CMA Final · Strategic Financial Management · Portfolio Theory and Practice
Two assets A and B have standard deviations of 10% and 20% respectively. A portfolio holds 50% in each and the correlation coefficient between them is 0.5. What is the portfolio standard deviation (approximately)?
The portfolio standard deviation is about 13.2%. Variance equals 25 plus 100 plus 50, which is 175, and its square root is roughly 13.2%. Simply averaging the two standard deviations to get 15% wrongly ignores the benefit of imperfect correlation.
- A15.0%
- B13.2%Correct
- C12.5%
- D10.0%
Explanation
Variance = (0.5^2 x 100) + (0.5^2 x 400) + 2 x 0.5 x 0.5 x 0.5 x 10 x 20 = 25 + 100 + 50 = 175. Standard deviation = sqrt(175) = 13.23%, about 13.2%. The 15% option is the simple weighted average of the standard deviations, which ignores diversification.
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