RESEARCHTHESIS

MonteCarloSimulationinRealEstateInvestment

PresentedBy;

TysonWarnett

3527490

RMITUNIVERSITY

OMGT2280PROPERTYINDUSTRYPROJECT

2

ACKNOWLEDGEMENTS

ThisthesisonMonteCarlosimulationandhowitmaybeusedwithintheRealEstate

industry primarily arises from a risk management perspective and its implementation in

investmentmarkets.Itwasintroducedtomeinmypostgraduatestudieswhilstundertaking

the unit ‘Investment Evaluation Techniques for Real Estate’. It was progressed on within

‘CorporatePropertyfinance’.BothoftheseunitswerelecturedbyMr.JohnGarimort.

I would like to acknowledge and thank Mr. John Garimort on his guidance and

discussionson the topic. For the replyof emails and the ‘short notice’meetings to clarify

particular aspects in asset allocation and the initiation of simulation model building and

directingmeonhowtoconstructit.

Iwouldliketoexpressmygratitudetomythesissupervisor,ProfessorNickBlismas

forprovidingdirectioninstructuringthedissertationandtakingthetimetoreadandeditmy

excessively longsentences!I’dalsoliketoacknowledgetheavailabilityhemadeformyself

andallotherstudentsduringabusysemester.

To RMIT University, particularly the School of Property, Construction and Project

Management, thank you for implementing a beneficial program and allowingmyself and

otherstudentstoundertakeresearchintoourowninterests.

Finally,tofriends,familyandfellowstudentsthatshowedsupport,orlistenedtomy

monotonousspeakingonthetopic,thankyou.

3

TABLEOFCONTENTS

ACKNOWLEDGEMENTS 2

LISTOFTABLESANDFIGURES 5

GLOSSARYOFTERMS 6

1. INTRODUCTION 8

1.1. RESEARCHPROBLEM 8

1.2. RESEARCHQUESTION 9

1.3. METHODOLOGY 9

1.4. STRUCTUREOFTHETHESIS 10

2. LITERATUREREVIEW 12

3. RESEARCHDESIGN 16

3.1. INTRODUCTION 16

3.2. METHODOLOGY 16

3.2.1. DATASOURCES 17

3.2.2. ECONOMICPERIODS 18

3.2.3. ASSETALLOCATION 20

3.2.4. SHARPERATIO 20

3.2.5. MONTECARLOSIMULATION 21

3.2.6. EFFICIENTFRONTIER 21

3.3. RESEARCHPROCEDURE 21

3.4. CONCLUSION 24

4. ANALYSISOFDATA 25

4.1. INTRODUCTION 25

4.2. ANALYSISOFDATA 25

4.2.1. PROPERTYRETURNS 25

4.2.2. GROWTHPERIOD 27

4.2.3. DECLINEPERIOD 30

4.2.4. STABLEPERIOD 34

4.3. SUMMARY,DISCUSSIONANDMAINFINDINGS 36

4

5. CONCLUSION 39

5.1. INTRODUCTION 39

5.2. CONCLUSIONONRESEARCHQUESTIONS 39

5.3. CONCLUSIONABOUTRESEARCHPROBLEM 39

5.4. IMPLICATIONSTOPRACTICE 40

5.5. LIMITATIONS 40

5.6. FURTHERRESEARCH 41

6. BIBLIOGRAPHY 43

APPENDIX1: 45

5

LISTOFTABLESANDFIGURES

Table3.1:Propertyreturns,foreachassetclass,ineacheconomiccondition

Table4.1:Meanpropertyreturnsbysector,ineacheconomicperiod

Table4.2:Outputdataofpropertyreturnsin‘Growth’Period

Table4.3:DeterministicmodelRanking,in‘Growth’period,bySharperatio

Table4.4:MonteCarlosimulationranking,in‘Growth’period,bySharperatio

Table4.5:Outputdataofpropertyreturnsin‘Decline’Period

Table4.6:DeterministicPortfolioRanking,in‘Decline’period,bySharperatio

Table4.7:MonteCarlosimulationranking,in‘Decline’period,bySharperatio

Table4.8:Mean-Returnrangeofoptimalportfolios,in‘Decline’period

Table4.9:Outputdataofpropertyreturnsin‘Stable’Period

Table4.10:DeterministicPortfolioRanking,in‘Stable’period,bySharpeRatio

Table4.11:MonteCarlosimulationranking,in‘Stable’period,bySharperatio

Table4.12:ComparisonofbestperformingportfoliosinDeterministic&Probabilisticmodels

Table7.1:2-assetclassportfoliosweightings

Table7.2:3-assetclassportfoliosweightings

Figure4.1:PropertyReturnsfromJune2005toMarch2014

Figure4.2:EfficientFrontierofPortfoliosin‘Growth’period.

Figure4.3:EfficientFrontierofPortfoliosin‘Decline’period.

Figure4.4:EfficientFrontierofPortfoliosin‘Stable’period.

Figure7.1:Top10Portfolios,bySharperatio,inGrowthperiod

Figure7.2:Top10Portfolios,bySharperatio,in‘Decline’period

Figure7.3:Top10Portfolios,bySharperatio,in‘Stable’period

6

GLOSSARYOFTERMS

Asset Allocation: An investment strategy that aims to balance risk and return through

adjustinganinvestmentamongdifferentassets.

DeterministicModeling:Astatisticalmodelwherevariablesaredeterminedbyparametersin

themodelandarebasedoninitialconditions.

Diversification:Diversificationisariskmanagementtechniquethatmixesaspecifiedamount

ofassetclasseswithinaportfolio.

EfficientFrontier:Asetofoptimalportfolios thatoffers thehighestexpected return fora

definedlevelofriskorthelowestriskforagivenlevelofexpectedreturn.

Mean-Variance:Theprocessofweighingrisk(variance)againstexpectedreturn.

PortfolioRisk:Onestandarddeviation,or68%ofallprobableoutcomes,unlessotherwise

stated.

ProbabilisticModeling:Statisticalanalysistoolthatestimates,basedonprobability,anoutput

occurring.MonteCarlosimulationisaprobabilisticmodel.

SharpeRatio:Ameasureforcalculatingrisk-adjustedreturn.Thisratioiscommonlyusedin

industrypractice.

StandardDeviation:Astatisticalmeasureofhowfarasetofdataisfromitsmean.Themore

spreadapartthedata,thehigherthedeviation.

StochasticModeling:Astatisticalmodelthatisforthepurposeofestimatingtheprobability

ofoutcomes.Oneormoreofthevariableswithinthemodelarerandom.Alsoreferredtoas

ProbabilisticModeling.

Variability:Thestatisticaldistributionofdatapointsfromitsmeanvalue.

7

Volatility:Theamountofuncertaintyorriskaboutthesizeofchangesinadatapointsvalue.

8

1. INTRODUCTION

Assetallocationistheprocessofmixingassetweightwithinaportfoliotoyieldthemost

favourablerisk-returntrade-off(Cardona1998;Seiler,Webb&Myer1999;Sing&Ong2000).

Thisresearchwillinvestigateifvaryingassetallocationduringdifferenteconomicphases(i.e.

growth,declineandstable),optimizesandenhancestheperformanceofaportfolio,when

comparedtoanassetallocationthatremainsstatic.

The investigation will be undertaken by using Monte Carlo simulation as a risk

management tool to determine the most likely risk-adjusted returns of each portfolio.

PortfolioperformancewillbemeasuredbyaSharperatio,thisfactorsportfolioriskalongwith

portfolioreturntoenableatrueindicationofrisk-adjustedportfolioperformance.

Initial portfolio performance, prior to Monte Carlo simulation, is measured through

deterministicmodeling,thatcontainsnorandomnessandtheoutputwouldalwaysproduce

thesamerisk-adjustedreturnaslongastheinitialinputsremainedthesame.

There are three economic periods that bothMonte Carlo simulation and deterministic

modeling will be operated within. Each economic period produced asset returns and

deviationsthatdifferentacrosstheentirecycle.Thisproducedtheopportunitytoenhance

portfolioperformancethroughtheselectionoftheappropriateportfoliothatproducedthe

highestrisk-adjustedreturnineachperiod.

1.1. RESEARCHPROBLEM

The body of knowledge within this research area is limited. Most research on Asset

Allocationhasbeenconductedondifferentassetclasses,suchasequitiesandfixedinterest.

Studiesthathaveincludedpropertyasanassetclass,aremostlyconcernedwiththeassetas

partofamixed-assetportfolio.Oftheremainingresearchthatdoesfocusupon‘withinreal

estate’ asset allocation, most examines the diversification of property by property-type,

geographical regionor economic industries (Mueller 1993;Mueller&Ziering1992). There

werenostudies found thatexamineassetallocation,basedonMonteCarlo simulation, in

differingeconomicconditions.

9

Riskmanagement is becoming of interest in tightening financialmarkets,with it being

rankedbyfinancialexecutivesasoneoftheirmostimportantobjectives(Froot,Scharfstein&

Stein1993).Mostmeansofaddressingthisobjectiveisthroughratiosandinterpretationof

thoseratiosbythedecisionmaker/fundmanager.Theseratiosareoftenderivedfromhistoric

datathathasnorandomnessattached,thusmakingthedecisionmakersjudgementofthis

dataandhowitisimplementedforfutureforecastsincreasinglyimportant.Asthefutureis

alwaysuncertain,thereneedbeatoolthatassistsandincreasestheprobabilityofthedecision

makersjudgementoccurring.MonteCarlosimulationcanaddressthissituation.

1.2. RESEARCHQUESTION

Economic conditions are a major factor affecting the performance of a real estate

portfolio(Mueller1993).Achangeineconomicperformancecanplacesignificantpressureon

fund managers and institutional investors for them to meet specified benchmarks in all

periods,inordertosatisfyclients’expectationsandtheirfinancialpositions.Thisresearchsets

out to determine if using computer simulation modeling, in the form of aMonte Carlo

Simulation, can assist decision makers in effective choices to enhance and optimize the

performanceofarealestateportfolio.

