portfolio mag 1[1]

8/6/2019 Portfolio Mag 1[1]

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Portfolio TheoryPortfolio Theory

PORTFOLIO Management


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Portfolio ManagementPortfolio Management What is Portfolio Management Service?What is Portfolio Management Service?

It refers to professional services rendered forIt refers to professional services rendered formanagement of portfolio of others namely clientsmanagement of portfolio of others namely clients

or customers with the help of experts inor customers with the help of experts ininvestment advisory services.investment advisory services.

Some Aspects of Portfolio Management?Some Aspects of Portfolio Management? A proper investments decision making of what toA proper investments decision making of what to

buy and sellbuy and sell

Proper money management in terms of investmentProper money management in terms of investmentin basket of assets so as to satisfy the assetin basket of assets so as to satisfy the assetpreferences of investorpreferences of investor

Reduce the risk and increase returns.Reduce the risk and increase returns.


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Process of Portfolio ManagementProcess of Portfolio Management

Specification andquantification ofinvestor objectives,constraints andpreferences

Relevant economicsocial, political sectorsand securityconsiderations

Portfolio policiesand strategies

Capital Marketexpectations

MonitoringInvestor relatedInput factors

Portfolio construction andRevision, asset allocation,Portfolio Optimization,security selection,implementationAnd execution

Monitoring economicand marketInput factors

Attainment ofInvestor objectives,performancesmeasurement


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Efficient Portfolios and Efficient FrontierEfficient Portfolios and Efficient Frontier

A portfolio that provides the greatestA portfolio that provides the greatest

expected return for a given level of risk, orexpected return for a given level of risk, or

equivalently, the lowest risk for a givenequivalently, the lowest risk for a givenexpected return (also called optimal portfolio)expected return (also called optimal portfolio)

An efficient portfolio is that portfolio whichAn efficient portfolio is that portfolio which

has no alternative withhas no alternative with The same ER(P) and lower SD(P)The same ER(P) and lower SD(P)

The same SD(P) and higherER (P)The same SD(P) and higherER (P)

A higherER (P) and lower SD (p)A higherER (P) and lower SD (p)


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Efficient Portfolios and Efficient FrontierEfficient Portfolios and Efficient Frontier

Risk-Return Possibilities for Assets and Portfolios


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A) Investment SettingA) Investment Setting..


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Required rate of return andRequired rate of return and

components of Required ratecomponents of Required rate

1)1) RealReal RiskRisk FreeFree RateRate ofof ReturnReturn

2)2) ExpectedExpected InflationInflation PremiumPremium

3)3) RiskRisk PremiumPremium

FunctionallyFunctionally;;ROR=ROR=F(RFRreal,expectedF(RFRreal,expected inflation,inflation, riskrisk Premium)Premium)


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Diff BetweenDiff BetweenRFRRFR real &real &RFRRFR nominal,nominal,compute both measures.compute both measures.

RFRRFR realreal == ofof interestinterest isis thethe priceprice thethe investorinvestor chargeschargesforfor thethe deferraldeferral ofof currentcurrent consumptionconsumption.. TheThe priceprice isisinfluencedinfluenced byby subjectivesubjective andand objectiveobjective factorsfactors.. ChangesChanges inineithereither ofof thesethese factorsfactors occuroccur graduallygradually overover timetime..

SubjectiveSubjective factorsfactors areare basedbased onon individualindividualconsumerconsumer preferencepreference forfor currentcurrent consumptionconsumption

ObjectiveObjective factorsfactors relatesrelates toto thethe entireentireinvestmentinvestment opportunityopportunity setset availableavailable inin ananeconomyeconomy.. ThisThis isis determineddetermined byby longlong termterm realrealgrowthgrowth raterate ofof thethe economyeconomy.. WhenWhen thethe growthgrowthraterate isis higher,higher, investorsinvestors whowho supplysupply capitalcapitaldemanddemand aa higherhigher raterate ofof returnreturn.. OnOn thethe otherother

handhand borrowersborrowers areare readyready toto paypay aa highhigh raterate ofofreturnreturn


