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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
http://screen.finance.yahoo.com/stocks.html -
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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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