Rebalancing Multiple Assets with Mutual Price Impact

We find asymptotically optimal trading policies for long-term investors with constant relative risk aversion, in a multiple-assets market where expected returns and covariances are constant, and the execution price of each asset is linear in the trading intensities of all assets. Trading towards the frictionless target is optimal when the current portfolio differs from the target by a principal portfolio - an eigenvector of the inverse price-impact times the covariance matrices. Optimal policies approach the frictionless target along nonlinear, power-shaped paths, trading faster in more liquid directions, while tolerating wider oscillations along less liquid directions