CIE XYZ colour space is sometimes recommended in literature for photorealistic rendering computations because it allows one to simultaneously handle all perceivable colours at much lower computational cost than by using spectral rendering.In this paper we show that XYZ is actually a poor choice for such computations, since it is not closed under the componentwise multiplication which is a typical operation in a rendering system. We also discuss why this rather obvious fact has not received much attention yet, and give pointers to alternative solutions.