I used Extreme Value Theory to separate extreme negative returns from extreme positive returns, then, I calculated the VaR for both. I need to know what could be the interpretation of VaR for positive returns? Thanks in advance.
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What do you model? If negative returns are losses, then what is your interest in the "risk" of the positive ones. Most naturally you could look at quantiles of your distribution. The 1%-quantile is the negative of $VaR_{99\%}$. The $99\%$-quanile could be of interest if you want to know about the right end of the distribution.
The concept of Oemga ration compares losses and gains in the tails.
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$\begingroup$ Thanks for your answer..Actually, I measure the VaR for positive and negative returns to show the asymmetry.. I found that VaR for negative returns are bigger than those in positive returns. If the interpretation of VaR for negative returns is " the largest percentage of the portfolio value that you might lose" , I think that for positive returns, the interpretation of VaR could be as following : " the minimum gain that you may have" .. What do you think? $\endgroup$ Commented Nov 5, 2015 at 15:18
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$\begingroup$ The interpretation of VaR for losses is: only in x% of the cases you lose more than VaR. The interpretation of a "VaR" for profit is: only in x% of the cases you win more than this. $\endgroup$– Richi WaCommented Nov 5, 2015 at 15:26