12- 1 Chapter 12 Return, Risk and the Security Market Line CHAPTER OUTLINE Announcements, surprises and expected returns Announcements, surprises and expected

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Chapter 12Chapter 12Return, Risk and theReturn, Risk and theSecurity Market LineSecurity Market Line

CHAPTER OUTLINECHAPTER OUTLINE•Announcements, surprises and Announcements, surprises and expected returnsexpected returns•Efficient frontier and capital asset Efficient frontier and capital asset lineline•Risk: systematic and unsystematicRisk: systematic and unsystematic•Diversification, systematic risk and Diversification, systematic risk and unsystematic risk unsystematic risk •Systematic risk and betaSystematic risk and beta•The security market lineThe security market line•More on betaMore on beta•Multifactor modelsMultifactor models•A Brief History of Testing CAPMA Brief History of Testing CAPM•The Fama-French Three-Factor The Fama-French Three-Factor ModelModel

© 2009 McGraw-Hill Ryerson © 2009 McGraw-Hill Ryerson LimitedLimited

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

Our goal in this chapter is to define risk more Our goal in this chapter is to define risk more precisely, and discuss how to measure it. precisely, and discuss how to measure it.

In addition, we will quantify the relation In addition, we will quantify the relation between risk and return in financial markets.between risk and return in financial markets.


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Expected and Unexpected ReturnsExpected and Unexpected Returns

The return on any stock traded in a financial market The return on any stock traded in a financial market is composed of two parts.is composed of two parts. The normal, or expected, part of the return is the The normal, or expected, part of the return is the

return that investors predict or expect.return that investors predict or expect. The uncertain, or risky, part of the return comes from The uncertain, or risky, part of the return comes from

unexpected information revealed during the year.unexpected information revealed during the year.

Total Return-Expected Return=Unexpected ReturnTotal Return-Expected Return=Unexpected Return

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Announcements and NewsAnnouncements and News Firms make periodic announcements about events that may

significantly impact the profits of the firm. Earnings Product development Personnel

The impact of an announcement depends on how much of the announcement represents new information.

When the situation is not as bad as previously thought, what seems to be bad news is actually good news.

When the situation is not as good as previously thought, what seems to be good news is actually bad news.

News about the future is what really matters. Market participants factor predictions about the future into the expected

part of the stock return. Announcement = Expected News + Surprise News


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Systematic and Unsystematic RiskSystematic and Unsystematic Risk

Systematic risk is risk that influences a large number of assets. Also called market risk.

Unsystematic risk is risk that influences a single company or a small group of companies. Also called unique risk or firm-specific risk.Total risk = Systematic risk + Unsystematic risk

R- E(R)= U=Systematic portion+ Unsystematic portionR- E(R)= U=Systematic portion+ Unsystematic portion

= m + = m +


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Diversification and RiskDiversification and Risk In a large portfolio:

Some stocks will go up in value because of positive company-specific events, while

Others will go down in value because of negative company-specific events.

Unsystematic risk is essentially eliminated by diversification, so a portfolio with many assets has almost no unsystematic risk.

Unsystematic risk is also called diversifiable risk. Systematic risk is also called non-diversifiable risk.


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The Systematic Risk PrincipleThe Systematic Risk Principle

What determines the size of the risk premium on a What determines the size of the risk premium on a risky asset?risky asset?

The systematic risk principle states:The systematic risk principle states:

The reward for bearing risk depends only on the The reward for bearing risk depends only on the systematic risk of an investment. systematic risk of an investment.

So, no matter how much total risk an asset has, only So, no matter how much total risk an asset has, only the the systematicsystematic portion is relevant in determining the portion is relevant in determining the expected return (and the risk premium) on that asset.expected return (and the risk premium) on that asset.

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Measuring Systematic RiskMeasuring Systematic Risk

To be compensated for risk, the risk has to be special. Unsystematic risk is not special. Systematic risk is special.

The Beta coefficient () measures the relative systematic risk of an asset.

Assets with Betas larger than 1.0 have more systematic risk than average.

Assets with Betas smaller than 1.0 have less systematic risk Assets with Betas smaller than 1.0 have less systematic risk than average.than average.

Because assets with larger betas have greater systematic risks, Because assets with larger betas have greater systematic risks, they will have greater expected returns.they will have greater expected returns.

Note that not all Betas are created equally.Note that not all Betas are created equally.


