Lecture 8: Capital Asset Pricing Model
RSM 332
Capital Market Theory
Rotman School of Management
University of Toronto
Mike Simutin
November 2/3, 2011
Capital Asset Pricing Model
RSM 332, 1/25
Why Is This Important?
Capital Asset Pricing Model (CAPM) is THE workhorse
model in Finance
CAPM is very widely used both by academics and practitioners
CAPM is a very common way to measure performance of
investment strategies
It also allows us to identify undervalued securities
CAPM gives us a way to measure required return on a project
(e.g., new factory) and decide whether or not to go ahead
with it
It is a way to obtain the discount rate necessary to calculate
the present value of a firm’s future cash ﬂows
CAPM allows us to measure risk and determine its market
price
Capital Asset Pricing Model
RSM 332, 2/25
CAPM Assumptions
Investors are risk averse and maximize expected utility that
depends only on mean and variance of returns
Assets returns are jointly normally distributed
Investors cannot inﬂuence prices (they are pricetakers)
Investors have identical expectations about asset returns
Investors plan for one identical holding period
Investors can borrow or lend an unlimited amount at the
riskfree rate
There are no market imperfections (e.g., taxes, transaction
costs, shortselling restrictions, etc.)
All assets are infinitely divisible
Capital Asset Pricing Model
RSM 332, 3/25
Towards the CAPM
MPT allows us to determine how an individual investor should
allocate his or her wealth optimally
CAPM allows us to aggregate the actions of all investors to
determine expected returns of any security
Several insights led Sharpe (along with Treynor and Lintner) to
derive the CAPM:
Expected Return, Percent
0
1
2
3
4
5
6
7
8
Standard Deviation, Percent
0
5
10
15
20
25
30
35
40
45
50
55
60
65
MVP
Individual securities
Efficient Frontier
R
F
Capital Market Line
M
•
Portfolio M has the highest
attainable Sharpe ratio
•
All investors hold Portfolio M
•
M must contain all risky assets
•
In equilibrium, excess demand
for any asset must be zero
After some (quite simple) mathematical manipulations, we can derive the
CAPM
Capital Asset Pricing Model
RSM 332, 4/25
Capital Asset Pricing Model
Define the
beta
of any security
i
as
β
i
≡
Cov
(
R
i
,
R
M
)
Var
(
R
M
)
=
σ
iM
σ
2
M
=
ρ
iM
σ
i
σ
M
σ
2
M
=
ρ
iM
σ
i
σ
M
CAPM
states that the expected return on this security is
E
(
R
i
)
=
R
f
+
β
i
·
[
E
(
R
M
)
−
R
f
]
Expected return
on security
i
=
Riskfree
rate
+
Beta of
security
i
·
Market risk
premium
Capital Asset Pricing Model
RSM 332, 5/25
CAPM: Simple Example
You collect the following data:
Historical market risk premium is 6.5% per year
Expected return on the TBills is 1% per year
According to finance.google.com, Apple’s beta is 1.28
What is the expected annual return on Apple’s stock?
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 Fall '08
 RAYMONDKAN
 Capital Asset Pricing Model, capital asset pricing, Asset Pricing Model

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