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Diff BetweenDiff BetweenRFRRFR real &real &RFRRFR nominal,nominal,compute both measures compute both measures

RFRRFR nominalnominal:: TheThe inflationinflation premiumpremium (IP)(IP) isisanan adjustmentadjustment toto thethe RFRRFR realreal toto compensatecompensate

investorsinvestors forfor expectedexpected changeschanges inin thethe pricesprices andandmoneymoney marketmarket conditionsconditions beingbeing tightenedtightened ororeasedeased duedue toto changeschanges inin thethe inflationaryinflationary

expectationsexpectations..

RFR real= ((1+RFR nominal )/(1+IP))-1.

RFR nominal= (1+RFR real) (1+IP) -1

RFR nominal = RFR real + IP


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Diff BetweenDiff BetweenRFRRFR real &real &RFRRFR nominal,nominal,compute both measurescompute both measures

Therefore RFR nominal is the RFR realTherefore RFR nominal is the RFR realadjusted foradjusted for

Expected Inflation PremiumExpected Inflation Premium

Relative easiness or tightness in the capitalRelative easiness or tightness in the capitalmarketmarket

RFR realRFR real== ((1+RFR nominal )/(1+IP))((1+RFR nominal )/(1+IP)) -- 11


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Diff BetweenDiff BetweenRFRRFR real &real &RFRRFR nominal,nominal,compute both measures...compute both measures...

UST Rate] 6%

IP 2%

RFR nominal ?

1+RFR nominal 1.06

1+IP 1.02

RFR real= ((1+RFR nominal )/(1+IP))-1

1.039216

RFR real 0.039216

Real returns means, we remove the effect of InflationNominal returns means, that the effect of inflationhave been included

Compute RFR nominal

UST Rate] 3%

IP 2%

RFR real ?

1+RFR nominal 1.03

1+IP 1.02

RFR nominal= (1+RFR real) (1+IP) -1

1.0506

RFR nominal 0.0506


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Risk Premium and sources ofRisk Premium and sources of

fundamental riskfundamental riskTheThe increaseincrease inin thethe requiredrequired raterate ofof

returnreturn overover thethe nominalnominal riskrisk freefree raterate

isis knownknown asas riskrisk premiumpremium..

RpRp isis whatwhat thethe investorsinvestors demanddemand forforthethe uncertaintyuncertainty associatedassociated withwith thethe

investmentinvestment..E=E= ((11+RFR+RFR realreal )+()+(11+IP)+IP) +(+(11+RP)+RP)--11


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Risk Premium and sources ofRisk Premium and sources of

fundamental riskfundamental risk SourcesSources ofof fundamentalfundamental riskrisk..

1)1) BusinessBusiness riskrisk

2)2) FinancialFinancial riskrisk

3)3) LiquidityLiquidity riskrisk

4)4) ExchangeExchange raterate riskrisk5)5) PoliticalPolitical riskrisk..


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Warm up: Risk Premiums andWarm up: Risk Premiums and

Portfolio theoryPortfolio theory--ModernModern portfolioportfolio theory,theory, isis basedbased onon onon thethe ideaidea

thatthat thethe riskrisk premiumpremium forfor anyany securitysecurity isis aa

functionfunction ofof itsits riskrisk ofof aa diversifieddiversified portfolioportfolio..

--HoldingHolding aa diversifieddiversified portfolioportfolio reducesreduces riskrisk..

--TheThe riskrisk thatthat cannotcannot bebe eliminatedeliminated throughthrough

diversificationdiversification isis calledcalled marketmarket riskrisk oror systematicsystematicriskrisk..

--


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Warm up: Risk Premiums andWarm up: Risk Premiums and

Portfolio theory..Portfolio theory..The most important lesson of modernThe most important lesson of modern

portfolio theory is that the risk premiumportfolio theory is that the risk premium

for individual security is based only on itsfor individual security is based only on itssystematic risk, not on its risk as a standsystematic risk, not on its risk as a standalone investment.alone investment.

