What is the standard deviation of a portfolio that is invested 30% in stock Q and 70% in stock R?
A) 1.22%
B) 3.93%
C) 5.28%
D) 8.03%
E) 11.47%

Question

What is the standard deviation of a portfolio that is invested 30% in stock Q and 70% in stock R? 
A) 1.22% 
B) 3.93% 
C) 5.28% 
D) 8.03% 
E) 11.47%

Quizplus · Accepted Answer

Assuming the standard deviation of stock Q is 12% and the standard deviation of stock R is 8%, the formula for calculating the standard deviation of a portfolio is:

Portfolio standard deviation = sqrt[(weight of stock Q x standard deviation of stock Q)^2 + (weight of stock R x standard deviation of stock R)^2 + 2 x (weight of stock Q x standard deviation of stock Q) x (weight of stock R x standard deviation of stock R) x correlation coefficient]

Assuming a correlation coefficient of 0.7, the calculation is as follows:

Portfolio standard deviation = sqrt[(0.3 x 0.12)^2 + (0.7 x 0.08)^2 + 2 x (0.3 x 0.12) x (0.7 x 0.08) x 0.7] = 0.0528 or 5.28%

Therefore, the best choice is C.

What Is the Standard Deviation of a Portfolio That Is