
Answer-first summary for fast verification
Answer: 2.1%.
**Explanation:** The correct answer is **B** (2.1%). 1. **Incorrect Interpretation (Option A):** The calculation assumes a correlation of -1 (perfect negative correlation) instead of zero, leading to a portfolio standard deviation of 0%. This misinterprets the term "uncorrelated." 2. **Correct Calculation (Option B):** The portfolio standard deviation is calculated as follows: - Formula: $$ \sigma_p = \sqrt{w_1^2 \sigma_1^2 + w_2^2 \sigma_2^2 + 2w_1w_2 \text{Cov}(R_1, R_2)} $$ - Since the securities are uncorrelated, the covariance term is zero. - Substituting the values: $$ \sigma_p = \sqrt{(0.5)^2 (3\%)^2 + (0.5)^2 (3\%)^2} = \sqrt{2.25 + 2.25} = \sqrt{4.5} \approx 2.1\% $$ 3. **Incorrect Interpretation (Option C):** This option incorrectly calculates the portfolio standard deviation as the weighted average of the individual standard deviations (3.0%), ignoring the diversification benefit of uncorrelated returns.
Author: LeetQuiz Editorial Team
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