  We investigate the distributions of epsilon-drawdowns and epsilon-drawups of
the most liquid futures financial contracts of the world at time scales of 30
seconds. The epsilon-drawdowns (resp. epsilon- drawups) generalise the notion
of runs of negative (resp. positive) returns so as to capture the risks to
which investors are arguably the most concerned with. Similarly to the
distribution of returns, we find that the distributions of epsilon-drawdowns
and epsilon-drawups exhibit power law tails, albeit with exponents
significantly larger than those for the return distributions. This paradoxical
result can be attributed to (i) the existence of significant transient
dependence between returns and (ii) the presence of large outliers
(dragon-kings) characterizing the extreme tail of the drawdown/drawup
distributions deviating from the power law. The study of the tail dependence
between the sizes, speeds and durations of drawdown/drawup indicates a clear
relationship between size and speed but none between size and duration. This
implies that the most extreme drawdown/drawup tend to occur fast and are
dominated by a few very large returns. We discuss both the endogenous and
exogenous origins of these extreme events.