The primary aim of the research is to determine the applicability of Monte Carlo

simulationasanassetallocationtoolwithintherealestatesector.Specifically,thequestion

is;

Does altering real estate asset allocation during differing economic conditions,

basedonMonteCarlosimulation,enhanceportfolioperformance?

1.3. METHODOLOGY

Toinvestigateandanswerthisquestion,theprobabilisticmodel-MonteCarloSimulation,

wasusedtomodelhistoricdatatoproducearangeofportfolioreturns.Theportfolioasset

allocationispredeterminedandcanbeseeninTable7.1&7.2inAppendix1.Theresultsof

thesimulationdetermine iftheassetallocationtool,duringdifferenteconomicconditions,

enhances portfolio performance. The simulation enables fund managers to identify the

10

portfolioperformanceoverthedifferingeconomicconditions,i.e.willaparticularportfolio

perform as efficiently in a ‘Stable’ period as it does in a ‘Growth’ period? Portfolio

performanceismeasuredonarisk/returnbasis,notreturn-only.

Whilstthisdissertationdoesnotindicatetheprobabilityoffuturereturns,itprovidesthe

basisofhowtomodelMonteCarlosimulation,foroptimalassetallocationanddiversification

benefits. Historic risk/return data can be substituted for forecasted returns and standard

deviationswhereaprobabilisticoutcomemaybederived.

This methodology is advantageous amongst the two types of simulation models

(deterministicandprobabilistic) thatareoftenused in investment strategy to forecast the

risk-return of a prospective investment. The variables of a probabilistic model, unlike a

deterministicmodelthatusesfixedsingle-pointinputvariables,thevariablesarerepresented

by probability distributions (Byrne 1996). A comparison between the returns of the two

modelsismadeinthedataanalysis.

1.4. STRUCTUREOFTHETHESIS

Aprobabilisticmodelisbeneficialastheex-returnsanassetprovidescannotbeforecasted

withcertainty,howeverusing thepast returns indifferentphasesofeconomicconditions,

alongwith thevariability, i.e. standarddeviation, themodelcanproducea rangeof ‘most

likely’ figures for the decisionmaker to then interpret and act upon (Byrne 1996). It also

enablesthedecisionmakertouseanefficientfrontiertodeterminewhichassetsproducethe

mostefficientreturnsforaspecifiedlevelofrisk.

Thefollowingchaptersofthisdissertationfocusesonreviewingrelevantliterature,model

methodology,dataanalysisandconclusionofthemodelfindings.Chapter2reviewsliterature

that have relevance to this dissertation. This included aspects of asset allocation,

diversification,ModernPortfolioTheoryandMonteCarloSimulation.Chapter3focusesupon

theresearchdesign,includingimportantaspectssuchastheSharperatioandtheprocedure

ofMonteCarlosimulationmodelling.

Chapter4analysestheoutputdatafromtheMonteCarlosimulationaftertheMonteCarlo

simulation inChapter3wasundertaken. Itwill comparereturnsandresultsbetweentime

11

periodsand iteratehowMonteCarlo simulation,asa riskmanagement tool, canenhance

portfolioperformance.Chapter5concludesthedissertation,discussesthelimitationsofthis

studyandprovidesarangeoffurtherresearchthatmaybeconductedtoenhancethetopic.

12

2. LITERATUREREVIEW

Literature on stochastic computer simulation of asset allocation is limited within real

estate. There is a plethora of research that focuses upon asset allocation and portfolio

optimization,thoughthemassofthisresearchisfocuseduponthemoreliquidassetsincapital

markets,i.e.stocksandgovernmentbonds(Amencetal.2011;Cardona1998;Faff,Gallagher

&Wu2005).However,HarryMarkowitz’sModernPortfolioTheory(MPT)wasonestrategy

thatreappearedinalmosteverypieceofliterature(Detemple,Garcia&Rindisbacher2003;

Fisher&Liang2000;Seiler,Webb&Myer1999;Sing&Ong2000;Viezer1999,2000).

In 1952,Markowitzwas the first to discuss the concept of diversification through the

formal development of the MPT (Seiler, Webb & Myer 1999). However research has

demonstratedthatthemean-varianceconcept,whichisbasedontheprocessofweighting

variance(risk)againstreturnsinanormalandindependentdistribution,islimitedwhenasset

returns are skewed and form an abnormal distribution (Sing&Ong 2000). Therefore, the

mean-varianceconceptandMPTmaynotbethebestconceptformeasuringanddetermining

optimalassetallocationwithinrealestate,oratleastonitsown.Informationasymmetries,

hightransactioncosts,illiquidity,uniquenessofassetcharacteristics,privatepropertyrights,

tax,landuselegislationaresomeofthereasonswhycapitalmarkettheories,suchasMPT,do

notadequatelyperformwithinrealestatemarkets(Coleman&Mansour2005;Souza2014).

From the literature that has been reviewed,most agree that diversification and asset

allocationhaveevolvedasimportanttoolstomitigateriskinrealestateportfolios(Coleman

& Mansour 2005) and are intimately related to risk management (Amenc et al. 2011).

Optimizingportfolioperformanceforanindividual’slevelofrisktolerance(Cardona1998)is

as important an aspect of portfolio management as pursuing superior returns (often

correlatedwithhigherrisk).

Tactical and Strategic Allocation are other strategies that can be used to structure a

diversified portfolio (Cardona 1998). Typically, strategic allocation is what the populace

considerwhentheyhearthebroadterm‘assetallocation’.Targetallocationsareestablished

fordifferentassetclasses,inthisinstance,office,retailandindustrial,andtheseholdingsare

periodically rebalanced to theoriginal targetsas the investment returnsskewtheposition

13

(Cardona1998).Tacticalallocationattemptstooverweightorunderweightintoaparticular

assettoimprovereturns,ortakeadvantageofthatoutperformingassetclass(Cardona1998).

Rebalancingassets,asdoneinstrategicallocation,canbedifficulttoimplementinrealestate

duetoilliquidity,hightransactioncostsandtimeperiodofpurchasingandsellingassets.The

strategythispaperisconcernedwithistacticalallocation.

Tacticalassetallocationisbeginningtoreceiveincreasedinterestbyindustrypractitioners

inordertobeatthemarket(Chong&Phillips2014).Ittakesadvantagesofopportunitiesin

financialmarketswherecertainaspectsappearoutofline(Anson2004).Intheinstancesof

this dissertation, it takes opportunities where asset allocation can be altered to enhance

portfolioperformanceandnotablyoutperformthemarket.Itcomparestherelativevalueof

eachassetclassandoverweighsorunderweighstheassetclasswhenriskadjustedreturns

appeartooutperformthemarketorspecificbenchmark(Anson2004).

Indeterminingwhichassettotacticallyoverweighorunderweightoenhanceportfolio

performance,MonteCarloSimulation,asatool,canassistindeterminingtheprobabilityof

returnsforeachassetclassatapredeterminedrisklevel(Pyhrr1973).Theliteraturerelating

totheapplicationofMonteCarloSimulationinrealestateinvestmentislimited.Perhapsthe

mostrelevantpieceofliteratureisPyhrr(1973).Pyhrrshowsastep-by-stepapproachonhow

computer simulationmodels are usefulwithin the investment decision process. Thework

focusesuponaprobabilisticrateofreturn,whilstincorporatingbusinessandfinancialriskand

outlinesthemethodologiesforassessingprobabilitydistributioninputsintothemodel(Pyhrr

1973).

Pyhrrstatesthatariskanalysismodelshouldbeprobabilistic,sincethevaluesoftheinput

variablesareuncertain,thustheassociatedprobabilitydistributiondrivenbytheoutputof

themodel,must be a range, rather than single-value estimates to reflect this uncertainty

(Pyhrr1973).ThisiswhereMonteCarlomaybeutilised.Singlepointvaluemodels,suchas

DiscountedCashFlow(DCF),assumethatbothinputandoutputvariablesareestimatedas

certainvaluesmodelingonlyonescenario,producinganinefficientdecisionmakingtooland

exposingtheinvestmenttoincreasedriskiftheestimatedinputsareincorrect.

14

Take the same input values for a DCF,Monte Carlo simulation would create random

varieties on each input (often within a standard deviation) and produce thousands of

outcomesforeachoutput(Thomopoulos2013).Amean-averageoftheseoutcomesmakeit

amoreefficientdecisionmakingtoolandreducesriskasitfactorstheuncertainvariability

andcomplexitiesoftherealworld.

MonteCarloSimulationisreadilyusedandresearchedamongstindustriesoutsideofReal

Estate,fromharborprotection(Males&Melby2011)totheManhattanProjectinthe1940s,

whereitwastheprominenttoolinthedevelopmentofthehydrogenbomb(Thomopoulos

2013).ThemodelhasbeenusedinawiderangeofapplicationssincetheManhattanProject,

where itgained itsvalidity. Itwasdeemedthatas longastheprobabilitydistributionsand

parametersvaluesselectedwereauthentic,themodelispowerfulenoughtoassistindecision

making as crucial as constructing a hydrogen bomb, such as the Manhattan Project

(Thomopoulos2013).Sincethisproject,therehasbeennoobviousorcompellingevidenceto

suggestMonteCarlosimulationisineffectiveasadecisionmaking/riskmanagementtool.

The model is now extensively used in all industries and government decisions

(Thomopoulos2013).Inreferencetoharborprotection,MalesandMelbystate;

“Monte Carlo simulation modeling that incorporates engineering and economic

impactsisaworthwhilemethodforhandlingthecomplexitiesinvolvedinrealworld

problems”(2011,p1).

AlthoughtheManhattanProjectandharborprotectiondiffersubstantiallyfromfinancial

marketsandrealestateinvestment,usingriskmanagementtoolsfromotherindustriesoffer

riskmanagementprinciplesthatmaybeadjustedandimplementedtosuitthedemandsof

thesituation.

