USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)

-Refer to Exhibit 6.11. Calculate the expected standard deviation of the two-stock portfolio.
A) 0.1367
B) 0.1872
C) 0.1169
D) 0.20
E) 0.3950

Question

USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
 
-Refer to Exhibit 6.11. Calculate the expected standard deviation of the two-stock portfolio.
A) 0.1367 
B) 0.1872 
C) 0.1169 
D) 0.20 
E) 0.3950

Quizplus · Accepted Answer

Using the formula for the standard deviation of a two-stock portfolio: 
σp = [w1^2 × σ1^2 + w2^2 × σ2^2 + 2w1w2σ1σ2ρ12]^0.5 
where:
w1 = weight of stock 1 = 0.4
w2 = weight of stock 2 = 0.6
σ1 = standard deviation of stock 1 = 0.15
σ2 = standard deviation of stock 2 = 0.10
ρ12 = correlation coefficient between stocks 1 and 2 = 0.2

Plugging in the values: 
σp = [(0.4^2×0.15^2) + (0.6^2 × 0.10^2) + 2(0.4)(0.6)(0.15)(0.10)(0.2)]^0.5
σp = [0.009 + 0.0036 + 0.00432]^0.5
σp = 0.1169

Therefore, the expected standard deviation of the two-stock portfolio is 0.1169, or choice C.