Today’s low-rate slow growth markets are challenging institutional investors to more carefully analyse correlations between investment strategies and portfolio performance.

1. Today’slow-rate slow growthmarketsare challenginginstitutionalinvestorstomore carefully
analyse correlationsbetweeninvestmentstrategiesandportfolioperformance.
Portfolio Performance Evaluation
Performance evaluationinvolves-
Performance measurement- Tocalculate return
Performance attribution- Todetermine sourcesof portfolioreturn
Performance appraisal- Todrawconclusionwhetherthe performance wasprimarilyaffectedby
investmentdecision,byoverallmarketorbychance
Performance measurement- Portfolioreturnsreferstogainorlossrealizedbyaninvestment
portfoliooverperiodof time.
Portfolioreturns can be calculatedin differentways-
Parameterrequiredto calculate return-
a) Tenure b) Cashflow-Multiple orsingle c) AmountInvestedd) MarketValue
- Itsimplycalculatesthe percentagedifference fromperiodtoperiodof the
total portfolioNAV andincludesincome fromdividendandinterest.
EndingMarket Value- Beginningmarketvalue
BeginningMarketValue
HPR= P1+D1 −1
P0
Where: HPR - holding period return
• P1P1 – price at the end of the period
• P0P0 – price at the beginning of the period
• D1D1 – dividend at the end of the period
So, HPR is the total return earned by an investor over a single period and it includes all cash
flows occurring at the end of the period.
HPR is a valuable tool when you want to calculate the rate of return on an investment over one
period assuming that no additions or withdrawals of money occur meanwhile
CAGRisthe total returnexpressedasanannualized
return.For individual investmentsorportfoliowithoutcashflow CAGRis the bestmeasure.

2. CAGR is not correct method to calculate returns with multiple transactions due to following
reasons
 Due to interim transactions ending market value does not reflect correct growth rate
 Multiple transaction will have varying investment periods
- The TWRR calculates the compounded rate of growth
over a stated evaluation period of one unit of money initially invested in the portfolio. The time-
weighted rate of return is a geometric mean return over the whole investment period: It requires
HPR to be calculated covering each period that has an external cash flow.
TWRR=(1+HPR1)×(1+HPR2)×...×(1+HPRT)−−−−−−−−−−−−
−−−−−−−−−−−−−−−−−−−−−−−−−−√T−1
- The MWRR isan internal rate of returnon all funds
investedduringthe evaluationperiodincludingthe beginningvalueof the portfolio.
- MWRR isan average growthrate of all fundsinthe account.It is affectedbyboth
the returnsgeneratedonthe assetsandtimingof external cashflow.Foreg.If the assets appreciate
firstand thendepreciate,thentimingof cashflow will significantlyaffectthe MWRR.Let say if cash
flowoccursafter appreciation periodbutbefore the decline,the MWRRwill be lowerasmore funds
were exposedtodecline thantoincrease.
In contrastTWRR isonlylinkingof Holdingperiodreturnandisnotaffectedbyexternalcash flow.
Generally,TWRRisusedforportfolioevaluation becauseitreflectsonlythe returnof the assetsand
not the impactof addingor withdrawingfunds.
If Portfoliomanagercontrolsthe timingof additionand withdrawals of fundsthenMWRRis
appropriate forperformance reporting.
What is Attribution Analysis
Attributionanalysisisasophisticatedmethodforevaluatingthe performance of aportfolioorfund
manager. Performance attributionisatool usedto evaluate portfoliomanagersthatdecomposes
the account’sreturn vs.an appropriate benchmark.The analysisillustratesthe decisionsmade by
the portfoliomanager. Performanceattributiondetermineshow the portfoliomanager’sasset
allocationandselectionof securitiesaffectsthe portfolio’sperformancewhencomparedtoa
benchmark.
BREAKING DOWN Attribution Analysis
Performance Attribution=AllocationEffect+SelectionEffect+InteractionEffect
Pure Sector AllocationEffect- It measuresthe portfoliomanager’sabilitytoeffectivelyallocatethe
portfolio’sassetstovarioussectors.A sectorreferstoassetsorsecuritiesthatare groupedwithina
certainclassificationsuchas Banking,Pharma,orInformationTechnology.Positive allocationoccurs

