2018 capital market assumptions - sellwood consulting llc · emerging markets equity ... not to...

2018CapitalMarketAssumptionsFebruary2018

TABLEOFCONTENTS

TableofContents.....................................................................................................................................................................1

INTRODUCTION.......................................................................................................................................................................2

INFLATION.................................................................................................................................................................................6

FIXEDINCOME..........................................................................................................................................................................7

CashEquivalents...............................................................................................................................................................10

Low‐DurationFixedIncome........................................................................................................................................11

CoreFixedIncome............................................................................................................................................................12

Non‐CoreFixedIncome..................................................................................................................................................13

Core‐PlusFixedIncome.................................................................................................................................................14

Long‐DurationFixedIncome.......................................................................................................................................15

USTreasuryInflationProtectedSecurities(TIPS).............................................................................................16

Short‐TermUSTreasuryInflationProtectedSecurities(TIPS)....................................................................16

EQUITY.......................................................................................................................................................................................17

USLarge‐CapEquity........................................................................................................................................................18

USSmall‐CapEquity........................................................................................................................................................20

USEquity..............................................................................................................................................................................22

Non‐USLarge‐CapEquity..............................................................................................................................................22

Non‐USSmall‐CapEquity..............................................................................................................................................24

EmergingMarketsEquity..............................................................................................................................................24

Non‐USEquity....................................................................................................................................................................25

ALTERNATIVES......................................................................................................................................................................26

RealEstate...........................................................................................................................................................................26

DiversifiedInflation‐Related........................................................................................................................................27

MarketableAlternatives................................................................................................................................................28

Non‐MarketableAlternatives......................................................................................................................................28

RISK.............................................................................................................................................................................................29

CORRELATIONCOEFFICIENTS........................................................................................................................................33

APPENDIX:SOURCES...........................................................................................................................................................35

1

INTRODUCTIONSellwoodConsultingupdatesitscapitalmarketsassumptionsonanannualbasis.Our2018assumptionsreflectinformationasofDecember31,2017,unlessotherwisenoted.Thisreportdocumentsourprocessforcreatingthesecapitalmarketsassumptions,andweprovidedetailedmethodologyforeach.Severalover‐archingprinciples,however,informallofouranalysis:

1. Webelievethatforward‐lookingcapitalmarketassumptionsareanimportant,butfarfromtheonlyimportant,inputforproperlyconstructingportfolios.Greatcareshouldbetakennottorelyonlyonmean‐varianceanalysiswhenconstructingportfolios.Ananalysisthatreliesonlyonmean‐varianceanalysiswillover‐allocatetoassetswithinsignificantlysuperiorrisk/returnestimates,andassetsthatarelessliquidorlessfrequentlypriced,resultingininferiordiversificationandtheassumptionofunintendedrisks.

2. Ourassumptionsareforward‐lookinginnatureandreflectaten‐yearhorizon.Theyareappropriateforanalysisofportfolioswithlong‐term(10yearorgreater)horizons.Forportfolioswithshorterhorizons,alternatemethodsofanalysisshouldbeemployed.

3. Wepurposefullyusedifferentmethodstoestimatereturnandrisk.Thefirstpartofthispaperexplainsthedifferentmethodsweemploytoestimatethefuturereturnofeachindividualassetclass.Laterinthepaper,weexplainamorestandardizedapproachtoestimatingfutureriskofthesameassetclasses.

4. Ourreturnassumptionsutilizeabuild‐upapproachbasedonthecurrentvaluesoftheindividualdriversofexpectedreturnthatareuniquetoeachassetclass.

5. Forassetclasseswherethemarketprovidesacurrentviewofforward‐lookingreturns,ourassumptionsheavilyweightthemarketview.

6. Wherepossible,allofourreturnassumptionsincorporatecurrentvaluations.Wherewehaveidentifiedacurrentvaluationanditslong‐termmean,ourestimatesconsidera50%reversionfromthecurrentvaluationleveltoitslong‐termmeanoverthenexttenyears.

7. Ourassumptionsarepresentedinnominalterms.Wherewehaveusedhistoricalreturnsinourinputanalysis,wehavealwaystransformedthemtoreal,after‐inflation,returns,soastostripouthistoricalinflation.Attheendofthebuild‐upprocess,whereappropriate,weaddthemarket’scurrentmeasureofforward‐lookinginflationbacktotheassumptionstocreateforward‐lookingnominalreturnassumptions.

8. Ourbasereturncalculationsareofandforcompoundreturns.Aftercalculatingacompoundreturnandariskassumption,wecombinethetwomathematicallytocalculateanarithmeticaverageexpectedreturn,whichisanecessaryinputformean‐varianceanalysis.

2

9. Ourassumptionsarepassiveinnatureandassumenoactivemanagement.

10. Ourapproachtomodelingtheexpectedriskofeachassetcategoryismulti‐faceted.First,weexaminethehistoricalstandarddeviationofthereturnsforaproxyindexfortheassetcategory(boththefullhistoryandmostrecent10years).Next,weexaminethehistoricalworst‐caseannualreturnexperience(orinthecaseofassetcategoriesthatarenotpricedtomarket,themaximumtwo‐yearpeak‐to‐troughexperience)fortheassetclass.Ifnecessary,weadjustourriskestimatesupwardtoensurethattheactualworst‐caseexperiencehadatleasta2%probabilityofoccurring(onceevery50years)underourassumedreturnandriskdistributionparameters.Finally,forassetclasseswhereourconfidenceinthedataavailableforexaminationislimited,wequalitativelyadjustourriskassumptiontoreflectthisuncertainty.

11. Ourcorrelationcoefficientassumptionsaremostlyderivedfromhistory,withanemphasis

ontherecentpast.Weseekaproxyforeachassetcategorywehavemodeledwithaslongahistoryaspossible,andthencalculateourcorrelationassumptionsusingasimpleaverageofthefollowing,foreachpairofassetcategories:

Longest‐termcorrelation 10‐yearcorrelation 5‐yearcorrelation 3‐yearcorrelation

Thisapproachpurposefullyoverweightstherecentpast,whileacknowledgingthelong‐termpast.Itisalsoamoreconservativemeasureforcorrelationbenefittoaportfolio,becauserecentcorrelationshavebeenhigherthantheyhavebeenhistorically.

12. Weroundourassumptionstothenearest10basispoints,inthecaseofarithmeticaveragereturn,andnearest25basispoints,inthecaseofrisk.

13. OurassumptionsareapplicabletoUS‐based,non‐taxableinvestors.FortaxableclientslocatedintheUnitedStates,wemaintainaseparatemethodologythatconsiderstheeffectsoftaxesonexpectedreturnsandrisk.

14. Wehavestrivedtoconstructasetofassumptionsthatisstraightforward,explainable,fullydocumented,andreplicablebyotherresearchers.Ourassumptionsareascomplexasnecessarybutnomorecomplexthannecessary,andtheyhavenohiddenconstraints.Wecouldmakethemmorecomplicated,butwedonotbelievethatdoingsowouldmakethembetter.

Insummaryform,our2018forward‐lookingassumptionsfollowonthenextpage.

3

NominalCompoundReturn Risk

NominalArithmeticReturn

SharpeRatio

Inflation 1.96% 3.00% 2.00% ‐‐‐CashEquivalents 1.79% 1.00% 1.80% ‐‐‐Low‐DurationFixedIncome 2.55% 3.00% 2.60% 0.25CoreFixedIncome 2.57% 5.00% 2.70% 0.16Core‐PlusFixedIncome 2.58% 5.25% 2.70% 0.15Non‐CoreFixedIncome 2.58% 14.25% 3.50% 0.06Long‐DurationFixedIncome 2.47% 10.25% 3.00% 0.07TIPS 2.12% 6.25% 2.30% 0.05Short‐TermTIPS 2.28% 3.75% 2.30% 0.13USEquity 4.46% 18.75% 6.10% 0.14USLarge‐CapEquity 4.48% 18.75% 6.10% 0.14USSmall‐CapEquity 4.25% 20.00% 6.10% 0.12Non‐USEquity 5.83% 23.75% 8.30% 0.17Non‐USLarge‐CapEquity 5.80% 23.25% 8.20% 0.17Non‐USSmall‐CapEquity 6.05% 28.00% 9.50% 0.15EmergingMarketsEquity 6.56% 29.25% 10.30% 0.16RealEstate 4.57% 19.00% 6.20% 0.15DiversifiedInflation‐Related 3.65% 14.50% 4.60% 0.13MarketableAlternatives 4.12% 11.75% 4.80% 0.20Non‐MarketableAlternatives 6.52% 29.75% 10.30% 0.16

GlobalEquities

Alternatives

FixedIncome

4

Historicalreturndistributions(historicalrealreturns,plusourassumedfutureinflation)aredepictedbelowinblue,andourforward‐lookingassumedreturndistributionsareshownintan:

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INFLATION

Modeled:USCPI‐UInflationCompoundReturn:1.96%

ArithmeticAverageReturn:2.00%Risk:3.00%

Themarkettellsusitsexpectationforforward‐lookingten‐yearinflation,andourassumptionreflectsthatmarketassumption.OnDecember31,2017,themarket’syieldfora10‐YearUSTreasuryBondwas2.40%,andtherealyieldfora10‐YearTIPSsecuritywas0.44%.Thedifferencebetweenthetwoapproximatesthemarket’sinflationexpectationoverthenexttenyears,1.96%.TheFederalReservehaspublishedthisinflationapproximation–theso‐called“TIPSbreakevenspread”–since2003.Thefollowingchartdepictsthefullhistoryofthismeasure,laidagainsttheactualsubsequentinflation(asmeasuredbytheConsumerPriceIndex,“CPI”)thatoccurredoverthefollowingfiveyears.Wehavechosentodepictthefive‐yearTIPSbreakevenspreadandsubsequentfive‐yearinflation,becausethe10‐yearvaluesdonotyetoffersufficientdataforevaluation.Withtheexceptionofespeciallyilliquidmarketperiods,whichdistortthemeasurebecauseofliquiditydifferencesbetweenTIPSandnominalTreasuryBonds,themeasurehasdoneafairjobofpredictingsubsequentinflationanddoesnotappeartobebiasedpositivelyornegatively.

