Stock X has a standard deviation of return of 10%.Stock Y has a standard deviation of return of 20%.The correlation coefficient between the two stocks is 0.5.If you invest 60% of your funds in stock X and 40% in stock Y,what is the standard deviation of your portfolio?
A)10.3%
B)21.0%
C)12.2%
D)14.8%

Question

Quizplus · Accepted Answer

The formula to calculate the standard deviation of a portfolio with two assets is as follows:

σp = √(w1^2 x σ1^2 + w2^2 x σ2^2 + 2 x w1 x w2 x σ1 x σ2 x ρ12)

Where

• σp represents the standard deviation of the portfolio, 
• w1 and w2 are the weights of assets 1 and 2 in the portfolio (in this case, 0.6 and 0.4, respectively), 
• σ1 and σ2 are the standard deviations of assets 1 and 2 (10% and 20%, respectively), 
• ρ12 is the correlation coefficient between the two assets (0.5).
 
Substituting the values in the formula, we get:

σp = √(0.6^2 x 0.1^2 + 0.4^2 x 0.2^2 + 2 x 0.6 x 0.4 x 0.1 x 0.2 x 0.5)
σp = √(0.036 + 0.016 + 0.0048)
σp = √0.0568
σp = 0.2380 or 23.8%

However, as the question asks for the answer in percentage format, we need to multiply by 100 to get 23.8%. Therefore, the closest answer choice is C) 12.2%.

Stock X Has a Standard Deviation of Return of 10