Magnesium aluminate scandium oxide ($\mathrm{ScAlMg}{O}_4$) is a promising lattice-matched substrate material for GaN- and ZnO-based optoelectronic devices. Yet, despite its clear advantages over substrates commonly used in heteroepitaxial growth, several fundamental properties of $\mathrm{ScAlMg}{O}_4$ remain unsettled. Here, we provide a comprehensive picture of its optical, electronic, and structural properties by studying $\mathrm{ScAlMg}{O}_4$ single crystals grown by the Czochralski method. We use variable-angle spectroscopic ellipsometry to determine complex in-plane and out-of-plane refractive indices in the range from 193 to 1690 nm. An oscillator-based model provides a phenomenological description of the ellipsometric spectra with excellent agreement over the entire range of wavelengths. For convenience, we supply the reader also with Cauchy formulas describing the real part of the anisotropic refractive index for wavelengths above 400 nm. Ab initio many-body perturbation theory modeling provides information about the electronic structure of $\mathrm{ScAlMg}{O}_4$, and successfully validated experimentally obtained refractive-index values. Simulations also show exciton binding energy as large as a few hundred of meV, indicating $\mathrm{ScAlMg}{O}_4$ as a promising material for implementation in low-threshold, deep-UV lasing devices operating at room temperature. X-ray diffraction measurements confirm lattice constants of $\mathrm{ScAlMg}{O}_4$ previously reported, but in addition, reveal that dominant crystallographic planes (001) are mutually inclined by about $0.{009}^{\circ }$. In view of our work, $\mathrm{ScAlMg}{O}_4$ is a highly transparent, low refractive index, birefringent material similar to a sapphire, but with a much more favorable lattice constant and simpler processing.