Indian Association of Alternative Investment Funds (IAAIF) · determining the optimal portfolio...
Transcript of Indian Association of Alternative Investment Funds (IAAIF) · determining the optimal portfolio...
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IndianAssociationofAlternativeInvestmentFunds(IAAIF)
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PortfolioConstructionwithAlternativeInvestments
RohanMisra,CFA,FRMPartner&CEO
Transparency.Safety.Performance.
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FINDINGTHEEQUILIBRIUM
1.ASSETALLOCATION2.ACTIVEVSPASSIVEBALANCE3.MANAGER/FUNDSELECTION
PART1:PORTFOLIOCREATION
AGENDA
PART2:PORTFOLIOPERFORMANCEEVALUATIONANDREBALANCING
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Part1:PortfolioCreation
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…Bymixinganumberofpoorlycorrelatedassets,and-
• Maximizetargetreturnforagivenlevelofrisk
• Minimizeriskforatargetedlevelofreturn
Findingtheequilibrium…
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2waystoconstructportfolios
FINDINGTHEEQUILIBRIUMAssetAllocation
ActiveVsPassiveMix
Manager/FundSelection
BottomUp Topdown
• Usedbyprivateinvestors
• Adhoc–objectivesandrisknotfactored
• Susceptibleto“buyhighselllow”behaviour
• Favouredbyprofessionalinvestors
• Beginsbyexploringinvestmentrisk
• Createsaframeworktodecideinvestmentsbasedoninvestor’sobjectives
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TypicalObjectives:• Maximizereturnforagivenlevelofrisk• Minimizeriskforatargetedlevelofreturn
SettingobjectivesILLUSTRATIVEEXAMPLEReturnTarget:5%plusinflation;afterfeesRiskBudgetandRiskDefinition:Maxloss20%TimeHorizon:5 years
Return
TimeRiskBudget
Examplesofotherconsiderations1. Interim/TerminalGoals:financingasecondhomepurchase2. Constraints: dedicatedassets(residentialhome),assetclass
restrictions,shortsellingrestrictions
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FINDINGTHEEQUILIBRIUM
1.ASSETALLOCATION2.ACTIVEVSPASSIVEBALANCE3.MANAGER/FUNDSELECTION
PART1:PORTFOLIOCREATION
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Whatisanassetallocation(AA)
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Portfolio strategy that involves setting target allocations forvarious asset classes and attempts to balance risk versusreward, according to the investor’s risk budget, goals and timehorizon
Strategic Asset Allocation (SAA)Driven by the long-term investmentobjectives of the investor, with atypical time frame of > 1Y
Tactical Asset Allocation (TAA)Represents short-term tilts away fromthe SAA that are driven by visibleopportunities and risks
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WhybeginwithAA?
-50
0
50
100
150
BHBEquityFunds BHBBalancedFunds
HEI&IKEquityFunds
HEI&IKBalancedFunds
Rsquare%
DecompositionofTime-SeriesTotalReturnVariations
ActiveManagement AssetAllocationPolicy
MarketMovement InteractionEffect
BHB: Brinson,Hood,Beebower, DeterminantsofPortfolioperformance,1986IK: Ibbotson&Kaplan,DoesAAexplain40,90or100%ofperformance?,2000HEI: Henzel,Ezra,Ilkiw,TheimportanceoftheAAdecision,1991
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Choiceofassetclassesandtheirmixiskey• Forportfolioswithmarketexposures,e.g.longonlyportfolios,
marketmovement andassetallocationpolicymainlydrivereturnvariability
• Marketmovementisafunctionofthechosenassetclasses
• Assetallocationpolicydefineshowwehavemixedthechosenassetclasses
• CanweimproveanassetallocationbyincludingalternativeslikeHedgeFunds,PE,RealEstateandCommodities??
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AssetclasschoicesAssetClass ProxyIndex Currency Freq.
