Answer-first summary for fast verification
Answer: 15.53
The standard deviation is just the square root of the variance. The variance is given by: \[\sigma^2_{A+B} = w_A^2 \sigma^2_A + w_B^2 \sigma^2_B + 2w_A w_B \text{Cov}(A, B)\] \[= 0.3^2 \times 1234.56 + 0.7^2 \times 243.56 + 2 \times 0.3 \times 0.7 \times 25.56\] \[= 241.19\] So the standard deviation of the portfolio (combined returns from these securities) is given by: \[\sigma_{A+B} = \sqrt{241.19} = 15.53\]
Author: Nikitesh Somanthe
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An investor invests 30% of his assets in security A and 70% in security B. The variance of returns for security A is 1234.56, and that of B is 243.56. The covariance between securities A and B is 25.56. What is the standard deviation of the combined returns from these securities?
A
18.89
B
14.78
C
15.53
D
13.45
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