Risk premiums are based on systematicRisk premiums are based on systematicrisk and that systematic (or market risk )risk and that systematic (or market risk )is measured by beta.is measured by beta.


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General Relationship betweenGeneral Relationship between

Risk & ReturnRisk & Return FundamentalRiskFundamentalRisk SystematicRiskSystematicRisk

E

E

Fundamental

Risk

Systematic Risk B

RFR RFR

L

AH

E=RFR+B(Rm-RFR)

SML


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Define SML, and discuss the factors that causeDefine SML, and discuss the factors that cause

movement along, changes in slope and shifts of SMLmovement along, changes in slope and shifts of SML

TheThe relationshiprelationship betweenbetween expectedexpectedreturnreturn andand levellevel ofof systematicsystematic riskrisk isis

calledcalled thethe SMLSML.. TheThe equationequation ofof SMLSMLisisE= RFR+ B (E(Rm)-RFR)

E( R) = expected return

RFR= Risk Free rate of return.

E(Rmkt)= expected market return

Beta = level of systematic risk


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InIn thethe precedingpreceding equation,equation, thethe quantityquantity (E(Rmkt(E(Rmkt--RFR)RFR) isis calledcalled thethe marketmarket riskrisk premiumpremium andand thethequantityquantity ofof B(E(RmktB(E(Rmkt--RFR)RFR) isis calledcalled thethe securityssecuritys

riskrisk premiumpremium.. TheseThese areare bothboth premiumspremiums bothbothrelativerelative toto thethe riskrisk freefree raterate ofof returnreturn..

TheThe precedingpreceding equationequation isis anan equationequation forfor aa linelineinin aa slopeslope interceptintercept formform.. TheThe interceptintercept-- RFRRFR andand

thethe slopeslopeE

(R

mktE

(R

mkt--R

FR)R

FR)

areare determineddetermined inin thethemarketmarket.. E(E( RR )) isis thethe YY--variablevariable whichwhich isis aafunctionfunction ofof beta,beta, whichwhich isis thethe xx--variablevariable..

ThusThus SMLSML showsshows expectedexpected returnreturn asas aa functionfunction ofofsystematicsystematic risk,risk, givengiven thethe riskrisk freefree raterate ofof returnreturn

andand thethe riskrisk premiumpremium requiredrequired byby thethe investorinvestor


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SinceSince thethe marketmarket riskrisk premiumpremium (E(Rmkt(E(Rmkt--RFR)RFR) isis thethe premiumpremium forfor unitunit ofof marketmarket risk,risk,

betabeta isis measuredmeasured inin unitsunits ofof marketmarket riskrisk.. IfIf aasecuritysecurity hashas 11..22 unitsunits ofof marketmarket risk,risk, itsits riskriskpremiumpremium isis equalequal toto 11..22 marketmarket premiumspremiums..

WhetherWhether youyou considerconsider totaltotal riskrisk oror

systematicsystematic risk,risk, thethe riskierriskier thethe securitysecuritygreatergreater thethe expectedexpected returnreturn..


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RISK cont..RISK cont..

TotalTotal RiskRisk == SystematicSystematic ++ UnsystematicUnsystematicRiskRisk

SystematicSystematic RiskRisk isis alsoalso calledcalled NonNon--

diversifiablediversifiable RiskRisk oror MarketMarket RiskRisk

UnsystematicUnsystematic RiskRisk isis alsoalso calledcalled

DiversifiableDiversifiable RiskRisk oror UniqueUnique RiskRisk


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The Security market line (SML)The Security market line (SML)

TheThe relationshiprelationship betweenbetween expectedexpectedraterate ofof returnreturn andand thethe levellevel ofof

systematicsystematic riskrisk isis calledcalled thethe securitysecuritymarketmarket lineline..


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RFR

E

Beta

SML

Movement along the SML indicates that the Risk level of an individual

security has changed (its systematic risk or fundamental risk has changed

More Risk

Less Risk


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E= RFR + Beta (R market-RFR)

E(return) = RFR + Beta (R market-RFR)systematic risk Risk Premium

Y-variable intercept slope

Rmkt-RFR= market risk prmBeta( Rmkt-RFR)= security risk premium.


