  The joint distribution of maximum increase and decrease for Brownian motion
up to an independent exponential time is computed. This is achieved by
decomposing the Brownian path at the hitting times of the infimum and the
supremum before the exponential time. It is seen that an important element in
our formula is the distribution of the maximum decrease for the three
dimensional Bessel process with drift started from 0 and stopped at the first
hitting of a given level. From the joint distribution of the maximum increase
and decrease it is possible to calculate the correlation coefficient between
these at a fixed time and this is seen to be -0.47936... .
