CAPM Capital Marktet Line - CML Security Market Line - SML
Capital Asset Pricing Model - CAPM
Ludˇek Benada
Department of Finance, office - 402
e-mail: benada@econ.muni.cz
CAPM Capital Marktet Line - CML Security Market Line - SML
Content
1 CAPM
2 Capital Marktet Line - CML
3 Security Market Line - SML
CAPM Capital Marktet Line - CML Security Market Line - SML
Content
1 CAPM
2 Capital Marktet Line - CML
3 Security Market Line - SML
CAPM Capital Marktet Line - CML Security Market Line - SML
CAPM
One of the most famous models in financial theory and
practice
CAPM Capital Marktet Line - CML Security Market Line - SML
CAPM
One of the most famous models in financial theory and
practice
Originated in the 1960s
CAPM Capital Marktet Line - CML Security Market Line - SML
CAPM
One of the most famous models in financial theory and
practice
Originated in the 1960s
It extends the concept introduced by H. Markowitz, it is a
special case of the M & M Model (1958)
CAPM Capital Marktet Line - CML Security Market Line - SML
CAPM
One of the most famous models in financial theory and
practice
Originated in the 1960s
It extends the concept introduced by H. Markowitz, it is a
special case of the M & M Model (1958)
It is a basic tool for financial analysis
CAPM Capital Marktet Line - CML Security Market Line - SML
CAPM
One of the most famous models in financial theory and
practice
Originated in the 1960s
It extends the concept introduced by H. Markowitz, it is a
special case of the M & M Model (1958)
It is a basic tool for financial analysis
Despite its shortcomings, it is widely used:
CAPM Capital Marktet Line - CML Security Market Line - SML
CAPM
One of the most famous models in financial theory and
practice
Originated in the 1960s
It extends the concept introduced by H. Markowitz, it is a
special case of the M & M Model (1958)
It is a basic tool for financial analysis
Despite its shortcomings, it is widely used:
Asset valuation
CAPM Capital Marktet Line - CML Security Market Line - SML
CAPM
One of the most famous models in financial theory and
practice
Originated in the 1960s
It extends the concept introduced by H. Markowitz, it is a
special case of the M & M Model (1958)
It is a basic tool for financial analysis
Despite its shortcomings, it is widely used:
Asset valuation
Investment decision-making
CAPM Capital Marktet Line - CML Security Market Line - SML
CAPM
One of the most famous models in financial theory and
practice
Originated in the 1960s
It extends the concept introduced by H. Markowitz, it is a
special case of the M & M Model (1958)
It is a basic tool for financial analysis
Despite its shortcomings, it is widely used:
Asset valuation
Investment decision-making
Financial asset management
CAPM Capital Marktet Line - CML Security Market Line - SML
CAPM
One of the most famous models in financial theory and
practice
Originated in the 1960s
It extends the concept introduced by H. Markowitz, it is a
special case of the M & M Model (1958)
It is a basic tool for financial analysis
Despite its shortcomings, it is widely used:
Asset valuation
Investment decision-making
Financial asset management
Trading
CAPM Capital Marktet Line - CML Security Market Line - SML
CAPM
One of the most famous models in financial theory and
practice
Originated in the 1960s
It extends the concept introduced by H. Markowitz, it is a
special case of the M & M Model (1958)
It is a basic tool for financial analysis
Despite its shortcomings, it is widely used:
Asset valuation
Investment decision-making
Financial asset management
Trading
Monetary policy
CAPM Capital Marktet Line - CML Security Market Line - SML
Financial asset management
A portfolio consisting at leas of one ri and one rf
CAPM Capital Marktet Line - CML Security Market Line - SML
Financial asset management
A portfolio consisting at leas of one ri and one rf
The opportunity to invest in rf determines the shape of
Efficient frontier
CAPM Capital Marktet Line - CML Security Market Line - SML
Financial asset management
A portfolio consisting at leas of one ri and one rf
The opportunity to invest in rf determines the shape of
Efficient frontier → straightline, segment of a line
CAPM Capital Marktet Line - CML Security Market Line - SML
Financial asset management
A portfolio consisting at leas of one ri and one rf