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New SML

Old SML

E

Beta

When there is an increase in the market risk Premiumthe SML rotates counterclockwise

RFR


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When there is decrease in the market risk Premium the

SML rotates clockwise

New

SML

Old

SML


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RFR2

RFR2

New SML

Old SML

Increase in expected

rate or real rate

SML will undergo a parallel shift if the capital market

conditions changes and there is rise in the expected rate


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SummarySummary

MovementMovement alongalong thethe SML,SML, refersrefers toto aachangechange inin thethe systematicsystematic riskrisk ofof thethe investorinvestor

ChangesChanges inin thethe slopeslope ofof thethe SML,SML, reflectsreflects ananinvestorsinvestors attitudeattitude towardstowards riskrisk thatthat affectsaffectsthethe marketmarket riskrisk prmprm

ParallelParallel shiftshift inin thethe SMLSML reflectsreflects aa changechange

inin thethe nominalnominal RFRRFR egeg expectedexpected growthgrowth andandinflationinflation


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Summary..Summary..

The trade off between risk & Return is shown byThe trade off between risk & Return is shown bymovement along the SML.movement along the SML.

The slope of the SML reflects the market risk premium.The slope of the SML reflects the market risk premium.

If market risk premium increases, SML will rotateIf market risk premium increases, SML will rotatecounterclockwise.counterclockwise.

IF market risk premium decreases, SML will rotateIF market risk premium decreases, SML will rotateclockwise.clockwise.

IF inflation expectation increases, SML will shiftIF inflation expectation increases, SML will shiftupwards in parallel fashion.upwards in parallel fashion.

IF inflation expectations decreases, SML will shiftIF inflation expectations decreases, SML will shiftdownwards in a parallel fashion.downwards in a parallel fashion.


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B)Asset AllocationB)Asset AllocationDecisionDecision


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Steps in Portfolio managementSteps in Portfolio managementprocess.process.

Describe Return Objectives of capitalDescribe Return Objectives of capitalpreservation, Capital Appreciation,preservation, Capital Appreciation,current Income and Total return.current Income and Total return.

Describe Investment Constraints ofDescribe Investment Constraints ofliquidity, time horizon, tax, legal,liquidity, time horizon, tax, legal,unique needs and preferencesunique needs and preferences


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B) Introduction toB) Introduction toPortfolio ManagementPortfolio Management


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Steps in portfolio managementSteps in portfolio management

Write a policy statement (goals andWrite a policy statement (goals and

constraints)constraints)

Develop a investment strategyDevelop a investment strategy

Implement a planImplement a plan

Monitor and update.Monitor and update.


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Define Risk Aversion and cite evidenceDefine Risk Aversion and cite evidencethat suggests that investors are generallythat suggests that investors are generally

Risk averseRisk averse !!

RiskRisk aversionaversion refersrefers toto thethe factfact thatthatindividualindividual prefersprefers lessless toto moremore riskrisk..

RiskRisk AverseAverse investorinvestor1)1) PreferPrefer lowerlower toto higherhigher riskrisk forfor aa givengiven

levellevel ofof ExpectedExpected returnreturn

2)2) WillWill onlyonly expectexpect aa riskierriskier investmentinvestment ififtheythey areare compensatedcompensated withwith higherhigherreturnreturn


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E

O*

H

S

G

I3 I2 I1

pr

p

Preferred

Direction

E

Risk

The curved lines represent indifference curve because all investmentsthat lie along each curve are equally preferred.

ImpNote: IC are positively sloped, whereas IC we have examined ineconomics were negatively sloped. This is because in economics analysiswe had a combination of 2 goods and now we have good (expectedreturn) & one bad (Risk ). A higher or more preferred curve lies in thenorth west direction.