‐2.0%

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2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017

TIPSBreakevenSpreadandSubsequentCPI‐ 5Years

Subsequent5‐YearCPI 5‐YearBreakevenSpread

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FIXEDINCOMEFixedincomereturnsareverydependentonentryyields.FortheBloombergBarclaysAggregateIndex,since1976,going‐inyieldshaveexplained85%ofsubsequent10‐yearreturns:

Itwouldbetemptingtosimplysetourbond‐marketassumptionsasthecurrentyield,buttodosowouldbetoignoreprospectsforchanginginterestrates,changingcompositionofthebondbenchmarks,andthenegativeeffectsofbonddefaults.Instead,webuildavaluationmodelforeachbondcategoryforwhichweassumeareturn.Still,currentyieldsanchorouranalysis:ineachcase,thecompoundreturnassumptionthatwecalculatewiththismodelisclosetothecurrentnominalyieldfortheassetclass.Allofourfixedincomeassumptionsuseanidenticalbuilding‐blockmodelasourbaseanalysis,butwehavemadesomequalitativeadjustmentstotheanalysis,wherenoted.Ourbuildingblockmodelbeginswiththefixedincomeassetclass’scurrentrealyieldandduration.Wethenexaminethelong‐termaverageoftherealyield,andassumethatovertheprospectiveten‐yearperiod,theasset’srealyieldrevertshalfwaytothataverage.Forassetcategoriesthatpayayieldspreadascompensationforhigherrisk,weusesimilarcalculationstoassumethereversionoftheyieldspreadhalfwaytoitshistoricalaverage.Forthemostpart,weassumethatlong‐termaveragedefaultandrecoveryrateswillpersistintotheprospectiveten‐yearperiod.1Giventheseinputs,wecancalculatetheasset’sexpectedforward‐looking10‐yearreturnusingarithmetic.

1OursourceforhistoricaldefaultandrecoveryratesforallbondsisMoodys.

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BloombergBarclaysAggregateYield&Subsequent10‐YearReturn

BarclaysAggregateYield Subsequent10‐YearReturn

R2=0.85

7

WeuseaUSTreasuryBondasourfirstfixedincomebuildingblock–theblockuponwhichwestackyieldspreadsandinflation.Tocalculatetheforward‐lookingten‐yearreturnforTreasuryBonds,webeginwithtoday’srealyieldandassumeten‐yearreversionhalfwaytothelong‐termaveragemeanrealyield.Tocapturethelongesttimehorizonpossible,wecalculateallrealyieldsbyadjustingthenominalyieldbyaninflationseries2.Weassumethatthereversiontoameanrealyieldwilloccurinevenincrementsineachofthefuturetenyears.Weassumefurtherthatthesecurity’sdurationwillstayconstantovertheten‐yearperiod.Thelastbuildingblock,thoughitisassumedtobezeroforaTreasurysecurity,isanassumeddefaultrate,adjustedforanassumedrecoveryrate.Finally,becauseallofthisanalysisiscalculatedinrealterms,weaddbackthemarket’sinflationassumptiontoarriveatanominalreturnassumption.Ourcalculationsforthe2‐,5‐,10‐,and20‐YearUSTreasuryBondsfollow.Ourassumptionsare:Maturity: 2years 5years 10years 20yearsDuration: 1.86years 4.67years 8.77years 14.50yearsCurrentRealYield: 0.12% 0.34% 0.44% 0.61%Long‐TermAverageRealYield: 1.60% 2.00% 2.27% 2.51%CumulativeYieldChange(10Years): +0.74% +0.83% +0.92% +0.95%ExpectedDefaultRate: 0% 0% 0% 0%

2 Since2003,ourrealyieldsarebasedontheconstantmaturityTIPSyieldscalculatedbytheFederalReserveformaturitieslongerthan2years.Priorto2003,inordertocalculaterealyieldsweadjustedtheapplicableyieldwiththeprior12‐monthcoreCPIindex.Forexample,fora5‐yearTreasurybond,wecalculateahistoricalrealyieldseriesbysubtractingprior12‐monthcoreCPIfromhistorical5‐yearTreasurybondyieldspriorto2003,andbyusingthethen‐current5‐yearTIPSbreakevenyieldafter2003.Becauseofitslowervolatility,thecoreCPIindexhasprovenabetterpredictorofsubsequentCPIinflationthanhastheCPIindexitself.

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Foreachassumptionweaddourinflationassumptiontotheexpectedannualizedcompoundreturn.Basedonthiscalculationwearriveatthefollowingcompoundreturnassumptions: Ourprojectednominal10‐yearannualizedreturnforeachTreasuryBondis:

2Year 5Year 10Year 20Year2.28% 2.29% 2.01% 1.62%

2-Year Treasurys -- Total ReturnYear 0 1 2 3 4 5 6 7 8 9 10 Cumulative AnnualizedStarting Real Yield 0.12% 0.20% 0.27% 0.34% 0.42% 0.49% 0.57% 0.64% 0.71% 0.79% 0.86%Duration 1.86 1.86 1.86 1.86 1.86 1.86 1.86 1.86 1.86 1.86 1.86 Parallel Yield Change 0.07% 0.07% 0.07% 0.07% 0.07% 0.07% 0.07% 0.07% 0.07% 0.07% 0.74%12-month return -0.01% 0.06% 0.13% 0.21% 0.28% 0.35% 0.43% 0.50% 0.58% 0.65%Compound Factor 99.99% 100.06% 100.13% 100.21% 100.28% 100.35% 100.43% 100.50% 100.58% 100.65% 3.22% 0.32%

market 10-year inflation 1.96%

nominal 10-yr annualized return 2.28%

5-Year Treasurys -- Total Return

Year 0 1 2 3 4 5 6 7 8 9 10 Cumulative AnnualizedStarting Real Yield 0.34% 0.42% 0.51% 0.59% 0.67% 0.76% 0.84% 0.92% 1.01% 1.09% 1.17%Duration 4.67 4.67 4.67 4.67 4.67 4.67 4.67 4.67 4.67 4.67 4.67

Parallel Yield Change 0.08% 0.08% 0.08% 0.08% 0.08% 0.08% 0.08% 0.08% 0.08% 0.08% 0.83%

12-month return -0.05% 0.03% 0.12% 0.20% 0.28% 0.37% 0.45% 0.53% 0.62% 0.70%

Compound Factor 99.95% 100.03% 100.12% 100.20% 100.28% 100.37% 100.45% 100.53% 100.62% 100.70% 3.30% 0.33%market 10-year inflation 1.96%


10-Year Treasurys -- Total ReturnYear 0 1 2 3 4 5 6 7 8 9 10 Cumulative AnnualizedStarting Real Yield 0.44% 0.53% 0.62% 0.72% 0.81% 0.90% 0.99% 1.08% 1.17% 1.27% 1.36%Duration 8.77 8.77 8.77 8.77 8.77 8.77 8.77 8.77 8.77 8.77 8.77 Parallel Yield Change 0.09% 0.09% 0.09% 0.09% 0.09% 0.09% 0.09% 0.09% 0.09% 0.09% 0.92%12-month return -0.36% -0.27% -0.18% -0.09% 0.00% 0.09% 0.19% 0.28% 0.37% 0.46%Compound Factor 99.64% 99.73% 99.82% 99.91% 100.00% 100.09% 100.19% 100.28% 100.37% 100.46% 0.48% 0.05%



20-Year Treasurys -- Total ReturnYear 0 1 2 3 4 5 6 7 8 9 10 Cumulative AnnualizedStarting Real Yield 0.61% 0.70% 0.80% 0.89% 0.99% 1.08% 1.18% 1.27% 1.37% 1.46% 1.56%Duration 14.50 14.50 14.50 14.50 14.50 14.50 14.50 14.50 14.50 14.50 14.50 Parallel Yield Change 0.09% 0.09% 0.09% 0.09% 0.09% 0.09% 0.09% 0.09% 0.09% 0.09% 0.95%12-month return -0.77% -0.67% -0.58% -0.48% -0.39% -0.29% -0.20% -0.10% -0.01% 0.09%Compound Factor 99.23% 99.33% 99.42% 99.52% 99.61% 99.71% 99.80% 99.90% 99.99% 100.09% -3.34% -0.34%



9

CashEquivalentsModeled:91‐DayT‐Bills

CompoundReturn:1.79%ArithmeticAverageReturn:1.80%

Risk:1.00%WeusethemodeloutlinedaboveforCashEquivalents.Assumptions(91‐DayT‐Bills):

Maturity: 91daysDuration: 0.25yearsCurrentRealYield: ‐0.44%Long‐TermAverageRealYield: 0.82%CumulativeYieldChange(10Years): +0.63%(halfwayfromcurrenttolong‐termaverage)ExpectedDefaultRate: 0%

Theseassumptionsyieldanominalcompoundreturnexpectationof1.79%:

Wecautionthatthereisaninherentproblemwithforecastinga10‐yearreturnforanassetthatmaturesevery91days.Nominalcashreturnsarehighlysensitivetonominalshort‐terminterestrates,whichweexpecttobeasvariableoverthenextdecadeastheyhavebeenhistorically.Asillustratedinthechartbelow,whileinvestorstypicallydemandapositiverealyieldfromcash,periodsofnegativerealreturntocashhaveexistedforconsiderableperiodsoftime–includingthemostrecentperiodsince2008.Ourriskassumptionreflectsanappropriaterangeofuncertaintyaroundourreturnprojectionforcashequivalents.

