Title: Optimal rebalancing frequency of functionally generated portfolios
Abstract: Functionally generated portfolios, such as constant weighted portfolios, have been shown to outperform the market capitalization index over long time horizons in a diverse volatile market. In actual applications time is discrete and one encounters the problem of determining how frequently to rebalance such a portfolio. We will show that the optimal frequency is determined by the angle at which geodesics in a certain geometry on the unit simplex intersect. The geometry is also intimately connected to an interesting Monge-Kantorovich optimal transport problem that is of independent interest.