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 p2= w1212+ w2222+ 2w1w2 Cov(r1r2) i2 = Variance of Security i Cov(r1r2) = Covariance of returns for Security 1 and Security 2 Two-Security Portfolio: Risk Matrix format:p2= w**w here represents the variance covariance matrix of returns 9-5 Lecture III p.5 FIN 6275 2p = W1212 + W2212 + 2W1W2 rp= W1r1 +W2r2 + W3r3 Cov(r1r2) +W3232 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 p2 = (Consider all pairwise covariance measures) p2= w**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: P2=w'w=wiwjCov(ri,rj)j=1ni=1n2=1ni2i=1nand Cov=1n(n1)wiwjCov(ri,rj)i=1nj=1jinP2=1n2+n1nCov9-9 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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