  We have studied the electronic properties of the ladder compound
$\alpha'$-NaV$_{2}$O$_{5}$, adopting a joint experimental and theoretical
approach. The momentum-dependent loss function was measured using electron
energy-loss spectroscopy in transmission. The optical conductivity derived from
the loss function by a Kramers-Kronig analysis agrees well with our results
from LSDA+U band-structure calculations upon application of an
antiferromagnetic alignment of the V~3$d_{xy}$ spins along the legs and an
on-site Coulomb interaction U of between 2 and 3 eV. The decomposition of the
calculated optical conductivity into contributions from transitions between
selected energy regions of the DOS reveals the origin of the observed
anisotropy of the optical conductivity. In addition, we have investigated the
plasmon excitations related to transitions between the vanadium states within
an effective 16 site vanadium cluster model. Good agreement between the
theoretical and experimental loss function was obtained using the hopping
parameters derived from the tight binding fit to the band-structure and
moderate Coulomb interactions between the electrons within the ab plane.
