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CHAPTER TEN

THE CAPITAL ASSET PRICING MODEL

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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

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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

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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

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THE CAPITAL MARKET LINETHE CAPITAL MARKET LINE

M

rP

P

CML

rfr

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THE CAPITAL MARKET LINE

• THE SEPARATION THEOREM– James Tobin identifies:

• the division between the investment decision and the financing decision

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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

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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

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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 and

• its covariance with the market returns

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THE SECURITY MARKET LINE (SML)

• THE SECURITY MARKET LINE

or

where

mim

rfmrf

rrrr ,2

Mirfrfi rrrr ,2 )(

2

,,

M

MiMi

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THE SECURITY MARKET LINE (SML)

• THE SECURITY MARKET LINE– THE BETA COEFFICIENT

• an alternative way to represent the covariance of a security

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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

iMiiMP X

1,,

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THE SECURITY MARKET LINE (SML)

THE SECURITY MARKET LINESML

E(r)

rrf

rM

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THE MARKET MODEL

• FROM CHAPTER 7– assumed return on a risky asset was related to

the return on a market index

iIIiiIi rr 1

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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

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THE MARKET MODEL

• MARKET INDICES– the most widely used and known are

• S&P 500

• NYSE COMPOSITE

• AMEX COMPOSITE

• RUSSELL 3000

• WILSHIRE 5000

• DJIA

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THE MARKET MODEL

• MARKET AND NON-MARKET RISK– Recall that a security’s total risk may be

expressed as

2222iiiIi

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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

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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

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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