The authors calculated the electronic structure of PtMnSb in order to explain the very high magnetooptical Kerr effect (over 2. 5 degree at 720 nm at room-temperature) of this compound. It is shown that this behavior is related to the unusual electronic properties of PtMnSb: it is a half-metallic ferromagnet like NiMnSb. The extreme asymmetry in the electronic structure of these compounds - metallic behavior for one spin direction and at the same time semiconducting behavior for the other spin direction - is responsible for the unusual magneto-optical properties.