The opportunity to invest in rf determines the shape of
Efficient frontier → straightline, segment of a line
Allows to identify the contribution of individual assets to Rp
and σp
CAPM Capital Marktet Line - CML Security Market Line - SML
Financial asset management
A portfolio consisting at leas of one ri and one rf
The opportunity to invest in rf determines the shape of
Efficient frontier → straightline, segment of a line
Allows to identify the contribution of individual assets to Rp
and σp
CAPM is an equilibrium model
CAPM Capital Marktet Line - CML Security Market Line - SML
Financial asset management
A portfolio consisting at leas of one ri and one rf
The opportunity to invest in rf determines the shape of
Efficient frontier → straightline, segment of a line
Allows to identify the contribution of individual assets to Rp
and σp
CAPM is an equilibrium model
The concept of the model is explicitly built on the
maximization of utility and the available set of investment
portfolios
CAPM Capital Marktet Line - CML Security Market Line - SML
Trading with securities
Quantification of systematic and unsystematic risk
CAPM Capital Marktet Line - CML Security Market Line - SML
Trading with securities
Quantification of systematic and unsystematic risk
Enables the identification of incorrectly valued assets
CAPM Capital Marktet Line - CML Security Market Line - SML
Monetary policy
The initial assumption is based on Tobin’s money demand
assumption
CAPM Capital Marktet Line - CML Security Market Line - SML
Monetary policy
The initial assumption is based on Tobin’s money demand
assumption
A modified version of the Tobin’s money demand
CAPM Capital Marktet Line - CML Security Market Line - SML
Monetary policy
The initial assumption is based on Tobin’s money demand
assumption
A modified version of the Tobin’s money demand
→ in addition to bonds, stocks are also substitutes for money
CAPM Capital Marktet Line - CML Security Market Line - SML
Monetary policy
The initial assumption is based on Tobin’s money demand
assumption
A modified version of the Tobin’s money demand
→ in addition to bonds, stocks are also substitutes for money
A rational subject makes decisions based on the von
Neumann-Morgenstein utility function
CAPM Capital Marktet Line - CML Security Market Line - SML
Assumptions of CAPM
The portfolio is compiled for one period
CAPM Capital Marktet Line - CML Security Market Line - SML
Assumptions of CAPM
The portfolio is compiled for one period
The information of ri and σi is known
CAPM Capital Marktet Line - CML Security Market Line - SML
Assumptions of CAPM
The portfolio is compiled for one period
The information of ri and σi is known
The investors are rational . . .
CAPM Capital Marktet Line - CML Security Market Line - SML
Assumptions of CAPM
The portfolio is compiled for one period
The information of ri and σi is known
The investors are rational . . .
Every investor is able to compare all permissible portfolios
CAPM Capital Marktet Line - CML Security Market Line - SML
Assumptions of CAPM
The portfolio is compiled for one period
The information of ri and σi is known
The investors are rational . . .
Every investor is able to compare all permissible portfolios
All assets are infinitely divisible
CAPM Capital Marktet Line - CML Security Market Line - SML
Assumptions of CAPM
The portfolio is compiled for one period
The information of ri and σi is known
The investors are rational . . .
Every investor is able to compare all permissible portfolios
All assets are infinitely divisible
There exists a risk-free asset . . .
CAPM Capital Marktet Line - CML Security Market Line - SML
Assumptions of CAPM
The portfolio is compiled for one period
The information of ri and σi is known
The investors are rational . . .
Every investor is able to compare all permissible portfolios
All assets are infinitely divisible
There exists a risk-free asset . . .
There is information efficiency
CAPM Capital Marktet Line - CML Security Market Line - SML
Assumptions of CAPM
The portfolio is compiled for one period
The information of ri and σi is known
The investors are rational . . .
Every investor is able to compare all permissible portfolios
All assets are infinitely divisible
There exists a risk-free asset . . .
