Analytical solutions of optimal portfolio rebalancing

We study optimal portfolio rebalancing in a mean-variance type framework and present new analytical results for the general case of multiple risky assets. We first derive the equation of the no-trade region, and then provide analytical solutions and conditions for the optimal portfolio under several simplifying yet important models of asset covariance matrix: uncorrelated returns, same non-zero pairwise correlation, and a one-factor model. In some cases, the analytical conditions involve one or two parameters whose values are determined by combinatorial, rather than numerical, algorithms. Our results provide useful and interesting insights on portfolio rebalancing, and sharpen our understanding of the optimal portfolio.