Tax-Aware Dynamic Asset Allocation

We consider dynamic asset allocation problems where the agent is required to pay capital gains taxes on her investment gains. These are very challenging problems because the tax owed whenever a security is sold depends on the cost basis, and this results in high‐dimensional problems, which cannot be solved exactly except in the case of very stylized problems with just one or two securities and relatively few time periods. In this paper, we focus on exact and average cost‐basis problems, make the limited use of losses (LUL) assumption and develop simple heuristic trading policies for these problems when there are differential tax rates for long‐ and short‐term gains and losses. We use information relaxation‐based duality techniques to assess the performance of these trading policies by constructing unbiased lower and upper bounds on the (unknown) optimal value function. In numerical experiments with as many as 80 time periods and 25 securities we find our best suboptimal policy is within 3–10 basis points of optimality on a certainty equivalent (CE) annualized return basis. The principal contribution of this paper is in demonstrating that while the primal problem remains very challenging to solve exactly, we can easily solve very large dual problem instances. Moreover, dual tractability extends to standard problem variations, including problems with random time horizons, no wash sales constraints, intertemporal consumption and recursive utility, as well as the step‐up feature of the U.S. tax code, among others.