  The growth-optimal portfolio optimization strategy pioneered by Kelly is
based on constant portfolio rebalancing which makes it sensitive to transaction
fees. We examine the effect of fees on an example of a risky asset with a
binary return distribution and show that the fees may give rise to an optimal
period of portfolio rebalancing. The optimal period is found analytically in
the case of lognormal returns. This result is consequently generalized and
numerically verified for broad return distributions and returns generated by a
GARCH process. Finally we study the case when investment is rebalanced only
partially and show that this strategy can improve the investment long-term
growth rate more than optimization of the rebalancing period.
