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Bus 315 - Week9 - Week 9 Portfolio Theory II Optimal Risky...

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Week 9 Portfolio Theory II: Optimal Risky Portfolios - Bodie et al., Ch. 7 1 Jorge Cruz Lopez - Bus 315: Investments
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Optimal Risky Portfolios Objective: To examine portfolio risk and to show how optimal portfolios are constructed. 2 Jorge Cruz Lopez - Bus 315: Investments
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Optimal Risky Portfolios 1. Diversification and Portfolio Risk. 2. Portfolios of Two Risky Assets. 3. Asset Allocation with Stocks, Bonds and Bills. 4. The Markowitz Portfolio Selection Model. 5. The Power of Diversification. 6. Risk Pooling, Risk Sharing, and Risk in the Long Run. 3 Jorge Cruz Lopez - Bus 315: Investments
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1. Diversification and Portfolio Risk 4 Jorge Cruz Lopez - Bus 315: Investments
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Portfolio Risk 5 Jorge Cruz Lopez - Bus 315: Investments
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Portfolio Diversification 6 Jorge Cruz Lopez - Bus 315: Investments
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2. Portfolios of Two Risky Assets 7 Jorge Cruz Lopez - Bus 315: Investments
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Two-Security Portfolio Return w 1 = proportion of funds in Security 1 w 2 = proportion of funds in Security 2 r 1 = return on Security 1 r 2 = return on Security 2 8 1 w n 1 i i 2 2 1 1 r w r w r p Jorge Cruz Lopez - Bus 315: Investments
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Two-Security Portfolio Expected Return w 1 = proportion of funds in Security 1 w 2 = proportion of funds in Security 2 E(r 1 ) = expected return on Security 1 E(r 2 )= expected return on Security 2 9 1 w n 1 i i ) ( ) ( ) ( 2 2 1 1 r E w r E w r E p Jorge Cruz Lopez - Bus 315: Investments
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Two-Security Portfolio Risk 1 2 = variance of Security 1 2 2 = variance of Security 2 Cov(r 1 ,r 2 ) = covariance of returns for Security 1 and Security 2 10 ) r , r ( Cov w w 2 w w 2 1 2 1 2 2 2 2 2 1 2 1 2 p Jorge Cruz Lopez - Bus 315: Investments
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Covariance 1,2 = Correlation coefficient of returns 1 = Standard deviation of returns for Security 1 2 = Standard deviation of returns for Security 2 11 2 1 2 , 1 2 1 ) , ( r r Cov Jorge Cruz Lopez - Bus 315: Investments
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Correlation Coefficients: Possible Values Range of values for 1,2 -1.0 < < +1.0 If = 1.0, the securities would be perfectly positively correlated If = - 1.0, the securities would be perfectly negatively correlated 12 Jorge Cruz Lopez - Bus 315: Investments
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Three-Security Portfolio 13 ) ( ) ( ) ( ) ( 3 3 2 2 1 1 r E w r E w r E w r E p ) , ( 2 ) , ( 2 ) , ( 2 3 2 3 2 3 1 3 1 2 1 2 1 2 3 2 3 2 2 2 2 2 1 2 1 2 r r Cov w w r r Cov w w r r Cov w w w w w p Jorge Cruz Lopez - Bus 315: Investments
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n-Security Portfolio 14 n i i i p r E w r E 1 ) ( ) ( n k j 1 k , j k j k j n 1 i 2 i 2 i 2 p ) r , r ( Cov w w 2 w Jorge Cruz Lopez - Bus 315: Investments
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Descriptive Statistics for Two Funds 15 Jorge Cruz Lopez - Bus 315: Investments
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Portfolio Weights and Expected Return 16
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