The answer by RGJ is not exact: the ball will always travel back up
The only difference is that:if the collision is inelastic $e<1$, if
the collision is elastic $e=1$,
But as correctly said by angel, it is almost impossible that this may
happen and the coefficient of restitution will be at most 0.99......
This because e is the ratio between the two values of the speeds
This answer somewhat explains it, but it left some confusion.
Why will the ball always travel up eh?
This is because of conservation of momentum. Let's ignore air resistance. The ball cannot come up higher than it was dropped because then it would get momentum from nowhere. The perfect scenario in which all the momentum is transferred from the ball to the wall back to the ball is $e = 1$. e is basically a measure of efficiency, how well the surface can "give back" momentum. Momentum can be lost to heat, "squishyness", etc. therefore in real life, $e < 1$.