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

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Finance

Florida Company (FC) and Minnesota Company (MC) are both servicecompanies. Their stock returns for the past three years were asfollows: FC: ?5 percent, 15 percent, 20 percent; MC: 8 percent, 8percent, 20 percent. What is the standard deviation of a portfoliowith 50 % of the funds invested in FC and 50 % in Mc ?(Ignore thecorrection for the loss of a degree of freedom set out in thetext)

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3.7 Ratings (367 Votes)

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

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Transcribed Image Text

Florida Company (FC) and Minnesota Company (MC) are both servicecompanies. Their stock returns for the past three years were asfollows: FC: ?5 percent, 15 percent, 20 percent; MC: 8 percent, 8percent, 20 percent. What is the standard deviation of a portfoliowith 50 % of the funds invested in FC and 50 % in Mc ?(Ignore thecorrection for the loss of a degree of freedom set out in thetext)

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