  The hadronic vacuum polarization can be determined from the vector correlator
in a mixed time-momentum representation. We explicitly calculate the
disconnected contribution to the vector correlator, both in the $N_f = 2$
theory and with an additional quenched strange quark, using non-perturbatively
$O(a)$-improved Wilson fermions. All-to-all propagators are computed using
stochastic sources and a generalized hopping parameter expansion. Combining the
result with the dominant connected contribution, we are able to estimate an
upper bound for the systematic error that arises from neglecting the
disconnected contribution in the determination of $(g-2)_\mu$.
