OPTIMAL REBALANCING OF PORTFOLIOS WITH TRANSACTION COSTS

Abstract. Rebalancing of portfolios with a concave utility function is consid-ered. It is proved that transaction costs imply that there is a no-trade region where it is optimal not to trade. For proportional transaction costs it is opti-mal to rebalance to the boundary when outside the no-trade region. With flat transaction costs, the rebalance from outside the no-trade region should be to an internal state in the no-trade region but never a full rebalance. The stan-dard optimal portfolio theory is extended to n-symmetric assets, general utility function, and more general stochastic processes. Examples are discussed. 1