I'm preparing for thesis defense and I've got simple question connected with Value at Risk backtesting. Portfolio VaR was calculated using historical simulation approach (250 days and 500days) and backtested with Kupiec test. In those portfolios where VaR was not properly estimated, there was always high frequency of exceedances so the Value at Risk was underestimated.
Why there was so many exceedances? The statistical important information was included in tails of distribution, because of lack of these tails the VaR was not properly estimated?
What should be done to improve the precision of estimation?