EC3333 Notes02

# EC3333 Notes02 - Lecture 2 Optimal Risky Portfolios...

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Lecture 2 Optimal Risky Portfolios

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Two-Security Portfolio: Return Portfolio Return Bond Weight Bond Return Equity Weight Equity Return p DE P D D E E r r w r w r ww rr =+ = = = = = () ( ) p DD EE Er w wEr = +
= Variance of Security D = Variance of Security E = Covariance of returns for Security D and Security E Two-Security Portfolio: Risk 2 D σ 2 E (, ) D E Cov r r ) , ( 2 2 2 2 2 2 E D E D E E D D p r r Cov w w w w + + = σσ

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Covariance = = = n s EY s Y EX s X s p Y X E Y X Cov 1 ) ) ( )( ) ( ( ) ( ) , ( 2 2 ) ( ) ( ) , ( X X E X X E X X σ = = =
ρ DE = Correlation coefficient of returns ρ DE = Cov(r D, r E ) /( σ D σ E ) σ D = Standard deviation of returns for Security D σ E = Standard deviation of returns for Security E Correlation

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Covariance and Correlation y Covariance and the correlation coefficient provide a measure of the way that the returns of two assets vary together y Portfolio risk depends on the correlation between the returns of the assets in the portfolio 2 (,) ( ,)2 P DD EE DE wwCovr r wwCovr r wwCovr r σ =+ +
Range of values for ρ 1,2 + 1.0 > ρ > -1.0 If ρ = 1.0, the securities would be perfectly positively correlated If

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## This note was uploaded on 10/30/2011 for the course ECON EC3333 taught by Professor Lu during the Spring '11 term at National University of Singapore.

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EC3333 Notes02 - Lecture 2 Optimal Risky Portfolios...

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