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Chapter 10Fundamentals of Corporate FinanceThird Edition
Risk,Return,
and Capital
Budgeting
Brealey Myers Marcus
slides by Matthew Will
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Topics Covered
?Measuring Beta
?Portfolio Betas
?CAPM and Expected Return
?Security Market Line
?Capital Budgeting and Project Risk
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Measuring Market Risk
Market Portfolio - Portfolio of all assets in the
economy,In practice a broad stock market
index,such as the S&P Composite,is used
to represent the market.
Beta - Sensitivity of a stock’s return to the
return on the market portfolio.
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Measuring Market Risk
Example - Turbo Charged Seafood has the
following % returns on its stock,relative to
the listed changes in the % return on the
market portfolio,The beta of Turbo
Charged Seafood can be derived from this
information.
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Measuring Market Risk
Month Ma r ke t R e t ur n % Tur bo R e tu r n %
1 + 1 + 0.8
2 + 1 + 1.8
3 + 1 - 0.2
4 - 1 - 1.8
5 - 1 + 0.2
6 - 1 - 0.8
Example - continued
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Measuring Market Risk
?When the market was up 1%,Turbo
average % change was +0.8%
?When the market was down 1%,Turbo
average % change was -0.8%
?The average change of 1.6 % (-0.8 to 0.8)
divided by the 2% (-1.0 to 1.0) change in
the market produces a beta of 0.8.
Example - continued
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Measuring Market Risk
B = = 0, 81, 62
?When the market was up 1%,Turbo
average % change was +0.8%
?When the market was down 1%,Turbo
average % change was -0.8%
?The average change of 1.6 % (-0.8 to 0.8)
divided by the 2% (-1.0 to 1.0) change in
the market produces a beta of 0.8.
Example - continued
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Measuring Market Risk
Example - continued
-0,8
-0,6
-0,4
-0,2
0
0,2
0,4
0,6
0,8
1
-0,8 -0,6 -0,4 -0,2 0 0,2 0,4 0,6 0,8 1
Ma r k e t R e tu r n %
T u r b o
r e tu r n %
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Portfolio Betas
?Diversification decreases variability from
unique risk,but not from market risk.
?The beta of your portfolio will be an
average of the betas of the securities in the
portfolio.
?If you owned all of the S&P Composite
Index stocks,you would have an average
beta of 1.0
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Measuring Market Risk
Market Risk Premium - Risk premium of market
portfolio,Difference between market return and
return on risk-free Treasury bills,0
2
4
6
8
10
12
14
0 0,2 0,4 0,6 0,8 1
B e ta
Ex
p
e
c
te
d
R
e
tu
r
n
(%
)
.
Market
Portfolio
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Measuring Market Risk
CAPM - Theory of the relationship between risk and
return which states that the expected risk premium
on any security equals its beta times the market
risk premium.
M ark et ris k p rem i u m = r - r
R i s k p rem i u m o n an y ass et = r - r
E x p ected R etu rn = r + B(r - r )
m f
f
f m f
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Measuring Market Risk
Security Market Line - The graphic representation
of the CAPM.
0 1
Beta
0
20
40
Ex
pe
cte
d R
etu
rn
(%
),
Rf
Rm Security Market Line
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Capital Budgeting & Project Risk
?The project cost of capital depends on the
use to 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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Capital Budgeting & Project Risk
Example - Based on the CAPM,ABC Company has a cost
of capital of 17%,(4 + 1.3(10)),A breakdown of the
company’s investment projects is listed below,When
evaluating a new dog food production investment,which
cost of 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
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Capital Budgeting & Project Risk
Example - Based on the CAPM,ABC Company has a cost
of capital of 17%,(4 + 1.3(10)),A breakdown of the
company’s 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 an
investment given the unique risk of the project.
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Derivation of CAPM
?Capital Market Line
?Individual's Efficient Frontier with Risk Free
Asset
E ( R )
Rf
?
M
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Derivation of CAPM
?Homogeneous Expectation--->One Market
Efficienf Frontier:Capital market Line (CML)
?The Slope of Capital Market Line is,
E ( R )
Rf
?
M
C M L
?
E( R m ) - R f
m
E( R m )
m?
M
fM RRE
?
?)(
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Derivation of CAPM
?Seurity Market Line (CAPM)
?If a portfolio is consisted of A and market
portfolio M with asset A,W%,and M,(1-
W%),then
E ( R )
Rf
?
M
A
C M L
),()1()()( MAP REWRWERE ???
? ? )21()1(2)1()( 222 E X PWWWWR iMMAP ???? ?????
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Derivation of CAPM
?對 W 取一階導數,
?When in equilibrium,W=0 and,
)()( MAP REREdWdR ??
P
MAAMMMAAMMAP W
dW
d
?
?????????? ????? 222 )2(
)()(| 0 MAWP REREdWdR ???
M
MAM
P
MAAMM
W
P
dW
d
?
??
?
????? 22
0|
?????
?
MP ?? ?
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Derivation of CAPM
?The slope of the portfolio in equilibrium then is:
?Since in equilibrium,the portfolio is equal the
market portfolio,the slope of the portfolio in
CML must equal to that of the market portfolio,
the equation can constructed as follows:
MMAM
MA
W
P
P RERE
d
dR
???? /)(
)()(|
20 ?
??
?
M
fM RRE
?
?)(
MMAM
MA RERE
??? /)(
)()(
2?
??
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Derivation of CAPM
?簡化上式：
?In market model:
?SML
? ? 2)()(
M
AM
fMfA RRERRE ?
????
AMAAA RR ??? ???
2
M
AM
A ?
?? ?
? ? AfMfA RRERRE ???? )()(
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Derivation of CAPM
E ( R )
Rf
?
M
S M L
1
E ( R m )
? ?
1
)()( fM
A
fA RRERRE ???
?