We have calculated the electronic structure of PtMnSb in order to explain the very high magneto-optical Kerr effect (over 2.5° 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