Lecture 9 - Capital Asset Pricing Model

Lecture 9 - Capital Asset Pricing Model - Required Reading...

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Finance - I (MGCR 341) – Prof. de Motta Capital Asset Pricing Model CAPM Finance - I (MGCR 341) – Prof. de Motta 2 Required Reading Sections 11.6 from Chapter 11 , “Optimal Portfolio Choice” from Berk and De Marzo , Corporate Finance. Chapter 12 , “The Capital Asset Pricing Model” from Berk and De Marzo , Corporate Finance. (Except Section 12.5: Extending the CAPM) Finance - I (MGCR 341) – Prof. de Motta 3 The Tangent or Efficient Portfolio Investments on the green line connecting the risk-free investment and the tangent portfolio provide the best risk - return trade-off available to an investor. Finance - I (MGCR 341) – Prof. de Motta 4 Example Your uncle currently has $100,000 to invest. The efficient portfolio has an expected return of 18.5% and a volatility of 13%. The risk free rate is 5%. If your uncle wants to have a volatility of 8% calculate how much he should invest in the efficient portfolio and the return that he should be expected from his $100,000 investment. Solution Let x be the weight of your uncle’s portfolio in the efficient portfolio (and hence, (1- x ) is the weight on the risk free asset) then: % 3 . 13 % 5 . 18 615 . 0 % 5 ) 615 . 0 1 ( ) ( ) 1 ( ) ( = × + × = = + = Eff f xEff R xE r x R E % 5 . 61 % 13 % 8 ) ( ) ( = = = x x R xSD R SD Eff xEff
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Finance - I (MGCR 341) – Prof. de Motta 5 Risk-Return Trade-off in the Efficient Frontier ) ( ) ( ) ( ) ( Eff P Eff P R SD R SD x R xSD R SD = = ) ) ( ( ) ( f Eff f P r R E x r R E + = Let’s consider a portfolio P located in the efficient frontier with weight x in the efficient portfolio (and hence, (1- x ) is the weight on the risk free asset). This portfolio has the following expected return and volatility: Plugging the x from the second equation in the first equation we obtain: ) ) ( ( ) ( ) ( ) ( f Eff Eff P f P r R E R SD R SD r R E + = Finance - I (MGCR 341) – Prof. de Motta 6 Risk-Return Trade-off in the Efficient Frontier ) ) ( ( ) ( ) ( ) ( f Eff Eff P f P r R E R SD R SD r R E + = ) ) ( ( ) ( ) , ( ) ( f Eff Eff Eff P f P r R E R Var R R Cov r R E + = () ( ) ) ( ) ( ) ( ) ( ) , 1 ) , ( Eff Eff p Eff Eff Eff f Eff P R Var R SD R SD R xVar R R x r x Cov R R Cov = = = + = Finance - I (MGCR 341) – Prof. de Motta 7 The expected return of a portfolio P located in the efficient frontier is: where β P Eff is the beta of portfolio P with respect to the efficient portfolio and it is defined as: The expected return of a portfolio in the Efficient Frontier is determined by its beta, which depends on the covariance between the return of the portfolio and the return of the Efficient Portfolio. Risk-Return Trade-off in the Efficient Frontier ) ( ) , ( Eff Eff P Eff P R Var R R Cov ) ) ( ( ) ( f Eff Eff P f P r R E r R E + = Finance - I (MGCR 341) – Prof. de Motta 8 Problem (A project’s cost of capital) Alphatec is seeking to raise capital from a large group of investors to expand its operations. Suppose that the S&P 500 portfolio is the efficient portfolio of risky securities. The S&P 500 portfolio has volatility of 15% and a expected return of 10%. The investment is expected to have a volatility of 40% and a 50% correlation with the S&P 500. If the risk free rate if 4% what is the appropriate cost of capital for Alphatec’s expansion?
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Finance - I (MGCR 341) – Prof. de Motta 9 Solution
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Lecture 9 - Capital Asset Pricing Model - Required Reading...

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