Chapter 2Chapter 2

RISK AND RETURN BASICSRISK AND RETURN BASICS

Chapter 2 QuestionsChapter 2 Questions

• What are the sources of investment returns?What are the sources of investment returns?• How can returns be measured?How can returns be measured?• What is risk and how can we measure risk?What is risk and how can we measure risk?• What are the components of an investment’s What are the components of an investment’s

required return to investors and why might required return to investors and why might they change over time?they change over time?

Sources of Investment Sources of Investment ReturnsReturns

• Investments provide two basic types of Investments provide two basic types of return:return:

• Income returnsIncome returns– The owner of an investment has the right to The owner of an investment has the right to

any cash flows paid by the investment.any cash flows paid by the investment.

• Changes in price or valueChanges in price or value– The owner of an investment receives the The owner of an investment receives the

benefit of increases in value and bears the risk benefit of increases in value and bears the risk for any decreases in value.for any decreases in value.

Income ReturnsIncome Returns

• Cash payments, Cash payments, usually received usually received regularly over the life regularly over the life of the investment.of the investment.

• Examples: Coupon Examples: Coupon interest payments interest payments from bonds, from bonds, Common and Common and preferred stock preferred stock dividend payments.dividend payments.

Returns From Changes in Returns From Changes in ValueValue

• Investors also Investors also experience capital experience capital gains or losses as the gains or losses as the value of their value of their investment changes investment changes over time.over time.

• For example, a stock For example, a stock may pay a $1 dividend may pay a $1 dividend while its value falls from while its value falls from $30 to $25 over the $30 to $25 over the same time period.same time period.

Measuring ReturnsMeasuring Returns

• Dollar ReturnsDollar Returns– How much money was made on an investment How much money was made on an investment

over some period of time?over some period of time?– Total Dollar Return = Income + Price ChangeTotal Dollar Return = Income + Price Change

• Holding Period ReturnHolding Period Return– By dividing the Total Dollar Return by the By dividing the Total Dollar Return by the

Purchase Price (or Beginning Price), we can Purchase Price (or Beginning Price), we can better gauge a return by incorporating the size of better gauge a return by incorporating the size of the investment made in order to get the dollar the investment made in order to get the dollar return.return.

Annualized ReturnsAnnualized Returns

• If we have return or income/price change If we have return or income/price change information over a time period in excess of information over a time period in excess of one year, we usually want to annualize the one year, we usually want to annualize the rate of return in order to facilitate rate of return in order to facilitate comparisons with other investment returns.comparisons with other investment returns.

• Another useful measure:Another useful measure:Return Relative = Return Relative = Income + Ending ValueIncome + Ending Value

Purchase PricePurchase Price

Annualized ReturnsAnnualized Returns

Annualized HPR = (1 + HPR)Annualized HPR = (1 + HPR)1/n1/n – 1 – 1

Annualized HPR = (Return Relative)Annualized HPR = (Return Relative)1/n1/n – 1 – 1

• With returns computed on an annualized With returns computed on an annualized basis, they are now comparable with all other basis, they are now comparable with all other annualized returns.annualized returns.

Measuring Historic ReturnsMeasuring Historic Returns

• Starting with annualized Holding Period Starting with annualized Holding Period Returns, we often want to calculate Returns, we often want to calculate some measure of the “average” return some measure of the “average” return over time on an investment.over time on an investment.

• Two commonly used measures of Two commonly used measures of average:average:– Arithmetic MeanArithmetic Mean– Geometric MeanGeometric Mean

Arithmetic Mean ReturnArithmetic Mean Return

• The arithmetic mean is the “simple average” The arithmetic mean is the “simple average” of a series of returns. of a series of returns.

• Calculated by summing all of the returns in Calculated by summing all of the returns in the series and dividing by the number of the series and dividing by the number of values.values.

RRAA = ( = (HPR)/nHPR)/n• Oddly enough, earning the arithmetic mean Oddly enough, earning the arithmetic mean

return for n years is not generally equivalent return for n years is not generally equivalent to the actual amount of money earned by the to the actual amount of money earned by the investment over all n time periods.investment over all n time periods.

