Answer: 15.53

## Explanation The standard deviation is calculated as the square root of the variance. The portfolio variance formula for two assets is: \[ \sigma_p^2 = w_A^2 \sigma_A^2 + w_B^2 \sigma_B^2 + 2w_A w_B \text{Cov}(A, B) \] Where: - \(w_A = 0.3\) (30% weight in security A) - \(w_B = 0.7\) (70% weight in security B) - \(\sigma_A^2 = 1234.56\) (variance of security A) - \(\sigma_B^2 = 243.56\) (variance of security B) - \(\text{Cov}(A, B) = 25.56\) (covariance between A and B) Substituting the values: \[ \sigma_p^2 = (0.3)^2 \times 1234.56 + (0.7)^2 \times 243.56 + 2 \times 0.3 \times 0.7 \times 25.56 \] \[ \sigma_p^2 = 0.09 \times 1234.56 + 0.49 \times 243.56 + 0.42 \times 25.56 \] \[ \sigma_p^2 = 111.1104 + 119.3444 + 10.7352 \] \[ \sigma_p^2 = 241.19 \] The standard deviation is: \[ \sigma_p = \sqrt{241.19} = 15.53 \] Therefore, the standard deviation of the combined returns from these securities is **15.53**.

Author: Tanishq Prabhu