91-Day T-Bills -- Total ReturnYear 0 1 2 3 4 5 6 7 8 9 10 Cumulative AnnualizedStarting Real Yield -0.44% -0.37% -0.31% -0.25% -0.19% -0.12% -0.06% 0.00% 0.07% 0.13% 0.19%Duration 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 Parallel Yield Change 0.06% 0.06% 0.06% 0.06% 0.06% 0.06% 0.06% 0.06% 0.06% 0.06% 0.63%12-month return -0.45% -0.39% -0.33% -0.26% -0.20% -0.14% -0.08% -0.01% 0.05% 0.11%Compound Factor 99.55% 99.61% 99.67% 99.74% 99.80% 99.86% 99.92% 99.99% 100.05% 100.11% -1.69% -0.17%



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Historical RealCashYieldRealCashYield

FederalFundsRate

10

Low‐DurationFixedIncomeModeled:1‐3YearAggregateFixedIncome


Risk:3.00%OurLow‐DurationFixedIncomeassumptionreflectsa50%proportiontoboththe2‐YearTreasuryBondandcorporatebonds.Forhalftheassumedportfolio,then,weaddtoour2‐YearTreasurybondreturnexpectationaspreadfor1‐3yearcorporatebonds:Assumptions:

ProportioninCorporates: 50%SpreadDuration: 1.55yearsCurrentSpread: 0.52%Long‐TermAverageSpread: 1.27%CumulativeSpreadChange(10Yrs): +0.38%(halfwayfromcurrenttolong‐termaverage)

Finally,wemakeassumptionsfortheexpecteddefaultrateandrecoveryratefordefaulted1‐3yearcorporatesecurities.Thesecalculationsonlyapplytotheproportionoftheassumptionpertainingtocorporatesecurities.Thefollowingfiguresrepresentthehistoricalaveragefortheassetclass:Assumptions:

ExpectedDefaultRate: 0.15%ExpectedDefaultRecoveryRate: 44%Default/RecoveryReturnContribution: ‐0.08%Multipliedby0.5(halfofportfolio); ‐0.04%

Insummary,ourreturnassumptionforlow‐durationfixedincomebuildsupseveralsourcesofreturn:

2‐YearTreasuryReturn 2.28%SpreadEffect +0.32%DefaultEffect ‐0.04%ReturnAssumption 2.55%3

3Afterrounding.

1-3 Year Corporates -- Spread Effect (over Treasurys) Year 0 1 2 3 4 5 6 7 8 9 10 Cumulative AnnualizedStarting Spread 0.52% 0.56% 0.60% 0.63% 0.67% 0.71% 0.75% 0.78% 0.82% 0.86% 0.90%Duration 1.55 1.55 1.55 1.55 1.55 1.55 1.55 1.55 1.55 1.55 1.55 Parallel Yield Change 0.04% 0.04% 0.04% 0.04% 0.04% 0.04% 0.04% 0.04% 0.04% 0.04% 0.38%12-month return 0.46% 0.50% 0.54% 0.57% 0.61% 0.65% 0.69% 0.72% 0.76% 0.80%

Compound Factor 100.46% 100.50% 100.54% 100.57% 100.61% 100.65% 100.69% 100.72% 100.76% 100.80% 6.49% 0.63%

Proportion 50.00%

Spread Effect (Total) 0.32%

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Combiningthe2‐YearTreasuryBondreturnandtheexpectedreturnfromspread,andthensubtractingtheexpecteddefaultrateafteradjustingforrecovery,yieldsourreturnassumptionof2.55%incompoundterms.CoreFixedIncome

Modeled:USInvestment‐GradeAggregateandHedgedNon‐USAggregateFixedIncomeCompoundReturn:2.57%


Thebaselevelofourbuilding‐blockapproachforCoreFixedIncomeisthe5‐YearTreasuryBond,outlinedabove.Tothisexpectedreturn,weaddanexpectationforspreadreturn:

SpreadDuration: 3.35yearsCurrentSpread(BCAggregate): 0.36%Long‐TermAverageSpread: 0.55%CumulativeSpreadChange(10Yrs): +0.10%(halfwayfromcurrenttolong‐termaverage)

Ourassumptionsfordefaultandrecoveryratesareinlinewithhistory.Wesubtractadefaultcontributionbasedontheseinputvariables:Assumptions:

ExpectedDefaultRate: 0.15%ExpectedDefaultRecoveryRate: 44%Default/RecoveryReturnContribution: ‐0.08%

Insummary:

5‐YearTreasuryReturn 2.29%SpreadEffect +0.37%DefaultEffect ‐0.08%ReturnAssumption 2.57%

Addingthe5‐YearUSTreasuryBondreturn,theexpectedspreadreturn,andadjustingfordefaultsyieldsacompoundreturnexpectationof2.57%.

BC Aggregate -- Spread Effect (over Treasurys) Year 0 1 2 3 4 5 6 7 8 9 10 Cumulative AnnualizedStarting Spread 0.36% 0.37% 0.38% 0.39% 0.40% 0.41% 0.42% 0.43% 0.44% 0.45% 0.46%Duration 3.35 3.35 3.35 3.35 3.35 3.35 3.35 3.35 3.35 3.35 3.35 Parallel Yield Change 0.01% 0.01% 0.01% 0.01% 0.01% 0.01% 0.01% 0.01% 0.01% 0.01% 0.10%12-month return 0.33% 0.34% 0.35% 0.36% 0.37% 0.38% 0.39% 0.40% 0.41% 0.42%

Compound Factor 100.33% 100.34% 100.35% 100.36% 100.37% 100.38% 100.39% 100.40% 100.41% 100.42% 3.78% 0.37%

Proportion 100.00%


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WebelievethatthisapproachworksequallywellforUSAggregatefixedincomeandforNon‐USAggregatefixedincomewherethecurrencyexposureishedgedbacktotheUSdollar.Bystrippingoutcurrencyexposure,theNon‐USfixedincomeinvestorisleftwithaportfoliooffixedincomesecuritiesexpectingsimilarunderlyingcharacteristicstotheUSfixedincomeportfolio.Non‐CoreFixedIncome

Modeled:USandNon‐USBelow‐Investment‐Grade&EmergingMarketsFixedIncomeCompoundReturn:2.58%


OurNon‐CoreFixedIncomeassumptioncombinesUSbelow‐investment‐grade(highyield)bondsandemergingmarketssovereignbonds.Weassumea50%weightingtoeachassetclass.Thematurityofthehigh‐yieldindexiscurrently6.3years.Tomatchthismaturity,weassumethereturnforasynthetic6.3‐yearTreasurybondbyappropriatelyweightingtheexpectedreturnswecalculatedforthe5‐and10‐yearTreasurybonds.Thecurrentmaturityofanindexofemergingmarketssovereignbondsis11.7years.Tomatchthisduration,wecalculateaspreadoveraweightedaverageofexpectedreturnsfor10‐and20‐yearUSTreasuryBondsthatyieldsanexpectedreturnfora11.7‐yearTreasuryBond.Totheseexpectedreturns,wethenaddaspreadbuildingblock,andfinallysubtractadefaultbuildingblock. HighYieldBonds EmergingMarketDebt

Maturity: 6.3years 11.7years6.3‐YearTreasuryAssumedReturn: 2.21% 1.94%SpreadDuration: 3.74years 7.05yearsCurrentSpread: 3.63% 2.75%Long‐TermAverageSpread: 5.74% 3.52%CumulativeSpreadChange(10Yrs): +1.05% 0.39%

High Yield -- Spread Effect (over Treasurys) Year 0 1 2 3 4 5 6 7 8 9 10 Cumulative AnnualizedStarting Spread 3.63% 3.74% 3.84% 3.95% 4.05% 4.16% 4.26% 4.37% 4.47% 4.58% 4.68%Duration 3.74 3.74 3.74 3.74 3.74 3.74 3.74 3.74 3.74 3.74 3.74 Parallel Yield Change 0.11% 0.11% 0.11% 0.11% 0.11% 0.11% 0.11% 0.11% 0.11% 0.11% 1.05%12-month return 3.24% 3.34% 3.45% 3.55% 3.66% 3.76% 3.87% 3.97% 4.08% 4.18%

Compound Factor 103.24% 103.34% 103.45% 103.55% 103.66% 103.76% 103.87% 103.97% 104.08% 104.18% 43.94% 3.71%

Proportion 50.00%


EMD -- Spread Effect (over Treasurys)Year 0 1 2 3 4 5 6 7 8 9 10 Cumulative AnnualizedStarting Spread 2.75% 2.79% 2.83% 2.86% 2.90% 2.94% 2.98% 3.02% 3.06% 3.10% 3.14%Duration 7.05 7.05 7.05 7.05 7.05 7.05 7.05 7.05 7.05 7.05 7.05 Parallel Yield Change 0.04% 0.04% 0.04% 0.04% 0.04% 0.04% 0.04% 0.04% 0.04% 0.04% 0.39%12-month return 2.47% 2.51% 2.55% 2.59% 2.63% 2.67% 2.71% 2.75% 2.78% 2.82%

Compound Factor 102.47% 102.51% 102.55% 102.59% 102.63% 102.67% 102.71% 102.75% 102.78% 102.82% 29.87% 2.65%

Proportion 50.00%


13

Ourassumedreturncontributionfromourspreadbuildingblockapproach,beforeaccountingfordefaults,is(assuming50%oftheportfolioforeachassetclass):

HighYieldBonds EmergingMarketDebt1.85% 1.32%

Ourfinalbuildingblockisanadjustmentforexpecteddefaultandrecoveryrates.Thequalitycompositionoftheemergingmarketsdebtuniversehaschangedovertime,sowedonotapplyhistoricaluniverse‐widedefaultandrecoveryrates.Instead,weexaminethehistoricaldefaultandrecoveryratesbybondqualityratingandapplythoseratestothecurrentuniversequalitycomposition.Historically,investment‐gradeemergingmarketsissueshaveexperienced1.7%defaultrates.Speculative‐gradeemergingmarketsissueshaveexperienced18.3%defaultrates.Theuniverseiscurrently48%investmentgradeand52%speculativegrade;applyingtheseproportionsresultsinanexpecteddefaultrateof10.4%.Historicalrecoveryratesindefault,regardlessofrating,hasbeen65%.

