Bus 315 - Week12

Bus 315 - Week12 - Week 12 Equilibrium in Capital Markets...

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Week 12 Equilibrium in Capital Markets II: Index Models and the Arbitrage Pricing Theory - Bodie et al., Ch. 9 1 Jorge Cruz Lopez - Bus 315: Investments
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Index Models and the Arbitrage Pricing Theory Objective: To provide an introduction to index models and the APT and to discuss the nature and use of arbitrage. 2 Jorge Cruz Lopez - Bus 315: Investments
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Index Models and the Arbitrage Pricing Theory 1. A Single-Factor Security Market 2. The Single Index Model 3. Estimating the Single Index Model 4. Portfolio Construction and the Single-Index Model 5. Portfolio Management with the Single-Index Model 6. Multifactor Models 7. Arbitrage Pricing Theory 8. Individual Assets and the APT 9. A Multifactor APT 10. Where Should We Look For Factors? 11. The Multifactor CAPM and the APT 3 Jorge Cruz Lopez - Bus 315: Investments
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1. A Single-Factor Security Market 4 Jorge Cruz Lopez - Bus 315: Investments
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The Input List of the Markowitz Model To analyze an economy with n securities we need: n estimates of expected returns. n estimates of variances. (n 2 -n)/2 estimates of covariances. So we need to estimate 2n+(n 2 -n)/2 parameters with a sample of n observations. These are a lot of estimates! Therefore, we need to figure out a way to reduce the number of parameters that we need to estimate. 5 Jorge Cruz Lopez - Bus 315: Investments
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Single Factor Model • Returns on a security come from two sources: – Common macro-economic factors. – Firm specific events. • Possible common macro-economic factors: – GDP Growth – Interest Rates 6 Jorge Cruz Lopez - Bus 315: Investments
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Single Factor Model: Returns 7 i i i i e m r E r   ) ( • where events macro to i security of y sensitivit events specific firm ted unanticipa events macro ted unanticipa i security of return i i i e m r Jorge Cruz Lopez - Bus 315: Investments
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Single Factor Model: Variance 8 ) ( 2 2 2 2 i m i i e • where Risk Specific Firm ) ( Risk Systematic Risk Total 2 2 2 2 i m i i e Jorge Cruz Lopez - Bus 315: Investments
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Single Factor Model: Covariance 9 2 ) , ( ) , ( m j i j j i i j i e m e m Cov r r Cov • It simplifies the estimation of covariances! Jorge Cruz Lopez - Bus 315: Investments
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2. The Single Index Model 10 Jorge Cruz Lopez - Bus 315: Investments
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• The single index model makes the single factor model operational. • We use a broad index of securities such as the S&P/TSX Composite as a proxy for the common macroeconomic factor. • A simple regression is applied to paired data to estimate factor sensitivities. 11
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This note was uploaded on 12/06/2011 for the course BUS 315 taught by Professor N.a during the Spring '09 term at Simon Fraser.

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Bus 315 - Week12 - Week 12 Equilibrium in Capital Markets...

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