1313

11

Return, Risk, and the Security Return, Risk, and the Security Market LineMarket Line

22

Key Concepts and SkillsKey Concepts and Skills

Know how to calculate expected returnsKnow how to calculate expected returns Understand the impact of diversificationUnderstand the impact of diversification Understand the systematic risk principleUnderstand the systematic risk principle Understand the security market lineUnderstand the security market line Understand the risk-return trade-offUnderstand the risk-return trade-off Be able to use the Capital Asset Pricing ModelBe able to use the Capital Asset Pricing Model

33

Chapter OutlineChapter Outline

Expected Returns and VariancesExpected Returns and Variances PortfoliosPortfolios Announcements, Surprises, and Expected ReturnsAnnouncements, Surprises, and Expected Returns Risk: Systematic and UnsystematicRisk: Systematic and Unsystematic Diversification and Portfolio RiskDiversification and Portfolio Risk Systematic Risk and BetaSystematic Risk and Beta The Security Market LineThe Security Market Line The SML and the Cost of Capital: A PreviewThe SML and the Cost of Capital: A Preview

44

Expected ReturnsExpected Returns Expected returns are based on the probabilities Expected returns are based on the probabilities

of possible outcomesof possible outcomes In this context, “expected” means average if In this context, “expected” means average if

the process is repeated many timesthe process is repeated many times The “expected” return does not even have to The “expected” return does not even have to

be a possible returnbe a possible return

n

iiiRpRE

1

)(

55

Example: Expected ReturnsExample: Expected Returns

Suppose you have predicted the following Suppose you have predicted the following returns for stocks C and T in three possible returns for stocks C and T in three possible states of nature. What are the expected returns?states of nature. What are the expected returns?

StateState ProbabilityProbability CC TT BoomBoom 0.30.3 1515 2525 NormalNormal 0.50.5 1010 2020 RecessionRecession ?????? 22 11

RRCC = .3(15) + .5(10) + .2(2) = 9.9% = .3(15) + .5(10) + .2(2) = 9.9% RRTT = .3(25) + .5(20) + .2(1) = 17.7% = .3(25) + .5(20) + .2(1) = 17.7%

66

Variance and Standard Variance and Standard DeviationDeviation

Variance and standard deviation still Variance and standard deviation still measure the volatility of returnsmeasure the volatility of returns

Using unequal probabilities for the entire Using unequal probabilities for the entire range of possibilitiesrange of possibilities

Weighted average of squared deviationsWeighted average of squared deviations

n

iii RERp

1

22 ))((σ

77

Example: Variance and Standard Example: Variance and Standard DeviationDeviation

Consider the previous example. What are the variance Consider the previous example. What are the variance and standard deviation for each stock?and standard deviation for each stock?

Stock CStock C 22 = .3(15-9.9) = .3(15-9.9)22 + .5(10-9.9) + .5(10-9.9)22 + .2(2-9.9) + .2(2-9.9)22 = 20.29 = 20.29 = 4.5= 4.5

Stock TStock T 22 = .3(25-17.7) = .3(25-17.7)22 + .5(20-17.7) + .5(20-17.7)22 + .2(1-17.7) + .2(1-17.7)22 = 74.41 = 74.41 = 8.63= 8.63

88

Another ExampleAnother Example Consider the following information:Consider the following information:

StateState ProbabilityProbability ABC, Inc. (%)ABC, Inc. (%) BoomBoom .25.25 1515 NormalNormal .50.50 88 SlowdownSlowdown .15.15 44 RecessionRecession .10.10 -3-3

What is the expected return?What is the expected return? What is the variance?What is the variance? What is the standard deviation?What is the standard deviation?

