  We explore the anisotropy in low frequency conductivity as a function of hole
doping in multiorbital models of pnictides by analyzing the Drude weight in the
$x$ and $y$ directions of a ($\pi$, 0) spin-density wave state. A reduction in
the conductivity anisotropy with increased hole doping, and subsequent sign
reversal, both observed in experiments, is found to be a common trend in these
models. This behavior arises due to the interplay of low energy
orbitally-resolved density of states and the geometrical features of the Fermi
surface. An understanding of anisotropy in the electron doped regime, however,
would require additional ingredients.
