What is the standard deviation of a portfolio which is invested 20% in stock A,30% in stock B and 50% in stock C?
A)0.6%
B)0.9%
C)1.8%
D)2.2%
E)4.9%

Question

What is the standard deviation of a portfolio which is invested 20% in stock A,30% in stock B and 50% in stock C? 
A)0.6% 
B)0.9% 
C)1.8% 
D)2.2% 
E)4.9%

Quizplus · Accepted Answer

E(r)_Boom = (.20 F1F1F1S1F1F1F10 .15)+ (.30 F1F1F1S1F1F1F10 .10)+ (.50 F1F1F1S1F1F1F10 .05)= .03 + .03 + .025 = .085E(r)_Normal = (.20 F1F1F1S1F1F1F10 .09)+ (.30 F1F1F1S1F1F1F10 .06)+ (.50 F1F1F1S1F1F1F10 .07)= .018 + .018 + .035 = .071E(r)_Bust = (.20 F1F1F1S1F1F1F10 -.14)+ (.30 F1F1F1S1F1F1F10 .02)+ (.50 F1F1F1S1F1F1F10 .08)= -.028 + .006 + .04 = .018E(r)_Portfolio = (.10 F1F1F1S1F1F1F10 .085)+ (.70 F1F1F1S1F1F1F10 .071)+ (.20 F1F1F1S1F1F1F10 .018)= .0085 + .0497 + .0036 = .0618Var_Portfolio = [.10 F1F1F1S1F1F1F10 (.085 - .0618)²] + [.70 F1F1F1S1F1F1F10 (.071 - .0618)²] + [.20 F1F1F1S1F1F1F10 (.018 - .0618)²] = .000053824 + .000059248 + .000383688 = .00049676Std dev = F1F1F1S1F1F1F10.00049676 = .022288 = 2.2%

What Is the Standard Deviation of a Portfolio Which Is