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Lecture__04_Appendix

# Lecture__04_Appendix - Investment Management FINE 441...

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Investment Management, FINE 441, Lecture Notes 4 - Appendix Asset Allocation Cont’d Ruslan Goyenko Faculty of Management McGill University

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1 1 2 - Cov(r1r2) W 1 = + - 2Cov(r1r2) 2 W2 = (1 - W1) 2 2 2 E(r2) = .14 = .20 St 2 12 = .2 E (r1) = .10 = .15 St 1 ρ 2 Minimum-Variance Portfolio in case of 2 assets
W1 = (.2)2 - (.2)(.15)(.2) (.15)2 + (.2)2 - 2(.2)(.15)(.2) W1 = .6733 W2 = (1 - .6733) = .3267 Minimum-Variance Combination: ρ = .2

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rp = .6733(.10) + .3267(.14) = .1131 p = [(.6733)2(.15)2 + (.3267)2(.2)2 + 2(.6733)(.3267)(.2)(.15)(.2)] 1/2 p = [.0171] 1/2 = .1308 Minimum -Variance: Return and Risk with ρ = .2
W1 = (.2)2 - (-.3)(.15)(.2) (.15)2 + (.2)2 - 2(.2)(.15)(-.3) W1 = .6087 W2 = (1 - .6087) = .3913 Minimum -Variance Combination: ρ = -.3

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) 1 ( R E The Case of 2 Assets ) 2 ( R E ) ( P R E E(R) Asset 1 Asset 2 σ Perfectly Positive Correlation Perfectly Negative Correlation Imperfect Correlation; Between -1 and 1
Minimum-Variance Frontier E(R) Minimum-Variance Portfolio σ Individual Assets Individual Assets Minimum-Variance Frontier X Y Z

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Efficient Frontier 1 σ σ 2 σ E(R) Efficient Frontier (portfolios lying between points E and F) A R E 1 B R E 1 B R E 2 A R E 2 A B C D E F
Combining Risky and Risk-free Assets With proportion w% in the risky asset and (1-w)% in

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