Extreme Risk
 Is
there a possibility to model and forecast extreme financial risks?
How does the probability of large portfolio losses evolve over
time?Extreme Value Theory can help to find answers to the above questions. Given careful modeling of the portfolio return characteristics, it allows to make out-of-sample assessments about extreme return realizations. Considering time-varying extremes, we find a cyclic behavior in the probability of large losses. The figure illustrates results for a stock market index, namely for the German DAX portfolio during January 2, 1969 to December 31, 2002. The top panel gives a plot of an index of the extreme loss probability (alpha), where a higher level indicates a lower probability of crashes. In the bottom panel, daily negative returns are plotted jointly with the 1% and the 5% lower predicted loss quantiles. 
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