There is information efficiency
Investors have the same expectations:
CAPM Capital Marktet Line - CML Security Market Line - SML
Assumptions of CAPM
The portfolio is compiled for one period
The information of ri and σi is known
The investors are rational . . .
Every investor is able to compare all permissible portfolios
All assets are infinitely divisible
There exists a risk-free asset . . .
There is information efficiency
Investors have the same expectations:
→ ri , σi , σi,j
CAPM Capital Marktet Line - CML Security Market Line - SML
Separation theorem
The optimal mix of risky securities can be determined without
knowing the investor’s attitudes toward return and risk
CAPM Capital Marktet Line - CML Security Market Line - SML
Separation theorem
The optimal mix of risky securities can be determined without
knowing the investor’s attitudes toward return and risk
It is not necessary to consider the indifference curves of each
investor
CAPM Capital Marktet Line - CML Security Market Line - SML
Separation theorem
The optimal mix of risky securities can be determined without
knowing the investor’s attitudes toward return and risk
It is not necessary to consider the indifference curves of each
investor
This means that the risk portion of each investor’s portfolio is
the same
CAPM Capital Marktet Line - CML Security Market Line - SML
Modified versions of CAPM
The original model has strong assumptions . . .
CAPM Capital Marktet Line - CML Security Market Line - SML
Modified versions of CAPM
The original model has strong assumptions . . .
→ Effort to get closer to a reality
CAPM Capital Marktet Line - CML Security Market Line - SML
Modified versions of CAPM
The original model has strong assumptions . . .
→ Effort to get closer to a reality
Common modifications of CAPM:
CAPM Capital Marktet Line - CML Security Market Line - SML
Modified versions of CAPM
The original model has strong assumptions . . .
→ Effort to get closer to a reality
Common modifications of CAPM:
T-CAPM (Brennan, 1970)
CAPM Capital Marktet Line - CML Security Market Line - SML
Modified versions of CAPM
The original model has strong assumptions . . .
→ Effort to get closer to a reality
Common modifications of CAPM:
T-CAPM (Brennan, 1970)
Zero-Beta CAPM (Black, 1972)
CAPM Capital Marktet Line - CML Security Market Line - SML
Modified versions of CAPM
The original model has strong assumptions . . .
→ Effort to get closer to a reality
Common modifications of CAPM:
T-CAPM (Brennan, 1970)
Zero-Beta CAPM (Black, 1972)
M-CAPM (Merton, 1973)
CAPM Capital Marktet Line - CML Security Market Line - SML
Modified versions of CAPM
The original model has strong assumptions . . .
→ Effort to get closer to a reality
Common modifications of CAPM:
T-CAPM (Brennan, 1970)
Zero-Beta CAPM (Black, 1972)
M-CAPM (Merton, 1973)
IP-CAPM (Amihud & Mendelson, 1986)
CAPM Capital Marktet Line - CML Security Market Line - SML
Content
1 CAPM
2 Capital Marktet Line - CML
3 Security Market Line - SML
CAPM Capital Marktet Line - CML Security Market Line - SML
Capital market line
Market portfolio
CAPM Capital Marktet Line - CML Security Market Line - SML
Capital market line
Market portfolio (. . . relative representation of securities)
CAPM Capital Marktet Line - CML Security Market Line - SML
Capital market line
Market portfolio (. . . relative representation of securities)
→ use of indexes
CAPM Capital Marktet Line - CML Security Market Line - SML
Capital market line
Market portfolio (. . . relative representation of securities)
→ use of indexes
CML represents only efficient portfolios
CAPM Capital Marktet Line - CML Security Market Line - SML
Capital market line
Market portfolio (. . . relative representation of securities)
→ use of indexes
CML represents only efficient portfolios
The model identifies the costs of time and the costs of risk
CAPM Capital Marktet Line - CML Security Market Line - SML
Capital market line
Market portfolio (. . . relative representation of securities)
→ use of indexes
CML represents only efficient portfolios
The model identifies the costs of time and the costs of risk
¯Rp = rf +
¯rm − rf
σm
∗ σp
CAPM Capital Marktet Line - CML Security Market Line - SML
Derivation of CML
Graphic projection . . .
