  It is shown that the celebrated result of Sparre Andersen for random walks
and L\'evy processes has intriguing consequences when the last time of the
process in $(-\infty,0]$, say $\sigma$, is added to the picture. In the case of
no positive jumps this leads to six random times, all of which have the same
distribution - the uniform distribution on $[0,\sigma]$. Surprisingly, this
result does not appear in the literature, even though it is based on some
classical observations concerning exchangeable increments.