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Define Risk Aversion and cite evidenceDefine Risk Aversion and cite evidencethat suggests that investors are generallythat suggests that investors are generally

Risk averseRisk averse

The fact that most investors would buyThe fact that most investors would buyHome insurance, auto insurance etc,Home insurance, auto insurance etc,

indicates that they are risk averse.indicates that they are risk averse.


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Morkowitz Model contdMorkowitz Model contd

PortfolioPortfolio theorytheory isis basedbased isis basedbased onon thetheassumptionassumption thatthat thethe utilityutility ofof anan investorinvestor isis

aa functionfunction ofof twotwo factorsfactors..MeanMean (Expected(Expected Return)Return)

VarianceVariance (or(or itsits squaresquare rootroot SD)SD)

HenceHence itit isis alsoalso referredreferred toto asas thethe meanmean--variancevariance portfolioportfolio oror twotwo parameterparameterportfolioportfolio theorytheory


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List the assumptions about IndividualsList the assumptions about Individuals

Investment behavior of Markowitz ModelInvestment behavior of Markowitz Model

ReturnReturn distributiondistribution:: InvestorsInvestors looklook atat eacheachinvestmentinvestment opportunityopportunity asas aa probabilityprobability

distributiondistribution ofof expectedexpected returnreturn overover thethegivengiven investmentinvestment horizonhorizon..

UtilityUtility maximizationmaximization::

RiskRisk isis variabilityvariability :: InvestorsInvestors measuresmeasures RiskRisk

asas variancevariance oror standardstandard deviationdeviation ofofExpectedExpected returnreturn

RiskRisk AversionAversion::


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Calculate Expected Return for IndividualCalculate Expected Return for IndividualAsset and for a PortfolioAsset and for a Portfolio (expectational(expectational

data)data)

Expected Ret for Individual SecurityExpected Ret for Individual Security

E

( R ) = Sum P1R1+ P2R2+.PnRn (UsingE

xpectationE

( R ) = Sum P1R1+ P2R2+.PnRn (UsingE

xpectationReturns )Returns )

P1=probability that state 1 will occur.P1=probability that state 1 will occur.

R1=Asset return if the economy is in state 1R1=Asset return if the economy is in state 1

!

!n

i

iiRpRE

1

)(


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Expected return for a Portfolio of securitiesExpected return for a Portfolio of securities

(with Probability)(with Probability)

Suppose you have predicted the following returns forSuppose you have predicted the following returns forstocks C and T in three possible states of nature. Whatstocks C and T in three possible states of nature. Whatare the expected returns?are the expected returns?

StateState ProbabilityProbability CC TT

BoomBoom 0.30.3 0.150.15 0.250.25

NormalNormal 0.50.5 0.100.10 0.200.20

RecessionRecession 0.20.2 0.020.02 0.010.01

RRCC = .3(.15) + .5(.10) + .2(.02)= .099 = 9.99%= .3(.15) + .5(.10) + .2(.02)= .099 = 9.99%

RRTT = .3(.25) + .5(.20) + .2(.01)= .177 = 17.7%= .3(.25) + .5(.20) + .2(.01)= .177 = 17.7%


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Sate of World Probability Returns Expected Return

Expansion 0.25 0.05 0.0125Normal 0.5 0.15 0.075

Recession 0.25 0.25 0.0625

0.15E ( R ) =

Compute Expected Return-(Expectational

data)


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Calculate Expected for Individual Asset andCalculate Expected for Individual Asset and

for a Portfoliofor a Portfolio (Historic data)(Historic data)

months Returns

1 0.1

2 -0.153 0.02

4 0.25

5 -0.3

6 0.2

Total 0.12 Average 0.05


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Expected return for a Portfolio of securitiesExpected return for a Portfolio of securities

TheThe expectedexpected returnreturn onon aa portfolioportfolio ofofassetsassets isis simplysimply thethe weightedweighted averageaverage ofof

thethe returnsreturns onon theirtheir individualindividual assets,assets,weightedweighted byby theirtheir portfolioportfolio weightsweights..

ThusThus forfor aa 22 assetsassets portfolio,portfolio, thethe expectedexpected

returnreturn isis

!