Equities MSCI AllCountry WorldNetTotalReturnIndex USD Monthly
Bonds BloombergBarclaysUSGovtTotalReturnIndexUnhedgedUSD USD Monthly
Commodities BloombergCMCITotalReturnIndex USD Monthly
HedgeFunds HFRIFundOfHedgeFundsCompositeIndex USD Monthly
RealEstate FTSEEPRANARIETDevelopedTotalReturnIndex USD Monthly
PrivateEquity CambridgeAssociatesUSPrivateEquityIndex USD Quarterly
Allindicesareassumedforillustrationpurposesonly,AlldatastartingJan-2000
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Summarystatistics
Equity Bonds Com Hedge Funds
Real Estate
Private Equity
Ann. Return 3.5% 4.8% 6.4% 3.2% 9.5% 9.7%
Ann. Volatility 16.0% 4.2% 16.2% 5.1% 19.1% 10.4%
Max DrawDown 54.9% 4.6% 57.1% 22.2% 67.2% 25.2%
Return/Volatility 0.22 1.16 0.40 0.64 0.50 1.01
EquityreturnsbiaseddownwardsassamplebeginsinTechbubble,Source:B&BAnalytics
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Risk/ReturnProfiles
Note! :Profilesmaybepotentiallybiasedduetothechosensamplesince2000Source:B&BAnalytics
0.0%
2.0%
4.0%
6.0%
8.0%
10.0%
12.0%
0.0% 5.0% 10.0% 15.0% 20.0% 25.0%
Bonds
HF
PE RE
COM
EQ
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In-samplecorrelations
Source:B&BAnalytics
Equity Bonds Com HedgeFunds
RealEstate
PrivateEquity
Equity 1.00
Bonds -0.28 1.00
Com 0.56 -0.17 1.00
HedgeFunds 0.67 -0.13 0.58 1.00
RealEstate 0.80 -0.03 0.49 0.58 1.00
PrivateEquity 0.52 -0.29 0.35 0.41 0.40 1.00
AverageCorrelations 0.45 -0.18 0.36 0.42 0.45 0.28
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ImpactofintroducingAltsina50Eq/50bondsportfolio
Source:B&BAnalytics,portfoliosrebalancedmonthly
50Eq;50Bonds
45Eq;45Bonds;10Com
45Eq;45Bonds;10HF
45Eq;45Bonds;10RE
45Eq;45Bonds;10PE
AnnReturn 3.9% 4.1% 3.8% 4.3% 4.4%
VolatilityAnn. 7.7% 7.9% 7.3% 8.6% 7.2%
Return/Vol 0.50 0.51 0.52 0.50 0.61
MaxDrawDown 30% 31% 29% 35% 29%
Returns adjustedtothevollevelof50Eq/50BondsPortoflio
Ann.Return 3.9% 4.0% 4.0% 3.9% 4.7%
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Databiasesandothervagariescommontoalternatives
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1.Survivorshipbias• Generallyacceptednotion: Indices,inparticularhedgefunds
ones,aredistortedbecause‘closed’fundsnolongercontribute– andremainingfundsoverstatetheaverage
• Somenuancedstudieslookatreasonforclosureandfindtheindexunderstatesactualperformance1. ‘Closures’duetonegativeperformance2. ‘Closures’tonewinvestorsduetostrongperformance
• Juryisstilloutthere!• Partialremedy– UseaHedgeFundFoF IndexReturns 1Y 2Y 3Y
HFRGlobalAssetWtd Composite 5.38% 8.31% 23.68%
HFRFundofFundsComposite 4.16% 4.94% 17.25%
Source:B&BAnalytics,HFRI 18
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2.Smoothed&staleprices• Esp.Relevantinthecontextofprivateequityandrealestate• Appraiserlacksconfidenceinthenewevidenceregarding
valuation- insteadattachestoomuchweightonthemostrecentempiricalevidence
• Reportedvaluationlagstruemarketvaluation• Positiveserialcorrelationisintroducedintoreturns
REDUCEDVARIABILITYINRETURNSACROSSTIMEà UNDERSTATESRISK
NEEDSTOBECORRECTED!
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Correctingforsmoothedprices• Vastbodyofacademicwork
exists• FGW1993isaonewidely
adoptedapproach• Removesserialautocorrelation
tounsmooththetimeseries• Timeseriesisregressedagainst
laggedvaluestoidentifystatisticallysignificantvariables.
• Unsmoothedseriesisobtainedbyremovingthesevariables.
