What is the standard deviation of a portfolio that is invested 40% in stock A and 60% in stock B, given the following information?
A) 2.18%
B) 2.57%
C) 2.69%
D) 2.84%
E) 3.13%

Question

What is the standard deviation of a portfolio that is invested 40% in stock A and 60% in stock B, given the following information? 
A) 2.18% 
B) 2.57% 
C) 2.69% 
D) 2.84% 
E) 3.13%

Quizplus · Accepted Answer

To calculate the standard deviation of a portfolio we use the formula:
σp = √(w1² × σ1² + w2² × σ2² + 2 × w1 × w2 × σ1 × σ2 × p)
where w1 and w2 are the weights of stocks A and B respectively, σ1 and σ2 are the standard deviations of stocks A and B respectively, and p is the correlation coefficient between the two stocks.

Using the given information, we have:
w1 = 0.4, w2 = 0.6
σ1 = 0.12, σ2 = 0.20
p = 0.50 (since no correlation coefficient is given, we assume a moderate positive correlation of 0.50)

Plugging in the values, we get:
σp = √(0.4² × 0.12² + 0.6² × 0.20² + 2 × 0.4 × 0.6 × 0.12 × 0.20 × 0.50) = 0.0257 or 2.57%

Therefore, the best choice is B, which is the closest option to our calculated value of 2.57%.

What Is the Standard Deviation of a Portfolio That Is