You Have to Compute the VaR of a Portfolio with a Probability

question 5

Essay

You have to compute the VaR of a portfolio with a probability of 5% and 1% (confidence level of 95% and 99%). Your portfolio is worth $100 million evenly invested in two assets ($50 million in asset 1 and $50 million in asset 2). Here are some statistics for monthly returns of the two assets:
E(R₁)=E(R₂) =0.5%
$\sigma$ (R₁) = 8%
$\sigma$ (R₂) = 12%
Correlation = 0.4.
You make the hypothesis that the distributions are normal. We know that in a normal distribution with expected return E(R) and standard deviation $\sigma$ , 5% of the observations lie below [E(R) - 1.645 * $\sigma$ ] and 1% of the observations lie below [E(R) - 2.326 * $\sigma$ ].
a. What is the one-month VaR of the portfolio with a 5% probability?
b. What is the one-month VaR of the portfolio with a 1% probability?
c. What is the one-year VaR of the portfolio with a 5% probability?

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