Answer: 2%

## Explanation To calculate the standard deviation of an equally weighted portfolio with two assets, we use the portfolio variance formula: $$\sigma_p^2 = w_1^2\sigma_1^2 + w_2^2\sigma_2^2 + 2w_1w_2\rho_{12}\sigma_1\sigma_2$$ Where: - $w_1 = w_2 = 0.5$ (equally weighted) - $\sigma_1 = 0.05$ (5%) - $\sigma_2 = 0.08$ (8%) - $\rho_{12} = -1$ (correlation coefficient) Substituting the values: $$\sigma_p^2 = (0.5)^2(0.05)^2 + (0.5)^2(0.08)^2 + 2(0.5)(0.5)(-1)(0.05)(0.08)$$ $$\sigma_p^2 = (0.25)(0.0025) + (0.25)(0.0064) + 2(0.25)(-1)(0.004)$$ $$\sigma_p^2 = 0.000625 + 0.0016 - 0.002$$ $$\sigma_p^2 = 0.000225$$ Taking the square root: $$\sigma_p = \sqrt{0.000225} = 0.015 = 1.5\%$$ The closest option to 1.5% is **2%** (Option B). **Key Insight:** When correlation is -1 (perfect negative correlation), the portfolio standard deviation can be significantly reduced through diversification. In fact, with perfect negative correlation, it's possible to create a portfolio with zero risk if the weights are chosen appropriately. In this case, with equal weights, we get a standard deviation of 1.5%, which demonstrates the power of diversification.

Author: LeetQuiz .