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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 costs
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
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
THE CAPITAL MARKET LINETHE CAPITAL MARKET LINE
M
rP
P
CML
rfr
THE CAPITAL MARKET LINE THE SEPARATION THEOREM
•James Tobin identifies:the division between the investment
decision and the financing decision
THE CAPITAL MARKET LINE THE SEPARATION THEOREM
•to be somewhere on the CML, the investor initiallydecides to invest andbased 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 CML
THE 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 andits covariance with the market returns
THE SECURITY MARKET LINE (SML) THE SECURITY MARKET LINE
or
where
mim
rfmrf
rrrr ,2
Mirfrfi rrrr ,2 )(
2
,,
M
MiMi
THE SECURITY MARKET LINE (SML) THE SECURITY MARKET LINE
•THE BETA COEFFICIENTan alternative way to represent the
covariance of a security
THE SECURITY MARKET LINE (SML) THE SECURITY MARKET LINE
•THE BETA COEFFICIENTof a portfolio
– is the weighted average of the betas of its component securities
N
iMiiMP X
1,,
THE SECURITY MARKET LINE (SML)THE SECURITY MARKET LINE
SML
E(r)
rrf
rM
THE MARKET MODEL
FROM CHAPTER 7•assumed return on a risky asset was
related to the return on a market index
iIIiiIi rr 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 portfolio
THE MARKET MODEL
MARKET INDICES•the most widely used and known are
S&P 500NYSE COMPOSITEAMEX COMPOSITERUSSELL 3000WILSHIRE 5000DJIA
THE MARKET MODEL
MARKET AND NON-MARKET RISK•Recall that a security’s total risk may
be expressed as2222iiiIi
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
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
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
END OF CHAPTER 9