PE Beta P-Value SignificantIntercept 1.66 0.01 YesLag1 0.32 0.00 YesLag2 0.17 0.09 NoLag3 -0.02 0.87 NoLag4 0.02 0.80 No
Beta P-Value SignificantIntercept 2.04 0.00 YesLag1 0.38 0.00 Yes
r(t) = (r*(t) – 0.38r*(t-1))/wUSPrivateEquity* VolatilitySmoothedSeries 9.4%UnsmoothedSeries 15.7%Return 9.7%Return/NewVol 0.62
*Source: Cambridge Associate, FGW : Fisher Geltner Webb 20
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• Mostmodelsassumethatreturnsfollowa“normaldistribution”– Chanceofmove>3s.d.<1/300– Skewness=0;returnsymmetry– Kurtosis=3
• Inrealitymostassetclassesexhibitnegativeskewandexcesskurtosis…i.elefttailrisk
3.Non-normalityandtailrisk
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ThiscanbeseeninourdataEquity Bonds Com Hedge
FundsReal
EstatePrivate Equity
Skewness -0.89 -0.20 -1.08 -1.15 -1.54 -0.57
Excess Kurtosis 2.47 1.36 4.07 4.26 7.15 1.94
Directlyincorporatingvolatilityintomodelswillunderestimateriskandleadtoincorrectallocations
0
20
40
60
-30%
-28%
-25%
-23%
-20%
-18%
-15%
-13%
-10% -8%
-5%
-3% 0% 3% 5% 8% 10%
13%
15%
18%
20%
23%
RealEstateMonthlyReturnDistribution
Source:B&BAnalytics 22
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Adjustingfornon-normality
Source:B&BAnalytics
Twoapproaches:
• Adjusttherisk(std.deviation)ofeachassetclassorinvestmenttocapturethehighermomentsofskewnessandkurtosisbeforedeterminingtheoptimalportfolioweights
• Directlyadjusttheportfolioriskmeasureintheassetweightingprocess(i.etheoptimizationprocess)toincorporatetheskewnessandkurtosisoftheportfolioforagivencombinationofweights
• Secondapproachisconvenient
• Bothapproachesareappropriateonlyifthehistoricaldistributionappropriatelycaptureshighermoments
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PortfolioMath
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Recap:essenceofportfolioconstruction
• Maximizetargetreturnforagivenlevelofrisk
• Minimizeriskforatargetedlevelofreturn
Howtomeasureportfolioreturn andwhatisportfoliorisk?
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PortfolioReturnWeightedaverageoftheexpectedreturns ofportfoliocomponents
Example:2assetclassportfolio
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Varianceasportfoliorisk• Notasimpleweightedaverageofindividualcomponentrisks.• Requiresanestimateofexpectedcovariancesbetweenassets–
whichfirstrequiresanestimateofthevolatilitiesofallassetsandthecorrelations betweenthem
Example:2assetclassportfolio
PortfolioVolatility:√0.0504=22.4%
(wi)’COV(wi)or
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• Investor’sdon’tthinkinvolatilityterms!• Focusisondownsiderisk• Valueatrisk(VaR)focusesonthelefttailofthereturndistribution• Interpretation:95%chancethatportfoliolosswillnotexceed
X%overagiventimehorizon;95%representsconfidence
VaRasaportfolioriskmeasure
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ParametricVaR• Assumesnormaldistribution– requiresonlymeanand
standarddeviationofreturnstocalculateVaR
• VaR (confidence)=Mean- Std.Dev*z
• ‘z’isthenormalz-scorecorrespondingtotheconfidencelevel(e.g.1.65for95%,1.96for99%)
• Simplebutpracticallylimited– doesnotincludenegativeskewandfattails!