ExpectedDefaultRate: 10.4% ExpectedDefaultRecoveryRate: 65%

Wesubtracttheexpectedunrecovereddefaultfromthetotalyield:

DefaultRate

RecoveryRate

UnrecoveredRate

DefaultEffectonReturn

HighYield 2.8% 38% 62% ‐1.74%EMDebt 10.4% 65% 35% ‐3.62%Insummary: HighYield EMDebt Combined

TreasuryReturn 2.21% 1.94% ‐‐‐SpreadEffect +3.71% +2.65% ‐‐‐DefaultEffect ‐1.74% ‐3.62% ‐‐‐ReturnAssumption 4.18% 0.97% 2.58%WeaveragetheHighYieldandEmergingMarketsDebtassumptionstoarriveatourforward‐lookingcompoundreturnexpectationfornon‐corefixedincome:2.58%.Core‐PlusFixedIncome

Modeled:80%USInvestment‐GradeAggregate;20%Non‐CorePlusSectorsCompoundReturn:2.58%


Thisreturnassumptionexpectsareturncalculatedasfollows:

14

80%oftheexpectedreturnofCoreFixedIncome(2.57%) +20%oftheexpectedreturnofNon‐CoreFixedIncome(2.58%)Thisprocessyieldsanexpectedcompoundreturnof2.58%.Long‐DurationFixedIncome

Modeled:USLong‐TermGovernment/CreditFixedIncomeCompoundReturn:2.47%


Ourmodelassumes50%eachin(i)10‐and20‐YearUSTreasuryBondsand(ii)long‐durationUSinvestment‐gradecorporatebonds.Whilethecompositionofsomelong‐durationfixedincomeindexesdiffersslightlyfromthisapproach,webelievethatmostdifferenceswillcanceleachotherout.

TreasuryComponent

FortheTreasurycomponent,weuseourbasicmodeltoaveragetheexpectedreturnsfor10‐and20‐yearTreasuryBonds(outlinedabove)toapproximatethereturnofa15‐yearTreasuryBond.ThisaverageexpectedreturnfortheTreasurycomponentis1.81%.

SpreadComponent

Weaddaspreadcomponentconsistingoflong‐termUSinvestment‐gradecorporatebonds:

Assumptions:

ProportioninCorporates: 50%SpreadDuration: 13.90yearsCurrentSpread: 1.50%Long‐TermAverageSpread: 1.75%CumulativeSpreadChange(10Yrs): 0.12%(halfwayfromcurrenttolong‐termaverage)ExpectedDefaultRate: 0.15% ExpectedDefaultRecoveryRate: 44%

Long Corporates -- Spread Effect (over Treasurys) Year 0 1 2 3 4 5 6 7 8 9 10 Cumulative AnnualizedStarting Spread 1.50% 1.51% 1.52% 1.54% 1.55% 1.56% 1.57% 1.59% 1.60% 1.61% 1.62%Duration 13.90 13.90 13.90 13.90 13.90 13.90 13.90 13.90 13.90 13.90 13.90 Parallel Yield Change 0.01% 0.01% 0.01% 0.01% 0.01% 0.01% 0.01% 0.01% 0.01% 0.01% 0.12%12-month return 1.33% 1.34% 1.35% 1.37% 1.38% 1.39% 1.40% 1.42% 1.43% 1.44%

Compound Factor 101.33% 101.34% 101.35% 101.37% 101.38% 101.39% 101.40% 101.42% 101.43% 101.44% 14.74% 1.38%

Proportion 50.00%


15

Insummary:

TreasuryReturn 1.81%(averageof10‐and20‐yearTreasurys)SpreadEffect +0.69%(50%proportion)DefaultEffect ‐0.04%(50%proportion)ReturnAssumption 2.47%

USTreasuryInflationProtectedSecurities(TIPS)

Modeled:USTIPSCompoundReturn:2.12%


GiventhatthefirstUSTIPSissuancewasin1997,wearehesitanttorelyonany“long‐term”yieldorspreadaveragestofurthermodeltheassetclass.Instead,wemodelaproxyfortheBloombergBarclaysUSTIPSIndex,whichcurrentlyhasamaturityof7.9years.Aportfolioof42%5‐yearTreasuryBonds,and58%10‐yearTreasurybondsresultsinahypotheticalTreasurybondwith7.9‐yearmaturity.Assumingourinflationexpectationof1.96%peryearfortheprospective10‐yearperiod,theexpectedTIPSreturnissimplyaweightedaverageofourreturnexpectationsforthenominal5‐yearand10‐yearTreasurybonds.Applyingtheseweightstoourreturnprojectionsforthosebondsresultsina10‐yearTIPSreturnassumptionof2.12%:

(42%x2.29%)+(58%x2.01%)=2.12%.Short‐TermUSTreasuryInflationProtectedSecurities(TIPS)

Modeled:Short‐TermUSTIPSCompoundReturn:2.28%


WeemployasimilarprocesstoourTIPScalculationforourShort‐TermTIPSassumption,althoughwemodelaproxyfortheBloombergBarclaysUS0‐5YearTIPSIndex,whichcurrentlyhasamaturityof2.5years.Aportfolioof85%2‐yearTreasuryBondsand15%5‐yearTreasurybondsresultsinahypotheticalTreasurybondwith2.5‐yearmaturity.Assumingourinflationexpectationof1.96%peryearfortheprospective10‐yearperiod,theexpectedShort‐TermTIPSreturnissimplyaweightedaverageofourreturnexpectationsforthenominal2‐yearand5‐yearTreasurybonds.Applyingtheseweightstoourreturnprojectionsforthosebondsresultsina10‐yearShort‐TermTIPSreturnassumptionof2.28%:

(85%x2.28%)+(15%x2.29%)=2.28%.

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EQUITYToderiveourequityreturnassumptions,weusetwomethodologies:(i) abuilding‐blockapproachusingtheso‐calledShillerprice‐to‐earnings(P/E)measure;and(ii) anequityriskpremiumestimatethataveragesthecurrentimpliedequityriskpremium

basedonafreecashflowtoequitymodelandthehistoricalaverageequityriskpremium. EquityRiskPremium/BuildingBlockApproachFreeCashFlowtoEquityModel

WhereourbuildingblockscallforaP/Emeasure,weassumethatthiscurrentvaluationmetricwillreverthalfwaytoitslong‐termmeanovertheprospectiveten‐yearperiod.Ourapproachemploys“Shillerearnings,”whichrepresentaten‐yearaverage,adjustedforinflation.Webelievethatthisapproachappropriatelysmoothestheimpactofyear‐to‐yearearningsvolatility,andresearchshowsthatofallthevariedwaystocalculateaP/Eratio,theShillerP/Emeasurehashistoricallyshownthehighestpredictivepoweroverfuture10‐yearreturns.4Ourbuildingblockapproachisconsistentacrossequitycategories:

Assumed(Expected)USInflation+CurrentDividendYield+ExpectedRealEarningsGrowth+ReversioneffectofP/E(halfwaytolong‐termmean,over10years)

TheseinputsareavailablewithreliableandrobustdatafortheUSlarge‐capstockmarket,butnotforUSsmall‐capequitiesorforglobalequities.Forthisreason,wehavechosentoanchorourUSsmall‐capandglobalequityassumptionstoourUSlarge‐capequityassumptioninseveralways.

4 Vanguard.Forecastingstockreturns:Whatsignalsmatter,andwhatdotheysaynow?https://personal.vanguard.com/pdf/s338.pdf

CurrentDividendYield

ExpectedReal EarningsGrowth

Inflation

(+/‐)P/EReversionEffect

EquitySecurityReturn

CapitalizationPremiumImpliedEquityRiskPremium

Expected10‐YearTreasuryReturn

17

USLarge‐CapEquityModeled:USMid‐andLarge‐CapitalizationEquities


Risk:18.75%OurreturnassumptionsforUSlarge‐capequityaretheaverageoftwoseparateapproaches:(i) avaluation‐basedbuilding‐blockapproachand;(ii) afreecashflowtoequitymodel.

BuildingBlockApproachWefindtheShillerP/Emetrictobethemostusefulofvariousvaluationmetricsfromtheperspectiveofutilityinforecastingreturns.ThefollowingchartdepictstheShillerP/EmetricfortheUSmarket,since1951(thepost‐WWIIperiod).TheShillerP/Eatagivenpointintimeisdepictedonthehorizontalaxis,andthesubsequent10‐yearinflation‐adjustedreturnisdepictedontheverticalaxis.Wehavedecomposedthedataarrayintothreeeconomicregimes–thepost‐warboom(inblue;1951‐1965);thegreatinflationaryperiod(intan;1966‐1984);andthegreatmoderation(ingrey;1985‐2017).Examiningthedatathiswayyieldsusefulinsightsand,importantly,highpredictivepowerfortheShillerP/Emetricoversubsequentrealreturn.TheS&P500’scurrentpositiononthechartisindicatedbytheboldverticalline.

