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Q.3036 What would be the 95% parametric VaR of a portfolio made of two independently normally distributed stocks - A and B, with A ~ N(0.5, 1) and B ~ N(3, 15)? Assume that P = (A + B) | Financial Risk Manager Part 2 Quiz - LeetQuiz

Explanation:

Assuming P = A + B, then P ~ N(3.5, 16).

\begin{aligned} \text{VaR}(\alpha\%) &= [-\mu_{\text{r}} + \sigma_{\text{r}} \times Z_{\alpha}] \\ &= [-3.5 + 4 \times 1.645] \\ &= 3.08 \end{aligned}

Note. The sum of two independent normally distributed random variables is normal. Its mean is the sum of the two means, and its variance is the sum of the two variances

Where $\sigma_{\text{r}} = \sqrt{16} = 4$

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