The basic principle of Monte Carlo simulation is that is a methodology for analysing

problemswherethereareuncertainties(Males&Melby2011).Itisusefulinrepresentingreal

world situationswhere therearemanyuncertainvariablesbut theparameterorbehavior

values are known (Males & Melby 2011), e.g. the future expected return is unknown &

effected by many uncertain variables, although the parameters of historic returns and

variabilitythroughstandarddeviationareextremelyusefulindeterminingtheoutput.

15

Theliteraturereviewdemonstratesthatdiversificationthroughtacticalassetallocation

canenhanceportfolioperformance.Byalteringtacticalassetallocationtooverweighorunder

weighinhighrisk-adjustedreturnassets,indifferenteconomicperiods,canproducereturns

thataremorelikelytooutperformthemarket.MonteCarlosimulation,asatool,canbeused

todeterminewhichportfoliosandtheircorrespondingassetallocationweightsaremostlikely

toproducereturnsthatenhanceportfolioperformance.

16

3. RESEARCHDESIGN

3.1. INTRODUCTION

Thegoalof this research is toquantifyandmeasureriskamongst thecommercial real

estateinvestmentsector.Asrealestateinvestmentdecisionsinvolvemanycomplex,dynamic

anduncertainelements(Pyhrr1973),usingadeterministicmodeltoestimaterisk&return

valuesandassist indecisionmakingmaynotbethemostappropriatemodel,exposingthe

investortogreatersystematicrisk.

MonteCarlosimulationallowstheinvestortouseaprobabilitydistributionforeachasset

class (Retail,Office& Industrial) anddetermine theoptimal asset allocation.Optimization

occursbymixingassetweightstoconcludeaportfoliowiththemostfavourablerisk-reward

trade-off(Sing&Ong2000)measuredbyaSharpeRatio.

Furthermore, the results of probabilitymodelingwill provide data to plot an efficient

frontier,producingaborderlineofwhichportfoliosandtheassetallocationweightingsthat

provide themostefficientportfolios to suita specified riskperunitof return,or specified

returnperunitofrisk.

3.2. METHODOLOGY

InordertodetermineifMonteCarloSimulationcanassistdecisionmakersininterpreting

datatoenhanceportfolioperformance,acasestudyusingsecondarysourceswillbeutilised.

Theinvestigationisadeductiveapproachthatteststhereturnsfromdifferentassetallocation,

during differing economic cycles. Monte Carlo Simulation runs the asset allocation to

determineanexpectedrateofreturn.The inputs intothesimulationarequantitativedata

collectedfromMSCIData(formerlyknownasIPDData).

There are several reasons for selecting a case study. Firstly, using the historic data

obtainedfromMSCIoneachassetclass(Office,Industrial&Retail)ineacheconomicperiod

(Growth, Decline, Stable), allows the quantitative testing of probabilistic modeling to

determineifdiversifyingassetsinrespectiveeconomicperiodsenhancestheperformanceof

theoverallportfolio.

17

Secondly, by presenting the process in a case study format, it communicates to the

readershowtointerprettheinputandoutputdataofthemodel.Theprobabilisticmodel,or

anymodel,isonlyasaccurateastheinputsdeterminedbytheuserandtheinterpretationof

theoutputsreceivedofthoseinputs.MonteCarloSimulationisnoexception,themodelonly

providesprobabilisticoutputs,asnothinginrealitycanbeforecastedwithcertainty,therefore

understanding and interrupting the variables associated with the model is a critical

componenttorunninganeffectivesimulation.Manyinvestorsaresuspiciousthatthemodel

operateslikeablackbox,inwhichdataisfedandresultsappear,possiblywiththechancefor

unscrupulousmanipulationbyothers(Rowland2010).

Onceareaderunderstandsandiscapableofinterpretingthedata,theyarethenableto

implementthemodelintheirownpractice.DuetothecomplexityofMonteCarloSimulation

and the mathematical equations behind it, a case study provides the best approach of

transferringtheknowledgeintopractice.Manypapersfocusonthecomplexmathematical

equations behind the model, however in reality, the user does not need extensive

understandingoftheequationsbehindthemodel;theyneedtoknowhowtoit,itslimitations

andhowtointerpretwhatitproduces.

Thefollowingsectionscontainmaterialthatwillallowforunderstandingthecomponents

ofthemodel,enablingagreaterinterpretationoftheresearchprocedureandoutcomesin

Chapter4:AnalysisofData.

3.2.1. DATASOURCES

Thedatasourcesusedwithinthisresearchmodelingarefromreliablesources.Property

returnsareobtainedfromMSCI:IPDAustraliaQuarterlyDigest,September2015.MSCIData

holds real estate asset information on hundreds of institutional investors, whilst also

producing indexes for both privately held real estate portfolios and publicly listed

organisations(MSCI2016).Itprovidesquarterlydatareturnsforeachprimarysector(Retail,

Office, Industrial)overaperiodfromDecember1985toSeptember2015.Propertyreturns

(RollingAnnualReturns) foreachsectorhavebeenutilisedfromJune2005toMarch2014

(Table3.1).Thesecorrespondwiththeeconomicperiodsusedinmodeling.

18

Government Bond rates, were obtained from the Reserve Bank of Australia ‘Capital

MarketYield:GovernmentBondtables’.Thebondrateisusedastheriskfreerate,arateof

returnthatcarriesnoriskandtheinvestmentreturniscertain.Thebondrateisusedinthe

Sharperatioformula.

3.2.2. ECONOMICPERIODS

TheMonteCarloSimulationwasoperatedinthreedistincteconomicperiods.Eachperiod

representsdifferingeconomicconditionswherepropertyreturnssignificantlychangedinline

withtheMarketCycle(Figure3.1).Theseperiodswere;

• Growth:June2005–March2008

• Decline:June2008–March2011

• Stable:June11–March2014

These economic periods also coincide with the Global Financial Crisis (GFC), which

drastically affected the investmentmarket. The periods can also be perceived as Pre-GFC

(Growth),GFC(Decline)andPost-GFC(Stable).

The simulationwill determine, by probabilisticmeans, the portfolios that are likely to

producethehighestmeanreturnandSharperatios(risk/reward) ineacheconomicperiod.

Theprocedureofthemodelingwillbeexplainedinsection3.4.ResearchProcedure.

19

TotalReturn(RollingAnnual%pa)

Date/Period AllProperty Retail Office Industrial BondsJun-05 15.0 17.9 11.4 16.8 5.15

Sep-05 14.9 16.6 12.6 16.6 5.11

Dec-05 15.7 16.1 14.9 17.0 5.31

Mar-06 16.6 16.5 16.8 16.9 5.30

Jun-06 18.4 18.1 19.3 16.3 5.75

Sep-06 19.4 19.0 20.8 16.7 5.83

Dec-06 19.7 19.1 21.3 16.3 5.97

Mar-07 19.8 18.5 21.9 16.4 6.04

Jun-07 19.5 17.6 22.2 15.7 6.39

Sep-07 19.3 16.0 23.2 15.5 6.29

Dec-07 18.4 14.7 22.3 15.2 6.66

Mar-08 15.0 11.8 18.1 12.2 6.21

Jun-08 10.8 8.7 12.6 8.0 6.84Sep-08 5.7 5.2 6.0 3.7 5.48Dec-08 -0.1 0.2 -0.4 -2.1 3.43Mar-09 -3.2 -1.8 -4.0 -6.1 3.20Jun-09 -6.5 -4.1 -8.2 -8.9 4.47Sep-09 -5.4 -2.7 -7.5 -7.6 4.82Dec-09 -2.3 0.9 -5.0 -4.4 4.83Mar-10 1.3 3.7 -1.2 0.8 5.05Jun-10 6.3 7.1 5.1 6.1 4.71Sep-10 7.9 8.6 7.0 7.4 4.70Dec-10 9.4 9.5 9.0 8.8 5.19Mar-11 10.2 10.2 9.8 9.1 5.01Jun-11 10.5 10.6 10.0 9.7 4.76Sep-11 10.5 10.2 10.3 10.0 3.64Dec-11 10.3 9.7 10.3 9.8 3.13Mar-12 10.1 9.3 10.3 10.0 3.66Jun-12 9.9 9.1 10.2 9.6 2.33Sep-12 9.6 9.0 9.9 9.5 2.55Dec-12 9.4 9.1 9.6 9.2 2.69Mar-13 9.2 8.8 9.5 9.5 2.94Jun-13 9.2 8.8 9.4 9.8 2.69Sep-13 9.2 9.0 9.2 10.3 2.90Dec-13 9.2 9.1 9.0 10.9 2.96Mar-14 9.4 9.5 8.9 11.3 2.97

Table3.1:Propertyreturns,foreachassetclass,ineacheconomicconditionGrow

th

Decline

Stab

le

20

3.2.3. ASSETALLOCATION

AssetAllocationistheformationofadiversifiedportfolioutilizingdifferentassetclasses

(Cardona 1998). Asset classes usedwithin this case study are the threemain commercial

sectors;Retail,OfficeandIndustrial.Allocationinvolvesmixingassetweightsofaportfolioto

yieldthemostfavourablerisk/returntrade-off.Portfolioweights inthismodelareeither2

assetportfoliosor3assetportfolios,producingatotalof87differentportfolios.

A2-assetportfoliocontainsonly2assetclasses,i.e.Portfolio‘D’hasaweightingof85%

retail,15%office,0%industrial.3-assetportfolioscontainall3assetclasses,i.e.Portfolio‘XC’

hasaweightingof70%retail,15%office,15%industrial.Theweightingofeachportfoliocan

befoundinTable7.1&7.2inAppendix1.Theseweightsarenottheonlypossibleoptions,if

assetweightingweretobeadjustedby1%betweenportfolios,theremaybethousandsof

possibleweightingmixes.Assetallocationperformancewillbemeasuredonarisk-adjusted

return,primarilythroughaSharperatio.

