CAPM%20and%20WACC_post0

CAPM%20and%20WACC_post0 - CAPM and WACC Outline Were...

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CAPM and WACC
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THE UNIVERSITY OF BRITISH COLUMBIA Outline We’re looking for an explicit relationship between portfolio risk and expected return We then want to extend the risk-return relationship to individual securities Last topic will integrate what we’ve learned into a framework for determining the discount rate for capital budgeting
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THE UNIVERSITY OF BRITISH COLUMBIA Portfolio Frontier with Many Risky Assets Since assets are positively correlated, the frontier will look like this Any risk-return combo on and inside of the frontier is feasible Impossible to eliminate risk by combining risky assets in a portfolio (the minimum variance portfolio will not be risk free) Risk averse investors would choose a portfolio that is efficient : On the upper portion of the blue line, to the right of the minimum variance portfolio. 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.1 0.2 0.3 0.4 0.5 Standard Deviation Expected Return T-Bonds YHOO Corp-Bonds MSFT GE Gold Portfolio Frontier for Risky Assets Min. Var Portfolio
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THE UNIVERSITY OF BRITISH COLUMBIA Portfolio Frontier with Risky Assets and T-Bills Now we introduce an explicit risk-free asset that we can invest in: T-Bills What effect does this have on the shape of the efficient frontier? 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0 0.1 0.2 0.3 0.4 0.5 Standard Deviation Expected Return T-Bonds YHOO Corp-Bonds MSFT GE Gold T-Bills Portfolio Frontier for Risky Assets r f =
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THE UNIVERSITY OF BRITISH COLUMBIA Combining T-bills and GE Suppose we form a portfolio of T-Bills and GE stock. What are the expected return and the standard deviation if we invest: x in General Electric 1- x in T-Bills? Expected Return Variance But r f is risk free! It doesn’t vary (and thus does not co-vary with GE either), so Var(r f ) = Cov(r f , r GE ) = 0! Therefore: Standard Deviation (square root of above) ) ( ) 1 ( ) ( GE f Portf r xE r x r E + - = ( 29 ( 29 ( 29 ( 29 ) , ( 1 2 ) ( ) ( 1 2 2 GE f GE f Portf r r Cov x x r Var x r Var x r VAR - + + - = ( 29 ) ( 2 GE Portf r Var x r VAR = GE Portf x σ = GE Portf x =
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THE UNIVERSITY OF BRITISH COLUMBIA Combining T-bills and GE Now substitute for x in the expected return equation: Simplify to: Several points to note: Portfolio expected return E(r portf ) is a linear function of portfolio risk (as measured by standard deviation) σ portf The quantity E(r GE ) – r f is called the “ risk premium ” for General Electric. It measures how much additional expected return you earn above the risk free rate by investing in GE. The quantity is called the Sharpe or reward-to-risk ratio for GE. > It gives the risk premium per unit of risk (usually applied to portfolios, not single stocks). ) ( ) 1 ( ) ( GE GE Portf f GE Portf Portf r E r r E σ + - = Portf GE f GE f Portf r r E r r E - + = ) ( ) ( GE f GE r r E - ) (
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THE UNIVERSITY OF BRITISH COLUMBIA Portfolio Frontier with Many Assets The dashed line shows the risk-return combinations for a portfolio of T-Bills and General Electric. 0
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This note was uploaded on 04/09/2011 for the course COMM 298 taught by Professor Freedman during the Spring '09 term at UBC.

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CAPM%20and%20WACC_post0 - CAPM and WACC Outline Were...

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