!m

j

jjP REwRE1

)()(


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Variance and StandardDeviationVariance and StandardDeviation

individual securityindividual security (with probability)(with probability)

Variance and standard deviation still measure theVariance and standard deviation still measure thevolatility of returnsvolatility of returns

Using unequal probabilities for the entire rangeUsing unequal probabilities for the entire rangeof possibilitiesof possibilities

Weighted average of squared deviationsWeighted average of squared deviations

!!

n

iii

RERp1

22 ))((

Ri= return in state of the world I

Pi= probability of state I occurring

E (R )= expected return


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Calculating Variance & SD withCalculating Variance & SD with

expectational Dataexpectational Data

Sate roa ilit eturn i -E ^2 * i -E ^2Expansion 0.25 0.05 0.0125 0.15 0.01 0.0025

Normal 0.5 0.15 0.075 0.15 0 0

Recession 0.25 0.25 0.0625 0.15 0.01 0.0025

0 15 Variance 0.005

SD 0.005 .05 0.071

E ( R ) =

Expecte

eturn

Expecte

et


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Calculating Variance & SD withCalculating Variance & SD with

Historic DataHistoric Data


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Variance and Standard DeviationVariance and Standard Deviation

individual securityindividual security (with probability(with probability))

Consider the previous example. What are theConsider the previous example. What are thevariance and standard deviation for each stock?variance and standard deviation for each stock?

Stock CStock C

WW22 = .3(.15= .3(.15--.099).099)22 + .5(.1+ .5(.1--.099).099)22 + .2(.02+ .2(.02--.099).099)22 ==.002029.002029

WW = .045= .045

Stock TStock T

WW22 = .3(.25= .3(.25--.177).177)22 + .5(.2+ .5(.2--.177).177)22 + .2(.01+ .2(.01--.177).177)22 ==.007441.007441

WW = .0863= .0863


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Another ExampleAnother Example

Consider the following information:Consider the following information:

StateState ProbabilityProbability ABC, Inc.ABC, Inc.

BoomBoom 0.250.25 0.150.15 NormalNormal 0.500.50 0.080.08

SlowdownSlowdown 0.150.15 0.040.04

RecessionRecession 0.100.10 00--.03.03

What is the expected return?What is the expected return?What is the variance?What is the variance?

What is the standard deviation?What is the standard deviation?


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Portfolio VariancePortfolio Variance

However for a portfolioHowever for a portfolio

Portfolio variance = W1(R1-E(R1))^2+ W2(R2-E(R2))^2

Because, the variance and standard deviation of aportfolio reflects not only the variance and standarddeviation of the stocks in the portfolio but also howthe returns on the stock varies or move together.

These 2 measures of how the returns on the 2 stocksvary together are co variance and correlation


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Portfolio Variance and StandardPortfolio Variance and StandardDeviationDeviation

TheThe variance/standardvariance/standard deviationdeviation ofof aaportfolioportfolio reflectsreflects notnot onlyonly thethevariance/standardvariance/standard deviationdeviation ofof thethe stocksstocksthatthat makemake upup thethe portfolioportfolio..

ButBut alsoalso howhow thethe returnsreturns onon thethe stocksstockswhichwhich comprisecomprise thethe portfolioportfolio varyvary togethertogether..TwoTwo measuresmeasures ofof howhow thethe returnsreturns onon aa pairpairofof stocksstocks varyvary togethertogether areare thethe covariancecovarianceandand thethe correlationcorrelation coefficientcoefficient..


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Calculate CovarianceCalculate Covariance

CovarianceCovariance isis aa measuremeasure ofof howhow assetsassets movemovetogethertogether..

ITIT isis defineddefined asas thethe expectedexpected valuevalue ofof thetheproductproduct ofof thethe deviationdeviation betweenbetween randomrandomvariablevariable XX andand YY

COV(X,Y)COV(X,Y)


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Covariance contd..Covariance contd..

COV (X, Y)= P1 {(XCOV (X, Y)= P1 {(X--E (X)*(YE (X)*(Y--E (Y)}.E (Y)}.

