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What happens to portfolio variance when a. the correlation between securities decrease? b. the number of assets in the portfolio increases? (Assume correlation among assets are not perfect)

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Answer:

A)
Portfolio Variance = (w(1)^2 x SD(1)^2) + (w(2)^2 x SD(2)^2) + (2 x (w(1)*SD(1)*w(2)*SD(2)*q(1,2))

w(1) = the portfolio weight of the first asset

w(2) = the portfolio weight of the second asset

SD(1) = the standard deviation of the first asset

SD(2) = the standard deviation of the second asset

q(1,2)=the correlation between two assets class

So from above equation it is clear that a decrease in correlation between securities in a portfolio results in a decrease in portfolio variance.

B)

Since the assets with perfect correlation move together. So there is no perfect correlation so as the number of assets increases the portfolio variance decreases.


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