Yes, permitted. You need a license, which is something that can be denied for a multitude of common reasons. Gun ownership in Switzerland is taken seriously and very heavily regulated. And the same goes for bullet ownership. Read your wikipedia link; it reads nothing like what anyone in the USA would recognise.

Relative to the USA status quo, Swiss gun laws are like a far left socialist wet dream. No electable left-wing politician would ever imagine being able to get one tenth of Swiss-style laws passed in the USA.