3.2.4. SHARPERATIO

TheSharperatio is themostwidelyusedmeasureof risk-adjustedreturns in financial

analysis(Lee&Higgins2009).Theratiomeasurestheexcessreturnperunitofrisk,whererisk

ismeasuredbythestandarddeviationoftheexcessreturns(Johnston,Hatem&Scott2013)

andtheexcessreturnisthereturnbeyondtheriskfreerate(i.e.governmentbonds).Ahigh

Sharperatioispreferred.

TheformulaforaSharperatioisasfollow;

𝑆ℎ𝑎𝑟𝑝𝑒𝑅𝑎𝑡𝑖𝑜 = 𝑅𝑝 − 𝑅𝑓𝜎𝑝

Where;

𝑅𝑝 = 𝐴𝑣𝑒𝑟𝑎𝑔𝑒𝑅𝑒𝑡𝑢𝑟𝑛

𝑅𝑓 = 𝑅𝑖𝑠𝑘𝐹𝑟𝑒𝑒𝑅𝑎𝑡𝑒(𝐺𝑜𝑣𝑒𝑟𝑛𝑚𝑒𝑛𝑡𝐵𝑜𝑛𝑑𝑠)

𝜎𝑝 = 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛

21

‘𝜎𝑝?orStandardDeviationisthevariationaroundthemean.Inanormaldistribution,+/-

1standarddeviationfromthemeanreturnsaccountsfor68%(34%abovethemeanand34%

belowthemean)ofallprobableoutcomes,+/-2standarddeviationsaccountsfor95%ofall

probable outcomes and +/-3 standard deviation accounts for 99.7%. In calculating and

analysingtheSharperatio,+/-1standarddeviationisused.InundertakingtheMonteCarlo

simulation,+/-2standarddeviationswereused.

3.2.5. MONTECARLOSIMULATION

TheMonteCarlosimulationmakesuseofrandomnumberstoproduceaprobabilistic

outcome (Byrne 1996). The random numbers are pseudorandom, where the numbers

generated derive from predetermined parameters. The inputs are selected +/-2-standard

deviationsoftheaverageweightedreturnoftheportfolio,representing95%ofallprobable

outcomes.TheMonteCarlosimulationwillenable thedecisionmaker todeterminewhich

portfolio and its corresponding asset allocation weighting, may enhance portfolio

performance.Itwillalsoproducedatathatprovidearangeofefficientportfoliosthatmaybe

plottedalonganefficientfrontier.

3.2.6. EFFICIENTFRONTIER

Theefficientfrontierplotsthesetofportfoliosthatreturnthegreatestyieldperunitof

risk(Peterson2012)basedonacalculatedweightedcombinationofportfolioassets(Higgins

&Fang2012).TheX-Axiscontainstheportfoliorisk;theY-Axiscomprisestheportfolioreturn.

All portfolios that are along the efficient frontier are considered to be themost efficient

returningportfolios relative to the specific risk level (Best 2014). Portfolios locatedwithin

(below)thefrontieraredeemedinefficient,asforthesamelevelofrisktheycontain,agreater

returncanbeachievedthroughaportfolioalongthefrontier.Theportfoliothatoffersthe

lowest possible risk level for a rate of expected return is called theMinimum Variance

Portfolio.

3.3. RESEARCHPROCEDURE

Summarisingtheparticularaspectsoftheprobabilisticmodellinginsection3.2enablesa

comprehensiveunderstandingofhowthesimulationwasundertaken.Thefollowingstepsare

22

howMonte Carlo simulation was utilized to determine if altering asset allocation during

differingeconomicconditions,enhancesportfolioperformance.

Step1.

PropertydatawasextractedfromMSCI:IPDAustraliaDigest.Meanreturns,Variance

andStandardDeviationwereall calculated foreachasset class (retail,office, industrial) in

eacheconomicperiod(growth,decline,stable).

Step2.

AssetAllocationsweightingforeachportfolioweredetermined.Intotal,therewere87

portfolios. Where portfolios contained only 2 asset classes, an asset variance of 5% was

applied,forexample;

• ‘PortfolioA’allocated100%Retail/0%Office/0%industrial

• ‘PortfolioB’allocated95%Retail/5%Office/0%Industrial

• ‘PortfolioC’allocated90%Retail/10%Office/0%Industrial

Where portfolios contained all 3 asset classes, an asset variance of 10%was applied, for

example;

• ‘PortfolioXA’allocated90%Retail/5%Office/5%industrial

• ‘PortfolioXB’allocated80%Retail/10%Office/10%Industrial

• ‘PortfolioXC’allocated70%Retail/15%Office/15%Industrial

Forassetallocationofall87portfolios,refertoAppendix1.

Step3.

Foreachportfolio,theweightedmean-return,weightedrisk(standarddeviation)and

Sharperatiowerecalculated.Theweightedmean-returnwasachievedbymultiplyingeach

assetweightingbyassetreturnintherespectiveperiod.Assuch,theweighted-meanreturn

foragivenportfolioisthesumofallassetweightedreturns.Thefigureswererepeatedfor

eacheconomicperiod.

23

Step4.

Onceassetallocationandrisk/returndatahadbeencomputedbasedonhistoricdata,

the Monte Carlo simulation model was developed. In order to achieve the simulation, a

‘PseudorandomNumberGenerator’producedareturnforeachassetthatwasbetween+/-2

standarddeviationsof themeanasset return,within thateconomicperiod.Thiswas then

weightedwiththecorrespondingassetweightingfortheparticularportfoliotoproducethe

‘SimulationVariables’.

Step5.

TheMonteCarlosimulation,usingthepredetermined‘simulationvariables’,operates

1000iterationsthrougha‘What-IfAnalysis’,amanipulationofinputvariablesinordertoask

what the effectwill be on the output (Forgionne&Russell 2008). The input variables are

constrainedwithintheparametersofstandarddeviation.Thenumberofiterationsthatcan

beruninasimulationareuserspecifiedandcanbeaslittleas1or2orasmanyas1,000,000.

The results of the simulation are recorded as ‘Simulation Output’, which from the 1000

iterations, acquires themean average return,median return,minimum return,maximum

return,standarddeviationandtheSharperatio.Again,aseveryeconomicperiodhasdifferent

returns,itsrepeatedfortherespectiveperiod.

Step6.

Once the simulation has been processed and recorded for each portfolio in each

economic period, the portfolios are ranked accordingly tomean return (return only) and

Sharperatio(returnrelativetorisk).Thisallowsthedecisionmakertoquicklyanalysewhich

portfoliohasthegreatestreturnandwhichportfoliohasthegreatestreturnperunitofriskin

each period. However, it does not allow the decision maker to deem which portfolio is

probabletoachievethegreatestreturnrelativetoinvestorrisktolerance,anefficientfrontier

isusedforthispurpose.

Step7.

Onceallresultshavebeengraphedandaranking/comparisonhasbeencompleted,itis

easytodetermineifalteringassetallocationindifferenteconomicperiodstestedbyMonte

Carlosimulation iseffective inenhancingportfolioperformance.Forexample,thedecision

makercan realise that ‘PortfolioA’has thehighestSharpe ratio in thegrowthperiod,but

changingallocationcomposition,as themarketdeclines, to ‘PortfolioXC’willenhance the

24

portfolioreturnwithminimalrisk.Additionally,theresultsofMonteCarlosimulationcangive

the decision maker an advantage in minimizing the quantity of portfolios to investigate

throughinterpretingthedataappropriately.

3.4. CONCLUSION

Once the simulation model was created and the user was equipped with the

understandingandprocessofapplication,thealterationofthemodeltosuitmanyparticular

purposesissimplistic.Themodelcandeterminetheoptimalportfolioassetallocationsineach

economiccycle,orwhichportfoliostofurtheranalysewithouttheneedtocomprehensively

analyse eachoption. Themodels accuracy is subject to ensuring thedatausedwithin the

simulation is reliable.With falsified or flawed data, themodel will produce an unreliable

outputthatdecisionsshouldnotbebasedupon.

The model answered the research question, as found in the following chapter, that

altering asset allocation, based onMonte Carlo simulation, in differing economic periods,

enhancedportfolioperformancethroughdeliveringtheportfoliosandtheirassetallocation

weightsthatcontainthehighestrisk-adjustedreturns.Iftheuserwishestousethemodelfor

forecastedreturns,step1needbeforecastedreturndata,ratherthanhistoricdataandthe

samestepsmaybefollowed.

25

4. ANALYSISOFDATA

4.1. INTRODUCTION

Quantitativedataanalysisistheexpressionofaproblemusingmathematicalformulation

andthenmeasuringorestimatingvariablesinthecreatedmathematicalconstruct(Forgionne

&Russell2008).Thequantitativedataanalysedwilllookattheperformanceoftheproperty

marketandtheassetsectorineachrespectiveperiod.Itwillincludeacomparativeanalysis

ofassetallocationbetweenportfoliosandbetweeneconomicperiodstodetermineifusing

Monte Carlo simulation to determine asset allocation during different economic periods,

enhancesportfolioperformance.

Thestructureofthischapterwillanalysethepropertyreturnsineacheconomicperiod

and will provide the top ranking, risk-adjusted portfolios prior and post Monte Carlo

simulation.Priortothesimulation,thetopportfoliosarerankedbydeterministicmodeling

wherenorandomnessisinvolvedandthemodelwillalwaysproducethesameoutputfrom

the initial conditions. Post Monte Carlo simulation, the top portfolios are ranked by the

outputs of the simulation,where randomness has been included and the outputs are the

‘mostlikely’returnsafter1000iterationswithinthemodelparametershasbeenconducted.

ThisprovidesananalysesofhowMonteCarlosimulation,asatool,canenhanceportfolio

performance.ThereturnspostMonteCarlosimulationoffereddifferentassetallocationsthan

prior.PostsimulationconsistedofportfoliosthatcontainedhigherSharperatiosandhigher

risk-adjustedreturns.

4.2. ANALYSISOFDATA

4.2.1. PROPERTYRETURNS

Propertyrisk-adjustedreturnswithineacheconomicperioddifferedsignificantly.Ineach

economicperiod,thereisoneassetclassthatoutperformsthemarket(AllProperty)andeach

asset class takes turns in offering superior absolute returns than the other classes. These

returnscanbeseenbelowinTable4.1.

