  Statistics of drawdowns (loss from the last local maximum to the next local
minimum) plays an important role in risk assessment of investment strategies.
As they incorporate higher ($>$ two) order correlations, they offer a better
measure of real market risks than the variance or other cumulants of daily (or
some other fixed time scale) of returns. Previous results have shown that the
vast majority of drawdowns occurring on the major financial markets have a
distribution which is well-represented by a stretched exponential, while the
largest drawdowns are occurring with a significantly larger rate than predicted
by the bulk of the distribution and should thus be characterized as outliers.
In the present analysis, the definition of drawdowns is generalised to
coarse-grained drawdowns or so-called epsilon-drawdowns and a link between such
epsilon-outliers and preceding log-periodic power law bubbles previously
identified is established.
