A graph of the distribution of annual portfolio returns based on a Monte Carlo

A graph of the distribution of annual portfolio

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with strike price $90. A graph of the distribution of annual portfolio returns based on a Monte Carlo simulation appears below. From the simulation, the mean and standard deviation of changes in portfolio value over the next year are found to be –$241 and $5,835. If we use the normal-linear VaR model to compute a 95% 1-year VaR, we would get VaR = 1.65 * 5,835 – (–241) = $9,869. However, we would not expect this number to be very accurate. Why not? What is the actual 95% 1-year VaR statistic for this portfolio (data from the simulation is provided below)?
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