Arithmetic Mean ExampleArithmetic Mean Example

YearYear Holding Period ReturnHolding Period Return

11 10% 10%

22 30% 30%

33 -20% -20%

44 0% 0%

55 20% 20%

RRAA = ( = (HPR)/n = 40/5 = 8%HPR)/n = 40/5 = 8%

Geometric Mean ReturnGeometric Mean Return

• The geometric mean is the one return that, if The geometric mean is the one return that, if earned in each of the n years of an earned in each of the n years of an investment’s life, gives the same total dollar investment’s life, gives the same total dollar result as the actual investment.result as the actual investment.

• It is calculated as the nth root of the product It is calculated as the nth root of the product of all of the n return relatives of the of all of the n return relatives of the investment.investment.

RRGG = [ = [(Return Relatives)](Return Relatives)]1/n1/n – 1 – 1

Geometric Mean ExampleGeometric Mean Example

YearYear Holding Period ReturnHolding Period Return Return RelativeReturn Relative 11 10% 10% 1.10 1.10 22 30% 30% 1.30 1.30 33 -20% -20% 0.80 0.80 44 0% 0% 1.00 1.00 55 20% 20% 1.20 1.20

RRGG = [(1.10)(1.30)(.80)(1.00)(1.20)] = [(1.10)(1.30)(.80)(1.00)(1.20)]1/51/5 – 1 – 1

RRGG = .0654 or 6.54% = .0654 or 6.54%

Arithmetic vs. GeometricArithmetic vs. Geometric

To ponder which is the superior measure, To ponder which is the superior measure, consider the same example with a $1000 initial consider the same example with a $1000 initial investment. How much would be investment. How much would be accumulated?accumulated?

YearYear Holding Period Return Investment ValueHolding Period Return Investment Value 11 10% 10% $1,100$1,100 22 30% 30% $1,430$1,430 33 -20% -20% $1,144$1,144 44 0% 0% $1,144$1,144 55 20% 20% $1,373$1,373

Arithmetic vs. GeometricArithmetic vs. Geometric

• How much would be accumulated if you earned How much would be accumulated if you earned the arithmetic mean over the same time period?the arithmetic mean over the same time period?

Value = $1,000 (1.08)Value = $1,000 (1.08)55 = $1,469 = $1,469• How much would be accumulated if you earned How much would be accumulated if you earned

the geometric mean over the same time period?the geometric mean over the same time period?Value = $1,000 (1.0654)Value = $1,000 (1.0654)55 = $1,373 = $1,373• Notice that only the geometric mean gives the Notice that only the geometric mean gives the

same return as the underlying series of returns.same return as the underlying series of returns.

Investment StrategyInvestment Strategy

• Generally, the income returns from an investment are Generally, the income returns from an investment are “in your pocket” cash flows.“in your pocket” cash flows.

• Over time, your portfolio will grow much faster if you Over time, your portfolio will grow much faster if you reinvest these cash flows and put the full power of reinvest these cash flows and put the full power of compound interest in your favor.compound interest in your favor.

• Dividend reinvestment plans (DRIPs) provide a tool Dividend reinvestment plans (DRIPs) provide a tool for this to happen automatically; similarly, Mutual for this to happen automatically; similarly, Mutual Funds allow for automatic reinvestment of income.Funds allow for automatic reinvestment of income.

• See Exhibit 2.5 for an illustration of the benefit of See Exhibit 2.5 for an illustration of the benefit of reinvesting income.reinvesting income.

What is risk?What is risk?

• Risk is the uncertainty associated with the Risk is the uncertainty associated with the return on an investment.return on an investment.

• Risk can impact all components of return Risk can impact all components of return through:through:– Fluctuations in income returns;Fluctuations in income returns;– Fluctuations in price changes of the investment;Fluctuations in price changes of the investment;– Fluctuations in reinvestment rates of return.Fluctuations in reinvestment rates of return.

Sources of RiskSources of Risk

• Systematic Risk FactorsSystematic Risk Factors– Affect many investment returns simultaneously; Affect many investment returns simultaneously;

their impact is pervasive.their impact is pervasive.– Examples: changes in interest rates and the state Examples: changes in interest rates and the state

of the macro-economy.of the macro-economy.

