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Florida Company (FC) and Minnesota Company (MC) are both service companies. Their stock returns for the...

Florida Company (FC) and Minnesota Company (MC) are both service companies. Their stock returns for the past three years were as follows: FC: −5 percent, 15 percent, 20 percent; MC: 8 percent, 8 percent, 20 percent. What is the standard deviation of a portfolio with 50 % of the funds invested in FC and 50 % in Mc ?(Ignore the correction for the loss of a degree of freedom set out in the text)

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Expert Solution

Year Return FC Rfc Mean retrun Fc Mfc (Rfc-Mfc)^2 Return MC Rmc Mean Return MC =Mmc (Rmc-Mmc)^2 (Rfc-Mfc)(Rmc-Mmc)
1 -5.00% 10% 0.0225 8.00% 12.00% 0.0016 0.006
2 15.00% 10% 0.0025 8.00% 12.00% 0.0016 -0.002
3 20.00% 10% 0.01 20.00% 12.00% 0.0064 0.008
Total 30.00% 0.035 36.00% 0.0096 0.012
Mean return 10% 12.00%
Sample Variance=Variance Total/(n-1) 0.0175 0.0048
Covariance =0.0120/2= 0.006
Weight of FC =w1= 0.5
Weight of MC =w2= 1
Variance Portfolio= w1^2*var Fc+w2^2*varMc+2*w1*w2*CovarianceFcMc
            =0.50^2*0.0175+0.50^2*0.0048+2*0.50*0.50*0.0060
                               = 0.008575
So Variance of Portfolio= 0.008575
Standard Devaition = Sqaure root of Varaince = 0.092601

jeff jeffy answered 9 months ago
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