  We investigate the free energy of nearest-neighbor random walks on
$\mathbb{Z}^d$, endowed with a drift along the first axis and evolving in a
nonnegative random potential given by i.i.d. random variables. Our main result
concerns the ballistic regime in dimensions $d\geq4$, at which we show that
quenched and annealed Lyapunov exponents are equal as soon as the strength of
the potential is small enough.