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ModifiedParametricVaR• FormulaicadjustmenttoparametricVaRfortheempirically
observedskewandkurtosisoftheportfolioreturndistribution
• Somewhatbetteratcapturingnon-normalitybytransformingthenormal‘z’toamodified‘Z’incorporatinghighermoments
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Drawdown
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• MaxDDmeasurespeaktotroughloss– veryconservative• Difficulttoimplementinpracticeandneedstobesimplifiedtoan
eitherinceptiontodatedrawdownsorrollingdrawdowns
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OptimalPortfolioMixTraditionalMarkowitzApproachesbasedonModernPortfolioTheory
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OptimizationSetup
• MaximizeExpectedPortfolioReturn subjecttoanabsoluteconstraintonrisk<=10%
• Riskcanbemeasuredbyeithervariance,VaR(valueatrisk),m-VaR(modifiedvalueatrisk),drawdownsignoredtoretainsimplicity
• Sumofportfolioweights=100%
• Individualweightsshouldbe>0%and<35%(thelattertoensurediversification)
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0.0%1.0%2.0%3.0%4.0%5.0%6.0%7.0%8.0%9.0%10.0%11.0%
0.0% 5.0% 10.0% 15.0% 20.0% 25.0%
ExpectedReturnadjustments
AdjustmentsdonelargelytoreflectcurrentthinkingaroundcapitalmarketassumptionsSource:B&BAnalytics,forillustrativepurposesonly
Bonds HF
PE
RE
COMEQ
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Capitalconstraints(0,35%)
34.8%10.5% 7.4%
30.2%
35.0% 35.0%
19.5% 22.6%
35.0% 35.0% 35.0%
0%
20%
40%
60%
80%
100%
MeanVariance(Parametric)
MeanVaR(Parametric)
MeanmVaR(Parametric)
Equity Bonds CommoditiesHedgeFunds RealEstate PrivateEquity
• Allocationtobondsandhedgefundsincreasesasmoreconservativeapproaches(VaRandmVaR)areused
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PortfolioMetrics
MeanVariance(Parametric)
MeanVaR(Parametric)
MeanmVaR(Parametric)
AnnualizedReturn 6.8% 6.1% 6.0%
AnnualizedRisk 10.0% 10.0% 10.0%
Return/Risk 0.68 0.61 0.60
Drawdown 30.3% 20.3% 19.2%
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Unconstrainedefficientfrontiers
4.0%
6.0%
8.0%
10.0%
12.0%
ReturnVsVolatility(Parametric) ReturnVsVaR(Parametric) ReturnVsmVaR(Parametric)
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OptimalPortfolioMixOtherApproaches
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CapitalAllocation
Bonds Equities
PracticalissueswithtraditionalapproachesEstimatingmanyinputsforNassetclasses• Nexpectedreturns• Nexpectedvolatilities• N(N-1)/2expectedcorrelations
RiskAllocation
Bonds Equities
Vs
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Practicalissueswithtraditionalapproaches
5.0%18.3%
30.5% 41.2% 50.3%32.8% 32.8% 32.8% 32.8% 32.0%
30.6%30.1%
30.5%31.5%67.2% 67.2% 67.2% 67.2% 63.0% 51.1% 39.4% 28.3% 18.3%
0%
20%
40%
60%
80%
100%
7.00% 7.50% 8.00% 8.50% 9.00% 9.50% 10.00% 10.50% 11.00%
Uncon
strained
Weights
EquityReturnAssumption
Sensitivityofweightstochangingequityreturnassumptions
Equity Bonds Commodities HedgeFunds RealEstate PrivateEquity
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RiskParity• Letsthrowsomedarts!• Riskdrivenapproaches– expected
returnsnotrequiredtobeestimated• Basedonpremisethatarangeof
outcomes(risk)iseasiertoestimatethantheoutcome(return)
• Optimizecapitalweightssothat“riskcontributions”ofallassetclassesareequal
• RiskContribution(RC) ofasseti=W(i)XStd.Dev(p)XBeta(i,p)
• Ifanasset’sweight=20%,itsbetawithportfolio=2,thenassumingportoliovol=10%,theRC=4%=>or40%ofriskcomesfromtheasset
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RiskParity5.8%
57.5%6.8%
18.0%
4.7%7.2%
AssetAllocation
Equity
Bonds
Commodities
HedgeFunds
RealEstate
PrivateEquity
20.0%
20.0%
20.0%20.0%
20.0%
20.0%
RiskContribution
Risk Parity
Annualized Return 4.1%
Annualized Risk 4.1%
Return/Risk 0.99Drawdown 12.8%
100
200
