You Have to Compute the VaR (Value at Risk) of a Portfolio

Question

Examlex · Accepted Answer

The Answer is a. The expected return on the portfolio is zero.

\begin{array} { l } \sigma _ { p } ^ { 2 } = \left( 0.5 imes \sigma _ { 1 } ight) ^ { 2 } + \left( 0.5 imes \sigma _ { 2 } ight) ^ { 2 } + 2 imes 0.50 imes 0.5 imes 0.5 imes \sigma _ { 1 } imes \sigma _ { 2 } = 27.25 \\sigma _ { p } = 5.22 \%\end{array}

In dollar terms, the variance is equal to 5.22% *$100 million = $5.22 million.
Monthly VaR = 1.645 * 5.22%*100 million =8.59 million.
b. Under the assumption that the distributions are normal and identically independent (i.i.d.), the yearly VaR can be deducted from the monthly VaR by multiplying it by

\sqrt { 12 } :

Annual VaR

= \sqrt { 12 } imes 8.59 = 29.76

million.

You Have to Compute the VaR (Value at Risk) of a Portfolio

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