P=ProbabilityP=Probability

X= actual Return Security XX= actual Return Security X

E(X)=Expected Return of Security XE(X)=Expected Return of Security X

Y= actual Return Security YY= actual Return Security Y

E (Y)=Expected Return of Security YE (Y)=Expected Return of Security Y


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Calculate CoCalculate Co variance usingvariance using

Expectational dataExpectational data

1 2 3 4 5 1*4*5

P R1 R2 R1-E (R1 ) R2-E (R2 ) P*(R1-E (R1)*(R2-E(R2)0.25 0.05 0.32 -0.1 0.16 -0.004

0.5 0.15 0.14 0 -0.02 0

0.25 0.25 0.04 0.1 -0.12 -0.003E 6 -0.007COV R1, R2


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Calculate CoCalculate Co variance usingvariance using

Historic dataHistoric dataCOV (X, Y)= {(XCOV (X, Y)= {(X--E (X)*(YE (X)*(Y--E (Y)}E (Y)}

N

caculate Cov using Historic Data

year Stock 1 Stock 2 R1- E (R1 ) R2- E (R2 )

1 0.1 0.2 0.05 0.1 0.005

2 -0.15 -0.2 -0.2 -0.3 0.06

3 0.2 -0.1 0.15 -0.2 -0.03

4 0.25 0.3 0.2 0.2 0.045 -0.3 -0.2 -0.35 -0.3 0.105

6 0.2 0.6 0.15 0.5 0.075

Average 0.05 0.1 0.255

Cov R1, R2 0.0425


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Limitation of CovarianceLimitation of Covariance

InIn practicepractice itit isis difficultdifficult toto interpretinterpretcovariancecovariance.. BecauseBecause itit cancan taketake extremelyextremely

largelarge valuesvalues rangingranging fromfrom positivepositive totonegativenegative (same(same likelike variance)variance)

ToTo makemake thethe covariancecovariance ofof thethe 22 variablesvariableseasiereasier toto interpretinterpret wewe useuse correlationcorrelation


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CorrelationCorrelation

TheThe CorrelationCorrelation CoefficientCoefficient betweenbetween thethereturnsreturns onon twotwo stocksstocks cancan bebe calculatedcalculated

usingusing thethe followingfollowing equationequation::

CorrelationCorrelation (X,Y)=(X,Y)= COVCOV (X,(X, Y)/Y)/ SDSD ofof XX andandSDSD ofof YY


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Variance on a TwoVariance on a Two--AssetAssetPortfolioPortfolio

WX^WX^22*SD*SD XX ^22++ WY^WY^22*SD*SD YY ^ 22++22 WWX*WYX*WY *COV*COV (XY)(XY)

COVCOV (X,(X, Y)=Y)= CorrelationCorrelation (X,(X, Y)*Y)* SDSD ofof XXandand SDSD ofof YY


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Portfolio Variance contdPortfolio Variance contd

Weighted sum of theWeighted sum of the CovarianceCovariance andand

variances of thevariances of the AssetsAssets in a portfolio.in a portfolio.


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PORTFOLIO MANAGEMETN


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Efficient portfolio.Efficient portfolio.

Efficient portfolio.Efficient portfolio.

Risk and Return indifference curve &Risk and Return indifference curve &

Optimal portfolio.Optimal portfolio.

Optimal portfolio with borrowing andOptimal portfolio with borrowing and

lendinglending


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Proportion of A Proportion of B Expected Return Std Deviation

1.00 0.00 15.00 10.000.75 0.25 16.25 11.52

0.50 0.50 17.50 15.21

0.25 0.75 18.75 19.88

0.00 1.00 20.00 25.00

Efficient Portfolio, Portfolio options,

feasible region


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Efficient portfolio contdEfficient portfolio contd

Portfolio optionsPortfolio options

If just stocks offer the investor withIf just stocks offer the investor with

so many options, imagine the rangeso many options, imagine the range

of possibilities available to him whenof possibilities available to him when

he invests in a number of securities.he invests in a number of securities.


