1® 1999 South-Western College Publishing

Chapter 5Calculating Rates Of Return

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Using Rates Of Return

• UsesUses

– Comparing investments in different assetsComparing investments in different assets

– Measuring historical performanceMeasuring historical performance

– Determining future investmentDetermining future investment

– Estimating the cost of capitalEstimating the cost of capital

• Percentage Figures Standard PracticePercentage Figures Standard Practice

• Dollar Amount MeaninglessDollar Amount Meaningless

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Measuring Historical Performance

• Ex-Post Rates of ReturnEx-Post Rates of Return

– Realized rates of returnRealized rates of return

• Ex-Ante Rates of ReturnEx-Ante Rates of Return

– Expected rates of returnExpected rates of return

• Requires Knowledge of RiskRequires Knowledge of Risk

– Risk-return relationshipRisk-return relationship

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Determining Future Investment

• Estimate Estimate – Future returnFuture return– Future fluctuations of returnsFuture fluctuations of returns

• Historical AveragesHistorical Averages– Give best estimate of future returnsGive best estimate of future returns– Estimate future fluctuations of returnsEstimate future fluctuations of returns

• Next Year’s Returns Next Year’s Returns – May be dramatically differentMay be dramatically different

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Estimating Cost Of Capital

• Rates of ReturnRates of Return

– Used to estimate the firm’s cost of capitalUsed to estimate the firm’s cost of capital

– NPV calculationsNPV calculations

• Utilizing historical rates of returnUtilizing historical rates of return

– Calculated in more than one wayCalculated in more than one way

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Rate-Of-Return Calculations

• Different MethodsDifferent Methods– Yield different resultsYield different results

• Could Use Method Giving Best ResultCould Use Method Giving Best Result– Lack of standard would affect comparabilityLack of standard would affect comparability

• AIMRAIMR– Association of Investment Management and Association of Investment Management and

Research Research – Established strict guidelinesEstablished strict guidelines

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Simple Rates Of Return

• HPRHPR

– Holding period returnHolding period return

EMV - BMV + IEMV - BMV + I R =R = BMVBMV– Limitations Limitations (does not account for)(does not account for)

• Timing of cash dividendsTiming of cash dividends

• Accrued interestAccrued interest

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Capital gain or lossCapital gain or loss

Rate of return Rate of return components components

Cash flow yieldCash flow yield

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Approaches To Computing The Rate Of Return

• Linking MethodLinking Method– Calculate to each subperiodCalculate to each subperiod– Cash dividends date determines subperiodCash dividends date determines subperiod– Simple to calculateSimple to calculate

• Index MethodIndex Method superior calculation superior calculation

– Cash flows used to purchase additional unitsCash flows used to purchase additional units– Useful to understanding time weighted Useful to understanding time weighted

computations computations

10® 1999 South-Western College Publishing

Bond Returns

• Cash BasisCash Basis

– Ignores accrued interestIgnores accrued interest

• Accrual BasisAccrual Basis

– Bond interest accrues dailyBond interest accrues daily

– Price paid for bondsPrice paid for bonds

• Includes accrued interestIncludes accrued interest

– AIMR acceptedAIMR accepted

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After-Tax Rates Of Return

• Includes the Impact of TaxesIncludes the Impact of Taxes

– Ordinary incomeOrdinary income

– Capital gainsCapital gains

EMVEMVn n - BMV- BMVn n - N- N00(P(Pnn - P - P00)T)Tgg+ I+ Inn(I - T)(I - T) RRnn = = BMVBMVnn

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Inflation-Adjusted Rates Of Return

• Reduction of Purchasing PowerReduction of Purchasing Power

• Inflation Measured By CPIInflation Measured By CPI

– Consumer Price IndexConsumer Price Index

• Real Rate of Return Real Rate of Return

CPICPI11 - CPI - CPI00

h =h = CPICPI00

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Exchange Rates

• Falling DollarFalling Dollar

– Good for U. S. investors in foreign Good for U. S. investors in foreign countriescountries

– Bad for foreign investors in U. S.Bad for foreign investors in U. S.

