{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

CAPM_Proof

# CAPM_Proof - Capital Market Line(CML thus R P-r σ P = R...

This preview shows pages 1–9. Sign up to view the full content.

CAPM proof Suppose we hold the market portfolio, M , and we wish to invest a small amount α in an asset X , with beta β . Definition Let R M = return on the market portfolio R X = return on asset X σ M = volatility of the market portfolio σ X = volatility of X r = risk free rate P = M + α X (the new portfolio)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
CAPM proof So R P = R M + α R X 1 + α and σ 2 P = 1 1 + α 2 σ 2 M + α 1 + α 2 σ 2 X + 2 1 1 + α α 1 + α Cov ( M , X )
CAPM proof So R P = R M + α R X 1 + α and σ 2 P = 1 1 + α 2 σ 2 M + α 1 + α 2 σ 2 X + 2 1 1 + α α 1 + α Cov ( M , X ) = 1 1 + α 2 σ 2 M + 2 1 1 + α α 1 + α Cov ( M , X ) (since α 2 α )

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
CAPM proof Thus σ 2 P = 1 ( 1 + α ) 2 σ 2 M + 2 α Cov ( M , X ) = 1 ( 1 + α ) 2 σ 2 M + 2 α Cov ( M , X ) σ 2 M σ 2 M = 1 ( 1 + α ) 2 σ 2 M + 2 αβσ 2 M (by the definition of β ) = σ 2 M ( 1 + α ) 2 ( 1 + 2 βα )
CAPM Proof So σ P = σ M ( 1 + α ) 1 + 2 βα = σ M ( 1 + α ) ( 1 + βα ) (Since 1 + x 1 + 1 2 x )

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
CAPM Proof So σ P = σ M ( 1 + α ) 1 + 2 βα = σ M ( 1 + α ) ( 1 + βα ) (Since 1 + x 1 + 1 2 x ) If the new portfolio is efficient, it must lie on the

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Capital Market Line (CML) , thus R P-r σ P = R M-r σ M . CAPM Proof Thus R M + α R X 1 + α-r σ M ( 1 + βα ) 1 + α = R M-r σ M CAPM Proof Thus R M + α R X 1 + α-r σ M ( 1 + βα ) 1 + α = R M-r σ M so R M + α R X-r-α r 1 + βα = R M-r CAPM Proof Thus R M + α R X 1 + α-r σ M ( 1 + βα ) 1 + α = R M-r σ M so R M + α R X-r-α r 1 + βα = R M-r solving for R X gives R X = r + β ( R M-r )...
View Full Document

{[ snackBarMessage ]}