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Beta CoefficientsBeta CoefficientsTable 12.1


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Finding a Beta on the WebFinding a Beta on the Web

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Portfolio BetasPortfolio Betas The total risk of a portfolio has no simple relation to the The total risk of a portfolio has no simple relation to the

total risk of the assets in the portfolio.total risk of the assets in the portfolio. Recall the variance of a portfolio equationRecall the variance of a portfolio equation For two assets, you need two variances and the covariance.For two assets, you need two variances and the covariance. For four assets, you need four variances, and six covariances.For four assets, you need four variances, and six covariances.

In contrast, a portfolio Beta can be calculated just like the In contrast, a portfolio Beta can be calculated just like the expected return of a portfolio.expected return of a portfolio. That is, you can multiply each asset’s Beta by its portfolio That is, you can multiply each asset’s Beta by its portfolio

weight and then add the results to get the portfolio’s Beta.weight and then add the results to get the portfolio’s Beta. Example: Beta for IBM is 1.05, Beta for eBay is 1.45. You put half Example: Beta for IBM is 1.05, Beta for eBay is 1.45. You put half

your money into IBM and half into eBay. What is your portfolio your money into IBM and half into eBay. What is your portfolio Beta? (Answer = 0.50x1.05 + 0.5x1.45 = 1.25)Beta? (Answer = 0.50x1.05 + 0.5x1.45 = 1.25)

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Beta and the Risk PremiumBeta and the Risk Premium Consider a portfolio made up of asset A and a risk-free asset. Consider a portfolio made up of asset A and a risk-free asset.

For asset A, For asset A, E(RE(RAA)) = 20% and = 20% and AA = 1.6 = 1.6

The risk-free rate The risk-free rate RRff = 8%. For a risk-free asset, = 8%. For a risk-free asset, = 0 by definition = 0 by definition

• Note that if the investor borrows at the risk-free rate and invests the Note that if the investor borrows at the risk-free rate and invests the proceeds in asset A, the investment in asset A will exceed 100%.proceeds in asset A, the investment in asset A will exceed 100%.

% of Portfolio in Asset A% of Portfolio in Asset A Portfolio Expected ReturnPortfolio Expected Return Portfolio BetaPortfolio Beta

0%0% 88 0.00.0

2525 1111 0.40.4

5050 1414 0.80.8

7575 1717 1.21.2

100100 2020 1.61.6

125125 2323 2.02.0

150150 2626 2.42.4

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Portfolio Expected Returns and Portfolio Expected Returns and Betas for Asset ABetas for Asset A


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The Reward-to-Risk RatioThe Reward-to-Risk Ratio

Notice that all the combinations of portfolio expected Notice that all the combinations of portfolio expected returns and betas fall on a straight line.returns and betas fall on a straight line.

Slope (Rise over Run):Slope (Rise over Run):

What this tells us is that asset A offers a reward-to-risk ratio of 7.50%. In other words, asset A has a risk premium of 7.50% per “unit” of systematic risk.

7.50%

1.6

8%20%

β

RRE

A

fA

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The Basic ArgumentThe Basic Argument Recall that for asset A: Recall that for asset A: E(RE(RAA)) = 20% and = 20% and AA = 1.6 = 1.6 Suppose there is a second asset, asset B.Suppose there is a second asset, asset B.

For asset B: For asset B: E(RE(RBB)) = 16% and = 16% and AA = 1.2 = 1.2 Which investment is better, asset A or asset B?Which investment is better, asset A or asset B?

Asset A has a higher expected returnAsset A has a higher expected return Asset B has a lower systematic risk measureAsset B has a lower systematic risk measure

We can calculate some different possible portfolio expected returns and betas by We can calculate some different possible portfolio expected returns and betas by changing the percentages invested in asset B and the risk-free rate.changing the percentages invested in asset B and the risk-free rate.