99

PortfoliosPortfolios

A portfolio is a collection of assetsA portfolio is a collection of assets An asset’s risk and return are important in how An asset’s risk and return are important in how

they affect the risk and return of the portfoliothey affect the risk and return of the portfolio The risk-return trade-off for a portfolio is The risk-return trade-off for a portfolio is

measured by the portfolio expected return and measured by the portfolio expected return and standard deviation, just as with individual assetsstandard deviation, just as with individual assets

1010

Example: Portfolio WeightsExample: Portfolio Weights

Suppose you have $15,000 to invest and you Suppose you have $15,000 to invest and you have purchased securities in the following have purchased securities in the following amounts. What are your portfolio weights in amounts. What are your portfolio weights in each security?each security? $2000 of DCLK$2000 of DCLK $3000 of KO$3000 of KO $4000 of INTC$4000 of INTC $6000 of KEI$6000 of KEI

•DCLK: 2/15 = .133

•KO: 3/15 = .2

•INTC: 4/15 = .267

•KEI: 6/15 = .4

1111

Portfolio Expected ReturnsPortfolio Expected Returns

The expected return of a portfolio is the weighted The expected return of a portfolio is the weighted average of the expected returns of the respective assets average of the expected returns of the respective assets in the portfolioin the portfolio

You can also find the expected return by finding the You can also find the expected return by finding the portfolio return in each possible state and computing the portfolio return in each possible state and computing the expected value as we did with individual securitiesexpected value as we did with individual securities

m

jjjP REwRE

1

)()(

1212

Example: Expected Portfolio Example: Expected Portfolio ReturnsReturns

Consider the portfolio weights computed previously. If Consider the portfolio weights computed previously. If the individual stocks have the following expected returns, the individual stocks have the following expected returns, what is the expected return for the portfolio?what is the expected return for the portfolio? DCLK: 19.69%DCLK: 19.69% KO: 5.25%KO: 5.25% INTC: 16.65%INTC: 16.65% KEI: 18.24%KEI: 18.24%

E(RE(RPP) = .133(19.69) + .2(5.25) + .267(16.65) + .4(18.24) ) = .133(19.69) + .2(5.25) + .267(16.65) + .4(18.24)

= 15.41%= 15.41%

1313

Portfolio VariancePortfolio Variance

Compute the portfolio return for each state:Compute the portfolio return for each state:RRPP = w = w11RR11 + w + w22RR22 + … + w + … + wmmRRmm

Compute the expected portfolio return using the Compute the expected portfolio return using the same formula as for an individual assetsame formula as for an individual asset

Compute the portfolio variance and standard Compute the portfolio variance and standard deviation using the same formulas as for an deviation using the same formulas as for an individual assetindividual asset

1414

Example: Portfolio VarianceExample: Portfolio Variance

Consider the following informationConsider the following information Invest 50% of your money in Asset AInvest 50% of your money in Asset A StateState ProbabilityProbability AA BB BoomBoom .4.4 30%30% -5%-5% BustBust .6.6 -10%-10% 25%25%

What are the expected return and standard What are the expected return and standard deviation for each asset?deviation for each asset?

What are the expected return and standard What are the expected return and standard deviation for the portfolio?deviation for the portfolio?

Portfolio12.5%7.5%

1515

Another ExampleAnother Example

Consider the following informationConsider the following information StateState ProbabilityProbability XX ZZ BoomBoom .25.25 15%15% 10%10% NormalNormal .60.60 10%10% 9%9% RecessionRecession .15.15 5%5% 10%10%

What are the expected return and standard What are the expected return and standard deviation for a portfolio with an investment of deviation for a portfolio with an investment of $6,000 in asset X and $4,000 in asset Z?$6,000 in asset X and $4,000 in asset Z?

1616

Expected versus Unexpected Expected versus Unexpected ReturnsReturns

Realized returns are generally not equal to Realized returns are generally not equal to expected returnsexpected returns

There is the expected component and the There is the expected component and the unexpected componentunexpected component At any point in time, the unexpected return can be At any point in time, the unexpected return can be

either positive or negativeeither positive or negative Over time, the average of the unexpected Over time, the average of the unexpected

component is zerocomponent is zero

1717

Announcements and NewsAnnouncements and News

Announcements and news contain both an Announcements and news contain both an expected component and a surprise componentexpected component and a surprise component

It is the surprise component that affects a It is the surprise component that affects a stock’s price and therefore its returnstock’s price and therefore its return

