CHAPTER TEN
THE CAPITAL ASSET PRICING
MODEL
1
THE CAPM ASSUMPTIONS
• NORMATIVE ASSUMPTIONS
– expected returns and standard deviation cover a
one-period investor horizon
– nonsatiation
– risk averse investors
– assets are infinitely divisible
– risk free asset exists
– no taxes nor transaction costs
2
THE CAPM ASSUMPTIONS
• ADDITIONAL ASSUMPTIONS
– one period investor horizon for all
– risk free rate is the same for all
– information is free and instantaneously
available
– homogeneous expectations
3
THE CAPITAL MARKET LINE
• THE CAPITAL MARKET LINE (CML)
– the new efficient frontier that results from risk
free lending and borrowing
– both risk and return increase in a linear fashion
along the CML
4
THE CAPITAL MARKET LINE
THE CAPITAL MARKET LINE
CML
rP
M
rfr
sP
5
THE CAPITAL MARKET LINE
• THE SEPARATION THEOREM
– James Tobin identifies:
• the division between the investment decision and the
financing decision
6
THE CAPITAL MARKET LINE
• THE SEPARATION THEOREM
– to be somewhere on the CML, the investor
initially
• decides to invest and
• based on risk preferences makes a separate
financing decision either
– to borrow or
– to lend
7
THE MARKET PORTFOLIO
• DEFINITION: the portfolio of all risky
assets which contains
– complete diversification
– a central role in the CAPM theory which is the
tangency portfolio (M) with the CML
8
THE SECURITY MARKET
LINE (SML)
• FOR AN INDIVIDUAL RISKY ASSET
– the relevant risk measure is its covariance with
the market portfolio (si, M)
– DEFINITION: the security market line
expresses the linear relationship between
• the expected returns on a risky asset and
• its covariance with the market returns
9
THE SECURITY MARKET
LINE (SML)
• THE SECURITY MARKET LINE
 rm  rrf
r  rrf  
2
s
m


s i ,m

or r i  r  (r  r ) 
rf
2
rf
i ,M
where
 i,M
s i ,M

2
sM
10
THE SECURITY MARKET
LINE (SML)
• THE SECURITY MARKET LINE
– THE BETA COEFFICIENT
• an alternative way to represent the covariance of a
security
11
THE SECURITY MARKET
LINE (SML)
• THE SECURITY MARKET LINE
– THE BETA COEFFICIENT
• of a portfolio
– is the weighted average of the betas of its component
securities
N
 P ,M   X i  i ,M
i 1
12
THE SECURITY MARKET
LINE (SML)
THE SECURITY MARKET LINE
E(r)
SML
rM
rrf
 1.0

13
THE MARKET MODEL
• FROM CHAPTER 7
– assumed return on a risky asset was related to
the return on a market index
ri   iI   i1rI   iI
14
THE MARKET MODEL
• DIFFERENCES WITH THE CAPM
– the market model is a single-factor model
– the market model is not an equilibrium model
like the CAPM
– the market model uses a market index,
– the CAPM uses the market portfolio
15
THE MARKET MODEL
• MARKET INDICES
– the most widely used and known are
•
•
•
•
•
•
S&P 500
NYSE COMPOSITE
AMEX COMPOSITE
RUSSELL 3000
WILSHIRE 5000
DJIA
16
THE MARKET MODEL
• MARKET AND NON-MARKET RISK
– Recall that a security’s total risk may be
expressed as
s   s s
2
i
2
iI
2
i
2
i
17
THE MARKET MODEL
• MARKET AND NON-MARKET RISK
– according to the CAPM
• the relationship is identical except the market
portfolio is involved instead of the market index
18
THE MARKET MODEL
• MARKET AND NON-MARKET RISK
– Why partition risk?
• market risk
– related to the risk of the market portfolio and to the beta of
the risky asset
– risky assets with large betas require larger amounts of
market risk
– larger betas mean larger returns
19
THE MARKET MODEL
• MARKET AND NON-MARKET RISK
– Why partition risk?
• non-market risk
– not related to beta
– risky assets with larger amounts of sI will not have
larger E(r)
• According to CAPM
– investors are rewarded for bearing market risk not nonmarket risk
20