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(L10)BasicCAPM(f)2

# (L10)BasicCAPM(f)2 - Lecture#10 The Capital Asset Pricing...

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Primbs/Investment Science 1 Lecture #10 The Capital Asset Pricing Model (CAPM 1) Reading: Luenberger Chapter 7, Sections 1 – 4

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Primbs/Investment Science 2 CAPM CAPM Market Equilibrium The Capital Asset Pricing Model Consequences of CAPM
Primbs/Investment Science 3 Market Equilibrium Under the one fund theorem, everyone will buy the same single fund of risky assets. Question: What is that fund? Answer: The Market Portfolio!!!! The market portfolio: A portfolio of every stock in the market in proportion to that stock’s representation in the entire market.

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Primbs/Investment Science 4 Computation of the Market Portfolio Each asset’s weight in the market portfolio is market) of value (\$ i) asset of value (\$ = i w These weights are called capitalization weights .
Primbs/Investment Science 5 Example Security Shares Outstanding Price(\$) Capitalization Weight Jazz 10,000 6 60,000 3/20 Classical 30,000 4 120,000 3/10 Rock 40,000 5.5 220,000 11/20 Total 400,000 1 Jazz Classical Rock 3/20 3/10 11/20

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Primbs/Investment Science 6 The Capital Market Line σ r r f x M r M σ σ σ - + = M f M f r r r r The capital market line : - M f M r r σ The slope is often called the price of risk .
Primbs/Investment Science 7 Example Given: 05 . 0 = f r 12 . 0 = M r 15 . 0 = M σ You would like to earn 20% on average. What will be the standard deviation of your portfolio. Clearly, you would like your portfolio to lie on the Capital Market Line, hence σ σ - + = M f M f r r r r Solve for 3214 . 0 = σ σ 15 . 0 ) 05 . 0 12 . 0 ( 05 . 0 20 . 0 - + =

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Primbs/Investment Science 8 CAPM CAPM Market Equilibrium The Capital Asset Pricing Model Consequences of CAPM
Primbs/Investment Science 9 CAPM Theorem : (Capital Asset Pricing Model) If the market portfolio M is efficient, the expected return of any asset i satisfies i r ) ( f M i f i r r r r - = - β where 2 M iM i σ σ β = (1) All investors are Markowitz mean-variance investors. (2) Short selling is allowed. (3) There exists a risk free asset. (4) Investors share same predictions of means, variances and covariances Assume :

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Primbs/Investment Science 10 Proof of CAPM x x i σ r r f M r M σ M
Primbs/Investment Science 11 Proof of CAPM Consider a portfolio of α in asset i (1- α ) in the market portfolio Expected return: M i r r r ) 1 ( α α α - + = Standard Deviation: 2 2 2 2 ) 1 ( ) 1 ( 2 M iM i σ α σ α α σ α σ α - + - + = weights: This portfolio has: σ r M r M σ

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Primbs/Investment Science 12 Proof of CAPM At α= 0 , the curve and the capital market line are tangent. i.e., they have the same slope. Slope of Capital Market Line= - M f M r r σ Slope of portfolio at α= 0. 0
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