– U. S. industry more competitiveU. S. industry more competitive

– Foreign securities become more valuableForeign securities become more valuable

– Foreigners shy away from U. S. marketsForeigners shy away from U. S. markets

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Rate Of Return Adjusted For Foreign Exchange Risk

fxfxnn (DC / FC) (DC / FC) RRDD = (1 + R = (1 + RLL) - 1) - 1 fxfx00 (DC / FC) (DC / FC)

Alternative MethodAlternative Method

RRDD = (1 + R = (1 + Rfxfx) (1 + R) (1 + RLL) - 1) - 1

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Average Rate Of Return• Measuring Returns Across YearsMeasuring Returns Across Years• Arithmetic AverageArithmetic Average

– Adds the realized rate of return over Adds the realized rate of return over different periodsdifferent periods

– Correct for one period of timeCorrect for one period of time– Unbiased estimate of future expected Unbiased estimate of future expected

rates of returnrates of return• Geometric MethodGeometric Method

– Compounds rates of returnCompounds rates of return– Measures actual growth of assetsMeasures actual growth of assets

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Adjusted Rate Of Return

• Accounts for the Timing of Cash DividendsAccounts for the Timing of Cash Dividends

• Called Time-Weighted Rate of ReturnCalled Time-Weighted Rate of Return

• Called Called Rate of ReturnRate of Return in Rest of Textbook in Rest of Textbook

• AIMR ApprovedAIMR Approved

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Importance Of Indexes

• Stock IndexesStock Indexes– Measure the general performance of an economyMeasure the general performance of an economy

• Benchmark For Gauging PerformanceBenchmark For Gauging Performance– Money managerMoney manager– Bond fund managerBond fund manager

• Serves as a Guide for Mutual Fund PerformanceServes as a Guide for Mutual Fund Performance• Assess Overall Direction of the MarketAssess Overall Direction of the Market• Estimates Statistical Parameters Estimates Statistical Parameters BetaBeta• Used as Underlying Securities in Derivatives Used as Underlying Securities in Derivatives

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Indexes Differ

• By Which and How Many SecuritiesBy Which and How Many Securities

• By How the Index is Adjusted for ChangeBy How the Index is Adjusted for Change

• By Method Used to Adjust IndexBy Method Used to Adjust Index

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Types Of Indexes

• Price-Weighted IndexPrice-Weighted Index

• Value-Weighted IndexValue-Weighted Index

• Equally Weighted IndexEqually Weighted Index

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Price-Weighted Index

• ValueValue

– Found by adding the prices of each Found by adding the prices of each security and dividing by a divisorsecurity and dividing by a divisor

• Divisor Divisor

– Adjusted for stock dividends and splits Adjusted for stock dividends and splits and other changesand other changes

• Easy to MimicEasy to Mimic

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Value-Weighted Indexes

• ValueValue

– Based on the total market value of a Based on the total market value of a securitysecurity

• Market CapitalizationMarket Capitalization

– The greater the market capitalization the The greater the market capitalization the greater the securities influencegreater the securities influence

• Not affected by stock dividends or splitsNot affected by stock dividends or splits

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Equally Weighted Index

• ValueValue

– Give each security the same weightGive each security the same weight

• Arithmetic MethodArithmetic Method

• Results in higher values than geometricResults in higher values than geometric

• Multiplicative MethodMultiplicative Method

– GeometricGeometric

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Stock Indexes

• Most are Value-WeightedMost are Value-Weighted

– Automatically adjusting for stock splitsAutomatically adjusting for stock splits

– Weight based on market capitalizationWeight based on market capitalization

• Easy to Develop and MaintainEasy to Develop and Maintain

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Bond Indexes

• Track Different Segments of Bond MarketTrack Different Segments of Bond Market

• Incorporate Total Returns (1970’s)Incorporate Total Returns (1970’s)

• Prior Indexes Ignored Coupon PaymentsPrior Indexes Ignored Coupon Payments

• Bonds Change Because Bonds Change Because – Of finite maturity Of finite maturity change riskchange risk

– Call featuresCall features

• Pricing Problems Due to Lack of TradingPricing Problems Due to Lack of Trading

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Differences In Bond Indexes

• Weighting MethodsWeighting Methods

• Reinvest of Intramonth Cash FlowsReinvest of Intramonth Cash Flows

• Maturity Structure of IndexMaturity Structure of Index

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Tracking Rates Of Return Over Time

• Common Stock is More Volatile than Common Stock is More Volatile than BondsBonds

• Common Stock Offers Higher Return than Common Stock Offers Higher Return than BondsBonds

• Positive Relationship Between Risk and Positive Relationship Between Risk and

ReturnReturn