% of Portfolio in Asset B% of Portfolio in Asset B Portfolio Expected ReturnPortfolio Expected Return Portfolio BetaPortfolio Beta

0%0% 88 0.00.0

2525 1010 0.30.3

5050 1212 0.60.6

7575 1414 0.90.9

100100 1616 1.21.2

125125 1818 1.51.5

150150 2020 1.81.8


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Portfolio Expected Returns and Betas for Asset BPortfolio Expected Returns and Betas for Asset B


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Expected Returns and Betas for Both AssetsExpected Returns and Betas for Both Assets

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The Fundamental ResultThe Fundamental Result The situation we have described for assets A and B cannot persist in a The situation we have described for assets A and B cannot persist in a

well-organized, active marketwell-organized, active market Investors will be attracted to asset A (and buy A shares)Investors will be attracted to asset A (and buy A shares) Investors will shy away from asset B (and sell B shares)Investors will shy away from asset B (and sell B shares)

This buying and selling will makeThis buying and selling will make The price of A shares increase ; The price of B shares decreaseThe price of A shares increase ; The price of B shares decrease

This price adjustment continues until the two assets plot on exactly the This price adjustment continues until the two assets plot on exactly the same line. That is, until same line. That is, until

The reward-to-risk ratio must be the same for all assets in a competitive financial market.The reward-to-risk ratio must be the same for all assets in a competitive financial market. If one asset has twice as much systematic risk as another asset, its risk premium will If one asset has twice as much systematic risk as another asset, its risk premium will

simply be twice as large.simply be twice as large. Because the reward-to-risk ratio must be the same, all assets in the market must plot on Because the reward-to-risk ratio must be the same, all assets in the market must plot on

the same line.the same line.

B

fB

A

fA

β

RRE

β

RRE


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The Fundamental ResultThe Fundamental Result


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The Security Market Line, SMLThe Security Market Line, SML The Security market line (SML) is a graphical representation of

the linear relationship between systematic risk and expected return in financial markets.

For a market portfolio,

The term E(RM) – Rf is often called the market risk premium because it is the risk premium on a market portfolio.

For any asset i in the market: Setting the reward-to-risk ratio for all assets equal to the market

risk premium results in an equation known as the capital asset pricing model.

fRMRE1

fRMRE

MβfRMRE

fMi

fi RREβ

RRE

ifMfi βRRERRE


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The Security Market LineThe Security Market Line

The Capital Asset Pricing Model (CAPM) is a theory of risk and return for securities on a competitive capital market.

The CAPM shows that E(Ri) depends on: Rf, the pure time value of money. E(RM) – Rf, the reward for bearing systematic risk. i, the amount of systematic risk.

ifMfi βRRERRE


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The Security Market LineThe Security Market Line

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A Closer Look at BetaA Closer Look at Beta

R – E(R) = mR – E(R) = m + + , where , where mm is the systematic portion is the systematic portion of the unexpected return.of the unexpected return.

mm = = [ [RRMM –– E(RE(RMM))]] So, So, R – E(R) = R – E(R) = [ [RRMM –– E(RE(RMM))] + ] + In other words:In other words:

A high-Beta security is simply one that is relatively A high-Beta security is simply one that is relatively sensitive to overall market movementssensitive to overall market movements

A low-Beta security is one that is relatively insensitive to A low-Beta security is one that is relatively insensitive to overall market movements.overall market movements.

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Decomposition of Total ReturnsDecomposition of Total Returns


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Unexpected Returns and BetaUnexpected Returns and Beta

Figure 12.5

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Where Do Betas Come From?Where Do Betas Come From? A security’s Beta depends on:A security’s Beta depends on:

How closely correlated the security’s return is with How closely correlated the security’s return is with the overall market’s return, andthe overall market’s return, and

How volatile the security is relative to the market.How volatile the security is relative to the market. A security’s Beta is equal to the correlation A security’s Beta is equal to the correlation

multiplied by the ratio of the standard deviations.multiplied by the ratio of the standard deviations.

m

iMii σ

σR,RCorrβ

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Where Do Betas Come From?Where Do Betas Come From?Table 12.4

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Using a Spreadsheet to Calculate BetaUsing a Spreadsheet to Calculate Beta

Security Market2001 10% 8%2002 -8% -12%2003 -4% 16%2004 40% 26%2005 12% 22%

Average: 10% 12%Std. Dev.: 18.87% 15.03%

Correlation: 0.72 =CORREL(D10:D14,E10:E14)

Beta: 0.90

Using a Spreadsheet to Calculate Beta

To illustrate how to calculate betas, correlations, and covariances using a spreadsheet,we have entered the information from Table 12.4 into the spreadsheet below. Here, we use Excel functions to do all the calculations.

by n instead of n-1. Verify that you get a Beta of about 0.72 if you use the COVAR function divided by the variance of the Market Returns (Use the Excel function, =VAR).

