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?

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NNikitesh

Last updated: February 2, 2026 at 10:22

18.89

14.78

15.53

13.45

Explanation:

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:

$\sigma_{A+B} = \sqrt{241.19} = 15.53$

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