FIN2101
BUSINESS FINANCE II
Module 2
Capital Asset Pricing Model
(CAPM)
Student Activities
Reading
Text,Chapter 6 (pp,210-21 only)
Text Study Guide,Chapter 6 (part only)
Study Book,Module 2 (inc,Appendices 2.1,2.2 & 2.3)
Tutorial Work
Tutorial Workbook,Self Assessment Activity 2.1
Text Study Guide,Chapter 6,T/F 9 & 10,MC 13 to 15,
Problems 5,7 & 8
Capital Asset Pricing Model
CAPM describes how prices of individual
securities are determined.
Portfolio theory.
An asset’s return is equal to the risk-free rate
plus a risk premium equal to the asset’s beta
multiplied by the market risk premium.
Linear relationship between return and risk.
Risk and Return
Return is a function of risk
Higher risk warrants a higher return
Return = Risk-free return + risk premium
Risk
Total risk:
= unsystematic risk + systematic risk
= unique risk + market risk
= diversifiable risk + non-diversifiable risk
Expected Return - Single Asset
n
1=i
ii
Pr k = k
Risk - Single Asset
n
1i
i
2
ik Pr k - k?
1 -n
k - k
n
1i
2
i
k
Expected Return & Risk of a
Portfolio
n
1j=
jjp k w = k
211,221
2
2
2
2
2
1
2
1k rw2w w w p
Correlation Coefficient
A measure of the relation between the
returns on two securities.
Can be + or - or 0.
Diversification is of greatest benefit in risk
reduction when the correlation between the
returns on the two securities is negative.
Efficient Frontier
Holding the correlation coefficient constant,we
could change the weights of the two assets in the
portfolio.
We could then determine a number of expected
risk and return coordinates for the portfolio and
plot these in risk-return space.
It is possible to derive a complete curve by
simply varying the weights by small increments.
Efficient Frontier
We could examine a number of two-asset
portfolios and derive their curves by changing
the weights of the assets.
From these the efficient frontier is derived.
The efficient frontier is the envelope curve of
all of the individual curves.
Efficient Frontier
Consists of only those portfolios of risky
assets that give the highest possible return for
a given level of risk.
Dominance principle.
Each investor will try to hold a portfolio on
the efficient frontier.
Personal preference will determine where on
the frontier.
Indifference Curves
Show the investor’s trade-off between risk
and return.
The steeper the slope,the more risk averse
the investor.
The higher the indifference curve,the greater
the utility.
Efficient Frontier and Investor
Utility
All points along the efficient frontier are
potentially optimal.
Portfolio selection depends on risk tolerance.
An investor will choose the portfolio that is
tangent to the highest attainable indifference
curve.
Risk Tolerance
Conservative investors select portfolios at the
left end of the efficient frontier.
Aggressive investors select portfolios at the
right end of the efficient frontier.
Capital Market Line (CML)
The efficient frontier is concerned with
portfolios of risky assets.
A risk-free asset increases the investment
options available:
zero variance and a certain return
zero covariance with any other asset
no risk
New efficient frontier - CML.
CML
Options are:
100% risk-free asset (10% return)
Combination of risky & risk-free assets
Through borrowing,an increased investment
in risky assets
Risk-free Lending
Purchase of the risk-free asset = risk-free
lending.
Such an investor would choose a point on the
CML between RF and M.
Risk-free Borrowing
Buy the risky portfolio with available funds
and then borrow at the risk-free rate to
acquire further assets.
Higher returns means higher risk.
Lie beyond point M on the CML.
Market Portfolio M
Contains all risky assets in proportion to their
market value.
It is a completely diversified portfolio,
affected only by systematic risk (due to
macroeconomic factors).
Capital Market Line (CML)
Represents all possible market investments
proportionately.
The new efficient frontier (dominance
principle).
Shows trade-off between expected return and
risk for all efficient portfolios.
Linear & positive relationship between risk &
return.
CAPM
When the market is in equilibrium,an asset is
expected to provide a return commensurate
with its systematic risk.
CAPM looks at an asset’s systematic risk in
relation to the market as a whole.
Risk is the volatility of the asset’s returns
relative to the volatility of the market
portfolio’s returns.
