Stock X has a standard deviation of return of 10%. Stock Y has a standard deviation of return of 20%. The correlation coefficient between stocks is 0.5. If you invest 60% of the funds in stock X and 40% in stock Y, what is the standard deviation of a portfolio?
A) 10%
B) 20%
C) 12.2%
D) None of the above

Question

Quizplus · Accepted Answer

The formula for combining the standard deviations of two stocks in a portfolio is:

Portfolio SD = (w1^2 × SD1^2 + w2^2 × SD2^2 + 2 × w1 × w2 × SD1 × SD2 × correlation)^0.5

where w1 and w2 are the weights of the two stocks in the portfolio, SD1 and SD2 are the standard deviations of the returns of the two stocks, and correlation is the correlation coefficient between the two stocks.

Substituting the given values,

Portfolio SD = (0.6^2 × 0.1^2 + 0.4^2 × 0.2^2 + 2 × 0.6 × 0.4 × 0.1 × 0.2 × 0.5)^0.5

= (0.36 × 0.01 + 0.16 × 0.04 + 0.024)^0.5

= 0.122 or 12.2%

Therefore, the answer is C, 12.2%.

Stock X Has a Standard Deviation of Return of 10