CA Final · Advanced Financial Management · Portfolio Management
Kapoor Investments holds a two-security portfolio: 50% in Security X (standard deviation 10%) and 50% in Security Y (standard deviation 20%). The correlation coefficient between X and Y is +0.5. What is the portfolio standard deviation, to two decimals?
The portfolio standard deviation is 13.23%. Portfolio variance is 25 + 100 + 50 = 175 once the covariance term at correlation 0.5 is included, and its square root is 13.23%. The weighted average of 15% would be correct only if correlation were perfectly positive.
- A13.23%Correct
- B15.00%
- C11.18%
- D17.50%
Explanation
Variance = (0.5)^2(10)^2 + (0.5)^2(20)^2 + 2(0.5)(0.5)(0.5)(10)(20) = 25 + 100 + 50 = 175. The standard deviation is the square root of 175, which is 13.23%. The 15% option is the weighted average of the standard deviations, which holds only when correlation is +1. The 11.18% option assumes zero correlation (square root of 125).
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