CHAPTER SIX

The Returns and Risks from Investing

CHAPTER SIX

The Returns and Risks from Investing

Cleary / Jones

Investments: Analysis and Management

Learning ObjectivesLearning ObjectivesLearning ObjectivesLearning Objectives

To define “return” and state its two To define “return” and state its two componentscomponents

To explain the relationship between To explain the relationship between return and riskreturn and risk

To identify the sources of riskTo identify the sources of risk

To describe the different methods of To describe the different methods of measuring returnsmeasuring returns

Learning ObjectivesLearning ObjectivesLearning ObjectivesLearning Objectives

To describe the different methods To describe the different methods of measuring riskof measuring risk

To discuss the returns and risks To discuss the returns and risks from investing in major financial from investing in major financial assets in the pastassets in the past

Asset ValuationAsset ValuationAsset ValuationAsset Valuation

Function of both Function of both returnreturn and and riskrisk– At the centre of security analysisAt the centre of security analysis

How should realized return and risk How should realized return and risk be measured?be measured?– The realized risk-return tradeoff is The realized risk-return tradeoff is

based on the pastbased on the past– The expected future risk-return tradeoff The expected future risk-return tradeoff

is uncertain and may not occuris uncertain and may not occur

Return ComponentsReturn ComponentsReturn ComponentsReturn Components

Returns consist of two elements:Returns consist of two elements:– Yield:Yield: Periodic cash flows such as Periodic cash flows such as

interest or dividends (income return)interest or dividends (income return) ““Yield” measures relate income return to a Yield” measures relate income return to a

price for the securityprice for the security

– Capital Gain Or Loss:Capital Gain Or Loss: Price appreciation Price appreciation or depreciationor depreciation

The change in price of the assetThe change in price of the asset

Total Return = Yield +Price ChangeTotal Return = Yield +Price Change

Risk SourcesRisk SourcesRisk SourcesRisk Sources Interest Rate RiskInterest Rate Risk

– Affects market Affects market value and resale value and resale price price

Market RiskMarket Risk– Overall market Overall market

effectseffects Inflation RiskInflation Risk

– Purchasing power Purchasing power variabilityvariability

Business RiskBusiness Risk

Financial RiskFinancial Risk– Tied to debt financingTied to debt financing

Liquidity RiskLiquidity Risk– Time and price Time and price

concession required to concession required to sell securitysell security

Exchange Rate RiskExchange Rate Risk Country RiskCountry Risk

– Potential change in Potential change in degree of political degree of political stabilitystability

Risk TypesRisk TypesRisk TypesRisk Types

Two general types:Two general types:– Systematic (market) riskSystematic (market) risk

Pervasive, affecting all securities, cannot be Pervasive, affecting all securities, cannot be avoidedavoided

Interest rate or market or inflation risksInterest rate or market or inflation risks

– Nonsystematic (unique) riskNonsystematic (unique) risk Unique characteristics specific to a securityUnique characteristics specific to a security

Total Risk = General Risk + Specific Total Risk = General Risk + Specific RiskRisk

Measuring ReturnsMeasuring ReturnsMeasuring ReturnsMeasuring Returns

Total Return compares Total Return compares performance over time or across performance over time or across different securitiesdifferent securities

Total Return is a percentage Total Return is a percentage relating all cash flows received relating all cash flows received during a given time period, denoted during a given time period, denoted CFCFtt +(P +(PE E - P- PBB), to the start of period ), to the start of period price, Pprice, PBB

B

BEt

P)P(PCFTR

Measuring ReturnsMeasuring ReturnsMeasuring ReturnsMeasuring Returns

Total Return can be either positive Total Return can be either positive or negativeor negative– When cumulating or compounding, When cumulating or compounding,

negative returns are a problemnegative returns are a problem A Return Relative solves the A Return Relative solves the

problem because it is always problem because it is always positivepositive

RR CF PPt E

B

1 TR

Measuring ReturnsMeasuring ReturnsMeasuring ReturnsMeasuring Returns

To measure the level of wealth To measure the level of wealth created by an investment rather created by an investment rather than the change in wealth, returns than the change in wealth, returns need to be cumulated over timeneed to be cumulated over time

