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Implications of the CAPM

Lecture 3.3: The Capital Asset Pricing Model:

ImplicationsInvestment Analysis

Fall, 2012

Anisha Ghosh

Tepper School of BusinessCarnegie Mellon University

November 15, 2012

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Implications of the CAPM

Implication 1: All Investors Hold the Market Portfolio

All Investors Hold the Market Portfolio

All investors will choose to hold a portfolio of risky assets in proportions thatduplicate representation of the assets in themarket portfolio (M)

if IBM stock represents 3%of all risky assets, then the marketportfolio contains 3%IBM stock and each investor will take 3%of themoney that will be invested in all risky assets and place it in IBM stock

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Implications of the CAPM

Implication 1: All Investors Hold the Market Portfolio

All Investors Hold the Market Portfolio

All investors will choose to hold a portfolio of risky assets in proportions thatduplicate representation of the assets in themarket portfolio (M)

if IBM stock represents 3%of all risky assets, then the marketportfolio contains 3%IBM stock and each investor will take 3%of themoney that will be invested in all risky assets and place it in IBM stock

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Implications of the CAPM

Implication 2: The Market Portfolio is Mean-Variance

Efficient

The Market Portfolio is Mean-Variance Efficient

The market portfolio lies on the efficient frontier and is also the tangency

portfolio to the optimal capital allocation line (CAL) derived by each and every

investor.

Thecapital market line(CML), the line from the risk free rate through

the market portfolio,M, is also the best attainable capital allocation line

(offers the highest Sharpe ratio)All investors holdMas their optimal risky portfolio, differing only in the

amount invested in it versus in the risk free asset

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Implications of the CAPM

Implication 2: The Market Portfolio is Mean-Variance

Efficient

The Market Portfolio is Mean-Variance Efficient

The market portfolio lies on the efficient frontier and is also the tangency

portfolio to the optimal capital allocation line (CAL) derived by each and every

investor.

Thecapital market line(CML), the line from the risk free rate through

the market portfolio,M, is also the best attainable capital allocation line

(offers the highest Sharpe ratio)All investors holdMas their optimal risky portfolio, differing only in the

amount invested in it versus in the risk free asset

I li i f h CAPM

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Implications of the CAPM

Implication 2: The Market Portfolio is Mean-Variance

Efficient

The Market Portfolio is Mean-Variance Efficient

The market portfolio lies on the efficient frontier and is also the tangency

portfolio to the optimal capital allocation line (CAL) derived by each and every

investor.

Thecapital market line(CML), the line from the risk free rate through

the market portfolio,M, is also the best attainable capital allocation line

(offers the highest Sharpe ratio)All investors holdMas their optimal risky portfolio, differing only in the

amount invested in it versus in the risk free asset

I li ti f th CAPM

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Implications of the CAPM

Implication 3: Risk Premium on the Market Portfolio

Risk Premium on the Market Portfolio

The risk premium on the market portfolio will be proportional to its risk,

2M, and the degree of risk aversion, A, of the representative investor:

E(RM) RF=A2M

the more risk averse investors are, the greater premium they will

require for holding the risky asset portfolioMrelative to the riskless

asset

Implications of the CAPM

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Implications of the CAPM

Implication 3: Risk Premium on the Market Portfolio

Risk Premium on the Market Portfolio

The risk premium on the market portfolio will be proportional to its risk,

2M, and the degree of risk aversion, A, of the representative investor:

E(RM) RF=A2M

the more risk averse investors are, the greater premium they will

require for holding the risky asset portfolioMrelative to the riskless

asset

Implications of the CAPM

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Implications of the CAPM

Implication 4: Risk Premium on Individual Assets

Risk Premium on Individual Assets

The risk premium on individual assets will be proportional to the risk

premium on the market portfolio, M, and the beta coefficient of the

security relative to the market portfolio:

E(Ri) RF = i[E(RM)RF]

wherei = Cov(Ri, RM)

Var(RM)

Beta measures the extent to which returns on the asset and the market

move together.

Implications of the CAPM

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Implications of the CAPM

Implication 4: Risk Premium on Individual Assets

Risk Premium on Individual Assets

The risk premium on individual assets will be proportional to the risk

premium on the market portfolio, M, and the beta coefficient of the

security relative to the market portfolio:

E(Ri) RF = i[E(RM)RF]

wherei = Cov(Ri, RM)

Var(RM)

Beta measures the extent to which returns on the asset and the market

move together.