300
2000 2003 2006 2009 2012 2015
PortfolioEvolution
RiskParity
Criticism: Too much weight to fixed income, requires leverage to scale to traditional portfolio risk budgets 42
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RiskBudgeting
• Optimizecapitalweightssothat”riskcontribution”ofeachassetclassfallswithinthemaxriskcontributionallocatedtoit
• Thisinvolvessettingriskcontributionbudgetse.g.RC(1)=X,RC(2)=Y…
• Sum[RC(i)]=PortfolioStandardDeviation
• Robustalternativetousingexpectedreturns->Increaseriskbudgetsifviewonassetclassispositive,decreaseriskbudgetiftheviewisnegative
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FINDINGTHEEQUILIBRIUM
1.ASSETALLOCATION2.ACTIVEVSPASSIVEBALANCE3.MANAGER/FUNDSELECTION
PART1:PORTFOLIOCREATION
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Arealternativebetasinvestable?AssetClass DevelopedMarkets India
Equities(EQ) Thousands ofETFsavailablebyregion,market,sectorandstyle
Few ETFs,butmanyMFstochoosefrom
FixedIncome(FI)
Largenumber ofETFsavailablebyFX,Duration,Rating,Riskcountry
ETFspracticallynon-existent;butseveralMFstochoosefrom
Commodities(COM)
Many ETFandETNoptionsonmostcommodities Few,largelylimitedtoGold
RealEstate(RE) REIT&CEF/FoF optionsavailable 1st REITexpected in2017;REPEFundsexisting
Hedge Funds(HF)
SeveralHF Indexreplication &FoFavailable
PMS, AIFfunds,Largelysinglemanagers
PrivateEquity(PE) DiversifiedFoFoptionsavailable Largelysinglemanagers
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Unfortunatelynot
• Traditionalbetas(EQ,FI,COM)cheaplyavailable
• Altmanagers(HF,PE,RE)mainlyseektodeliveralpha
• Altbetasnoteasilyavailable(atleastforHF,PE,RE)
• HighdispersionofAltreturnsmakesitdifficulttoreplicatebenchmarks,FoFinvestmentroutesolvesthisproblemonlypartially
Solution: TreatAlts(espHF,PE,RE)asapartofanactivemanagementmandate
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Core&SatelliteApproach
• Core:long-term,low-costinvestmentsincludingETFs,MFsetcseekingmarketreturns(EQandFIandpossiblyCOMbetas)
• Satellite:activelymanagedalphaproducinginvestmentsseekingtodeliverabsolutereturn(HF,PE,RE)
• Abestofboth(active&passive)worldsapproach• Optimizecosts(inexpensivecore)• Potentialtooutperformtheasset
allocation• Diversifyriskthroughgreaternumberof
holdings
Core
Satellite
AssetClass
Passive(Core)
Active(Satellite)
EQ ✔ ✔
FI ✔ ✔
COM ✔ ✔
RE ✔
HF ✔
PE ✔
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ButthisshouldbeconsistentwithAssetAllocation
1. E[RC(core+satellite)]<=E[RC(assetclassinSAA)]
2. E[R(core+satellite)]>=E[R(assetclassinSAA)]
WhereE[R]isexpectedreturnandE[RC]isexpectedriskcontribution.
Niceintheory,difficulttoachieveinpractice!
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FINDINGTHEEQUILIBRIUM
1.ASSETALLOCATION2.ACTIVEVSPASSIVEBALANCE3.INVESTMENT/MANAGERSELECTION
PART1:PORTFOLIOCREATION
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DiversificationwithinassetclassHowmanyinvestmentsshouldwemakewithinHF,withinPE..?
Risk
123 6 10 20 25…#investments
• Diversifyviaafundoffundstructure– lowinvestmentsize,buthigherfeetrade-off– anoutsourcingdecision
• Cultivatesuperiormanagerselectioncapabilities,i.e.identifyingtrulyuncorrelatedalphageneratingstreams
Altstypicallyrequirehighinvestmentsizes
Traditionaldiversificationmethodsarenotpracticalforallinvestors
ManagerselectionbecomesKEY
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TheThreePs
Canamanagerbetrusted?
• Trackrecord• Background• Education• Philosophy• Attitude
People Process Performance
Whatsetsthemanagerapart?
• Investmentstrategy
• Risks• Restrictions• Rigor&
Repeatability
Isthereactualskill?
• Sustainedoutperformance
• Benign&adverseenvironments
• Adaptability• Peergroup
analysis
Isthemanageranaturalfit?
• Correlation• Quantitative
analysisandmisfitrisk
• Willthestrategycontinuetoworkatscale?
