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.