Download - 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)