M2 and M3 - Risk and Return

8/6/2019 M2 and M3 - Risk and Return

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Lecture

RISK AND RETURN BASICS


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Chapter 2 QuestionsWhatarethe sources of investmentreturns?

How can returns bemeasured?

How can wecomputereturns oninvestments outside oftheirhomecountry?


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Chapter 2 QuestionsWhat is risk andhow is itmeasured?

How is expectedreturn andriskestimated via scenario analysis?

Whatarethecomponents ofaninvestments requiredreturn to investors

and whymighttheychange overtime?


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Sources of Investment

ReturnsInvestments providetwo basictypes ofreturn:

Incomereturns

The ownerofan investmenthas therightto anycash flows paid bythe investment.

Changes in price orvalue

The ownerofan investmentreceives the benefit ofincreases in valueand bears therisk foranydecreases in value.


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Income ReturnsCashpayments,usuallyreceived

regularly overthelife oftheinvestment.

Examples: Coupon

interestpaymentsfrom bonds,Common andpreferred stockdividendpayments.


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Returns From Changes

in ValueInvestors alsoexperiencecapital gains

orlosses as the valueoftheir investmentchanges overtime.

Forexample, a stockmaypaya $1 dividend

while its value falls from$30 to $25 overthesametimeperiod.


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Investment StrategyGenerally, the incomereturns froman investmentarein yourpocketcash flows.

Overtime, yourportfolio will grow much faster ifyoureinvestthesecash flows andputthe fullpowerofcompound interest in your favor.

Dividendreinvestmentplans (DRIPs) provideatoolforthis to happen automatically; similarly, MutualFunds allow forautomaticreinvestment of income.

See Exhibit 2.5 foran illustration ofthe benefit ofreinvesting income.


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Measuring ReturnsDollarReturns How muchmoney was made on an investment

oversomeperiod oftime? Total Dollar Return = Income + Price Change

Holding Period Return Bydividing the Total Dollar Return bythe

Purchase Price (orBeginning Price), wecanbettergaugeareturn by incorporating the size ofthe investmentmade in orderto getthedollarreturn.


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Annualized ReturnsIf wehavereturn or income/pricechangeinformation overatimeperiod in excess of

oneyear, we usually wantto annualizetherate ofreturn in orderto facilitatecomparisons with other investmentreturns.

Anotherusefulmeasure:

Return Relative = Income + Ending Value

Purchase Price


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Annualized ReturnsAnnualized HPR = (1 + HPR)1/n 1

Annualized HPR = (Return Relative)1/n 1

Withreturns computed on an

annualized basis, theyare nowcomparable withall otherannualizedreturns.


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Returns on Overseas

InvestmentsA holding periodreturn on a foreigninvestment generally needs to betranslated back into thehomecountryreturn.

Iftheexchangeratehas changed over

thelife ofthe investment, thehomecountryreturn (HCR) can be verydifferentthan the foreign return (FR).


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Returns on Foreign

InvestmentsHCR Relative = FR Relative (Current

Exchange Rate/Initial Exchange Rate)

HCR=(1 + FR)Current Exchange Rate 1

Initial Exchange Rate


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Measuring Historic

ReturnsStarting withannualized Holding PeriodReturns, we often wantto calculate

somemeasure ofthe averagereturnovertime on an investment.

Two commonly usedmeasures ofaverage:Arithmetic Mean

Geometric Mean


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Arithmetic Mean ReturnThearithmeticmean is the simpleaverageofa series ofreturns.

Calculated by summing all ofthereturns inthe series anddividing bythe numberofvalues.

RA = (7HPR)/n

Oddlyenough, earning thearithmeticmeanreturn forn years is not generallyequivalentto theactualamount ofmoneyearned bytheinvestment overall n timeperiods.


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Geometric Mean ReturnThe geometricmean is the onereturn that, ifearned in each ofthe n years ofan

investments life, gives the sametotaldollarresultas theactual investment.

It is calculatedas the nthroot oftheproductofall ofthe n return relatives ofthe

investment.

RG

= [4(Return Relatives)]1/n 1


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Arithmetic vs.

GeometricTo ponderwhich is the superiormeasure,

considerthe sameexample witha $1000

initial investment. How much would beaccumulated?

Year Holding Period Return Investment Value

1 10% $1,100

2 30% $1,4303 -20% $1,144

4 0% $1,144

5 20% $1,373


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Scenario AnalysisWhilehistoricreturns, orpastrealizedreturns, are important, investmentdecisions

are inherently forward-looking.We often employ scenario orwhat if?analysis in orderto make betterdecisions,given the uncertain future.

Scenario analysis involves looking atdifferentoutcomes forreturns along withtheirassociatedprobabilities of occurrence.


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Expected Return

ExampleEconomic Conditions Probability Return

Strong .20 40%

Average .50 12%

Weak .30 -20%

E(R) = .20(40%) + .50 (12%) + .30 (-20%)E(R) = 8%


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What is risk?Risk is the uncertaintyassociated withthereturn on an investment.

Risk can impactallcomponents ofreturnthrough:

Fluctuations in incomereturns;

Fluctuations in pricechanges ofthe investment;

Fluctuations in reinvestmentrates ofreturn.


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Sources of RiskSystematic Risk Factors Affectmany investmentreturns simultaneously;

their impact is pervasive.

Examples: changes in interestrates andthe stateofthemacro-economy.

Asset-specific Risk Factors Affect only one ora small numberof investment

returns;come fromthecharacteristics ofthespecific investment.

Examples: poormanagement, competitivepressures.


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How can we measure

risk?Sincerisk is relatedto variabilityanduncertainty, wecan usemeasures of

variabilityto assess risk.The varianceand its positive squareroot, thestandarddeviation, are suchmeasures. Measure totalrisk ofan investment, the

combinedeffects of systematicandasset-specificrisk factors.

Variance of Historic Returns

W2 = [7(Rt-RA)2]/n-1


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Standard Deviation of

Historic ReturnsYear Holding Period Return

1 10% RA = 8%

2 30% W2 = 3703 -20% W = 19.2%

4 0%

5 20%

W2 = [(10-8)2+(30-8)2+(-20-8)2+(0-8)2+(20-8)2]/4

= [4+484+784+64+144]/4

= [1480]/4


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Components of ReturnRecall from Chapter1 thattherequiredrateofreturn on an investment is the sum ofthe

risk-freerate (RFR) ofreturn available in themarketandarisk premium (RP) tocompensatethe investor forrisk.

Required Return = RFR + RP

The Capital Market Line (CML) is a visualrepresentation ofhow risk is rewarded in themarket for investments.


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Components of Return

Over TimeWhatchanges therequiredreturn on aninvestment overtime?

Anything thatchanges therisk-freerate ortheinvestments risk premium. Changes in therealrisk-freerate ofreturn andthe

expectedrate of inflation (both impacting thenominalrisk-freerate, factors that shiftthe CML).

Changes in the investments specificrisk (amovementalong the CML) andthepremiumrequired in themarketplace forbearing risk(changing the slope ofthe CML).


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The CapitalAsset

Pricing Model (CAPM)

Rj

= Rf

+ (Rm

Rf

) Bj

Bj = Cov (Rj, Rm)/Var(Rm)

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M2 and M3 - Risk and Return