ch07 - 9-1 Lecture III(Chapter 7(7th/8th/9thedition 9-2...

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Unformatted text preview: 9-1 Lecture III (Chapter 7 (7th/8th/9thedition)) 9-2 Lecture III – p.2 FIN 6275 The Investment Decision Top-down process with 3 steps: 1.Capital allocation between the risky portfolio and risk-free asset 2.Asset allocation across broad asset classes 3.Security selectionof individual assets within each asset class 9-3 Lecture III – p.3 FIN 6275 rp= W1r1 +W2r2 Wi= Proportion of funds in Security i ri= Expected return on Security i Two-Security Portfolio: Return Matrix format:rp= w’*r 9-4 Lecture III – p.4 FIN 6275 σp2= w12σ12+ w22σ22+ 2w1w2 Cov(r1r2) σi2 = Variance of Security i Cov(r1r2) = Covariance of returns for Security 1 and Security 2 Two-Security Portfolio: Risk Matrix format:σp2= w’*Σ*w here Σrepresents the variance covariance matrix of returns 9-5 Lecture III – p.5 FIN 6275 σ2p = W12σ12 + W22σ12 + 2W1W2 rp= W1r1 +W2r2 + W3r3 Cov(r1r2) +W32σ32 Cov(r1r3) + 2W1W3 Cov(r2r3) + 2W2W3 Three-Security Portfolio 9-6 Lecture III – p.6 FIN 6275 rp= Weighted average of the n securities rp= w’*r σp2 = (Consider all pairwise covariance measures) σp2= w’*Σ*w In General, For an n-Security Portfolio: 9-7 Lecture III – p.7 FIN 6275 Risk Reduction with Diversification Number of SecuritiesSt. DeviationMarket Risk Unique Riskm 9-8 Lecture III – p.8 FIN 6275 The Power of Diversification Remember: If we define the average variance and average covariance of the securities as: We can then express portfolio variance as: σP2=w'Σw=wiwjCov(ri,rj)j=1n∑i=1n∑σ2=1nσi2i=1n∑and Cov=1n(n−1)wiwjCov(ri,rj)i=1n∑j=1j≠in∑σP2=1nσ2+n−1nCov9-9 Lecture III – p.9 Lecture III – p....
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ch07 - 9-1 Lecture III(Chapter 7(7th/8th/9thedition 9-2...

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