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McGraw Hill/Irwin Copyright 2009 by The McGraw-Hill Companies, Inc. All rights

Fundamentals

of Corporate

Finance

Sixth Edition

Richard A. Brealey

Stewart C. Myers

Alan J. Marcus

Chapter 12

McGraw Hill/Irwin Copyright 2009 by The McGraw-Hill Companies, Inc. All rights

Risk, Return and Capital

Budgeting

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Topics Covered

Expected Returns and Variances

Portfolios

Announcements, Surprises, and Expected Returns

Risk: Systematic and Unsystematic Diversification and Portfolio Risk

Systematic Risk and Beta

The Security Market Line and CAPM

The SML, the Cost of Capital and Capital

Budgeting: A Preview

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Expected Returns

Expected returns are based on theprobabilities of possible outcomes

In this context, expected means average

if the process is repeated many times The expected return does not even have to

be a possible return

=

=n

i

iiRpRE

1

)(

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Example: Expected Returns

Suppose you have predicted the following returnsfor stocks C and T in three possible states ofnature. What are the expected returns? State Probability C T

Boom 0.3 0.15 0.25 Normal 0.5 0.10 0.20 Recession ??? 0.02 0.01

RC= .3(.15) + .5(.10) + .2(.02) = .099 = 9.9%

RT = .3(.25) + .5(.20) + .2(.01) = .177 = 17.7%

V i d S d d

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12- 5 Variance and Standard

Deviation

Variance and standard deviation still measurethe volatility of returns

Using unequal probabilities for the entire

range of possibilitiesWeighted average of squared deviations

=

=n

i

ii RERp1

22 ))((

E l V i d

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12- 6 Example: Variance and

Standard Deviation

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

Stock C

2 = .3(.15-.099)2 + .5(.1-.099)2 + .2(.02-.099)2 = .

002029 = .045

Stock T

2

= .3(.25-.177)2

+ .5(.2-.177)2

+ .2(.01-.177)2

= .007441

= .0863

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Portfolios

A portfolio is a collection of assets An assets risk and return are important to

how the stock affects the risk and return of

the portfolio The risk-return trade-off for a portfolio is

measured by the portfolio expected return and

standard deviation, just as with individualassets

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Example: Portfolio Weights

Suppose you have $15,000 to invest and youhave purchased securities in the following

amounts. What are your portfolio weights in

each security? $2,000 of DCLK $3,000 of KO

$4,000 of INTC

$6,000 of KEI

DCLK: 2/15 = .133

KO: 3/15 = .2

INTC: 4/15 = .267

KEI: 6/15 = .4

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Portfolio Expected Returns

The expected return of a portfolio is the weightedaverage of the expected returns of the respective

assets in the portfolio

You can also find the expected return by finding

the portfolio return in each possible state andcomputing the expected value as we did with

individual securities

=

=

m

j

jjP REwRE1

)()(

t t

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12- 10 xamp e: xpecte ort o o

Returns

Consider the portfolio weights computedpreviously. If the individual stocks have thefollowing expected returns, what is theexpected return for the portfolio?

DCLK: 19.65%KO: 8.96% INTC: 9.67%

KEI: 8.13% E(R

P) = .133(19.65) + .2(8.96) + .267(9.67)

+ .4(8.13) = 10.24%

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Portfolio Variance

Compute the portfolio return for each state:R

P= w

1R

1+ w

2R

2+ + w

mR

m

Compute the expected portfolio return using

the same formula as for an individual asset Compute the portfolio variance and standard

deviation using the same formulas as for an

individual asset

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Example: Portfolio Variance

Consider the following information Invest 50% of your money in Asset A

State Probability A B

Boom .4 30% -5%

Bust .6 -10% 25%

What is the expected return and standard

deviation for each asset?

What is the expected return and standard

deviation for the portfolio?

Portfolio

12.5%7.5%

E t d U t d

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12- 13 Expected versus Unexpected

Returns

Realized returns are generally not equal toexpected returns

There is the expected component and the

unexpected component At any point in time, the unexpected return can be

either positive or negative

Over time, the average of the unexpected

component is zero

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Announcements and News

Announcements and news contain both anexpected component and a surprise

component

It is the surprise component that affects astocks price and therefore its return

This is very obvious when we watch how

stock prices move when an unexpected

announcement is made, or earnings are

different from anticipated

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Efficient Markets

Efficient markets are a result of investorstrading on the unexpected portion of

announcements

The easier it is to trade on surprises, themore efficient markets should be

Efficient markets involve random price

changes because we cannot predict surprises

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Systematic Risk

Risk factors that affect a large number ofassets

Also known as non-diversifiable risk or

market risk Includes such things as changes in GDP,

inflation, interest rates, etc.

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Unsystematic Risk

Risk factors that affect a limited number ofassets

Also known as unique risk and asset-specific

risk Includes such things as labor strikes, part

shortages, etc.