R²=0.878

R²=0.880

R²=0.8744

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Starting‐PointShillerP/EValuation

Long‐TermShillerP/Eversus10‐yrInflation‐AdjustedReturnsByEconomicRegime,Since1951(Postwarperiod)

CurrentValue PostwarBoom GreatInflation GreatModeration

18

Forthevaluation‐basedbuildingblockapproachcomponentofUSLarge‐CapEquityreturn,wecreateourbuildingblocksfromtheS&P500Index:

1.96% Inflation 1.84% CurrentDividendYield 1.53% Long‐TermCompoundAverageRealEarningsGrowth(Since1871) Forthevaluationbuildingblock,wemeasureexpectedP/Ereversionhalfwaytolong‐termmean: ShillerP/E Current 32.25

Long‐TermAverage 16.81 AnnualReversionEffect ‐3.15% (halfwaytolong‐termaverage)

ThebuildingblocksapproachresultsinanexpectedcompoundreturnforUSLarge‐CapEquityof2.17%.ThisapproachrepresentshalfofourcalculationforLarge‐CapUSEquity.EquityRiskPremium/DiscountedFreeCashFlowModelFortheimpliedequityriskpremium,wereferenceandmodifyadiscountedfreecashflowmodelcreatedbyProfessorAswathDamodaranoftheSternSchoolofBusiness5thatusesafreecashflowtoequityapproachtoaccountfordividendsaswellasstockbuybacks.Ourmodifiedfree‐cash‐flow‐to‐equitymodelemploysseveralinputvariables:Beginning(current)S&P500level= 2,673.61Baseyearfreecashflowtoequity,S&P500= $108.286ExpectedS&P500earningsgrowthovernext5years= 6.10%7ExpectedS&P500earningsgrowthforyears5‐10= 2.01%8WeapplyastandarddiscountedcashflowmethodologytothesevariablesandsolvefortherateofgrowththatmakesthediscountedforecastedvalueoftheS&P500identicaltotoday’svalue.

2,673.61108.28 1.061

1108.28 1.061

1108.287 1.061

1108.28 1.061

1108.28 1.061

1108.28 1.061 1.0201

0.0201 1

SolvingforryieldstheexpectednominalreturnfortheS&P500overthenext10years,undertheseassumptions.Thatrateofreturnis6.95%.Subtractingourassumed10‐YearTreasuryreturnof2.01%resultsinanexpectedequityriskpremiumof4.95%.

5 http://pages.stern.nyu.edu/~adamodar/ 62017S&P500Dividends=$48.12+buybacks=$60.16.7I/B/E/Sanalystconsensusearningsgrowthoverthenextyearis7.05%.Historically,theI/B/E/Sconsensusanalystforecasthasoverstatedsubsequentactualearningsgrowthby15.6%.Wereduceourassumptionforearningsgrowthby13.5%(1‐(1/1.156))accordingly.

8 Ourforecastedreturnforthe10‐yearTreasuryBond,asaproxyfortheten‐yearrisk‐freerate.

19

Thisimpliedequityriskpremiumishigherthanwhathistoryhasdelivered.Tocorrectforthis,weaveragethecurrentimpliedforward‐lookingequityriskpremium(4.95%)andthelong‐termhistoricalgeometricaveragerealizedequityriskpremium(4.62%)toderiveanequityriskpremiumestimateof4.78%forUSLarge‐CapEquity.Substitutingthisassumedequityriskpremiumintothemodelresultsinareturnestimateof6.79%.CombiningtheTwoApproachesAveragingtheexpectedreturnsgeneratedbythebuilding‐blocksapproachandthediscountedfreecashflowmodelyieldsanexpectedcompoundreturnof4.48%.USSmall‐CapEquity

Modeled:USSmall‐CapitalizationEquitiesCompoundReturn:4.25%


OurreturnassumptionforUSSmall‐CapEquityusesasimilarbuildingblocksapproachasourapproachforUSLarge‐Cap.Becausedataismuchmorelimitedforsmall‐capequitiesthanforlarge‐capequities,weevaluatesmall‐capequitiesrelativetolarge‐capequitiesratherthanrelativetotheirownhistory.ForUSSmall‐CapEquity,wecomparethebuild‐upmethodfortheRussell2000IndexandS&P500Indexoverthelongestcommontimeperiodforthetwoindexes(1979‐2017).Thebuild‐upmethodisonlyhalfofourUSLarge‐CapEquityassumedreturn,sowedividethepremiuminhalfandaddorsubtractitfromourfinalUSLarge‐CapEquityreturn.Whileourassumptionmodelsthefulluniverseofsmall‐capstocks,thedataweuseexcludescompanieswithnegativeearnings.Ouranalysishasshownthat,ascomparedtousingthedatafromthefulluniverseofsmall‐capstocks,usingthedatasetthatexcludesnegativeearnershasyieldedhigherpredictivepoweroverfuturereturnsofthefullindex,whichincludesthenegativeearners.OurbuildingblocksforUSSmall‐CapEquityareasfollows:

1.96% Inflation 1.25% CurrentDividendYield 2.47% Long‐TermRealEarningsGrowth WemeasureexpectedP/Ereversionhalfwaytolong‐termmean: ShillerP/E Current 31.20

Long‐TermAverage 21.63 AnnualReversionEffect ‐1.80% (halfwaytolong‐termaverage)

20

Thebuild‐upapproachresultsinanexpectedcompoundreturnforUSSmall‐CapEquityof1.92%,anegativepremiumof0.76%relativetoUSLarge‐CapEquityusingasimilarmethodologyoverthelongestcommontimeperiod(1988‐2017)forwhichwehavereliabledata. USLarge‐CapBuild‐up 2.69% USSmall‐CapBuild‐up 1.92% Small‐CapPremium ‐0.76%

Since1994,thisapproachhassystematicallyunderstatedsubsequent10‐yearreturnstosmall‐capstocks,by0.30%peryear:

Toaccountforthisbias,wetakethedifferencebetweenthemodel’scurrentpredictedpremium(‐0.76%)andthelong‐termaveragepredictedpremium(‐0.30%)andapplyonlythedifferential.Then,weaddonlyhalfofthatdifferentialtoourassumptionforUSLarge‐CapEquities,becausethebuilding‐blockscalculationitselfrepresentedonlyhalfofourcalculationofUSLarge‐CapEquityreturn.

USLarge‐CapAssumedReturn4.48% Small‐CapPremium ‐0.23%(halfofthecalculatedpremium) ReturnAssumption 4.25%Ourmodelingresultsinanegativereturnpremiumforsmall‐capstocksrelativetolarge‐capstocks.Historyhasshownthatsmall‐capstockshaveoutperformedtheirlarge‐capcounterpartsonlywhenbeginningatarelativevaluationdiscount,whichisnotthecasetoday:

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Predicted(SmallCap‐LargeCap)AverageSince94

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USEquity

Modeled:USEquities,AllCapitalizationsCompoundReturn:4.46%


OurreturnassumptionforUSEquityisintendedtomodeltheentireUSequitymarket.Itassumesthecurrentweightingoflarge‐andsmall‐capitalizationequitiesintheUSequitymarket–92%large,and8%small9.TheseweightsareappliedtotheunderlyingUSLarge‐CapandUSSmall‐CapEquityassumptionstoyield4.46%incompoundterms:

(92%x4.48%)+(8%x4.25%)=4.46%.

Non‐USLarge‐CapEquityModeled:Non‐USLarge‐CapitalizationEquities,DevelopedandEmerging


Risk:23.25%Webuildseparateassumptionsfordevelopedandemergingnon‐USmarkets,andthenweighthemaccordingtocurrentmarketweightstoconstructourNon‐USLarge‐CapEquityassumption,whichisintendedtomodelequitiesofbothdevelopedandemergingmarkets.OverthelongestcommonperiodforwhichwehavebothUS(S&P500Index)andnon‐USdevelopedmarkets(MSCIEAFEIndex)earningsdata(since1993),non‐USdevelopedmarketshavegrownatonly53%timestherateofUSlarge‐capitalizationstocks,inrealterms.Weapplythis

9FTSE/Russell.

LargeCapOutperforms

SmallCapOutperforms

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RealativeValue(Sm

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RatioofUSSmall‐CaptoUSLarge‐CapShillerP/EandSubsequent10‐YearRelativePerformance

RatioofUSSmall‐CaptoUSLarge‐CapShillerP/E AverageRelativeValuation

22

proportiontoourassumedlong‐termearningsgrowthrateforUSlarge‐capitalizationstocks(1.53%)toyieldanassumednon‐USdevelopedmarketsearningsgrowthrateof0.81%.Fordevelopedmarkets,ourassumedbuildingblocksareasfollows: 1.96% Inflation 2.94% CurrentDividendYield 0.81% AdjustedCompoundAverageRealEarningsGrowth WemeasureexpectedP/Ereversionhalfwaytolong‐termmean: ShillerP/E Current 17.8

Long‐TermAverage 13.410 AnnualReversionEffect ‐1.41%(halfwaytolong‐termaverage)

Thisapproachyieldsanexpectedcompoundreturnfordeveloped‐marketsNon‐USLarge‐CapitalizationEquitiesof4.29%,apremiumof2.12%relativetoourcalculationofUSLarge‐CapEquityusingsimilarbuild‐upmethodology.

USLarge‐CapBuild‐up 2.17% Non‐USDevelopedBuild‐up 4.29% Non‐USDevelopedPremium +1.06%(assumeshalfofUSLarge‐Capapproach) USLarge‐CapAssumedReturn4.48% Non‐USDevelopedPremium +1.06% ReturnAssumption 5.54%Ouremergingmarketsequityapproachisdetailedbelow.Theassumedcompoundreturnis6.56%.Developedmarketscurrentlycomprise75%,andemergingmarkets25%,ofthenon‐UStotalequitymarketcapitalization.Applyingthoseweightstoourdevelopedandemergingmarketsassumptionsyieldsanon‐USlarge‐capitalizationcompoundreturnassumptionof5.80%. 10OverthelongestcommonperiodforwhichwehavebothUS(S&P500)andDevelopedNon‐US(MSCIEAFE)earningsseries(since1995),EAFEhastradedatanaveragevaluationlevelapproximately78%oftheleveloftheS&P500.Weapplythisfractiontoourassumptionforthelong‐termP/EofUSlarge‐capitalizationstockstoarriveatourassumedlong‐termaveragevaluationleveltowhichweexpectnon‐USlarge‐capitalizationstockstorevert.