This is very obvious when we watch how stock This is very obvious when we watch how stock prices move when an unexpected prices move when an unexpected announcement is made or earnings are different announcement is made or earnings are different than anticipatedthan anticipated

1818

Efficient MarketsEfficient Markets

Efficient markets are a result of investors Efficient markets are a result of investors trading on the unexpected portion of trading on the unexpected portion of announcementsannouncements

The easier it is to trade on surprises, the The easier it is to trade on surprises, the more efficient markets should bemore efficient markets should be

Efficient markets involve random price Efficient markets involve random price changes because we cannot predict changes because we cannot predict surprisessurprises

1919

Systematic RiskSystematic Risk

Risk factors that affect a large number of Risk factors that affect a large number of assetsassets

Also known as non-diversifiable risk or Also known as non-diversifiable risk or market riskmarket risk

Includes such things as changes in GDP, Includes such things as changes in GDP, inflation, interest rates, etc.inflation, interest rates, etc.

2020

Unsystematic RiskUnsystematic Risk

Risk factors that affect a limited number of Risk factors that affect a limited number of assetsassets

Also known as unique risk and asset-Also known as unique risk and asset-specific riskspecific risk

Includes such things as labor strikes, part Includes such things as labor strikes, part shortages, etc.shortages, etc.

2121

ReturnsReturns

Total Return = expected return + unexpected Total Return = expected return + unexpected returnreturn

Unexpected return = systematic portion + Unexpected return = systematic portion + unsystematic portionunsystematic portion

Therefore, total return can be expressed as Therefore, total return can be expressed as follows:follows:

Total Return = expected return + systematic Total Return = expected return + systematic portion + unsystematic portionportion + unsystematic portion

2222

DiversificationDiversification Portfolio diversification is the investment in Portfolio diversification is the investment in

several different asset classes or sectorsseveral different asset classes or sectors Diversification is not just holding a lot of assetsDiversification is not just holding a lot of assets For example, if you own 50 Internet stocks, you For example, if you own 50 Internet stocks, you

are not diversifiedare not diversified However, if you own 50 stocks that span 20 However, if you own 50 stocks that span 20

different industries, then you are diversifieddifferent industries, then you are diversified

2323

Table 13.7Table 13.7

2424

The Principle of DiversificationThe Principle of Diversification

Diversification can substantially reduce the Diversification can substantially reduce the variability of returns without an equivalent variability of returns without an equivalent reduction in expected returnsreduction in expected returns

This reduction in risk arises because worse than This reduction in risk arises because worse than expected returns from one asset are offset by expected returns from one asset are offset by better than expected returns from anotherbetter than expected returns from another

However, there is a minimum level of risk that However, there is a minimum level of risk that cannot be diversified away and that is the cannot be diversified away and that is the systematic portionsystematic portion

2525

Figure 13.1Figure 13.1

2626

Diversifiable RiskDiversifiable Risk

The risk that can be eliminated by combining The risk that can be eliminated by combining assets into a portfolioassets into a portfolio

Often considered the same as unsystematic, Often considered the same as unsystematic, unique or asset-specific riskunique or asset-specific risk

If we hold only one asset, or assets in the same If we hold only one asset, or assets in the same industry, then we are exposing ourselves to risk industry, then we are exposing ourselves to risk that we could diversify awaythat we could diversify away

2727

Total RiskTotal Risk

Total risk = systematic risk + unsystematic riskTotal risk = systematic risk + unsystematic risk The standard deviation of returns is a measure The standard deviation of returns is a measure

of total riskof total risk For well-diversified portfolios, unsystematic risk For well-diversified portfolios, unsystematic risk

is very smallis very small Consequently, the total risk for a diversified Consequently, the total risk for a diversified

portfolio is essentially equivalent to the portfolio is essentially equivalent to the systematic risksystematic risk

2828

Systematic Risk PrincipleSystematic Risk Principle

There is a reward for bearing riskThere is a reward for bearing risk There is not a reward for bearing risk There is not a reward for bearing risk

unnecessarilyunnecessarily The expected return on a risky asset The expected return on a risky asset

depends only on that asset’s systematic depends only on that asset’s systematic risk since unsystematic risk can be risk since unsystematic risk can be diversified awaydiversified away

2929

Table 13.8Table 13.8

3030

Measuring Systematic RiskMeasuring Systematic Risk How do we measure systematic risk?How do we measure systematic risk? We use the beta coefficient to measure We use the beta coefficient to measure

systematic risksystematic risk What does beta tell us?What does beta tell us?

