Portfolio selection with proportional transaction costs and predictability

We consider the portfolio selection problem for a multiperiod investor who seeks to maximize her utility of intermediate consumption facing multiple risky-assets and proportional transaction costs in the presence of return predictability. With the presence of transaction costs, this problem is very difficult to solve even numerically due to the curse of dimensionality. In this paper, we propose first several suboptimal rebalancing policies that are based on optimizing simple quadratic programs for a mean-variance investor who faces proportional transaction costs. Then, we propose some feasible rebalancing and consumption policies that can be easily computed even for many risky assets, for an investor with power utility, based on the proposed suboptimal policies. Finally, we show how to compute upper bounds and use them to study how the certainty equivalent losses of consumption, associated when using the approximate policies, depend on different problem parameters.