Cumulative Wealth Index, CWICumulative Wealth Index, CWInn, , over n periods, =over n periods, =

)nTR1)...(2TR1)(1TR1(0WI

Measuring International Measuring International ReturnsReturns

Measuring International Measuring International ReturnsReturns

International returns include any International returns include any realized exchange rate changesrealized exchange rate changes– If foreign currency depreciates, If foreign currency depreciates,

returns are lower in domestic returns are lower in domestic currency termscurrency terms

Total Return in domestic currency Total Return in domestic currency == 1

For.Curr. of Val.BeginFor.Curr. of Val.End

RR

Measures Describing a Measures Describing a Return SeriesReturn Series

Measures Describing a Measures Describing a Return SeriesReturn Series

TR, RR, and CWI are useful for a TR, RR, and CWI are useful for a given, single time periodgiven, single time period

What about summarizing returns What about summarizing returns over several time periods?over several time periods?– Arithmetic mean and Geometric mean Arithmetic mean and Geometric mean

Arithmetic mean, or simply mean,Arithmetic mean, or simply mean,

nX

X

Arithmetic Versus Arithmetic Versus GeometricGeometric

Arithmetic Versus Arithmetic Versus GeometricGeometric

Arithmetic mean does not measure Arithmetic mean does not measure the compound growth rate over timethe compound growth rate over time– Does not capture the realized change in Does not capture the realized change in

wealth over multiple periodswealth over multiple periods– Does capture typical return in a single Does capture typical return in a single

periodperiod Geometric mean reflects compound, Geometric mean reflects compound,

cumulative returns over more than cumulative returns over more than one periodone period

Geometric MeanGeometric MeanGeometric MeanGeometric Mean

Geometric mean defined as the n-Geometric mean defined as the n-th root of the product of n return th root of the product of n return relatives minus one, or G = relatives minus one, or G =

Difference between Geometric Difference between Geometric mean and Arithmetic mean mean and Arithmetic mean depends on the variability of depends on the variability of returns, sreturns, s

1)TR1)...(TR1)(TR1( n/1n21

sX1G1 222

Adjusting Returns for Adjusting Returns for InflationInflation

Adjusting Returns for Adjusting Returns for InflationInflation

Returns measures are not adjusted Returns measures are not adjusted for inflationfor inflation– Purchasing power of investment may Purchasing power of investment may

change over timechange over time– Consumer Price Index (CPI) is possible Consumer Price Index (CPI) is possible

measure of inflationmeasure of inflation

TR IA

TRCPI

11

1

Measuring RiskMeasuring RiskMeasuring RiskMeasuring Risk

Risk is the chance that the actual Risk is the chance that the actual outcome will be different than the outcome will be different than the expected outcomeexpected outcome

Standard Deviation measures the Standard Deviation measures the deviation of returns from the meandeviation of returns from the mean

s

X Xn 1

2 1/2

Risk PremiumsRisk PremiumsRisk PremiumsRisk Premiums

Premium is additional return earned or Premium is additional return earned or expected for additional riskexpected for additional risk– Calculated for any two asset classesCalculated for any two asset classes

Equity risk premium is the difference Equity risk premium is the difference between stock and risk-free returnsbetween stock and risk-free returns

Bond default premium is the difference Bond default premium is the difference between the return on long term between the return on long term corporate bonds and long term corporate bonds and long term government bondsgovernment bonds

Risk PremiumsRisk PremiumsRisk PremiumsRisk Premiums

Equity Risk Premium, ERP, =Equity Risk Premium, ERP, =

1RF1

CSTR1

The Risk-Return RecordThe Risk-Return RecordThe Risk-Return RecordThe Risk-Return Record

Since 1938, cumulative wealth indexes Since 1938, cumulative wealth indexes show stock returns dominate bond show stock returns dominate bond returnsreturns– Stock standard deviations also exceed bond Stock standard deviations also exceed bond

standard deviationsstandard deviations Annual geometric mean return for the Annual geometric mean return for the

time period between 1938 and 1997 for time period between 1938 and 1997 for Canadian common stocks is 10.9% with Canadian common stocks is 10.9% with standard deviation of 16.2%standard deviation of 16.2%