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No… the statement is correct. Variance formula for two assets is (w1*sd1)^2 + (w2*sd2)^2 + 2*w1*w2*sd1*sd2*rho. If rho = 1, then this formula reduces to (w1*sd1 + w2*sd2)^2. Standard deviation is the square root, w1*sd1 + w2*sd2.

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Why does rho=1 eliminate the entire third section from the equation though.. wouldn’t rho=0 do this?

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