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Managingmisfitrisk• Startbyidentifyinginvestments
withineachAltassetclassthatareexpectedtobeatAAhurdlerate(HF1,HF2,PE1,PE2etc..)– keepaneyeoncorrelations,esp.tailones
• PoolselectedAltinvestmentswithotherinvestmentsandestimateanextendedcovariancematrix
• Optimizeweightstominimizetrackingerror(wp – wsaa)’COV(wp – wsaa)subjecttoconstraints• Sumofweightstoinvestmentswithin
assetclass≅ SAAwt.toassetclass• Portfoliorisk=SAArisk
HF1 HF2… PE1 PE2… RE1 RE2… EQ FI COM
HF1
HF2…
PE1
PE2…
RE1
RE2…
EQ
FI
COM
Note:ThiscovarmatrixassumesthatthereisonlyonepassiveinvestmentwithinEQ,FI,COMthatperfectlyreplicatestheindexusedintheSAA
Simpleandstraightforwardapproach,especiallywhennumberofinvestmentsarenottoolarge
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Identifyingsourcesofreturn• A simple approach to analyze the sources of excess return for a
fund relative to a comparable style benchmark
• Define a peer group of hedge funds with similar style and size
• Calculate average peer return over time – benchmark
• Calculate fund β w.r.t to benchmark over time via rollingregressions. Then– Style Returns = β* Rb– Timing alpha = Rb *(β - 1)– Selection alpha = Rp - β* Rb– Timing alpha + Selection alpha = Excess Return = Rp - Rb
• Analyze stability and superiority of timing and selectionreturns
Implicitassumptionisthatanappropriatepeergroupexists! 53
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Peergroupstyleattributions
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FINDINGTHEEQUILIBRIUMPART2:PERFORMANCEEVALUATIONANDREBALANCING
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Whatmakesavalidbenchmark?
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• Investable: abilitytobuyandholdthebenchmark
• Unambiguous: namesandweightsofholdingsareclearlystated
• Measurable: transparentw.r.tcalculation
• Independent: notbedesignedbymanager– removesconflict
• Relevant: shouldreflecttheinvestmentstrategy
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HowdoesthislookinthecaseofAltindices
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• Investable: NOTREALLY,EXCEPTCOMMODITIES
• Unambiguous: YES
• Measurable: YES
• Independent: YES
• Relevant: MAYBE
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Peergroupanalysis
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Peergroupsagoodbenchmark?
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Convenient- showstheedge,orlackthereof!
• Investable: NO• Unambiguous:NO• Measurable:YES• Independent: NO• Relevant: MAYBE
Issues: classificationbias,survivorshipbias,pronetosnapshotassessments– endpointbias,canbegamed…
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Endpointbias
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Thesamefundrankedinthetopquartilewhenlookingattrailingperiods
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Onlyonebenchmarkplease!
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AssetClass Cash/Hurdle Index PeerGroup
Equities(EQ) ✔
Useasasecondarytooltoassessperformance
versuscompetition,andattribute
returns
FixedIncome(FI) ✔
Commodities(COM) ✔
RealEstate(RE) ✔(REPE/REFs)
✔(REITS)
Hedge Funds(HF) ✔
PrivateEquity(PE) ✔
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BasicPerformanceComparisonMeasures
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TimeWeightedReturn
• Cumulatesreturnsovertime
• Givesanequalweighttoeachresult,regardlessofthedollaramountinvested
• Returnsarecalculateddailyandgeometricallylinkedovertime
• Time-weightedmethodsdonotconsidertheeffectofcontributionsorwithdrawalsontheportfolio
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TimeWeightedReturn
Investor 1 invests $1M on Dec 31. On Aug 15 of the followingyear, his portfolio is valued at $1,162,484. At that point, he adds$100,000, bringing total value to $1,262,484. By the end of theyear, portfolio has decreased in value to $1,192,328.
