  We study the approximation of stochastic differential equations driven by a
fractional Brownian motion with Hurst parameter $H>1/2$. For the mean-square
error at a single point we derive the optimal rate of convergence that can be
achieved by any approximation method using an equidistant discretization of the
driving fractional Brownian motion. We find that there are mainly two cases:
either the solution can be approximated perfectly or the best possible rate of
convergence is $n^{-H-1/2},$ where $n$ denotes the number of evaluations of the
fractional Brownian motion. In addition, we present an implementable
approximation scheme that obtains the optimal rate of convergence in the latter
case.
