Inspired by random matrix work of A. Guionnet and D. Shlyakhtenko we define a trace on the graded algebra of a planar algebra and show that the GNS algebra is a factor which affords a subfactor realising the planar algebra we started with. This gives an alternative proof of an old result of S. Popa. The various other graded algebra structures, with slightly modified traces, give the tower obtained by iterating the basic construction. There is a matrix model for these traces as the large N limit of certain Wishart matrices