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It sounds like the P&L's you are given are not really the historical P&L's. Rather, you have some portfolio and market data currently; you have 260 days of historical market data changes; and you calculate what the P&L of the present portfolio would have been if the market moved as it did on that historical date from the current market data. You'...


If you have a covariance matrix, $Q$ the VaR is a measure of the standard deviation of the portfolio, ie. $$VaR, V \propto \sqrt{S^T Q S}$$ and, $$ \frac{\partial V}{\partial S} = \frac{QS}{V} $$ Suppose you had 3 assets, with large positions in the first two assets, and small position in the third, AND that the first two were perfectly negatively correlated,...


One way to look at answering this question is VAR Contribution. Evaluate VAR of the Portfolio, and then evaluate VAR of the Portfolio without the asset. The largest difference of VAR with the asset - VAR of the portfolio without the asset would be the asset which is contributing the most to VAR. You may want to correct the size of the portfolio for each ...


VaR is a loss function calculated from what's available in step 1, whose value is a magnitude, and whose sign indicates whether there is a portfolio loss, or a negative loss (which is actually a gain, given that VaR, as a loss, is ordinarily reported as a negative number). So to ask which asset, whose returns are available in step 2, is driving this loss ...


I figured it out now. When calculate the probability use Binominal itself, the result matches: $$\alpha=1-(P(4)+P(3)+P(2)+P(1)+P(0))=1-(0.134+0.214+0.257+0.205+0.081)=0.108$$


The reason the mean is negative is because the change in portfolio value is seen as a gain rather than a loss, so if the mean is positive, to calculate the respective VaR, we must use the formula of the profit, i.e $\mu - \sigma\Phi(\alpha)$

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