Using a single-particle atomistic pseudopotential method followed by a many-particle configuration interaction method, we investigate the geometry, electronic structure and optical transitions of a self-assembled InAs/GaAs quantum ring (QR), changing its shape continously from a lens-shaped quantum dot (QD) to a nearly one dimensional ring. We find that the biaxial strain in the ring is strongly asymmetric in the plane perpendicular to the QR growth direction, leading to giant optical anisotropy.