26

PropertyReturns

Period AllProperty Retail Office Industrial Bonds

Growth(June’05–Mar’08) 17.65% 16.83% 18.73% 15.98% 5.83%

Decline(June’09–Mar’11) 2.83% 3.78% 1.94% 1.22% 4.81%

Stable(June’11–Mar’14) 9.72% 9.35% 9.73% 9.98% 3.10%

Inthe‘Growth’period,fromJune‘05toMarch‘08,totalpropertyassetsreturned17.65%,

reachingapeakreturnof19.80%inMarch2007.The‘Office’sectorwaspreeminentwitha3-

yearannualizedreturnof18.73%,reaching23.20%atitshighestinSeptember2007.Retail

followed,witha3-yearannualizedreturnof16.83%andIndustrialreturning15.98%overthe

sameperiod.

OncethemarketenteredintodecliningstatusfromJune’08toMarch‘11,theretailsector

surpassed office sector considerablywith a 3.78% return, comparative to office returning

1.94%.Theretailsectoroutperformedtherealestatemarket,whichreturnedatotal2.83%.

However,meanreturnsdonotdepicttheperiodappropriately.Atthetroughofthecycle,

assetswerelosingmoney,withtheindustrialsectorexperiencingthepoorestperformance,

returning as low as -8.9% in June ‘09. In such volatile conditions, returns alone are poor

indicatorsforportfoliodecisionmakingandfactoringriskthroughstandarddeviationsareas

importantasthereturn,ifnotmoreimportant.

InJune’11,thepropertymarketstabilizedwitheachassetsectorprovidingsimilarreturns

(SeeTable3.1). Importantly in thisperiod, volatility (risk)wasat its lowestover the three

various periods,meaning that the returns over the entire 3-year periodwere stablewith

minimumvariancebetweenannualreturns.

ItisapparentwithinFigure4.1thatthemarkettookadownwardsshift,experiencingthe

mostdifficultperiodbetweenJune’08-March’11.Fromthere,themarketstabilizedwith

littleincreaseordecreaseintotalreturnsandcomparativereturnsbetweenassetclasses.The

variancewithintheassetclassthroughthedifferingeconomicperiodsistheprimaryinterest

inassetallocation.AscanbeseeninFigure4.1,oneassetclassdidnotdrasticallyoutperform

theothersthroughouttheentiremarketcyclee.g.officereturnssignificantlyoutperformed

retailandthemarketintheGrowthphase,howeverexperiencedunderperformancetoboth

Table4.1:Meanpropertyreturnsbysector,ineacheconomicperiod

27

-15.00%

-10.00%

-5.00%

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

June

-2005

Octob

er-2005

February-2006

June

-2006

Octob

er-2006

February-2007

June

-2007

Octob

er-2007

February-2008

June

-2008

Octob

er-2008

February-2009

June

-2009

Octob

er-2009

February-2010

June

-2010

Octob

er-2010

February-2011

June

-2011

Octob

er-2011

February-2012

June

-2012

Octob

er-2012

February-2013

June

-2013

Octob

er-2013

February-2014

AllProperty Retail Office Industrial Bonds

Growth StableDecline

retailandthemarketthroughoutthedecline.Thisiswheretacticalallocation,tooverweight

the investors position in the best performing asset class through different economic

conditions,byprobabilisticmeans,willenhanceportfolioperformance.

4.2.2. GROWTHPERIOD

In the ‘Growth’ period, itwas noticeable inTable 4.2 that the office sector provided

superiorresultsthantheothers.However,fromarisk/returnmeasure,theofficesector,due

toitslargerstandarddeviation,hadhigherriskandalowerSharperatioof3.218comparative

toRetailandOffice.

Relative to investor expectations, a Sharpe ratioof >1 is consideredacceptable, >2 is

consideredverygoodand>3inconsideredexcellent.FromevaluationofaSharperatio,all

assetreturnsareconsideredexcellentandthejudgementtopursuesuperiorreturnsis left

withthedecisionmaker.

Figure4.1:PropertyReturnsfromJune2005toMarch2014

28

Growth-TotalReturn(%),3yearAnnualised

Retail Office Industrial Bonds

ExpectedReturn 16.83% 18.73% 15.98% 5.83%

Variance 4.30% 16.05% 1.74% 0.27%

StandardDeviation 2.07% 4.01% 1.32% 0.52%

SharpeRatio 5.300 3.218 7.694 N/A

GiventhatOfficehassuperiorreturns,beingoverweightintheOfficesectorthroughan

asset allocation of R:0%/O:100%/I:0% during a growth period would deem to offer the

greatest return. Conversely this is not optimal and does not conform with the logic of

diversification,nordoesitproduceahighrankingSharperatio.

Table4.3belowdisplaystheTop6portfolios,rankedbySharperatio. Indeterministic

modeling,thesearethetop6portfoliosthatproducethehighestSharperatio.Astheyare

deterministic,theydonotprocessarangeofpossibleoutcomeswithinthevarianceofthe

portfolio.These rankingscanbecompared to the rankingsofportfoliosafterMonteCarlo

simulation,foundinTable4.4.

Top6Portfolios,bySharpeRatio

Portfolio AssetAllocation Portfolio

Risk

Portfolio

Return

Sharpe

Ratio

Sharpe

RankRetail Office Industrial

BA 0% 0% 100% 1.32% 15.98% 7.694 1

BB 5% 0% 95% 1.36% 16.02% 7.511 2

BC 10% 0% 90% 1.39% 16.06% 7.338 3

BD 15% 0% 85% 1.43% 16.11% 7.174 4

AT 0% 5% 95% 1.45% 16.12% 7.077 5

BE 20% 0% 80% 1.47% 16.15% 7.018 6

Table4.2:Outputdataofpropertyreturnsin‘Growth’Period

Table4.3:DeterministicmodelRanking,in‘Growth’period,bySharperatio

29

Asdeterministicmodeling iscommonlyusedwhereparametersarecertain, it isoften

notapplicableforinvestmentmodeling,asnothingiscertain.Theapplicationofprobabilistic

modeling,i.e.MonteCarlosimulation,isthoughttoaddressthisissue.

Once the simulation for thegrowthperiodwasprocessed, comparing resultsofboth

models,nosingleportfolioinTable4.3wasconsideredasanoptimalassetallocationmixthat

wouldenhanceportfolioperformance.Table4.4belowspecifiesthetop6optimalportfolios

by Sharpe ratio that enhanceportfolio performancewithin the growthperiod.After 1000

iterations,portfolio‘ZC’ismostprobabletoreturn16.57%withalowerriskandhigherSharpe

ratiothanthehighestrankedportfoliousingadeterministicmodel(Table4.3).

Noticeably, assets with high weighting in the office sector are not significantly

representedineithermodels,asportfoliosheavilyweightedwithinthisassetareassociated

higherriskthatisnotoutweighedbyhigherreturns,correspondingtolowerSharperatios.

Portfolio‘ZC’isconsideredtoproduce,onaverage,thegreatestreturnperunitofrisk.

Forexample,68%(+/-1standarddeviationor ‘portfoliorisk’)ofallprobableoutcomesare

likelytobebetween15.25%-17.88%,comparativetoportfolio‘BA’inTable4.3,asingle-value

estimate,producedameanreturnof15.98%and68%ofpossibleoutcomesbetween14.66%

-17.30%.

Whilsthigherabsolutereturnsmaybeachieved,inanilliquidinvestmentmarketthatis

realestate,thedecisiontopursuehigherreturnattheexpenseofincreasedriskisacritical

Top6Portfolios,bySharpeRatio

PortfolioAssetAllocation Portfolio

Risk

Portfolio

Return

Sharpe

Ratio

Sharpe

RankRetail Office Industrial

ZC 15% 15% 70% 1.31% 16.57% 8.172 1

BG 30% 0% 70& 1.28% 16.27% 8.130 2

ZB 10% 10% 80% 1.31% 16.34% 8.021 3

BH 35% 0% 65% 1.31% 16.25% 7.963 4

YI 45% 10% 45% 1.37% 16.70% 7.915 5

BF 25% 0% 75% 1.31% 16.17% 7.859 6

Table4.4:MonteCarlosimulationranking,in‘Growth’period,bySharperatio

30

decision.Ifaninvestorwishestoincreasetheirrisktolerancetopursuehigherreturns,the

portfolioslocatedalongefficientfrontierarethemostefficientportfolios,perunitofriskata

givenreturn.Figure4.2belowdemonstratestheefficientfrontierofallportfolioswithinthe

‘Growth’ period. If the investor was ‘risk seeking’, portfolio ‘T’ is probable to return, on

average,18.87%with1standarddeviationintherangeof14.47%-23.27%.

These results indicate that Monte Carlo simulation was effective in enhancing

portfolioperformancebyoptimizingassetallocationthatprovidedhigherrisk-adjustedreturn

&SharperatioswhilstalsoprovidingefficientportfoliosalongthefrontierinFigure4.2that

offeredhigherreturnsperunitofrisk.

4.2.3. DECLINEPERIOD

Inanalysingthe‘Decline’periodinsimilarformtothe‘Growth’period,Retailproved

to be the best performing sector, outperforming all asset classes and the total property

market.However,unlikeoffice in the ‘Growth’period, italsoexhibitedthehighestSharpe

ratio,meaningonaverage,itproducedthehighestreturns,withthelowestrisk.

TP

L

ZI

XE

ZE

ZCBG

BC

14.00%

15.00%

16.00%

17.00%

18.00%

19.00%

20.00%

0.00% 0.50% 1.00% 1.50% 2.00% 2.50% 3.00% 3.50% 4.00% 4.50% 5.00%

Return

RiskFigure4.2:EfficientFrontierofPortfoliosin‘Growth’period.

