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Unformatted text preview: Lecture 11 Review of CAPM Single I ndex Model 1 CAPMwhat is it? • CAPM predicts the relationship between the expected return on the security and its risk • Beta –a measure of the asset’s covariance with the overall market is the “correct” measure of risk for any asset • The market portfolio is the common risky portfolio (“One Mutual Fund” theorem) that all investors hold CAPM • The fair risk premium on asset i: • Define the asset’s beta as the contribution of the stock “i” to the variance of the market portfolio • Finally we obtain: ] ) ( [ ) , ( ) ( 2 f m m m i f i r r E r r Cov r r E = σ 2 ) , ( m m i i r r Cov σ β = ] ) ( [ ) ( f i f i r r E r r E m = β 01 . * ) , ( } { A r r Cov r r E m i f i = Security Market Line • SML exhibits the expected return – beta relationship: • SML graphs the individual asset risk premiums as a function of asset risk (beta). • Given the risk of an investment, SML provides the required rate of return for that investment. • Slope is equal to the risk premium of the market portfolio. 4 M Security Market Line • SML exhibits the expected return – beta relationship: • Fairly priced assets would be located exactly on the SML. • I f a stock is a good buy (i.e. underpriced), it would provide an expected return in excess of the fair return described by the SML. • positive alpha stocks are a good buy… 5 Security Market Line • Notice, if alpha > 0, everyone wants to buy • Notice, if alpha < 0, everyone wants to sell • Hence price is not in equilibrium unless alpha = 0 6 • Risk pr emium on an individual asset is pr opor tional to the r isk pr emium on mar ket por tfolio and the secur ity's “beta.” – E{r e } r f = β e [E{r m }  r f ] – • This r elationship defines the Secur ity M ar ket Line I mplications of the Capital Asset Pr icing M odel 1 β Security Market Line . r f E{r} E{r m } Slope = E{r m }  r f 2 ) , ( m m e e r r Cov σ β = I mplications of the Capital Asset Pr icing M odel • Risk pr emium on an individual asset is pr opor tional to the r isk pr emium on mar ket por tfolio and the secur ity's “beta.” – E{r e } r f = β e [E{r m }  r f ] • This r elationship defines the Secur ity M ar ket Line Suppose r f = 5%, β e = 0.5, and the mar ket r isk pr emium (E{r m }  r f ) is 8%. Fill out the missing values 1 β Security Market Line ? E{r} ? Slope = E{r m }  r f 0.5 ? I mplications of the Capital Asset Pr icing M odel • Risk pr emium on an individual asset is pr opor tional to the r isk pr emium on mar ket por tfolio and the secur ity's “beta.” – E{r e } r f = β e [E{r m }  r f ] – • This r elationship defines the Secur ity M ar ket Line Suppose r f = 5%, β e = 0.5, and the mar ket r isk pr emium (E{r m }  r f ) is 8%....
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This note was uploaded on 04/17/2008 for the course ECON 171A taught by Professor Yusim during the Spring '08 term at Brandeis.
 Spring '08
 Yusim
 Economics

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