Characteristic Line
We can plot the historical sensitivity of an
individual asset’s returns to the returns on the
market portfolio.
The characteristic line is a line of best fit
through the points.
Beta
The slope of the characteristic line is the
sensitivity of the asset’s returns relative to the
market returns and its measurement is called
the beta coefficient.
Beta is a measure of an individual asset’s
systematic risk relative to the market risk.
Beta of the market is 1.0.
Beta
2
k
mj
j
m
k,k C o v
= b
Sample Betas
Company Beta
Amcor 1.11
NAB 1.09
Coca Cola Amatil 1.05
BHP 0.99
CSR 0.90
Boral 0.84
Mayne Nickless 0.80
Coles Myer 0.65
Source,Ross et al,Fundamentals of Corporate Finance,p.346.
Portfolio Beta
n
1j
jjp
b w b
Security Market Line (SML)
SML is a graphical representation of the trade-
off between expected return and systematic
risk,as measured by beta,for every asset,
including inefficient portfolios.
Risk is labeled as beta,therefore beta can
replace variance as the measure of portfolio
risk.
Only interested in systematic risk.
Security Market Line (SML)
Called the CAPM and written for an individual asset
as follows:
FmjFj R - k b + R = k?
Security Market Line
bM = 1.0
Systematic Risk (Beta)
RF
km
Re
qu
ire
d R
et
ur
n
Risk
Premium
Risk-free
Return
FmjFj R - k b + R = k?
Example of SML Calculations
12%
6 - 121 6 k
1 b 12% ; k 6% ; R
j
mF
SML Example (Continued)
9%
6 - 120.5 6 k
0.5 b
15%
6 - 121.5 6 k
1.5 b
j
j
Security Market Line (SML)
In equilibrium,all assets (single assets and
portfolios of assets) will lie on the SML.
An asset which plots above the SML is under-
priced.
An asset which plots below the SML is over-
priced.
Security Market Line
Systematic Risk (Beta)
Rf
Re
qu
ire
d R
et
ur
n
Direction of
Movement
Direction of
Movement
Stock Y (Overpriced)
Stock X (Underpriced)
Lisa Miller at Basket Wonders is attempting to
determine the rate of return required by their stock
investors,Lisa is using a 6% RF and a long-term
market expected rate of return of 10%,A stock
analyst following the firm has calculated that the
firm beta is 1.2,What is the required rate of return on
the stock of Basket Wonders?
Determination of the Required
Rate of Return
KBW = RF+ bj(KM - RF)
KBW = 6% + 1.2(10% - 6%)
KBW = 10.8%
The required rate of return exceeds the market
rate of return as BW’s beta exceeds the market
beta (1.0).
BWs Required Rate of
Return
Lisa Miller at BW is also attempting to determine the
intrinsic value of the stock,She is using the constant
growth model,Lisa estimates that the dividend next
period will be $0.50 and that BW will grow at a
constant rate of 5.8%,The stock is currently selling for
$15.
What is the intrinsic value of the stock? Is the
stock over or underpriced?
Determination of the Intrinsic
Value of BW
The stock is OVERVALUED as the
market price ($15) exceeds the intrinsic
value ($10).
Determination of the Intrinsic
Value of BW
$0.50
10.8% - 5.8%
Intrinsic
Value =
= $10
Implications of CAPM
All investors hold the aggregate market
portfolio.
The market portfolio will be the optimal risky
portfolio.
Investors can obtain a desired risk-return
position by combining the risky portfolio
with borrowing/lending at the risk-free rate.
Separation Theorem
Investment is always made in the same risky
asset portfolio.
The only difference among investors is the
financing decision they make.
Division of investment and financing
decisions is the ‘separation theorem’.
CAPM Assumptions
Wealth maximisation
Risk and return are key factors
Homogeneous expectations
Identical time horizons
CAPM Assumptions
Free and simultaneous access to information
Risk-free asset
No taxes and transaction costs
Assets are marketable and divisible
Testing of CAPM
Is there a linear relationship between risk and
return?
Market portfolio
Testing of CAPM
Stability of beta
Conclusions
Unrealistic assumptions.
Does not describe what has occurred and is
therefore likely to be wrong.
Forecasting beta,the risk-free rate and the
market rate is so difficult that it renders the
model virtually useless.