31

Decline-TotalReturn(%),3yearAnnualised

Retail Office Industrial Bonds

ExpectedReturn 3.78% 1.94% 1.22% 4.81%

Variance 26.37% 51.72% 46.22% 0.86%

StandardDeviation 5.14% 7.19% 6.80% 0.93%

SharpeRatio -0.201 -0.399 -0.527 N/A

Giventhesituationofhighestreturnandlowestrisk,beingheavilyweightedinthis

assetclassislikelytoconformtosuperiorportfolioperformance.Table4.6,belowdepictsthe

top 6 portfolios in the ‘decline’ period prior to probabilistic modeling. All being heavily

weightedin‘Retail’

UsingDeterministicmodeling,PortfolioRiskofall6portfoliosmaybeskewed ina

marketdownturn.Regardless,astheSharperatiosare<1,theprobabilisticoutcomeforevery

portfolio,isnotsatisfactory.However,inanunstablemarket,itmaybemoreappropriateto

examineSharperatiosrelativetomarketconditionsandnotasabsolutefigures.

Monte Carlo simulation produced (refer Table 4.7), after 1000 iterations, a risk

associatedwithportfolio ‘B’ thatwas less thanestimated in thedeterministicmodel. This

indicatedthattheportfolioriskassociatedwithportfolio‘B’islikelytobelessthanassumed

throughdeterministicmodeling,whichprovidesnorandomnessinitsestimation.Asaresult,

portfolio‘B’offersahigherrisk-adjustedreturn/SharperatioafterMonteCarlosimulation.

Top6Portfolios,bySharpeRatio

PortfolioAssetAllocation Portfolio

Risk

Portfolio

Return

Sharpe

Ratio

Sharpe

RankRetail Office IndustrialA 100% 0% 0% 5.14% 3.78% -0.201 1

B 95% 5% 0% 5.24% 3.69% -0.214 2

BT 95% 0% 5% 5.22% 3.65% -0.222 3

C 90% 10% 0% 5.34% 3.59% -0.228 4

XA 90% 5% 5% 5.32% 3.56% -0.235 5

D 85% 15% 0% 5.44% 3.50% -0.240 6

Table4.5:Outputdataofpropertyreturnsin‘Decline’Period

Table4.6:DeterministicPortfolioRanking,in‘Decline’period,bySharperatio

32

However,portfolio‘D’,the6thrankedportfolioinbothmodels,hadgreaterriskthan

estimatedinthedeterministicmodel,signifyingthatthereisahigherriskassociatedwiththe

portfolio,revealedthroughasmallerSharperatio.

Contrarytodiversificationtheory, themostprobablepositiontoenhanceportfolio

performanceisportfolio‘B’or100%allocationtoretail.From1000iterations,MonteCarlo

simulationproducedameanportfolio returnof 3.73%.Within those iterations, therewas

downsiderisk(-1std.dev.)thattheportfoliomaylose,-2.00%overtheperiod.Theupside

mean-return(+1std.dev.)oftheperiodwas9.45%.

ProbabilisticReturnRange,2standarddeviations

Portfolio Mean Minimum Maximum

B 3.73% -2.00% 9.45%

A 3.69% -2.17% 9.55%

BS 3.63% -1.70% 8.96%

C 3.48% -1.94% 8.89%

XA 3.43% -2.12% 8.98%

D 3.51% -1.55% 8.56%

Top6Portfolios,bySharpeRatio

Portfolio AssetAllocation Portfolio

Risk

Portfolio

Return

Sharpe

Ratio

Sharpe

RankRetail Office IndustrialB 95% 5% 0% 5.73% 3.73% -0.189 1

A 100% 0% 0% 5.86% 3.69% -0.191 2

BS 90% 0% 10% 5.33% 3.63% -0.221 3

C 90% 10% 0% 5.41% 3.48% -0.246 4

XA 90% 5% 5% 5.55% 3.43% -0.248 5

D 85% 15% 0% 5.06% 3.51% -0.258 6

Table4.7:MonteCarlosimulationranking,in‘Decline’period,bySharperatio

Table 4.8: Mean-Return range of optimal portfolios, in

‘Decline’period

33

ThisiswhereMonteCarlosimulationmaysubstantiallyenhanceportfolioperformance.

Often,whentheinvestingsentimentisnegative,asinamarketdownturn,diversificationis

oftenusedasanimportanttooltomitigateriskinarealestateportfolio(Coleman&Mansour

2005). Monte Carlo simulation, as presented here, shows that diversification offers little

advantage of risk reductionwhen there is systematic ormarket risk (Viezer 2000). It also

provides realisticmeasure of risk associatedwith portfolio selection, where as previously

mentioned,canbepositivelyornegativelyskewedbydeterministicmodeling.

Theefficientfrontier,asshownbelowinFigure4.3,indicatesthatportfolio‘B’isthemost

efficient portfolio for the specified unit of risk. If an investor is risk averse, theminimum

varianceportfolioisportfolio‘XE’(R:50%/O:25%/I:25%),providingamorediversifiedportfolio

thattolerateslessvarianceinoverallrisk,althoughwhilstprovidinglowerabsoluterisk,has

moreriskperunitofreturncomparedtoportfolio‘B’.

Similarly, to the previous ‘Growth’ period, Monte Carlo simulation provides the

opportunitytoenhanceportfolioperformancebyselectingtheportfolio(portfolio ‘B’)that

offersthehighestrisk-adjustedreturn.Theassetallocation,bothpreandpostMonteCarlo

simulation is heavilyweightedwithin theRetail sector, emphasizing that overweighting in

Retailistheoptimalassetclasstoenhanceportfolioperformance.

BBSDE

XC

XE

XGYH

0.00%

0.50%

1.00%

1.50%

2.00%

2.50%

3.00%

3.50%

4.00%

4.50%

0.00% 1.00% 2.00% 3.00% 4.00% 5.00% 6.00% 7.00%

Return

RiskFigure4.3:EfficientFrontierofPortfoliosin‘Decline’period.

34

4.2.4. STABLEPERIOD

Allassetclassesinthe‘Stable’periodproducedcomparablerisk/returnoutputs,without

one asset class significantly outperforming another. Each asset class produced very high

Sharperatiosthatyieldexcellentinvestments.Thesevaluesarearesultofbylowgovernment

bondratesandhighriskpremiumsinalowriskmarket.Portfolioselectioninthisperiodis

likely to contain a positive return, regardless of decision. For the purpose of enhancing

portfolioperformance,MonteCarlosimulationwasusedtodeterminewhichassetallocation

weightingwillprovidesuperiorSharperatio.

Stable-TotalReturn(%),3yearAnnualised

Retail Office Industrial Bonds

ExpectedReturn 9.35% 9.73% 9.98% 3.10%

Variance 0.31% 0.27% 0.37% 0.43%

StandardDeviation 0.56% 0.52% 0.61% 0.65%

SharpeRatio 11.226 12.816 11.343 N/A

After examining the output data for total return in Table 4.9, the top 6 performing

portfolios, by deterministicmodeling, are heavilyweighted in the industrial sector. These

portfoliosinTable4.10,aswithinthepreviousperiods,aremeanaveragefromarangeofdata

inputs,andnotthemostprobableaveragefoundthroughMonteCarlosimulation.

Top6Portfolios,bySharpeRatio

PortfolioAssetAllocation Portfolio

Risk

Portfolio

Return

Sharpe

Ratio

Sharpe

RankRetail Office IndustrialAA 0% 100% 0% 0.52% 9.73% 12.816 1

T 5% 95% 0% 0.52% 9.71% 12.731 2AB 0% 95% 5% 0.52% 9.74% 12.731 3AC 0% 90% 10% 0.53% 9.75% 12.646 4

S 10% 90% 0% 0.52% 9.69% 12.646 5YA 5% 90% 5% 0.52% 9.72% 12.646 6

Table4.9:Outputdataofpropertyreturnsin‘Stable’Period

Table4.10:DeterministicPortfolioRanking,in‘Stable’period,bySharpeRatio

35

As all asset sectors have very similar mean-returns and Sharpe ratios, Monte Carlo

simulationwas able to weight asset allocation evenly across all sectors to determine the

maximum return for the minimum risk. The results, like the former periods, produced

portfolios that were opposed to the deterministic model. 3-asset class portfolios

outperformed all 2-asset class, reflecting true diversification theory. This is different than

othereconomicperiods,whereoneassetclasshasofferedasignificantoutperformanceand

topperformingportfolioscomprisedof2-assetclasses.

ThetopperformingportfolioafterMonteCarlosimulation,bySharperatio,isportfolio

‘YF’.Portfolio‘YF’returns0.21%lessthanPortfolio‘AA’inthedeterministicmodel,though

portfolio ‘YF’ carries 33.71% lessportfolio risk. The topperforming Sharpe ratioportfolios

after1000iterationsofprobabilisticmodelingarebelowinTable4.11.

Theefficientfrontierbelow(Figure4.4)indicatesthatifahigherreturnissought,portfolio

‘AQ’isthemostefficientportfoliotodoso.Itisprobablethatitwillreturn9.98%,thoughit

carriesahigherunitofriskforreturnthantheminimum-varianceportfolio(portfolio‘ZH’).As

portfolio‘XD’isbelowtheminimumvarianceportfolioontheefficientfrontier,thusforless

portfoliorisk,ahigherreturncanbeachievedinportfolio‘ZH’.Thisiswhatisknownasan

inefficientportfolio.

