationdecisionsinthepresence of liability constraints. This material
is borrowed from Martellini (2006ab). From
an academic standpoint, several authors have
attempted to cast the ALM problem in a
continuous-timeframework,andextendMertons
intertemporal selection analysis (see Merton
(1969, 1971)) to account for the presence of
liabilityconstraintsintheassetallocationpolicy.
Afirststepintheapplicationofoptimalportfolio
selectiontheorytotheproblemofpensionfunds
hasbeentakenbyMerton(1990)himself,who
studies the allocation decision of a university
thatmanagesanendowmentfund.Inasimilar
vein, Boulier et al. (1995) have formulated a
continuous-time dynamic programming model
ofpensionfundmanagement.Itcontainsallof
thebasicelementsformodelingdy
top related