  The hemispheric asymmetry of sunspot activity observed possesses a regular
component varying on a time scale of several solar cycles whose origin and
properties are currently debated. This paper addresses the question of whether
the long-term hemispheric asymmetry can result from random variations of solar
dynamo parameters in time and latitude. Scatter in the observed tilt angles of
sunspot groups is estimated to infer constraints on fluctuations in the dynamo
mechanism for poloidal field regeneration. A dynamo model with fluctuations in
the Babcock-Leighton type $\alpha$-effect is designed in accordance with these
constraints and then used to compute a large number of magnetic cycles for
statistical analyses of their hemispheric asymmetry. Hemispheric asymmetry in
the simulated dynamo results from the presence of an equator-symmetric part in
the oscillating magnetic field. The subdominant quadrupolar oscillations are
stochastically forced by dominant dipolar oscillations via the
equator-symmetric part of the fluctuating $\alpha$-effect. The amplitude and
sense of the asymmetry of individual cycles varies on a time scale of the order
of four dynamo-cycle periods. The variations are irregular, i.e. not periodic.
The model suggests that asymmetry in the polar magnetic fields in the solar
minima can be used as a precursor for asymmetry of sunspot activity in the
following solar cycle.