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Returns

Total Return = expected return + unexpectedreturn

Unexpected return = systematic portion +

unsystematic portion Therefore, total return can be expressed as

follows:

Total Return = expected return + systematicportion + unsystematic portion

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Diversification

Portfolio diversification is the investment inseveral different asset classes or sectors

Diversification is not just holding a lot of assets

For example, if you own 50 Internet stocks,

then you are not diversified

However, if you own 50 stocks that span 20

different industries, then you are diversified

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Table 11.7

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The Principle of Diversification

Diversification can substantially reduce thevariability of returns without an equivalentreduction in expected returns

This reduction in risk arises because worse-

than-expected returns from one asset areoffset by better-than-expected returns fromanother asset

However, there is a minimum level of riskthat cannot be diversified away - that is thesystematic portion

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Figure 11.1

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Diversifiable Risk

The risk that can be eliminated bycombining assets into a portfolio

Often considered the same as unsystematic,

unique, or asset-specific risk

If we hold only one asset, or assets in the

same industry, then we are exposing

ourselves to risk that we could diversify

away

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Total Risk

Total risk = systematic risk + unsystematic

risk

The standard deviation of returns is a

measure of total risk

For well-diversified portfolios, unsystematic

risk is very small

Consequently, the total risk for a diversified

portfolio is essentially equivalent to the

systematic risk

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Systematic Risk Principle

There is a reward for bearing risk

There is not a reward for bearing risk

unnecessarily

The expected return on a risky asset dependsonly on that assets systematic risk since

unsystematic risk can be diversified away

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Measuring Systematic Risk

How do we measure systematic risk?

We use the beta coefficient to measuresystematic risk

What does beta tell us? A beta of 1 implies the asset has the same

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

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

risk than the overall market

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Table 11.8

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Total versus Systematic Risk

Consider the following information: Standard Deviation Beta Security C 20% 1.25

Security K 30% 0.95

Which security has more total risk?

Which security has more systematic risk?

Which security should have the higher expected

return?

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Example: Portfolio Betas

Consider the previous example with the followingfour securities Security Weight Beta

DCLK .133 4.03

KO .2 0.84

INTC .267 1.05

KEI .4 0.59

What is the portfolio beta? .133(4.03) + .2(.84) + .267(1.05) + .4(.59) = 1.22

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Beta and the Risk Premium

Remember that the risk premium = expectedreturn risk-free rate

The higher the beta, the greater the risk

premium should be Can we define the relationship between the

risk premium and beta so that we can estimate

the expected return? YES!

12 31 Example: Portfolio Expected

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12- 31 Example: Portfolio ExpectedReturns and Betas

Rf

E(RA)

A

0%

5%

10%

15%

20%

25%

30%

0 0.5 1 1.5 2 2.5 3

Beta

Expecte

dReturn

12 32 Reward to Risk Ratio:

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12- 32 Reward-to-Risk Ratio:Definition and Example

The reward-to-risk ratio is the slope of the lineillustrated in the previous example Slope = (E(R

A) R

f) / (

A 0)

Reward-to-risk ratio for previous example =

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

(implying that the asset plots above the line)?

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

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Market Equilibrium

In equilibrium, all assets and portfolios musthave the same reward-to-risk ratio, and each

must equal the reward-to-risk ratio for the

market

M

fM

A

fA RRERRE

)()( =

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Security Market Line

The security market line (SML) is therepresentation of market equilibrium

The slope of the SML is the reward-to-risk

ratio: (E(RM) R

f) /

M

But since the beta for the market is

ALWAYS equal to one, the slope can be

rewritten

Slope = E(RM) R

f= market risk premium

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Capital Asset Pricing Model

The capital asset pricing model (CAPM)defines the relationship between risk and

return

E(RA) = R

f+

A(E(R

M) R

f)

If we know an assets systematic risk, we

can use the CAPM to determine its expected

return

This is true whether we are talking about

financial assets or physical assets

12- 36 Factors Affecting Expected

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12- 36 Factors Affecting ExpectedReturn

Pure time value of money measured by therisk-free rate

Reward for bearing systematic risk

measured by the market risk premium Amount of systematic risk measured by

beta

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Example: CAPM

Consider the betas for each of the assets givenearlier. If the risk-free rate is 3.15% and the market

risk premium is 9.5%, what is the expected return

for each?

Security Beta Expected Return DCLK 4.03 3.15 + 4.03(9.5) = 41.435%

KO 0.84 3.15 + .84(9.5) = 11.13%

INTC 1.05 3.15 + 1.05(9.5) = 13.125%

KEI 0.59 3.15 + .59(9.5) = 8.755%

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SML and Equilibrium

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Capital Budgeting & Project Risk

The project cost of capital depends on the useto which the capital is being put. Therefore,

it depends on the risk of the project and not

the risk of the company.

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C i i & j i

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Example - Based on the CAPM, ABC Company has a cost of

capital of 17%. [4 + 1.3(10)]. A breakdown of thecompanys investment projects is listed below. Whenevaluating a new dog food production investment, which costof capital should be used?

1/3 Nuclear Parts Mfr. B=2.0

1/3 Computer Hard Drive Mfr. B=1.3

1/3 Dog Food Production B=0.6

AVG. B of assets = 1.3

Capital Budgeting & Project Risk

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C i l B d i & P j Ri k

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Example - Based on the CAPM, ABC Company has a cost of

capital of 17%. (4 + 1.3(10)). A breakdown of the

companys investment projects is listed below. When

evaluating a new dog food production investment, which cost

of capital should be used?

R = 4 + 0.6 (14 - 4 ) = 10%

10% reflects the opportunity cost of capital on aninvestment given the unique risk of the project.

Capital Budgeting & Project Risk

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Q i Q i

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Quick Quiz

How do you compute the expected return

and standard deviation for an individual

asset? For a portfolio?

What is the difference between systematic

and unsystematic risk?

What type of risk is relevant for determining

the expected return?

How do you evaluate an appropriate level of

risk for a project?

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