Top6Portfolios,bySharpeRatio

Portfolio AssetAllocation Portfolio

Risk

Portfolio

Return

Sharpe

Ratio

Sharpe

RankRetail Office Industrial

YF 30% 40% 30% 0.37% 9.71% 17.740 1

ZG 35% 35% 30% 0.37% 9.67% 17.722 2

ZH 40% 40% 20% 0.37% 9.62% 17.716 3

XG 30% 35% 35% 0.37% 9.72% 17.711 4

YE 25% 50% 25% 0.38% 9.71% 17.585 5

XF 40% 30% 30% 0.38% 9.66% 17.412 6

Table4.11:MonteCarlosimulationranking,in‘Stable’period,bySharperatio

36

AQ

AL

XI

XG

ZH

XD

9.30%

9.40%

9.50%

9.60%

9.70%

9.80%

9.90%

10.00%

10.10%

0.00% 0.10% 0.20% 0.30% 0.40% 0.50% 0.60%

Return

Risk

4.3. SUMMARY,DISCUSSIONANDMAINFINDINGS

UsingMonteCarlosimulationenabledustoverifythatalteringassetallocation,during

differing economic conditions, enhancing portfolio performance. Monte Carlo simulation

used1000iterationsofpossibleoutcomestodeterminethemostprobableoutputs(portfolio

return,portfoliorisk&Sharperatio)ofeachportfolio.Theuseofapseudorandomprocess

generatesamorecompellingmodel.

The findingswithin the researchareextensive. Theportfolios thatoffered thehighest

absolutemean-return(oftenwithhigherrisk),wereinefficientonreturnperunitofrisk.That

is,fortheincreasedriskassociatedwiththeinvestment,thereturnofferedincompensation

wasinefficient.Theabsolutemean-returnsonadeterministicmodelwerefrequentlysimilar

to the returns from probabilistic modeling, meaning that the Monte Carlo simulation is

somewhataccurate inforecastingthemostprobablereturnandcanprovideconfidence in

decisionmaking.However,MonteCarlowas also able to determine asset allocations that

weremostlikelytoproducehigherSharperatios.

Figure4.4:EfficientFrontierofPortfoliosin‘Stable’period.

37

Diversification among 3-asset classes had inefficient Sharpe ratios in twoout of three

economicperiods.Resultsinthe‘Growth’and‘Decline’periodindicatebeingoverweightin

anoutperformingassetsectoroftenproducesagreaterreturnwithlessriskthandiversifying

acrossall 3asset classes. It isonly in the ‘Stable’periodwhereportfolio risk inall 3asset

classes had similar (and low) risk, that a 3-asset class portfolio enhanced portfolio

performance.Thisisanimportantfindingfortacticalassetallocation.

Undoubtedly,alteringassetallocationdoesenhanceportfolioperformance,howeverthe

discussionpointtakenfromthisresearchis,cantheseoptimalassetallocationsthatenhance

portfolioperformance,beobtainedthroughsimplistic/deterministicmodeling?Theseresults

indicatethatMonteCarloprovidesmorerealisticoutputs.

The table above (Table 4.12) shows that the Sharpe ratios associated with the most

probableoutcomeinprobabilisticmodeling(MonteCarlosimulation)outperformstheresults

from deterministic modeling in every economic condition, thus making asset allocation

decisions based on probabilistic modeling likely to significantly enhance portfolio

performance.

An important consideration in diversification strategies is that “whilst theoretically

diversification iscost free, inrealitythiscertainly isn't thecase.Therearecostsassociated

withoptimallydiversifyingaportfolioincludinghardcostsofdeveloping,implementingand

monitoring diversification schemes, along with opportunity costs resulting from changing

DeterministicvsProbabilisticComparison

Model PortfolioAssetAllocation Portfolio

ReturnPortfolioRisk

SharpeRatioRetail Office Industrial

GrowthPeriod

Deterministic BA 0% 0% 100% 15.98% 1.32% 7.694

Probabilistic ZC 15% 15% 70% 16.57% 1.31% 8.172

DeclinePeriod

Deterministic A 100% 0% 0% 3.78% 5.14% -0.201

Probabilistic B 95% 5% 0% 3.73% 5.73% -0.189

StablePeriod

Deterministic AA 0% 100% 0% 9.73% 0.52% 12.816

Probabilistic YF 30% 40% 30% 9.71% 0.37% 17.740

Table4.12:ComparisonofbestperformingportfoliosinDeterministic&Probabilisticmodels

38

market conditions and reduced flexibility of capital deployment” (Fisher & Liang 2000).

Therefore,thecostsassociatedwithbuying,sellingandleasingrealestatemustbemeasured.

39

5. CONCLUSION

5.1. INTRODUCTION

Theobjectiveofthisthesisstudywastogainanunderstandingontheapplicabilityand

implementationofMonteCarlosimulationinrealestateinvestment,specifically,whetherit

canenhanceportfolioperformancethroughalteringassetallocation.Throughtheliterature

review, a broad understanding of Monte Carlo simulation was attained and its

(non)implementationwithintherealestateindustry.Tacticalassetallocationwasconsidered

tobeapplicabletoMonteCarlosimulationtodirectdiversificationstrategies.

5.2. CONCLUSIONONRESEARCHQUESTIONS

This research concludes thatportfolioperformance canbeenhancedby alteringasset

allocation, during different economic conditions, based on Monte Carlo simulation. The

hypothesiswasconsideredvalidasMonteCarlosimulationrepeatedlyproducedportfolios

thathadgreaterSharperatiosandoutperformeddeterministic,orsingle-valuemodeling.This

meantthatportfoliosrankedthehighestafterprobabilisticmodeling,arelikelytoprovidea

greater returnperunitof risk,orhave less riskperunitof return than thehighest ranked

portfoliosafterdeterministicmodeling.

Producing portfolios with greater Sharpe ratios signifies that certain asset allocations

mixescanenhanceportfolioperformance.Changingtheportfoliopositionineacheconomic

periodthroughthetacticaladjustmentofassetallocationweighting,ratherthanremaining

staticinoneportfolioovertheentireeconomiccycle,willsignificantlyenhancerisk-adjusted

returns.

5.3. CONCLUSIONABOUTRESEARCHPROBLEM

Thecasestudyarguesthatusingprobabilisticmodelinggivesabetterrepresentationof

actual,ormostprobable return.Theprincipleof ‘lawof largenumbers’ states thatas the

samplesizegrowsorthefrequencyofeventsincreases,themean-averagewillrepresentthe

40

mostprobableoutcome.Thus,themean-averageofaportfolioreturnusingthedeterministic

maybea‘oneoff’andthemostprobablemean-averageislikelythemean-averageproduced

byMonteCarlo simulation. Theproblemwithdeterministicmodeling is that it uses single

valueparametersintheinitialconditions.Iftheconditionsdochange,theestimateislikely

becomeinvalid.ContrastedtoMonteCarlosimulation,ifconditionsdochange,itisunlikely

tosignificantlyaffect theoriginalestimate,as theoriginalestimatewas themean-average

basedoff1000possibleestimates.

5.4. IMPLICATIONSTOPRACTICE

The implication to industrypractice, is that the inclusionofMonteCarlo simulation in

decisionmakingtoolscansubstantiallyenhanceriskmanagement.Asmentionednumerous

timesthroughthestudy,usingasingle-pointaveragedoesnotreflectrealworldconditions,

asusingaformofpseudo-randomnesscan.EvenifMonteCarlosimulationdoesnotreturn

valuesthataredifferentfromsingle-pointmean-averages,itgivesconfidencetothedecision

maker that they have theoretically based their average off 1000 possible outcomes. The

decisionmakercanincreasetheamountofiterationstoanendlessextentandincreasethe

principlesof‘lawoflargenumbers’.

Aspropertyandinvestmentmarketscontinuetoconstrictlargereturnsor‘easygains’and

selectingtherightinvestmentorassetallocationbecomesincreasinglyimportant,thereisno

practical reason (given the decision maker has understanding of model context and

application)not to implementMonteCarlo simulation in investmentanalysis anddecision

making.Riskmanagementisbecominginherentlyimportant.

5.5. LIMITATIONS

The limitations of usingMonte Carlo simulation is within the data. The data used in

modelingmustbereliableanddeemedtohaveahighpercentageofforecastedaccuracy.If

parameterssetforpseudorandomareinaccurate,themodelwillreflectthisinaccuracyand

theoutput/estimatesarenotreliable.

Inthiscasestudy,historicdatawasusedforeaseofmodelling,gainingforecasteddata

for3differingeconomicperiodsalongwithforecasteddataforeachassetclassoverthose

41

periodswasinefficientforthetimeframeallocatedtocompletethisstudy.Inexperiencewith

MonteCarlosimulationpriortothisstudyresultedinsignificanttimelearninganddeveloping

themodelandlimitedtimeextractinginformationfromthemodel.Ifmoretimewasallocated

toextractingtheinformation,amorecomprehensiveanalysismayhavebeenconducted.

Allocation Variance may also limit the possibility to further enhance portfolio

performance.Inthisstudy,all2-assetportfolioshadavarianceof5%(ReferAppendix1,Table

7.1), i.e.Portfolio ‘A’allocatedR:100%/O:0%/I:0%,Portfolio ‘B’allocatedR:95%/O:5%/I:0%

etc.3-Assetportfolioshadavarianceof10%.Ifvariancewasreduced,wouldassetallocation

produceevenfurtherenhancementandwouldtheportfoliorankingschange?

5.6. FURTHERRESEARCH

Related to the limitations of the study, further research may be conducted with the

application of Monte Carlo simulation with forecasted data. Compiling appropriate and

reliabledatawouldtakeconsiderabletime,howeverifonehasaccess,itwouldbeinteresting

tooperatethemodelandrecordtheactualreturnstodeterminehowaccurateMonteCarlo

simulationwasinforecastingthemostprobableriskandreturn.

Researchmaybeconductedinthesizeofassetvariancewithinallocationweightings.If

asset variance was reduced, i.e. R:97.5%/O:1.25%/I:1.25%, would those portfolios with

smaller variance offer superior Sharpe ratios and further enhance portfolio performance?

Whatistheoptimalassetvariance?

ResearchontheapplicabilityofMonteCarlosimulationcanalsobefocusedongeographic

locationoftheassetratherthanAssetclass,i.e.Office:SydneyCBDvsOffice:MelbourneCBD.

Theamountofportfolio iterationsmaybe increasedordecreased todetermine if running

moreiterationsimprovestheaccuracyofoutputdata.