BUSINESS FINANCE II
Module 2
Capital Asset Pricing Model
(CAPM)
Student Activities
Reading
Text,Chapter 6 (pp,210-21 only)
Text Study Guide,Chapter 6 (part only)
Study Book,Module 2 (inc,Appendices 2.1,2.2 & 2.3)
Tutorial Work
Tutorial Workbook,Self Assessment Activity 2.1
Text Study Guide,Chapter 6,T/F 9 & 10,MC 13 to 15,
Problems 5,7 & 8
Capital Asset Pricing Model
CAPM describes how prices of individual
securities are determined.
Portfolio theory.
An asset’s return is equal to the risk-free rate
plus a risk premium equal to the asset’s beta
multiplied by the market risk premium.
Linear relationship between return and risk.
Risk and Return
Return is a function of risk
Higher risk warrants a higher return
Return = Risk-free return + risk premium
Risk
Total risk:
= unsystematic risk + systematic risk
= unique risk + market risk
= diversifiable risk + non-diversifiable risk
Expected Return - Single Asset
n
1=i
ii
Pr k = k
Risk - Single Asset
n
1i
i
2
ik Pr k - k?
1 -n
k - k
n
1i
2
i
k
Expected Return & Risk of a
Portfolio
n
1j=
jjp k w = k
211,221
2
2
2
2
2
1
2
1k rw2w w w p
Correlation Coefficient
A measure of the relation between the
returns on two securities.
Can be + or - or 0.
Diversification is of greatest benefit in risk
reduction when the correlation between the
returns on the two securities is negative.
Efficient Frontier
Holding the correlation coefficient constant,we
could change the weights of the two assets in the
portfolio.
We could then determine a number of expected
risk and return coordinates for the portfolio and
plot these in risk-return space.
It is possible to derive a complete curve by
simply varying the weights by small increments.
Efficient Frontier
We could examine a number of two-asset
portfolios and derive their curves by changing
the weights of the assets.
From these the efficient frontier is derived.
The efficient frontier is the envelope curve of
all of the individual curves.
Efficient Frontier
Consists of only those portfolios of risky
assets that give the highest possible return for
a given level of risk.
Dominance principle.
Each investor will try to hold a portfolio on
the efficient frontier.
Personal preference will determine where on
the frontier.
Indifference Curves
Show the investor’s trade-off between risk
and return.
The steeper the slope,the more risk averse
the investor.
The higher the indifference curve,the greater
the utility.
Efficient Frontier and Investor
Utility
All points along the efficient frontier are
potentially optimal.
Portfolio selection depends on risk tolerance.
An investor will choose the portfolio that is
tangent to the highest attainable indifference
curve.
Risk Tolerance
Conservative investors select portfolios at the
left end of the efficient frontier.
Aggressive investors select portfolios at the
right end of the efficient frontier.
Capital Market Line (CML)
The efficient frontier is concerned with
portfolios of risky assets.
A risk-free asset increases the investment
options available:
zero variance and a certain return
zero covariance with any other asset
no risk
New efficient frontier - CML.
CML
Options are:
100% risk-free asset (10% return)
Combination of risky & risk-free assets
Through borrowing,an increased investment
in risky assets
Risk-free Lending
Purchase of the risk-free asset = risk-free
lending.
Such an investor would choose a point on the
CML between RF and M.
Risk-free Borrowing
Buy the risky portfolio with available funds
and then borrow at the risk-free rate to
acquire further assets.
Higher returns means higher risk.
Lie beyond point M on the CML.
Market Portfolio M
Contains all risky assets in proportion to their
market value.
It is a completely diversified portfolio,
affected only by systematic risk (due to
macroeconomic factors).
Capital Market Line (CML)
Represents all possible market investments
proportionately.
The new efficient frontier (dominance
principle).
Shows trade-off between expected return and
risk for all efficient portfolios.
Linear & positive relationship between risk &
return.
CAPM
When the market is in equilibrium,an asset is
expected to provide a return commensurate
with its systematic risk.
CAPM looks at an asset’s systematic risk in
relation to the market as a whole.
Risk is the volatility of the asset’s returns
relative to the volatility of the market
portfolio’s returns.