3. whenthe portfolioisoverweightedinasegmentthatoutperformsthe benchmarkand
underweighted inasegmentthatunderperformsthe benchmarkandvice versafornegative
allocation.
[(Portfoliosectorweight) – (Benchmarksector weight)]
X
[(SectorBenchmark return)- (PortfolioBenchmarkReturn)]
Example of Pure SectorAllocationEffect
Sector
Beginning
Weight
Sector
Return
Total
Return
Portfolio Pharma 10% 5% 7.50%
Nifty50 Pharma 4% 4.5% 3.50%
[(10.00%) – (4.00%)] X[4.5%-3.5%]
(6.00%) X (1%) = 0.0006
In thisexample,the allocationeffectispositive since the portfoliomanagerover weightedthe basic
Pharma sector,whichperformedbetterthanthe total benchmarkreturn
SelectionEffect- It measuresthe portfoliomanager’sabilitytoselectsecuritieswithinagivensector
relative toa benchmark. The withinsectorselectionreturn isassumingthatthe managerweights
each sectorinthe portfoliointhe same proportionasinthe overall benchmark.
(Benchmarksectorweight)]
X
[( (PortfolioSectorReturn) –(SectorBenchmarkreturn)]
From the previousexample data,selectioneffectwill asfollows-
[(4%) X (5.00%-4.5%)] = 0.0002
InteractionEffect - It measuresthe combinedimpactof assigningweightstobothsectorsand
individualsecurity.A decisiontoincrease the allocationof asecuritywill alsoincrease the weighting
of the sectorto whichthe securitybelongs.
[(Portfoliosectorweight) –(Benchmarksectorweight)]
X
[( (PortfolioSectorReturn) –(SectorBenchmarkreturn)]

4. [(10.00%) – (4.00%)] X[5%-4.5%] = 0.0003
FixedIncome PortfolioAttribution-
Fixedincome assetsmanagementcomprisesasetof strategiesforanticipatingyieldcurve
movementsandfortakingadvantage of yieldcurve shape amongothersstrategiessuchassecurities
selection.Performance attribution triestoexplainthe sourcesof the returnthatmanagershave as
an outcome of theirstrategies. Interestrate andDurationare typicallythe dominantfactorinreturn.
Fixedincome microattributiondecomposestotal returnof afixed-income portfoliointotwogroups
of components:
 Effectof external interestenvironment(outof manager’scontrol)
 Contributionof the investmentmanager
External Interestrate effect- Itcan be subdividedintotwocomponents-
 ExpectedInterestrate effect- First,a simulationof whatthe manager’sbenchmarkwould
have returnedif interestrate have movedinthe mannerof forwardcurve. Foreg if part of
the benchmarkisinvestedin10 yearpaperyielding7% andthe 1 monthforwardrate for9
year11 monthsecurityis7.1%, the expectedreturniscalculatedassumingrate movedto
7.1%. Thismust be done for all securitiesaggregated.Itisthe expectedinterestrate effect.
It doesnotconsideranyaction of the manager or whatactuallyhappenedtorates.
 UnexpectedInterestrate effect- The benchmarkreturnissimulatedbasedonwhatactually
happenedtointerestrate.Itstill doesnotconsideranyactionof the manager.
The nextfoursimulationscapture value addedorlostversusthe indexbyactionsof the
manager-
Interestrate management
Measuresthe manager’sabilitytopredictchangesininterestratesandadjustthe portfolioduration
and convexity.We compare the duration/convexityof the portfolioasif eachbondwas a riskfree
bondand compare the overall positionagainstactual treasuryyieldstocapture the durationand
convexitychanges. Itcanbe subdividedintoduration,convexity,andyield-curve shapeattributes.
Sector/Quality management
Looksat whathappenstoyieldspreadsonthe actual sector andqualityof bondsa portfolio
managerholds(i.e.non-treasurybonds).Soif amanager overweightscorporate bondsandthe
corporate bondspreadwidens,the portfoliowillunderperformagainst atreasury-onlyportfolio
Security Selection
Looksat the actual bondsselected.Soinourpreviousexample,if the corporate bondsactuallyheld
by the managerdidnot widenasmuchas the overall corporate bondsector,the managerwould
have a positive securityselectionforthe sectorsince hisorherbondsoutperformedtheir
benchmark.It’sbasicallythe same assecurityselectionforequities.
Trading Effect
Thisis the fixedincome plugfigure.Itcatchesthingslike transaction/tradingcostsetc.

