Transaction fees and optimal rebalancing in the growth-optimal portfolio

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 distr...