Finally,atheoreticalcasestudyusingmonetaryvalueswouldbeinterestingtodetermine

the final financial positions using the differentmodels (deterministic vs probabilistic) and

different asset allocation in the differing economic conditions.Would the outcomeof the

formerstudyaddtotheconclusionofthisstudy?Thismaybedeterminedbyanincreaseor

42

decreaseon,forexample,a$10millionpropertyportfoliousingdifferentassetallocationsin

thedifferenteconomicperiods.

43

6. BIBLIOGRAPHY

Amenc, N, Goltz, F, Martellini, L & Milhau, V 2011, 'Asset Allocation and PortfolioConstruction',inTheTheoryandPracticeofInvestmentManagement,JohnWiley&Sons,Inc.,pp.159-203.

Anson,M2004,'StrategicversusTacticalAssetAllocation',JournalofPortfolioManagement,vol.30,no.2,pp.8-22.

Best,MJa2014,Portfoliooptimization,Chapman&Hall/CRC.Byrne,PJ1996,Risk,uncertaintyanddecision-makinginpropertydevelopment,2nded.edn,

Spon,LondonMelbourne.Cardona,JC1998,'TheAssetAllocationDecision',ABABankingJournal,vol.90,no.2,p.94.Chong, J & Phillips, G 2014, 'Tactical Asset Allocation with Macroeconomic Factors', The

JournalofWealthManagement,vol.17,no.1,pp.58-69,7.Coleman,M&Mansour,A2005,'RealEstateintheRealWorld:DealingwithNon-Normality

andRiskinanAssetAllocationModel',Journalofrealestateportfoliomanagement,vol.11,no.1,pp.37-53.

Detemple, JB, Garcia, R & Rindisbacher, M 2003, 'A Monte Carlo Method for OptimalPortfolios',TheJournalofFinance,vol.58,no.1,pp.401-46.

Faff,R,Gallagher,DR&Wu,E2005,'TacticalAssetAllocation:AustralianEvidence',AustralianJournalofManagement,vol.30,no.2,pp.261-82.

Fisher, JD & Liang, Y 2000, 'Is sector diversification more important than regionaldiversification?',RealEstateFinance,vol.17,no.3,pp.35-40.

Forgionne,G&Russell,S2008,UnambiguousGoalSeekingThroughMathematicalModeling.Froot, K, Scharfstein, D & Stein, J 1993, 'Risk Management: Coordinating Corporate

InvestmentandFinancingPolicies',JournalofFinance,vol.48,no.5,p.1629.Higgins, D & Fang, F 2012, 'Analysing the Risk and Return Profile of Chinese Residential

PropertyMarkets',PacificRimPropertyResearchJournal,vol.18,no.2,pp.149-62.Johnston, K, Hatem, J & Scott, E 2013, 'A note on the evaluation of long-run investment

decisionsusingthesharperatio',JournalofEconomicsandFinance,vol.37,no.1,pp.150-7.

Lee, S & Higgins, D 2009, 'Evaluating the Sharpe Performance of the Australian PropertyInvestmentMarkets',PacificRimPropertyResearchJournal,vol.15,no.3,pp.358-70.

Males,R&Melby,J2011,'MonteCarlosimulationmodelforeconomicevaluationofrubblemound breakwater protection in Harbors', Selected Publications from ChineseUniversities,vol.5,no.4,pp.432-41.

MSCI2016,AssetClass:RealEstate,viewed01/04/20162016,<https://www.msci.com/real-estate>.

Mueller, GR 1993, 'Refining Economic Diversification Strategies for Real Estate Portfolios',JournalofRealEstateResearch,vol.8,no.1,p.55.

Mueller, GR & Ziering, BA 1992, 'Real Estate Portfolio Diversification Using EconomicDiversification',JournalofRealEstateResearch,vol.7,no.4,p.375.

Peterson,S2012,InvestmentTheoryandRiskManagement,Wileyfinanceseries,Wiley,NewYork.

Pyhrr,SA1973,'AComputerSimulationModeltoMeasuretheRiskinRealEstateInvestment',RealEstateEconomics,vol.1,no.1,pp.48-78.

Rowland,P2010,AustralianPropertyInvestmentandFinancing,LawbookCo,Sydney.Seiler,MJ,Webb, JR&Myer, FCN 1999, 'Diversification Issues in Real Estate Investment',

JournalofRealEstateLiterature,vol.7,no.2,pp.163-79.

44

Sing,TF&Ong,SE2000,'AssetAllocationinaDownsideRiskFramework',Journalofrealestateportfoliomanagement,vol.6,no.3,pp.213-24.

Souza,LA2014,'ModernRealEstatePortfolioManagement(MREPM):ApplicationsinModernand Post-Modern Real Estate Portfolio Theory (MREPT/PMREPT)', D.B.A. thesis,GoldenGateUniversity.

Thomopoulos,NT2013,EssentialsofMonteCarloSimulation:StatisticalMethodsforBuildingSimulationModels,StatisticalMethodsforBuildingSimulationModels,SpringerNewYork:NewYork,NY,NewYork,NY.

Viezer,TW1999,'ConstructingRealEstateInvestmentPortfolios:HowtoUseModelsandaFewToolstoBuildaDiversePortfolio',BusinessEconomics,vol.34,no.4,pp.51-8.

---- 2000, 'Evaluating "within real estate" diversification strategies', Journal of real estateportfoliomanagement,vol.6,no.1,pp.75-95.

45

APPENDIX1:

2ASSETCLASSPORTFOLIO

Portfolio AssetVariance 5% Retail Office Industrial Total

A 100% 0% 0% 100%

B 95% 5% 0% 100%

C 90% 10% 0% 100%

D 85% 15% 0% 100%

E 80% 20% 0% 100%

F 75% 25% 0% 100%

G 70% 30% 0% 100%

H 65% 35% 0% 100%

I 60% 40% 0% 100%

J 55% 45% 0% 100%

K 50% 50% 0% 100%

L 45% 55% 0% 100%

M 40% 60% 0% 100%

N 35% 65% 0% 100%

O 30% 70% 0% 100%

P 25% 75% 0% 100%

Q 20% 80% 0% 100%

R 15% 85% 0% 100%

S 10% 90% 0% 100%

T 5% 95% 0% 100%

AA 0% 100% 0% 100%

AB 0% 95% 5% 100%

AC 0% 90% 10% 100%

AD 0% 85% 15% 100%

AE 0% 80% 20% 100%

AF 0% 75% 25% 100%

AG 0% 70% 30% 100%

AH 0% 65% 35% 100%

AI 0% 60% 40% 100%

Table7.1:2-assetclassportfoliosweightings

46

AJ 0% 55% 45% 100%

AK 0% 50% 50% 100%

AL 0% 45% 55% 100%

AM 0% 40% 60% 100%

AN 0% 35% 65% 100%

AO 0% 30% 70% 100%

AP 0% 25% 75% 100%

AQ 0% 20% 80% 100%

AR 0% 15% 85% 100%

AS 0% 10% 90% 100%

AT 0% 5% 95% 100%

BA 0% 0% 100% 100%

BB 5% 0% 95% 100%

BC 10% 0% 90% 100%

BD 15% 0% 85% 100%

BE 20% 0% 80% 100%

BF 25% 0% 75% 100%

BG 30% 0% 70% 100%

BH 35% 0% 65% 100%

BI 40% 0% 60% 100%

BJ 45% 0% 55% 100%

BK 50% 0% 50% 100%

BL 55% 0% 45% 100%

BM 60% 0% 40% 100%

BN 65% 0% 35% 100%

BO 70% 0% 30% 100%

BP 75% 0% 25% 100%

BQ 80% 0% 20% 100%

BR 85% 0% 15% 100%

BS 90% 0% 10% 100%

BT 95% 0% 5% 100%

47

3ASSETCLASSPORTFOLIO

PortfolioAssetVariance 10%

Retail Office Industrial Total

XA 90% 5% 5% 100%

XB 80% 10% 10% 100%

XC 70% 15% 15% 100%

XD 60% 20% 20% 100%

XE 50% 25% 25% 100%

XF 40% 30% 30% 100%

XG 30% 35% 35% 100%

XH 20% 40% 40% 100%

XI 10% 45% 45% 100%

YA 5% 90% 5% 100%

YB 10% 80% 10% 100%

YC 15% 70% 15% 100%

YD 20% 60% 20% 100%

YE 25% 50% 25% 100%

YF 30% 40% 30% 100%

YG 35% 30% 35% 100%

YH 40% 20% 40% 100%

YI 45% 10% 45% 100%

ZA 5% 5% 90% 100%

ZB 10% 10% 80% 100%

ZC 15% 15% 70% 100%

ZD 20% 20% 60% 100%

ZE 25% 25% 50% 100%

ZF 30% 30% 40% 100%

ZG 35% 35% 30% 100%

ZH 40% 40% 20% 100%

ZI 45% 45% 10% 100%

Table7.2:3-assetclassportfoliosweightings

48

ZC

BGZB

BH

YI

BF

BI

ZD

BE

BD16.00%

16.10%

16.20%

16.30%

16.40%

16.50%

16.60%

16.70%

16.80%

1.26% 1.28% 1.30% 1.32% 1.34% 1.36% 1.38% 1.40% 1.42%

Return

Risk

YF

ZG

ZH

XG

YE

XF

ZF YG

XE

YH

9.60%

9.62%

9.64%

9.66%

9.68%

9.70%

9.72%

9.74%

0.36% 0.37% 0.38% 0.39% 0.40% 0.41%

Return

Risk

ZC

BGZB

BH

YI

BF

BI

ZD

BE

BD16.00%

16.10%

16.20%

16.30%

16.40%

16.50%

16.60%

16.70%

16.80%

1.26% 1.28% 1.30% 1.32% 1.34% 1.36% 1.38% 1.40% 1.42%

Return

Risk

Figure7.2:Top10Portfolios,bySharperatio,in‘Decline’period

Figure7.1:Top10Portfolios,bySharperatio,in‘Growth’period

Figure7.3:Top10Portfolios,bySharperatio,in‘Stable’period