EDHEC Study_ALM Decisions in Private Banking

7/30/2019 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


2/522 EDHEC RISK AND ASSET MANAGEMENT RESEARCH CENTRE

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



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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


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.



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


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


1-MerrillLynch&CapgeminiWorldWealthReport2006availableatwww.us.capgemini.com/worldwealthreport06


17/52

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



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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

2. Asset-Liability Management as a TrulyClient-Driven Approach to Private Banking



19/52


20/52

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



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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



2-Amean-revertingmodelforrealestatepriceshasalsobeenusedfortheillustrationswhererealestatewasintroduced.

3-OthercompetingmodelscanofcoursebeusedinALMsimulationsandoptimization,buttheyaremostlyconsistentinspiritwiththisparticularmodel,whichwehavechosenbecauseitrepresentsastandardexampleofastate-of-the-artALMmodelwhichismadeavailableforpublicusebytheCasualtyActuarialSociety(CAS)andtheSocietyofActuaries(SOA)(seereferencelistforexactreferencesofthepaperandawebsitewherethepapercanbedownloaded).


22/52

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).



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



Exhibit2:Surplusoptimizationwithaliability-matchingportfolio


24/52


25/52

4. Illustrations of the Usefulness of anALM Approach to PWM


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)


26/52

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-Wethusassumeawaythecomplexityrelatedtomortalityrisk,whichcanbedealtwiththroughanannuitycontractprovidedforbyaninsurancecompany.


27/52

(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



Exhibit5:Efficientfrontierinamean-variancesurplusspace


28/52

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



Exhibit7:Distributionoffinalsurplus/deficit

Exhibit8:AMandALMefficientfrontiersinamean-variancesurplusspace

WeightsStocksBondsLiab-PF

Expectedsurplus

Volatilityofsurplus

Prob(S


29/52

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



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.



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.



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.



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.



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.


35/52



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).


36/52



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


37/52

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



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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

Documents

EDHEC Study_ALM Decisions in Private Banking