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Feasible region:Feasible region:

The collection of all possible portfolioThe collection of all possible portfolio

options represented by the brokenoptions represented by the broken

egg shaped region is referred to asegg shaped region is referred to as

the feasible regionthe feasible region


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However, the investor should not beHowever, the investor should not bebewildered away by the range ofbewildered away by the range of

possibilities, because what matters to him ispossibilities, because what matters to him isthe efficient portfolio.the efficient portfolio.

A portfolio is efficient if (and only if) thereA portfolio is efficient if (and only if) thereis no alternative with.is no alternative with.

Same returnSame return--low SDlow SDHigher ReturnHigher Return--same SDsame SD

Higher RetHigher Ret--lower SD.lower SD.


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Efficient Portfolio.


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Risk ReturnRisk Return

indifference Curveindifference CurveOnce the efficient frontier isOnce the efficient frontier is

delineated the next question is, what isdelineated the next question is, what is

the optimal portfolio.the optimal portfolio.Now we come to the concept ofNow we come to the concept of

Indifference curveIndifference curve

All the points lying on the IC provideAll the points lying on the IC providethe same level of satisfaction.the same level of satisfaction.


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Optimal portfolio.Optimal portfolio.

Given the efficient frontier and the riskGiven the efficient frontier and the riskreturn indifference curve, the optimalreturn indifference curve, the optimal

portfolio is found at the point of tangencyportfolio is found at the point of tangencybetween the efficient frontier and the Riskbetween the efficient frontier and the Riskreturn indifference curve.return indifference curve.

The portfolio thatThe portfolio that yieldsyields the highest level ofthe highest level of

expectedexpected utilityutility. In portfolio theory, it is the. In portfolio theory, it is theportfolio located at the point on theportfolio located at the point on the efficientefficientfrontierfrontier where the investor'swhere the investor's indifferenceindifferencecurvecurve is tangent to the efficient frontieris tangent to the efficient frontier


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E

O*

H

S

G

I3 I2 I1

pr

p

Optimal

Portfolio.


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RISK

Systematic

RiskUnsystematic

Risk

-cannot be diversified

away

-Beta (slope of

regression line ) is a

measure of the

systematic Risk CAPM

-can be diversified

away

-Standard Deviation is

a measure of

Unsystematic Risk


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ConclusionConclusion

The risk/return tradeoff is the balance between theThe risk/return tradeoff is the balance between thedesire for the lowest possible risk and the highestdesire for the lowest possible risk and the highestpossible return.possible return.

Higher risk equals greater possible return.Higher risk equals greater possible return. Diversification lowers the risk of your portfolio.Diversification lowers the risk of your portfolio.

The concept of the optimal portfolio attempts toThe concept of the optimal portfolio attempts toshow how rational investors will maximize theirshow how rational investors will maximize theirreturn for the level of risk that is acceptable toreturn for the level of risk that is acceptable tothem.them.

CAPM describes the relationship between risk andCAPM describes the relationship between risk andexpected return and serves as a model for theexpected return and serves as a model for thepricing of risky securitiespricing of risky securities


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There are three main practices that canThere are three main practices that canhelp you ensure the best diversification:help you ensure the best diversification:

1.1. Spread your portfolio among multiple investmentSpread your portfolio among multiple investmentvehicles such as cash, stocks, bonds,vehicles such as cash, stocks, bonds, mutual fundsmutual funds,,

and perhaps even some real estate.and perhaps even some real estate.

2.2. Vary the risk in your securities. You're notVary the risk in your securities. You're notrestricted to choosing only blue chip stocks. In fact,restricted to choosing only blue chip stocks. In fact,it would be wise to pick investments with variedit would be wise to pick investments with varied

risk levels; this will ensure that large losses arerisk levels; this will ensure that large losses areoffset by other areas.offset by other areas.

3.3. Vary your securities by industry. This willVary your securities by industry. This willminimize the impact of specific risks of certainminimize the impact of specific risks of certain

industries.industries.


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THANK YOU

portfolio mag 1[1]

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