CA Final · Advanced Financial Management · Portfolio Management
Asha Investments holds a two-asset portfolio: 50% in Asset X (standard deviation 20%) and 50% in Asset Y (standard deviation 10%). The correlation between X and Y is zero. What is the portfolio standard deviation?
The portfolio standard deviation is about 11.2%. With zero correlation, variance equals 0.25 x 400 plus 0.25 x 100, which is 125, and its square root is roughly 11.18%. Simply averaging the standard deviations to get 15% would assume perfect positive correlation.
- A15.0%
- B11.2%Correct
- C12.5%
- D10.0%
Explanation
With zero correlation the covariance term vanishes. Variance = 0.25 x 400 + 0.25 x 100 = 100 + 25 = 125. SD = sqrt(125) = 11.18%, about 11.2%. The 15% option is the weighted average of SDs, which is only right if correlation is +1.
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