30 Pages Posted: 6 Jan 2014 Last revised: 9 Jan 2016
Date Written: January 8, 2016
We consider dynamic asset allocation problems where the agent is required to pay capital gains taxes on her investment gains. This is a very challenging problem because the tax owed whenever a security is sold depends on the cost-basis, i.e. the price(s) at which the shares of the security was originally purchased. This feature results in high-dimensional and path-dependent 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. The asset allocation problem with taxes has several variations depending on: (i) whether we use the exact or average cost-basis and (ii) whether we allow the full use of losses (FUL) or the limited use of losses (LUL). In this paper we focus on the exact and average cost-basis LUL cases since these problems are the most realistic and challenging to solve. We develop simple heuristic trading policies for these problems when there are differential tax rates for long- and short-term gains/losses. We then use duality techniques based on information relaxations 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 sub-optimal policy is within 3 to 10 basis points of optimality on a certainty-equivalent annualized return basis. The principal contribution of this paper is in demonstrating that much larger problems can now be tackled through the use of sophisticated optimization techniques and duality methods based on information-relaxations. More specifically, 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, inter-temporal consumption and recursive utility, and the step-up feature of the U.S. tax code, among others.
Keywords: Dynamic asset allocation, taxes, sub-optimal control, duality, information relaxations
JEL Classification: G11, C44, C61, C63
Suggested Citation: Suggested Citation