5. Performance Appraisal- The final stage of the performanceevaluationprocessis performance
appraisal.Performance appraisal isdesignedtoassesswhetherthe investmentresultsare due to
luckor skill.Five commonlyusedmeasuresare-
Jensen’sAlpha- Alphaisthe difference betweenthe actual returnandreturnrequiredto
compensate forsystematicrisk. Onex ante basis,the SML and CAPMprojectedreturntobe:
RE = RF+ BE(RM-RF)
RE= ExpectedReturn
RF= RiskFree Rate of Return
RM= ExpectedReturnonmarket
BE = PortfolioBeta(systematicrisk)
TreynorMeasure- The Treynorratio,also knownasthe reward-to-systematicriskratio,isa
performance metricfordetermininghow muchexcessreturnwasgeneratedforeachunitof
systematicrisktakenonby a portfolio.Systematicriskismeasuredbya portfolio's beta.Beta
measuresthe tendencyof aportfolio'sreturntochange inresponse tochangesinreturnfor the
overall market. A higherTreynorratioresultmeansa portfolioisamore suitable investment.
TA= Rp- RF
BA
Rp= ExpectedReturn
RF= RiskFree Rate of Return
Ba = PortfolioBeta(systematicrisk)
Sharpe Ratio- Sharpe ratiois a measure of excessportfolioreturnoverthe risk-free rate relative to
itsstandard deviation(TotalRisk). Itrepresentsthe additionalamountof returnthatan investor
receivesperunitof increase inrisk.The Sharpe ratioisa relative measure of risk-adjustedreturn.It
considersstandarddeviation,whichassumesasymmetrical distributionof returns.Forasymmetrical
returndistributionwithaSkewnessgreaterorlesserthanzeroandKurtosisgreaterorlesserthan3,
the Sharpe ratio may not be a goodmeasure of performance.
SP= Rp- RF
Std Dev
InformationRatio- The informationratioalsoseekstoevaluaterisk-adjustedreturn inrelationtoa
benchmark.Ratherthanusinga risk-free investmentforcomparisonpurposes,the informationratio
commonlymeasuresthe rate of returnof an investmentportfolioagainsta benchmark index. Itis
the active returnof the funddividedbyitstrackingerror,where active returnisthe difference
betweenthe fund’sreturnandthatof itsbenchmarkindex,andtrackingerroristhe standard
deviationof the active return.Essentially,the informationratiotellsaninvestorhow muchexcess
returnis generatedfromthe amountof excessrisktakenrelative tothe benchmark.

6. IRp= Active Return
Active Risk
Active Return- PortfolioReturnlessBenchmarkReturn
Active Risk- Standarddeviationof active return
The M2
Measure- The conceptbehindthe M² ratiois to create a portfolioPthat mimicsthe riskof
the marketportfoliobyalteringthe weightsof the actual portfolioPandthe risk-free assetuntil
portfolioPhasthe same total risk as the market.The returnon the mimickingportfolioPis
determinedandcomparedwiththe marketreturn.A portfoliothatmatchesthe returnof the
marketwill have anM² value equal tozerowhile aportfoliothatoutperformswill have apositive
value. Byusingthe M² measure,itispossible torankportfoliosandalsotodeterminewhich
portfoliosbeatthe marketona risk-adjustedbasis. -
M2
= Rf + σp X Sharpe Ratioof Portfolio