Returns

(Using the =AVERAGE function)(Using the =STDEV function)

Excel also has a covariance function, =COVAR, but we do not use it because it divides

Note: The Excel Format is set to percent, but the numbers are entered as decimals.


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Why Do Betas Differ?Why Do Betas Differ?

Betas are estimated from actual data. Different Betas are estimated from actual data. Different sources estimate differently, possibly using different sources estimate differently, possibly using different data.data. For data, the most common choices are three to five years For data, the most common choices are three to five years

of monthly data, or a single year of weekly data.of monthly data, or a single year of weekly data. To measure the overall market, the S&P 500 stock market To measure the overall market, the S&P 500 stock market

index is commonly used.index is commonly used. The calculated betas may be adjusted for various statistical The calculated betas may be adjusted for various statistical

reasons.reasons.


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Extending CAPMExtending CAPM

The CAPM has a stunning implication: The CAPM has a stunning implication: What you earn on your portfolio depends only on What you earn on your portfolio depends only on

the level of systematic risk that you bearthe level of systematic risk that you bear As a diversified investor, you do not need to worry As a diversified investor, you do not need to worry

about total risk, only systematic risk.about total risk, only systematic risk. But, does expected return depend only on Beta? But, does expected return depend only on Beta?

Or, do other factors come into play?Or, do other factors come into play? The above bullet point is a hotly debated The above bullet point is a hotly debated

question.question.

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Multifactor ModelsMultifactor Models

No single factor (market risk) that determines No single factor (market risk) that determines systematic risk and develop multifactor systematic risk and develop multifactor models. If we apply this principle we obtain models. If we apply this principle we obtain the following formula:the following formula:

E(Ri) =Rf +[ E (Rm)-Rf] X βi1+ [Second Factor Premium] X E(Ri) =Rf +[ E (Rm)-Rf] X βi1+ [Second Factor Premium] X βi2+ [Third Factor Premium] X βi3 +βi2+ [Third Factor Premium] X βi3 +……

where βi2 = sensitivity of stock i to factor 2. where βi2 = sensitivity of stock i to factor 2.


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Arbitrage Pricing ModelArbitrage Pricing Model

Arbitrage Pricing Model was developed in Arbitrage Pricing Model was developed in 1976. The model advocates that various 1976. The model advocates that various economic factors affect stock returns and that economic factors affect stock returns and that stock returns reach their equilibrium level stock returns reach their equilibrium level because of arbitrage principle.because of arbitrage principle.

If equilibrium is violated, investors can earn If equilibrium is violated, investors can earn abnormal returns by forming risk-free abnormal returns by forming risk-free arbitrage portfolios.arbitrage portfolios.


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The Fama-French Three-Factor ModelThe Fama-French Three-Factor Model

Professors Gene Fama and Ken French argue that two Professors Gene Fama and Ken French argue that two additional factors should be added.additional factors should be added.

In addition to beta, two other factors appear to be In addition to beta, two other factors appear to be useful in explaining the relationship between risk and useful in explaining the relationship between risk and return.return. Size, as measured by market capitalizationSize, as measured by market capitalization The book value to market value ratio, i.e., B/MThe book value to market value ratio, i.e., B/M

Whether these two additional factors are truly sources Whether these two additional factors are truly sources of systematic risk is still being debated.of systematic risk is still being debated.

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Returns from 25 Portfolios Formed Returns from 25 Portfolios Formed on Size and Book-to-Marketon Size and Book-to-Market

Note that the portfolio containing the smallest cap and Note that the portfolio containing the smallest cap and the highest book-to-market have had the highest returns.the highest book-to-market have had the highest returns.

Table 12.5


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Useful Internet SitesUseful Internet Sites http://finance.yahoo.com (A terrific source of financial (A terrific source of financial

information)information) www.theonlineinvestor.com (source for an earnings calendar) (source for an earnings calendar) http://earnings.nasdaq.com (to see recent earnings surprises)(to see recent earnings surprises) www.portfolioscience.com (helps you analyze risk) (helps you analyze risk) www.ibbotson.com (A source to purchase betas) (A source to purchase betas) www.money.com (Another source for betas) (Another source for betas) www.moneychimp.com (for a CAPM calculator and other (for a CAPM calculator and other

interesting tools)interesting tools)

Documents

12- 1 Chapter 12 Return, Risk and the Security Market Line CHAPTER OUTLINE Announcements, surprises and expected returns Announcements, surprises and expected