CHAPTER NINE
THE CAPITAL ASSET
PRICING MODEL
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 costsTHE 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 expectationsTHE 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 CMLTHE CAPITAL MARKET LINE
THE CAPITAL MARKET LINE
M r
P CML
rfr
THE CAPITAL MARKET LINE
THE SEPARATION THEOREM
•
James Tobin identifies:
the division between the investment decision and the financing decisionTHE 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
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 CMLTHE SECURITY MARKET LINE (SML)
FOR AN INDIVIDUAL RISKY ASSET
•
the relevant risk measure is its covariance with the market portfolio (i, M)•
DEFINITION: the security market line expresses the linear relationship between
the expected returns on a risky asset and
its covariance with the market returnsTHE SECURITY MARKET LINE (SML)
THE SECURITY MARKET LINE
or
where
m i m
rf m
rf
r r r
r 2 ,
M i rf
i rrf r r
r ( 2 )
,2 , ,
M M i M
i
THE SECURITY MARKET LINE (SML)
THE SECURITY MARKET LINE
•
THE BETA COEFFICIENT
an alternative way to represent the covariance of a securityTHE 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
Ni
M i i M
P
X
1
,
,
THE SECURITY MARKET LINE (SML)
THE SECURITY MARKET LINE
E(r)
SMLrrf rM
THE MARKET MODEL
FROM CHAPTER 7
•
assumed return on a risky asset was related to the return on a market indexiI I
i iI
i
r
r
1
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 portfolioTHE MARKET MODEL
MARKET INDICES
•
the most widely used and known are
S&P 500
NYSE COMPOSITE
AMEX COMPOSITE
RUSSELL 3000
WILSHIRE 5000
DJIATHE MARKET MODEL
MARKET AND NON-MARKET RISK
•
Recall that a security’s total risk may be expressed as2 2
2 2
i i
iI
i
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 indexTHE 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
THE MARKET MODEL
MARKET AND NON-MARKET RISK
•
Why partition risk?
non-market risk– not related to beta
– risky assets with larger amounts of I will not have larger E(r)
According to CAPM– investors are rewarded for bearing market risk not non-market risk