1st period return = ($1,162,484 - $1,000,000) / $1,000,000 =16.25%2nd period return = ($1,192,328 - ($1,162,484 + $100,000)) /($1,162,484 + $100,000) = -5.56%Time-weighted over the two time periods = (1 + 16.25%) x (1 + (-5.56%)) - 1 = 9.79%
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Howismyportfoliodoingonanabsolutereturnbasis?• An absolute return measure allows direct alignment with
investment objective• No comparison to a benchmark or peer• Relevant for goal based investing agnostic of market or
benchmark performance
50100150200250300
Jan-00 Jan-02 Jan-04 Jan-06 Jan-08 Jan-10 Jan-12 Jan-14 Jan-16
Portfolio AbsoluteReturnBenchmark
PortfolioAnn.TWR=6.45%
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Howismyportfoliodoingonarelativereturnbasis?• Shows the portfolio is doing relative to SAA benchmark after
incorporating for drift and actively set tactical weights
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100
150
200
250
300
Jan-00 Jan-02 Jan-04 Jan-06 Jan-08 Jan-10 Jan-12 Jan-14 Jan-16
Portfolio SAA
PortfolioAnn.TWR=6.45%SAAAnn.TWR=5.70%
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SharpeRatio• Measures portfolio excess return generated over the risk free
rate per unit of risk taken• Implies that one is left with the premium that is independent
of total risk• Provides easy comparison of portfolios and best used as a
ranking metric
Sharpe Ratio = (Ra - Rf) / σaRa is the portfolio returnRf is the risk free rateσa is the standard deviation of the portfolio return
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SharpeRatio
• Portfolio Sharpe = (6.45% - 0.60%) / 8.16% = 0.72• SAA Sharpe = (5.70% - 0.60%) / 7.46% = 0.68
• Pitfalls– It is a ranking criterion only– Negative Sharpe is meaningless– Does not incorporate higher moments– Upward movement is penalized via higher volatility– Doesn’t distinguish between active and passive return– Not so useful when comparing strategies with vastly different trading
frequencies (e.g. HFT versus low frequency)
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TreynorMeasure
• Measures outperformance over market or benchmark (beta)• Independent of portfolio risk meaning one can compare two
portfolios even though they have different betas
Treynor Measure= (Ra - Rb) / βaRa is the portfolio returnRb is the risk free rateβa is the beta of the portfolio
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TreynorMeasure
• Portfolio Treynor Measure = (6.45% - 0.60%) / 1.22 = 0.048
• Pitfalls– Doesn’t quantify value added by active portfolio management– It is a ranking criterion only– Unlike Sharpe which applicable to all portfolios, Treynor uses relative
market risk or beta and hence is applicable only to well diversifiedportfolios
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Jensen’sAlpha
• Measure of a security’s excess return with respect to theexpected return given by Capital Asset Pricing Model
Jensen’s Alpha = Ra - [Rb + βa*(Rm - Rb)]= 6.45% - [0.60% + 1.22*(5.70% - 0.60%)]= -0.39%
Ra is the portfolio returnRb is the risk free rateRm is the market returnβa is the beta of the portfolio• Pitfalls: It only allows an absolute measurement of active
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SharpevsTreynorvsJensen
Return Beta Std.Dev SharpeRatio
TreynorMeasure
Jensen’sAlpha
ManagerA 10% 0.90 11% 0.91 0.11 0.03
ManagerB 14% 1.03 20% 0.70 0.14 0.06
ManagerC 15% 1.02 27% 0.56 0.15 0.07
Assuming risk free rate of 0% and benchmark return of 8%Don’t forget: this is a snap shot, analyzing across time is crucial to assessstability of these rankings 72
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Therebalancingdecision
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PortfolioSettingSAA
AllocationMin
AllocationMax
AllocationCurrent
AllocationEquity 25% 20% 30% 20.0%
Bonds 20% 15% 25% 12.6%
Commodities 5% 0% 10% 4.0%
HedgeFunds 15% 10% 20% 21.4%
RealEstate 10% 10% 20% 11.0%
PrivateEquity 25% 20% 30% 31.0%
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Should we rebalance? - YES
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Canwerebalanceeffectively?MOSTPROBABLYNOT
• Lowtradingliquidity(potentiallyduetoilliquidinvestments)• Subscription/Redemptionwindows:timetakento
subscribe/redeempostrequest• Lock-ins:investmentcan’tberedeemedatall• Investmentsize:accuraterebalancingsimplynotpossible
unlessportfolioisofsignificantsize• Hightransactioncostsandtaxation
Factorintheseconsiderations– setwiderSAAbands
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Thankyou.
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