CMA Intermediate · Financial Management and Business Data Analytics · Risk and Return
Stock A and Stock B each have a standard deviation of 10%. Their weights in a portfolio are 50% each, and the correlation between them is 0.2. What is the portfolio standard deviation?
The portfolio standard deviation is 7.75%. Portfolio variance equals 25 plus 25 plus 10 for the covariance term, which is 60, and the square root is about 7.75%. This is below 10% because the correlation of 0.2 is less than one, giving diversification benefit.
- A10.00%
- B7.75%Correct
- C5.48%
- D7.35%
Explanation
Variance = 0.25x100 + 0.25x100 + 2x0.5x0.5x0.2x100 = 25 + 25 + 10 = 60. SD = sqrt(60) = 7.75%. Using 10% ignores diversification; 7.35% is not derived from the data.
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