• Asset-specific Risk FactorsAsset-specific Risk Factors– Affect only one or a small number of investment Affect only one or a small number of investment

returns; come from the characteristics of the returns; come from the characteristics of the specific investment.specific investment.

– Examples: poor management, competitive Examples: poor management, competitive pressures.pressures.

How can we measure risk?How can we measure risk?

• Since risk is related to variability and Since risk is related to variability and uncertainty, we can use measures of uncertainty, we can use measures of variability to assess risk.variability to assess risk.

• The variance and its positive square root, the The variance and its positive square root, the standard deviation, are such measures.standard deviation, are such measures.– Measure “total risk” of an investment, the Measure “total risk” of an investment, the

combined effects of systematic and asset-specific combined effects of systematic and asset-specific risk factors.risk factors.

• Variance of Historic ReturnsVariance of Historic Returns

22 = [ = [(R(Rtt-R-RAA))22]/n-1]/n-1

Standard Deviation of Standard Deviation of Historic ReturnsHistoric Returns

YearYear Holding Period ReturnHolding Period Return

11 10% R 10% RAA = 8% = 8%

22 30% 30% 22 = 370 = 370 33 -20% -20% = 19.2% = 19.2% 44 0% 0% 55 20% 20%22 = [(10-8) = [(10-8)22+(30-8)+(30-8)22+(-20-8)+(-20-8)22+(0-8)+(0-8)22+(20-8)+(20-8)22]/4]/4 = [4+484+784+64+144]/4= [4+484+784+64+144]/4 = [1480]/4= [1480]/4

Using the Standard Using the Standard DeviationDeviation

• If returns are normally distributed, the If returns are normally distributed, the standard deviation can be used to standard deviation can be used to determine the probability of observing a determine the probability of observing a rate of return over some range of rate of return over some range of values.values.

Coefficient of VariationCoefficient of Variation

• The coefficient of variation is the ratio of the The coefficient of variation is the ratio of the standard deviation divided by the return on the standard deviation divided by the return on the investment; it is a measure of risk per unit of investment; it is a measure of risk per unit of return.return.

CV = CV = /R/RAA

• The higher the coefficient of variation, the The higher the coefficient of variation, the riskier the investment.riskier the investment.

• From the previous example, the coefficient of From the previous example, the coefficient of variation would be:variation would be:

CV =19.2%/8% = 2.40CV =19.2%/8% = 2.40

Components of ReturnComponents of Return

• The required rate of return on an The required rate of return on an investment is the sum of the nominal investment is the sum of the nominal risk-free rate (Nominal RFR) and a risk risk-free rate (Nominal RFR) and a risk premium (RP) to compensate the premium (RP) to compensate the investor for risk.investor for risk.

• Required Return = Nominal RFR + RPRequired Return = Nominal RFR + RP• Or to be more technically correct:Or to be more technically correct:• RR = (1 + Nom RFR) x (1 + RP) - 1RR = (1 + Nom RFR) x (1 + RP) - 1

The Risk-Return The Risk-Return RelationshipRelationship

• The Capital Market Line (CML) is a The Capital Market Line (CML) is a visual representation of how risk is visual representation of how risk is rewarded in the market for investments.rewarded in the market for investments.

• The greater the risk, the greater the The greater the risk, the greater the required return, so the CML slopes required return, so the CML slopes upward.upward.

Components of Return Components of Return Over TimeOver Time

• What changes the required return on an What changes the required return on an investment over time?investment over time?

• Anything that changes the risk-free rate or Anything that changes the risk-free rate or the investment’s risk premium.the investment’s risk premium.– Changes in the real risk-free rate of return and the Changes in the real risk-free rate of return and the

expected rate of inflation (both impacting the expected rate of inflation (both impacting the nominal risk-free rate, factors that shift the CML).nominal risk-free rate, factors that shift the CML).

– Changes in the investment’s specific risk (a Changes in the investment’s specific risk (a movement along the CML) and the premium movement along the CML) and the premium required in the marketplace for bearing risk required in the marketplace for bearing risk (changing the slope of the CML).(changing the slope of the CML).