In: Finance
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)
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 |