23

Non‐USSmall‐CapEquityModeled:Non‐USSmall‐CapitalizationEquities,DevelopedandEmerging


Risk:28.00%

Asfarbackaswehavereliablepricedata(1994),non‐USsmall‐capstockshaveoutperformednon‐USlarge‐capstocksby0.45%peryear.ToourNon‐USLarge‐CapEquityassumption,weaddamoreconservativecompoundreturnpremiumof0.25%.Thisyieldsacompoundreturnassumptionof6.05%.Givenverylimiteddatafornon‐USsmall‐capequities,wearenotinclinedtomakeavaluationadjustmentbasedonreversiontoanaverage.EmergingMarketsEquity

Modeled:EmergingMarketsEquityCompoundReturn:6.56%


OurreturnassumptionforEmergingMarketsEquityisconstructedwithabuildingblocksapproach,butwithanadditionaladjustmenttothelong‐termearningsgrowthbuildingblock,givenlimiteddatahistoryforemergingmarketsstocks.OverthelongestcommonperiodforwhichwehavebothUS(S&P500Index)andemerging(MSCIEMIndex)marketsearnings(1995),emergingmarketearningshavegrownat3.08timestherateofUSlarge‐capitalizationstocks.Goingforward,wedonotexpectthisextraordinarygrowthratetocontinueindefinitelyandhavecutthelong‐termratioinhalfto1.54.Weapplythisproportiontoourassumedlong‐termearningsgrowthrateforUSlarge‐capitalizationstockstoyieldanassumedemergingmarketsearningsgrowthrateof2.35%.Ourassumedbuildingblocksareasfollows:

1.96% Inflation 2.21% CurrentDividendYield 2.35% AdjustedCompoundAverageRealEarningsGrowth(reducedby50%)

WemeasureexpectedP/Ereversionhalfwaytolong‐termmean:

ShillerP/E Current 15.0

Long‐TermAverage 14.411

11Since1995,thelongestdataseriesavailablefornon‐USmarketearnings,theaverageShillerP/Eratioforemergingmarketshasbeen18.6.Wenotethattheperiodsince1995hasgloballybeenaperiodofhighervaluationsthanhavehistoricallybeenexperienced.Forthisreason,wedonotassumethatemergingmarketsearningswillreverttotherelativelyhighlevel–instead,weassumethatemergingmarketswillcommandanaverageP/Eratio1.00higherthandevelopednon‐USmarketswill.

24

Annualreversioneffect‐0.20% (halfwaytolong‐termaverage)AddingthisP/Ereversionmeasuretotheotherbuildingblocksyieldsanexpectedcompoundreturnof6.32%,a4.15%premiumoversimilarlycalculatedUSLarge‐CapEquity:

USLarge‐CapBuild‐up 2.17% EmergingMarketsBuild‐up 6.32% EmergingMarketsPremium +4.15%AddinghalfofthispremiumtoourassumptionforUSLarge‐CapEquityyields6.56%: USLarge‐CapAssumedReturn4.48% EmergingMarketsPremium +2.08% ReturnAssumption 6.56%Non‐USEquity

Modeled:Non‐USEquities,AllRegions&CapitalizationsCompoundReturn:5.83%


OurreturnassumptionforNon‐USEquityisintendedtomodeltheentireNon‐USequitymarket.Itassumesthecurrentweightingoflarge‐capandsmall‐capmarketsequitiesintheinternationalequitymarket–86%large‐capand14%small‐cap12.TheseweightsareappliedtotheunderlyingNon‐USLarge‐CapEquityandNon‐USSmall‐CapEquityassumptions.Thisweightingyieldsacompoundreturnassumptionof5.83%:

(86%x5.80%)+(14%x6.05%)=5.83%.

12MSCI,MorningstarDirect

25

ALTERNATIVESAlternativeassetsshareacommonelementofnoteasilybeingmodeledwithpublic‐marketindexproxies.Aswell,wearemorereluctanttorelyontheirlong‐termhistory,givengrowthinassetsallocatedtosuchstrategiesoverthelastseveraldecadesandthedynamicnatureofstrategiesemployed.Instead,weemployabuild‐upapproachtoidentifyandmodeltheirsourcesofreturn.RealEstate

Modeled:Public(USEquityREITs)andOpen‐EndedPrivateCoreRealEstateCompoundReturn:4.57%


Ourexpectedreturnreflectsgoing‐incapratesforpublicequityandcoreprivaterealestate.ForpublicequityREITs,wecalculatethecurrentcaprate,definedasincomedividedbyprice,oftheFTSENAREITAllEquityREITSIndex:3.85%.ThefollowingchartdepictstheinverseofthecapratefortheequityREITbenchmark:itshistoricalprice‐to‐incomeratio.Thepresentlowcaprateisexplainedbyhighvaluationsrelativetotheindex’sownhistory.

OurcaprateassumptionforcoreprivaterealestateisbasedontheUrbanLandInstituteconsensusestimateoftheNCREIFcapitalizationrateasofDecember31,2017:5.30%incompoundterms.13Thiscapratereflectscurrentincomereturnonanunleveredbasisandexcludescapitalappreciation.

13 UrbanLandInstitute.http://uli.org/research/centers‐initiatives/center‐for‐capital‐markets/barometers‐forecast‐and‐data/uli‐real‐estate‐consensus‐forecast/

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NAREITAllEquityREITSValuation:Price/12‐MonthTrailingIncome

Price/Income AveragePrice/Income

26

Averagingthesetwocapratesyieldsareturnassumptionof4.57%.Wenotethattheprimarydriverofreturnforcorerealestateoverthelongtermhasbeenincome,notappreciation.ForequityREITS,inrealtermssince1973,historicalpriceappreciationhasaveraged0.33%peryear,andincomehasaveraged3.24%peryear.DiversifiedInflation‐Related

Modeled:Diversifiedportfoliocontaining1/3each:RealEstate,Commodities,andUSTIPSCompoundReturn:3.65%


Weassumeadiversifiedportfoliocontaining1/3eachinUSTIPS,RealEstate,andCommodities.TheUSTIPScomponentissimplyourexpectedreturnforUSTIPS,asoutlinedabove:2.12%,incompoundterms.TheRealEstatecomponentisourRealEstateAssumption:4.57%incompoundterms.FortheCommoditiescomponent,webuildamodelassumingthatcommodityreturncanbedecomposedintothreesources:collateralreinvestmentyield,commodityspotreturn,androllyield.Weassume0%forrollyield,knowingthatithasbeenpositiveandnegativeovervarioushistoricalperiods,asthebuyingandsellingbalancebetweencommodityinvestorsandcommodityconsumershasshifted.Overthelastdecade,rollyieldhasbeennegative.Forspotreturn,wecalculateaseriesofthelast10yearsofrealpricesfortheBloombergCommodityIndexandassumethatthecurrentrealpriceoftheindexwillreverthalfwaytoits10‐yearaverage,inevenincrementsoverthenext10years.ThecurrentrealspotpricefortheBloombergCommodityIndexis85.9,andits10‐yearaveragerealpriceis139.2.Revertinghalfwaytothisaveragerealpriceimpliesacompoundrealspotreturnof2.47%peryear.Insummary,fortheCommoditiescomponent: Collateral: 1.79%(ourassumednominalreturnforCashEquivalents) Spotreturn: 2.47%(halfwaytolong‐termaverage) Rollyield: 0.00% Commodityreturn: 4.26%FortheDiversifiedInflation‐Relatedassumption,weassumeacompoundreturnof:

1/3(TIPS)+1/3(RealEstate)+1/3(Commodities)=1/3(2.12%)+1/3(4.57%)+1/3(4.26%)=3.65%

27

MarketableAlternativesModeled:HedgeFundsofFunds,GlobalGTAA,&Daily‐ValuedAlternativeStrategies


Risk:11.75%Weassumeadiversifiedportfoliothatwilltendtoapproximatethefollowingmarketexposuresovertime: 30%USEquity 30%Non‐USEquity 20%CoreFixedIncome 20%Non‐CoreFixedIncomeWeightingthoseassumptionsaccordinglyresultsinacompoundreturnassumptionof4.12%.Thisapproachdoesnotexplicitlyreflecttheuseofleverageinmarketablealternativesstrategies.Alternativesvehiclesthatemployleveragecanearnhigherreturns,butduetothemechanicsofperformance‐basedfeeschedules,alsosubtracthigherfeesfromthosereturns.Giventhatourassumptionsetisintendedtobepassiveinnatureandnotreflectactivemanagement,forhedgefunds,weareassuminganindustryaveragehedgefundoffunds.Non‐MarketableAlternatives

Modeled:VentureCapital,PrivateEquity,&DistressedCredit,inLockupVehiclesCompoundReturn:6.52%


Weassumeadiversifiedportfoliothatwilltendtoapproximatethefollowingmarketexposuresovertime,plusapremiumforilliquidity: 50%USEquity 50%Non‐CoreFixedIncome +3.00%illiquidity/leveragepremiumWeightingthoseassumptionsaccordinglyresultsinacompoundreturnassumptionof6.52%.Giventhatourassumptionsetisintendedtobepassiveinnatureandnotreflectactivemanagement,weareassuminganindustry‐averageactivemanagerorcollectionofactivemanagers.