A beta of 1 implies the asset has the same A beta of 1 implies the asset has the same systematic risk as the overall marketsystematic risk as the overall market

A beta < 1 implies the asset has less systematic risk A beta < 1 implies the asset has less systematic risk than the overall marketthan the overall market

A beta > 1 implies the asset has more systematic A beta > 1 implies the asset has more systematic risk than the overall marketrisk than the overall market

3131

Total versus Systematic RiskTotal versus Systematic Risk

Consider the following information:Consider the following information: Standard DeviationStandard Deviation BetaBeta Security CSecurity C 20%20% 1.251.25 Security KSecurity K 30%30% 0.950.95

Which security has more total risk?Which security has more total risk? Which security has more systematic risk?Which security has more systematic risk? Which security should have the higher expected Which security should have the higher expected

return?return?

3232

Work the Web ExampleWork the Web Example Many sites provide betas for companiesMany sites provide betas for companies Yahoo Finance provides beta, plus a lot of Yahoo Finance provides beta, plus a lot of

other information under its key statistics linkother information under its key statistics link Click on the web surfer to go to Yahoo FinanceClick on the web surfer to go to Yahoo Finance

Enter a ticker symbol and get a basic quoteEnter a ticker symbol and get a basic quote Click on key statisticsClick on key statistics

3333

Example: Portfolio BetasExample: Portfolio Betas Consider the previous example with the following four Consider the previous example with the following four

securitiessecurities SecuritySecurity WeightWeight BetaBeta DCLKDCLK .133.133 2.6852.685 KOKO .2.2 0.1950.195 INTCINTC .267.267 2.1612.161 KEIKEI .4.4 2.4342.434

What is the portfolio beta?What is the portfolio beta? .133(2.685) + .2(.195) + .267(2.161) + .4(2.434) = .133(2.685) + .2(.195) + .267(2.161) + .4(2.434) =

1.9471.947

3434

Beta and the Risk PremiumBeta and the Risk Premium

Remember that the risk premium = expected Remember that the risk premium = expected return – risk-free ratereturn – risk-free rate

The higher the beta, the greater the risk The higher the beta, the greater the risk premium should bepremium should be

Can we define the relationship between the risk Can we define the relationship between the risk premium and beta so that we can estimate the premium and beta so that we can estimate the expected return?expected return? YES!YES!

3535

Example: Portfolio Expected Example: Portfolio Expected Returns and BetasReturns and Betas

0%

5%

10%

15%

20%

25%

30%

0 0.5 1 1.5 2 2.5 3

Beta

Exp

ecte

d R

etur

n

Rf

E(RA)

A

3636

Reward-to-Risk Ratio: Reward-to-Risk Ratio: Definition and ExampleDefinition and Example

The reward-to-risk ratio is the slope of the line The reward-to-risk ratio is the slope of the line illustrated in the previous exampleillustrated in the previous example

Slope = (E(RSlope = (E(RAA) – R) – Rff) / () / (AA – 0) – 0) Reward-to-risk ratio for previous example =Reward-to-risk ratio for previous example =

(20 – 8) / (1.6 – 0) = 7.5 (20 – 8) / (1.6 – 0) = 7.5 What if an asset has a reward-to-risk ratio of 8 What if an asset has a reward-to-risk ratio of 8

(implying that the asset plots above the line)?(implying that the asset plots above the line)? What if an asset has a reward-to-risk ratio of 7 What if an asset has a reward-to-risk ratio of 7

(implying that the asset plots below the line)?(implying that the asset plots below the line)?