Characteristic Line
We can plot the historical sensitivity of an
individual asset’s returns to the returns on the
market portfolio.
The characteristic line is a line of best fit
through the points.
Beta
The slope of the characteristic line is the
sensitivity of the asset’s returns relative to the
market returns and its measurement is called
the beta coefficient.
Beta is a measure of an individual asset’s
systematic risk relative to the market risk.
Beta of the market is 1.0.
Beta
2
k
mj
j
m
k,k C o v
= b
Sample Betas
Company Beta
Amcor 1.11
NAB 1.09
Coca Cola Amatil 1.05
BHP 0.99
CSR 0.90
Boral 0.84
Mayne Nickless 0.80
Coles Myer 0.65
Source,Ross et al,Fundamentals of Corporate Finance,p.346.
Portfolio Beta
n
1j
jjp
b w b
Security Market Line (SML)
SML is a graphical representation of the trade-
off between expected return and systematic
risk,as measured by beta,for every asset,
including inefficient portfolios.
Risk is labeled as beta,therefore beta can
replace variance as the measure of portfolio
risk.
Only interested in systematic risk.
Security Market Line (SML)
Called the CAPM and written for an individual asset
as follows:
FmjFj R - k b + R = k?
Security Market Line
bM = 1.0
Systematic Risk (Beta)
RF
km
Re
qu
ire
d R
et
ur
n
Risk
Premium
Risk-free
Return
FmjFj R - k b + R = k?
Example of SML Calculations
12%
6 - 121 6 k
1 b 12% ; k 6% ; R
j
mF
SML Example (Continued)
9%
6 - 120.5 6 k
0.5 b
15%
6 - 121.5 6 k
1.5 b
j
j
Security Market Line (SML)
In equilibrium,all assets (single assets and
portfolios of assets) will lie on the SML.
An asset which plots above the SML is under-
priced.
An asset which plots below the SML is over-
priced.
Security Market Line
Systematic Risk (Beta)
Rf
Re
qu
ire
d R
et
ur
n
Direction of
Movement
Direction of
Movement
Stock Y (Overpriced)
Stock X (Underpriced)
Lisa Miller at Basket Wonders is attempting to
determine the rate of return required by their stock
investors,Lisa is using a 6% RF and a long-term
market expected rate of return of 10%,A stock
analyst following the firm has calculated that the
firm beta is 1.2,What is the required rate of return on
the stock of Basket Wonders?
Determination of the Required
Rate of Return
KBW = RF+ bj(KM - RF)
KBW = 6% + 1.2(10% - 6%)
KBW = 10.8%
The required rate of return exceeds the market
rate of return as BW’s beta exceeds the market
beta (1.0).
BWs Required Rate of
Return
Lisa Miller at BW is also attempting to determine the
intrinsic value of the stock,She is using the constant
growth model,Lisa estimates that the dividend next
period will be $0.50 and that BW will grow at a
constant rate of 5.8%,The stock is currently selling for
$15.
What is the intrinsic value of the stock? Is the
stock over or underpriced?
Determination of the Intrinsic
Value of BW
The stock is OVERVALUED as the
market price ($15) exceeds the intrinsic
value ($10).
Determination of the Intrinsic
Value of BW
$0.50
10.8% - 5.8%
Intrinsic
Value =
= $10
Implications of CAPM
All investors hold the aggregate market
portfolio.
The market portfolio will be the optimal risky
portfolio.
Investors can obtain a desired risk-return
position by combining the risky portfolio
with borrowing/lending at the risk-free rate.
Separation Theorem
Investment is always made in the same risky
asset portfolio.
The only difference among investors is the
financing decision they make.
Division of investment and financing
decisions is the ‘separation theorem’.
CAPM Assumptions
Wealth maximisation
Risk and return are key factors
Homogeneous expectations
Identical time horizons
CAPM Assumptions
Free and simultaneous access to information
Risk-free asset
No taxes and transaction costs
Assets are marketable and divisible
Testing of CAPM
Is there a linear relationship between risk and
return?
Market portfolio
Testing of CAPM
Stability of beta
Conclusions
Unrealistic assumptions.
Does not describe what has occurred and is
therefore likely to be wrong.
Forecasting beta,the risk-free rate and the
market rate is so difficult that it renders the
model virtually useless.
