Lenny D. answered • 05/29/19
Financial Professional with many years of Wall Street Experience
An investor puts 42.00% of his investment into Cisco Systems, and the remaining 58.00% into Apple Computer. The standard deviation on Cisco Systems stock is 32.00%, while the standard deviation on Apple Computer is 25.00%.
Find the standard deviation of this portfolio if the correlation between the two stocks is 0.47.
. Let a= weight to Cisco and 1-a = weight to Apple
Portfolio Variance = a^2 Var(Cisco) + ((1-a)^2)Var(apple) +(1(1-a)Cov(Apple, cisco)
Lets handle the COV term first Cov = Corr*Std(cisco)*Std(apple) = .47*(0.32)(0.25)=.0376
Var Cisco = 32%^2 =.1024 var Apple =.25^2 =.0625
Now we square the portfolio weights. a^2 = .42^2 =.1764 (1-a)^2 =.3364
and a(1-a) = .42*.58 = .2436
Soooooooo
Portfolio Variance = (.1764)(.1024) +.3364(.0625) +.2436*.0376 = .04825
The stad deviation is the square root of the variance so portfolio ST DEV = (.04825)^(1/2)=21.965% which
If you have any questions on anything portfolio related please reach out. I managed very large portfolios on wall street for many years.