3737

Market EquilibriumMarket Equilibrium

In equilibrium, all assets and portfolios must In equilibrium, all assets and portfolios must have the same reward-to-risk ratio and they all have the same reward-to-risk ratio and they all must equal the reward-to-risk ratio for the marketmust equal the reward-to-risk ratio for the market

M

fM

A

fA RRERRE

)()(

3838

Security Market LineSecurity Market Line

The security market line (SML) is the The security market line (SML) is the representation of market equilibriumrepresentation of market equilibrium

The slope of the SML is the reward-to-risk ratio: The slope of the SML is the reward-to-risk ratio: (E(R(E(RMM) – R) – Rff) / ) / MM

But since the beta for the market is ALWAYS But since the beta for the market is ALWAYS equal to one, the slope can be rewrittenequal to one, the slope can be rewritten

Slope = E(RSlope = E(RMM) – R) – Rff = market risk premium = market risk premium

3939

The Capital Asset Pricing Model The Capital Asset Pricing Model (CAPM)(CAPM)

The capital asset pricing model defines the The capital asset pricing model defines the relationship between risk and returnrelationship between risk and return

E(RE(RAA) = R) = Rff + + AA(E(R(E(RMM) – R) – Rff))

If we know an asset’s systematic risk, we can If we know an asset’s systematic risk, we can use the CAPM to determine its expected returnuse the CAPM to determine its expected return

This is true whether we are talking about This is true whether we are talking about financial assets or physical assetsfinancial assets or physical assets

4040

Factors Affecting Expected Factors Affecting Expected ReturnReturn

Pure time value of money – measured by Pure time value of money – measured by the risk-free ratethe risk-free rate

Reward for bearing systematic risk – Reward for bearing systematic risk – measured by the market risk premiummeasured by the market risk premium

Amount of systematic risk – measured by Amount of systematic risk – measured by betabeta

4141

Example - CAPMExample - CAPM Consider the betas for each of the assets given earlier. Consider the betas for each of the assets given earlier.

If the risk-free rate is 2.13% and the market risk If the risk-free rate is 2.13% and the market risk premium is 8.6%, what is the expected return for each?premium is 8.6%, what is the expected return for each?

SecuritySecurity BetaBeta Expected ReturnExpected Return

DCLKDCLK 2.6852.685 2.13 + 2.685(8.6) = 25.22%2.13 + 2.685(8.6) = 25.22%

KOKO 0.1950.195 2.13 + 0.195(8.6) = 3.81%2.13 + 0.195(8.6) = 3.81%

INTCINTC 2.1612.161 2.13 + 2.161(8.6) = 20.71%2.13 + 2.161(8.6) = 20.71%

KEIKEI 2.4342.434 2.13 + 2.434(8.6) = 23.06%2.13 + 2.434(8.6) = 23.06%

4242

Figure 13.4Figure 13.4

4343

Quick QuizQuick Quiz How do you compute the expected return and standard How do you compute the expected return and standard

deviation for an individual asset? For a portfolio?deviation for an individual asset? For a portfolio? What is the difference between systematic and What is the difference between systematic and

unsystematic risk?unsystematic risk? What type of risk is relevant for determining the expected What type of risk is relevant for determining the expected

return?return? Consider an asset with a beta of 1.2, a risk-free rate of Consider an asset with a beta of 1.2, a risk-free rate of

5%, and a market return of 13%.5%, and a market return of 13%. What is the reward-to-risk ratio in equilibrium?What is the reward-to-risk ratio in equilibrium? What is the expected return on the asset?What is the expected return on the asset?

1313

4444

End of ChapterEnd of Chapter

4545

Comprehensive ProblemComprehensive Problem

The risk free rate is 4%, and the required return The risk free rate is 4%, and the required return on the market is 12%. What is the required on the market is 12%. What is the required return on an asset with a beta of 1.5?return on an asset with a beta of 1.5?

What is the reward/risk ratio?What is the reward/risk ratio? What is the required return on a portfolio What is the required return on a portfolio

consisting of 40% of the asset above and the consisting of 40% of the asset above and the rest in an asset with an average amount of rest in an asset with an average amount of systematic risk?systematic risk?