CHAPTER NINE THE CAPITAL ASSET PRICING MODEL. THE CAPM ASSUMPTIONS n NORMATIVE ASSUMPTIONS expected...

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