You have the following information for Stock A and Stock B: Expected rate of return Stock...

You have the following information for Stock A and Stock B:

Expected rate of return

Stock A: .12

Stock B: .06

Standard deviation:

Stock A: .9

Stock B: .5

Correlation between the two stocks: .80

If you invest $600 and $400 in Stock A and Stock B respectively, what is the standard deviation of the portfolio?

Expert Solution

Investment in A = $600
Investment in B = $400

Total Investment = $600 +$400 = $1000
Weight of A = $600/1000 =0.6
Weight of B = $400/1000 = 0.4

Variance of the Portfolio = [(Weight of Stock A)2 * (Standard Deviation of Stock A)2] + [(Weight of Stock B)2 * (Standard Deviation of Stock B)2] + [2 * Weight of A * Weight of B * Covariance between A and B]
                                                = [(0.6)2 * (0.9)2] + [(0.4)2 * (0.5)2] + [2 * 0.6 * 0.4 * 0.80]
                                                = [0.36 * 0.81] + [0.16 * 0.25] + [2 * 0.6 * 0.4 * 0.80]
                                                = [0.2916 + 0.04 + 0.384]
                                                = 0.7156

Standard Deviation of Portfolio = (Variance of the Portfolio)1/2
                                = (0.7156)1/2
                                = 0.8459

jeff jeffy answered 1 year ago

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