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You own a portfolio of two stocks (X and Y), with 40% of the portfolio invested in Stock X
You own a portfolio of two stocks (X and Y), with 40% of the portfolio invested in Stock X. You have observed over many years that the variance of your portfolio value is 0.0144 and that the correlation between the stock X and stock Y is 0.7. If the standard deviation of Stock X is 0.20, what is the standard deviation of the stock Y?
Expert Solution
Portfolio variance = (Weight of Stock X in portfolio*standard deviation of stock X in portfolio)^2+(Weight of Stock Y in portfolio*standard deviation of stock Y in portfolio)^2+2*(Weight of Stock X in portfolio*standard deviation of stock X in portfolio)*(Weight of Stock X in portfolio*standard deviation of stock X in portfolio)*correlation between stock X and Y
So we have
0.0144=(0.4*0.2)^2+(0.6*Y)^2+2*(0.4*0.2)*(0.6*Y)*0.7
0.36Y^2+0.0672Y=0.0080
Solving we get Y=0.0825
Thus standard deviation of stock Y is 0.0825
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