CAPM Capital Marktet Line - CML Security Market Line - SML
Derivation of CML
Graphic projection . . .
Using the similarity of right triangles . . .
CAPM Capital Marktet Line - CML Security Market Line - SML
Content
1 CAPM
2 Capital Marktet Line - CML
3 Security Market Line - SML
CAPM Capital Marktet Line - CML Security Market Line - SML
Security market line
Represents the relation between E(ri ) and σi,m for each asset
CAPM Capital Marktet Line - CML Security Market Line - SML
Security market line
Represents the relation between E(ri ) and σi,m for each asset
The model applies for efficient and inefficient securities and
also for portfolios
CAPM Capital Marktet Line - CML Security Market Line - SML
Security market line
Represents the relation between E(ri ) and σi,m for each asset
The model applies for efficient and inefficient securities and
also for portfolios
Individual securities are not efficient
CAPM Capital Marktet Line - CML Security Market Line - SML
Security market line
Represents the relation between E(ri ) and σi,m for each asset
The model applies for efficient and inefficient securities and
also for portfolios
Individual securities are not efficient
→ SML always located under CML
CAPM Capital Marktet Line - CML Security Market Line - SML
Security market line
Represents the relation between E(ri ) and σi,m for each asset
The model applies for efficient and inefficient securities and
also for portfolios
Individual securities are not efficient
→ SML always located under CML
The risk of market portfolio:
σm = w1,mσ1,m + w2,mσ2,m + · · · + wn,mσn,m
CAPM Capital Marktet Line - CML Security Market Line - SML
Security market line
Represents the relation between E(ri ) and σi,m for each asset
The model applies for efficient and inefficient securities and
also for portfolios
Individual securities are not efficient
→ SML always located under CML
The risk of market portfolio:
σm = w1,mσ1,m + w2,mσ2,m + · · · + wn,mσn,m
An equilibrium relation between the return and the risk by an individual a
CAPM Capital Marktet Line - CML Security Market Line - SML
Security market line
Represents the relation between E(ri ) and σi,m for each asset
The model applies for efficient and inefficient securities and
also for portfolios
Individual securities are not efficient
→ SML always located under CML
The risk of market portfolio:
σm = w1,mσ1,m + w2,mσ2,m + · · · + wn,mσn,m
An equilibrium relation between the return and the risk by an individual a
rei = rf +
rm − rf
σ2
m
∗ σi,m
CAPM Capital Marktet Line - CML Security Market Line - SML
Beta coefficient
βi measures the systematic risk
CAPM Capital Marktet Line - CML Security Market Line - SML
Beta coefficient
βi measures the systematic risk of security
CAPM Capital Marktet Line - CML Security Market Line - SML
Beta coefficient
βi measures the systematic risk of security or portfolio (βp)
CAPM Capital Marktet Line - CML Security Market Line - SML
Beta coefficient
βi measures the systematic risk of security or portfolio (βp)
βi > 1 . . . aggressive security
CAPM Capital Marktet Line - CML Security Market Line - SML
Beta coefficient
βi measures the systematic risk of security or portfolio (βp)
βi > 1 . . . aggressive security
βi < 1 . . . defensive security
CAPM Capital Marktet Line - CML Security Market Line - SML
Beta coefficient
βi measures the systematic risk of security or portfolio (βp)
βi > 1 . . . aggressive security
βi < 1 . . . defensive security
βi = 1 . . . neutral, correctly priced security
Equilibrium model:
ri = rf + βi ∗ (rm − rf )
CAPM Capital Marktet Line - CML Security Market Line - SML
Beta coefficient
βi measures the systematic risk of security or portfolio (βp)
βi > 1 . . . aggressive security
βi < 1 . . . defensive security
βi = 1 . . . neutral, correctly priced security
Equilibrium model:
ri = rf + βi ∗ (rm − rf )
where we can derive,
βi =
σi,m
σ2
m