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Portfolio Risk & Return

Portfolio Risk & Return - n n σ p 2 = ∑ w i 2 σ...

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Portfolio Return and Risk inputs: r i = projected return on asset i. σ i 2 = projected variance of asset i. σ i = projected standard deviation (risk) of asset i. σ ij = projected covariance of asset i and asset j. ρ ij = ρ ji = projected correlation between asset i and j. ρ ij < 1 for all i, j. w i = weight of asset i, where w i = 1. • the investor must choose the w's n portfolio return = R p = w i r i . i=1 n n portfolio variance = σ p 2 = w i w j σ ij (covariance form) i=1 j=1 i=j n
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Unformatted text preview: n n σ p 2 = ∑ w i 2 σ i 2 + ∑ ∑ w i w j σ ij i=1 i=1 j=1 i ≠ j n n n since ρ ij = σ ij / σ i σ j , σ p 2 = ∑ w i 2 σ i 2 + ∑ ∑ w i w j σ i σ j ρ ij i=1 i=1 j=1 i ≠ j (correlation form) Portfolio risk = σ p = ( σ p 2 ) 1/2 Suppose n = 3, then σ p 2 = w 1 2 σ 1 2 + w 2 2 σ 2 2 + w 3 2 σ 3 2 + 2w 1 w 2 σ 1 σ 2 ρ 12 + 2w 1 w 3 σ 1 σ 3 ρ 13 + 2w 2 w 3 σ 2 σ 3 ρ 23...
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