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RISKOurriskassumptionsaremostlyderivedfromhistory,butwehaveenhancedhistoricalmetricswithqualitativeoverlaysinseveralassetcategories.Foreachassetcategory,webeganbyexaminingthefollowinghistoricalannualreturns:Inflation USCPICashEquivalents 91‐DayT‐BillsLow‐DurationFixedIncome BloombergBarclays1‐3YearGovernment/CreditCoreFixedIncome BloombergBarclaysUSAggregateCorePlusFixedIncome 80%CoreFixedIncome,20%Non‐CoreFixedIncomeNon‐CoreFixedIncome 50%MLHighYieldMasterII,50%JPMorganEMBIbackto1994;

100%MLHighYieldMasterIIbefore1994Long‐DurationFixedIncome BloombergBarclaysLongGovernment/CreditTIPS BloombergBarclaysUSTIPSShort‐TermTIPS BloombergBarclaysUS0‐5YearTIPSUSEquity Russell3000backto1979;S&P500before1979USLarge‐CapEquity Russell1000backto1979;S&P500before1979USSmall‐CapEquity Russell2000Non‐USEquity MSCIACWIexUSIMIbackto1994;MSCIEAFEbefore1994Non‐USLarge‐CapEquity MSCIACWIexUSbackto2001;MSCIEAFEbefore2001Non‐USSmall‐CapEquity MSCIACWIexUSSmallCapEmergingMarketsEquity MSCIEmergingMarketsRealEstate FTSENAREIT,NCREIFProperty,andNCREIFODCE(separately)DiversifiedInflation‐Related 1/3each:FTSENAREIT,BloombergBarclaysUSTIPS,Bloomberg

CommodityMarketableAlternatives HFRIFundofFunds;and30%ourUSEquityseries,30%ourNon‐US

Equityseries,20%ourCoreFixedIncomeseries,and20%ourNon‐CoreFixedIncomeseries(separately)

Non‐MarketableAlternatives Averageof2xourUSEquityseriesand2xourNon‐CoreFixedIncomeseries

Ineachcase,wecalculatedthelongest‐termstandarddeviationofreturnspossibleforthecategory.Then,wecalculatedthestandarddeviationofannualreturnsoverthelasttenyears.Theaverageofthesetwofiguresrepresentsourbase‐caseriskassumption.Next,weexaminedtheworstannualreturnforeachproxyindex,goingbackasfaraspossibleintohistory.Weassumedthisreturnastheworst‐casescenario.Insomecases,thenormalreturndistributionimpliedbyourreturnandriskassumptionssuggestedthattheactualworst‐casescenariohadlessthana2%probability(1in50years)ofoccurring.Becauseweareuncomfortableassumingthatobservedrealityisunlikely,weadjustedourriskassumptionupwarduntiltheworst‐casescenariohadatleasta2%probabilityofoccurringunderourassumednormalreturndistribution.Toperformthisprobabilityanalysisforprivaterealestate,weexaminedrollingtwo‐

29

yearperiodstoaccountforthefactthatdeclines,asmeasuredbyappraisalsandilliquidity,occurmoreslowlythaninpublicmarkets.Finally,basedonthisanalysisandourqualitativeassessmentofthequalityandlongevityofourreturndata,wemadeseveralqualitativeadjustments,wherenoted.Theresultsofthisriskanalysisfollow.Thefollowingtabledepictsactualstandarddeviationsofannualreturn,measuredinthelongterm(asfarbackashistorywillallow),forthelasttenyears,andtheaverageofthosetwofigures.AddingorsubtractingourqualitativeadjustmentresultsintheRiskAssumptionatthefarright.

LongestTerm 10Years Average

QualitativeAdjustment

RiskAssumption(Rounded)

Inflation 4.90% 0.91% 2.90% 0.00% 3.00%CashEquivalents 3.30% 0.44% 1.87% ‐0.75% 1.00%Low‐DurationFixedIncome 4.61% 1.51% 3.06% 0.00% 3.00%CoreFixedIncome 6.80% 2.99% 4.90% 0.00% 5.00%Core‐PlusFixedIncome 5.27% 4.40% 4.84% 0.50% 5.25%Non‐CoreFixedIncome 12.57% 15.68% 14.13% 0.00% 14.25%Long‐DurationFixedIncome 10.91% 9.42% 10.17% 0.00% 10.25%TIPS 6.00% 6.58% 6.29% 0.00% 6.25%Short‐TermTIPS 3.76% 3.77% 3.77% 0.00% 3.75%USEquity 17.10% 19.79% 18.44% 0.25% 18.75%USLarge‐CapEquity 17.16% 19.78% 18.47% 0.25% 18.75%USSmall‐CapEquity 18.90% 20.94% 19.92% 0.00% 20.00%Non‐USEquity 22.64% 24.66% 23.65% 0.00% 23.75%Non‐USLarge‐CapEquity 22.16% 24.10% 23.13% 0.00% 23.25%Non‐USSmall‐CapEquity 25.41% 30.60% 28.01% 0.00% 28.00%EmergingMarketsEquity 33.76% 35.37% 34.57% ‐5.25% 29.25%RealEstate 18.66% 19.33% 19.00% 0.00% 19.00%DiversifiedInflation‐Related 12.26% 14.56% 13.41% 1.00% 14.50%MarketableAlternatives 9.76% 9.44% 9.60% 2.26% 11.75%Non‐MarketableAlternatives 26.61% 32.66% 29.64% 0.00% 29.75%

StandardDeviationofReturns

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Thefollowingtableexaminestheprobabilityoftheactualexperiencedworstcaseoccurringunderourassumednormaldistributionofreturns,asimpliedbyourexpectedreturnandstandarddeviationofreturns,afteraccountingforqualitativeadjustmentstorisk.Wemeasuretheactualworst‐casescenarioin“sigmas,”orstandarddeviationsfromourassumedmeanreturn.Measuringthisway,weask,“Howlikelywastheactualexperiencedworstcase,accordingtothedistributionparameterswehaveassumed?”Wehavequalitativelyadjustedseveralassetclassestoensurethattheprobabilityoftheactuallyexperiencedworstcaseisalwaysgreaterthan2%,meaningweassumethattheexperiencedworstcasehasatleastaone‐in‐fifty‐yearchanceofhappeningunderourassumptions.Wehavemadesimilaradjustmentsforassetclasseswithlimitedreturnhistory,toensurethatourassumptionsimplythattheactualobservedworstcasewasatleasta3%probability(roughly,one‐in‐30‐yearchanceofhappening).Whenmakingqualitativeadjustmentstomeetthesecriteria,weadjustthenumbersonlyenoughtomeetthesecriteria.

ActualWorstCase,in

SigmasfromAssumption

ImpliedProbabilityofActualWorstCaseOccurring

CashEquivalents 0.02% (2011) 1.59 11.3%Low‐DurationFixedIncome 0.55% (1994) 0.67 50.3%CoreFixedIncome ‐2.92% (1994) 1.15 25.2%Core‐PlusFI ‐4.26% (1994) 1.31 19.1%Non‐CoreFixedIncome ‐18.86% (2008) 1.58 11.3%Long‐DurationFixedIncome ‐8.83% (2013) 1.16 24.6%TIPS ‐8.61% (2013) 1.74 8.3%Short‐TermTIPS ‐2.03% (2008) 1.16 24.5%USEquity ‐37.31% (2008) 2.32 2.0%USLarge‐CapEquity ‐37.60% (2008) 2.33 2.0%USSmall‐CapEquity ‐33.79% (2008) 2.00 4.5%Non‐USEquity ‐45.99% (2008) 2.30 2.2%Non‐USLarge‐CapEquity ‐45.24% (2008) 2.31 2.1%Non‐USSmall‐CapEquity ‐50.01% (2008) 2.12 3.4%EmergingMarketsEquity ‐53.33% (2008) 2.17 3.0%RealEstate ‐37.34% (1974) 2.29 2.2%DiversifiedInflation‐Related ‐28.61% (2008) 2.31 2.1%MarketableAlternatives ‐21.37% (2008) 2.20 2.7%Non‐MarketableAlternatives ‐56.17% (2008) 2.24 2.5%

AlternatebenchmarksforRealEstateandNon‐MarketableAlternatives:NCREIFProperty(2Years) ‐22.23% (2008‐9) 1.50 13.4%NCREIFODCE(2Years) ‐36.79% (2008‐9) 2.26 2.4%MarketableAlternatives(build‐up) ‐27.71% (2008) 2.74 0.6%

WorstYear

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OurqualitativeadjustmentstoRiskwereasfollows:CashEquivalents(‐0.75%)

Whilethelong‐termstandarddeviationofreturnstocashhasbeengreaterthan3%,thatvolatilitywasexperiencedathigherlevelsofcashreturn.Webelieveitisunlikelyforthedistributionofreturnstocashequivalentstobeaswideashistoricallyobserved,givenitscurrentlowlevelofreturn.Wequalitativelyadjusttherisktocashequivalentsdownwardby75basispoints.

Core‐PlusFixedIncome(+0.50%)

Whilebecauseofdiversificationeffectslong‐termvolatilityforourmodeledCore‐PlusserieshasbeenlowerthanthatforCoreFixedIncome,recent(last10years)volatilityhasbeenapproximately50%higher.Ourmodestadjustmentacknowledgesthattheriskierelementsinherentinplussectorsprovideawiderdistributionofreturns,regardlessoftheirmeasuredyear‐over‐yearvolatility.

USEquity,USLarge‐CapEquity,DiversifiedInflation‐Related(+0.25%,+0.25%,+1.00%)

Thesecategorieswereadjustedupwardtomaketheiractualworst‐caseexperiencegreaterthana2%probabilityofoccurringundertheassumeddistribution.

EmergingMarketsEquity(‐5.25%)

Giventhelimitedhistoryforapublic‐marketproxyforeachassetclass,wearereluctanttorelytooheavilyonhistoricallymeasuredvolatility.Assuch,weadjustedtheriskdownwardsuchthattheassetclass’sactualworstcase(2008)representsanapproximately3%probabilityofoccurrenceundertheassumeddistribution.

MarketableAlternatives(+2.26%)

Thisadjustmentaveragesourtwoapproachesformodelingthehistoryforthisassetcategory.Theupwardadjustmentmakestheriskassumptionhalfwaybetweenthehistoricallymeasuredvolatilityofeachapproach(HFRIFundofFundsIndex,andbuild‐upapproach).

