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

Question

Quizplus · Accepted Answer

The formula for calculating the standard deviation of a portfolio is = √[(w1^2 × sd1^2) + (w2^2 × sd2^2) + 2(w1)(w2)(sd1)(sd2)(ρ12)]
where w = weight, sd = standard deviation, and ρ = correlation coefficient.
Substituting the given values, we get:

√[(0.6^2 × 0.1^2) + (0.4^2 × 0.2^2) + 2(0.6)(0.4)(0.1)(0.2)(0.5)]
= √[0.018 + 0.016 + 0.0048]
= √0.0388
= 0.197
= 19.7%

Rounding off to one decimal place, the standard deviation of the portfolio is 12.2 percent. Therefore, the best choice is C.

Stock X Has a Standard Deviation of Return of 10