Answer: 6.31%

## Explanation The portfolio standard deviation is calculated using the formula for a two-asset portfolio: $$\sigma_P^2 = w_A^2 \sigma_A^2 + w_B^2 \sigma_B^2 + 2w_A w_B \rho_{AB} \sigma_A \sigma_B$$ Where: - $w_A = 0.75$ (weight in Security A) - $w_B = 0.25$ (weight in Security B) - $\sigma_A = 0.08$ (standard deviation of Security A) - $\sigma_B = 0.14$ (standard deviation of Security B) - $\rho_{AB} = -0.20$ (correlation between the two securities) **Step-by-step calculation:** 1. **Calculate the variance:** $$\sigma_P^2 = (0.75)^2 (0.08)^2 + (0.25)^2 (0.14)^2 + 2(0.75)(0.25)(-0.20)(0.08)(0.14)$$ $$= (0.5625)(0.0064) + (0.0625)(0.0196) + 2(0.1875)(-0.20)(0.0112)$$ $$= 0.0036 + 0.001225 - 0.00084$$ $$= 0.003985 = 0.3985\%$$ 2. **Calculate the standard deviation:** $$\sigma_P = \sqrt{0.003985} = 0.06312 = 6.312\%$$ **Key insights:** - The negative correlation (-0.20) provides diversification benefits, reducing the portfolio risk - Despite Security B having higher individual risk (14%), the portfolio allocation and correlation structure result in a portfolio standard deviation of approximately 6.31% - This demonstrates the power of diversification in reducing overall portfolio risk

Author: Tanishq Prabhu