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CORRELATIONCOEFFICIENTSOurforward‐lookingcorrelationassumptionsaremostlyderivedfromlong‐termhistorybutemphasizetherecentpast.Ourprocessfirstidentifiesareasonableproxyforeachassetcategory,typicallyanindexthatrepresentstheassetclass.Forseveralassetclasses,wehaveusedourjudgmenttoconstructaproxyreturnstreamfortheassetclassthateitherhasalongerhistoryforevaluation,ortoconstructamarketableproxyforanon‐marketableasset.Ourcorrelationassumptionsarebasedonthesereturnstreams:Inflation USCPICashEquivalents 91‐DayT‐BillsLow‐DurationFixedIncome BloombergBarclays1‐3YearGovernment/CreditCoreFixedIncome BloombergBarclaysUSAggregateCorePlusFixedIncome 80%CoreFixedIncome,20%Non‐CoreFixedIncomeNon‐CoreFixedIncome 50%MLHighYieldMasterII,50%JPMorganEMBIbackto1994;

100%MLHighYieldMasterIIbefore1994Long‐DurationFixedIncome BloombergBarclaysLongGovernment/CreditTIPS BloombergBarclaysUSTIPSShort‐TermTIPS BloombergBarclaysUS0‐5YearTIPSUSEquity Russell3000backto1979;S&P500before1979USLarge‐CapEquity Russell1000backto1979;S&P500before1979USSmall‐CapEquity Russell2000Non‐USEquity MSCIACWIexUSIMIbackto1994;MSCIEAFEbefore1994Non‐USLarge‐CapEquity MSCIACWIexUSbackto2001;MSCIEAFEbefore2001Non‐USSmall‐CapEquity MSCIACWIexUSSmallCapEmergingMarketsEquity MSCIEmergingMarketsRealEstate FTSENAREIT,NCREIF,andNCREIFODCEMarketableAlternatives HFRIFundofFundsDiversifiedInflation‐Related 1/3each:FTSENAREIT,BloombergBarclaysUSTIPS,Bloomberg

CommodityNon‐MarketableAlternatives Averageof2xtheNon‐CoreFixedIncomeseriesand2xtheUS

EquityseriesUsingthosestreams,weconstructedacorrelationmatrixthattakesthesimpleaverageoffourothercorrelationmatrices–constructedwith3years,5years,and10yearsofdata,andonewithasmuchdataaspossiblegoingbacktoeachseries’inception.Averagingthesefourmeasuresgivesacknowledgementtothelong‐termhistorywhileemphasizingtherecentpast,whencorrelationshavebeenhigherthanlong‐termhistoryhasdelivered.Thisapproachisthereforeconservativeinassumingthediversificationbenefitthatwillappearfromcorrelationinourmodeling.Wequalitativelyadjustedonlytherealestatecorrelationcoefficients,becauseoftheirilliquidity.OurassumedcoefficientsforrealestateaveragethecalculatedcoefficientsforpublicREITsandprivaterealestate.

33

Finally,weranourcalculatedcorrelationcoefficientsthroughtheIbbotsonstatisticalcorrelationmatrixtester,whichmadeslightadjustmentstoensurethatthematrixispositivesemi‐definite.Ourassumedreturncorrelationmatrixfollows:

Inflation

CashEquivalents

Low‐DurationFixedIncome

CoreFixedIncome

Core‐PlusFixedIncome

Non‐CoreFixedIncome

Long‐DurationFixedIncome

TIPS

STTIPS

USEquity

USLarge‐CapEquity

USSmall‐CapEquity

Non‐USEquity

Non‐USLarge‐CapEquity

Non‐USSmall‐CapEquity

EmergingMarketsEquity

RealEstate

DiversifiedInflation‐Related

MarketableAlternatives

Non‐MarketableAlternatives

Inflation

1.00

0.08

0.01

‐0.11

0.00

0.22

‐0.19

0.03

0.23

0.11

0.11

0.12

0.13

0.12

0.15

0.13

0.00

0.19

0.16

0.16

CashEquivalents

0.08

1.00

0.17

0.09

0.07

0.02

0.08

0.08

0.11

‐0.01

‐0.01

‐0.01

0.06

0.06

0.05

0.11

0.00

0.13

0.03

0.00

Low‐DurationFixedIncome

0.01

0.17

1.00

0.80

0.72

0.30

0.62

0.66

0.63

‐0.15

‐0.13

‐0.21

0.04

0.04

0.03

0.16

0.24

0.35

‐0.10

0.01

CoreFixedIncome

‐0.11

0.09

0.80

1.00

0.92

0.43

0.94

0.80

0.54

‐0.08

‐0.06

‐0.17

0.09

0.09

0.09

0.17

0.41

0.41

‐0.03

0.11

Core‐PlusFixedIncome

0.00

0.07

0.72

0.92

1.00

0.74

0.87

0.83

0.63

0.20

0.22

0.10

0.39

0.39

0.38

0.46

0.56

0.61

0.22

0.43

Non‐CoreFixedIncome

0.22

0.02

0.30

0.43

0.74

1.00

0.42

0.55

0.53

0.62

0.63

0.53

0.77

0.77

0.74

0.78

0.59

0.73

0.58

0.83

Long‐DurationFixedIncome

‐0.19

0.08

0.62

0.94

0.87

0.42

1.00

0.74

0.41

‐0.04

‐0.03

‐0.12

0.10

0.10

0.09

0.16

0.45

0.40

‐0.01

0.13

TIPS

0.03

0.08

0.66

0.80

0.83

0.55

0.74

1.00

0.83

0.05

0.07

‐0.02

0.26

0.26

0.27

0.36

0.41

0.58

0.11

0.25

STTIPS

0.23

0.11

0.63

0.54

0.63

0.53

0.41

0.83

1.00

0.12

0.13

0.05

0.32

0.32

0.33

0.43

0.31

0.63

0.18

0.29

USEquity

0.11

‐0.01

‐0.15

‐0.08

0.20

0.62

‐0.04

0.05

0.12

1.00

1.00

0.90

0.83

0.83

0.78

0.69

0.59

0.56

0.73

0.95

USLarge‐CapEquity

0.11

‐0.01

‐0.13

‐0.06

0.22

0.63

‐0.03

0.07

0.13

1.00

1.00

0.88

0.83

0.84

0.78

0.69

0.59

0.56

0.73

0.95

USSm

all‐CapEquity

0.12

‐0.01

‐0.21

‐0.17

0.10

0.53

‐0.12

‐0.02

0.05

0.90

0.88

1.00

0.70

0.70

0.68

0.56

0.55

0.51

0.69

0.85

Non‐USEquity

0.13

0.06

0.04

0.09

0.39

0.77

0.10

0.26

0.32

0.83

0.83

0.70

1.00

1.00

0.97

0.89

0.52

0.64

0.76

0.88

Non‐USLarge‐CapEquity

0.12

0.06

0.04

0.09

0.39

0.77

0.10

0.26

0.32

0.83

0.84

0.70

1.00

1.00

0.95

0.89

0.52

0.64

0.75

0.89

Non‐USSm

all‐CapEquity

0.15

0.05

0.03

0.09

0.38

0.74

0.09

0.27

0.33

0.78

0.78

0.68

0.97

0.95

1.00

0.86

0.50

0.63

0.76

0.84

EmergingMarketsEquity

0.13

0.11

0.16

0.17

0.46

0.78

0.16

0.36

0.43

0.69

0.69

0.56

0.89

0.89

0.86

1.00

0.49

0.67

0.64

0.79

RealEstate

0.00

0.00

0.24

0.41

0.56

0.59

0.45

0.41

0.31

0.59

0.59

0.55

0.52

0.52

0.50

0.49

1.00

0.77

0.35

0.64

DiversifiedInflation‐Related

0.19

0.13

0.35

0.41

0.61

0.73

0.40

0.58

0.63

0.56

0.56

0.51

0.64

0.64

0.63

0.67

0.77

1.00

0.43

0.68

MarketableAlternatives

0.16

0.03

‐0.10

‐0.03

0.22

0.58

‐0.01

0.11

0.18

0.73

0.73

0.69

0.76

0.75

0.76

0.64

0.35

0.43

1.00

0.74

Non‐MarketableAlternatives

0.16

0.00

0.01

0.11

0.43

0.83

0.13

0.25

0.29

0.95

0.95

0.85

0.88

0.89

0.84

0.79

0.64

0.68

0.74

1.00

SellwoodConsulting2018CorrelationCoefficientAssumptions

34

APPENDIX:SOURCESWearegratefultoseveralsourcesforouranalysis.Theywere:FRED,TheSt.LouisFedFederalReserveEconomicData

https://fred.stlouisfed.org/

FTSENAREIThttps://www.reit.com/data‐research/reit‐indexes/ftse‐nareit‐us‐real‐estate‐index‐historical‐values‐returnshttp://www.ftse.com/products/indices/russell‐us

ProfessorAswathDamodaran,SternSchoolofBusiness http://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/implpr.html

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2581517

ResearchAffiliateshttp://www.researchaffiliates.com

Blackrock http://www.blackrock.com

PIMCO http://www.pimco.com

Standard&Poors http://www.standardandpoors.com

UrbanLandInstitutehttp://uli.org/research/centers‐initiatives/center‐for‐capital‐markets/barometers‐forecast‐and‐data/uli‐real‐estate‐consensus‐forecast/

MorganStanleyCapitalInternationalhttp://www.msci.com/

Moodyshttps://www.moodys.com/researchdocumentcontentpage.aspx?docid=PBC_151031https://www.moodys.com/researchdocumentcontentpage.aspx?docid=PBC_154805

ProfessorRobertShillerhttp://www.econ.yale.edu/~shiller/data.htm

Vanguardhttps://personal.vanguard.com/pdf/s338.pdf

ThisworkislicensedunderaCreativeCommonsAttribution‐NoDerivatives4.0InternationalLicense.Toviewacopyofthislicense,visithttp://creativecommons.org/licenses/by‐nd/4.0/.

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