Financial Risk Manager Part 1
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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?
Explanation:
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.