Stock J has a standard deviation of 67 percent and Stock K has a standard deviation of 51 percent. The correlation between the two stocks is -0.10. What is the standard deviation of a portfolio of the two assets with 35 percent invested in Stock J?
A) 46.23%
B) 38.64%
C) 41.07%
D) 35.19%
E) 43.82%

Question

Quizplus · Accepted Answer

The formula for calculating the standard deviation of a portfolio with two assets is: 
Portfolio standard deviation = (w1^2 * σ1^2 + w2^2 * σ2^2 + 2w1w2σ1σ2ρ)^0.5 
where: 
w1 and w2 are the weights of asset 1 and asset 2 in the portfolio 
σ1 and σ2 are the standard deviations of asset 1 and asset 2 
ρ is the correlation coefficient between the two assets

Using the formula, we can plug in the given information: 
w1 = 0.35 
w2 = 0.65 
σ1 = 0.67 
σ2 = 0.51 
ρ = -0.1

Portfolio standard deviation = (0.35^2 * 0.67^2 + 0.65^2 * 0.51^2 + 2*0.35*0.65*0.67*0.51*(-0.1))^0.5 
= 0.3864 or 38.64%

Therefore, the answer is B.

Stock J Has a Standard Deviation of 67 Percent and Stock