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Friday, January 10, 2014

Haugh, Iyengar & Wang on Asset Allocation

Martin Haugh, Garud Iyengar, and Chun Wang have posted Tax-Aware Dynamic Asset Allocation on SSRN with the following abstract:

We consider dynamic asset allocation problems where the investor is required to pay capital gains taxes on her investment gains. This is a very challenging problem because the tax to be paid whenever a security is sold depends on the tax basis, i.e. the price(s) at which 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 tax-basis and (ii) whether we allow the full use of losses (FUL) or the limited use of losses (LUL). We consider all of these variations in this paper but focus mainly on the exact tax-basis LUL case since this problem is perhaps the most realistic and generally the most challenging. We develop several sub-optimal trading policies for this problem and use duality techniques based on information relaxations to assess their performance. Our numerical experiments consider problems with as many as 20 securities and 20 time periods. 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. We show in fact that the dual formulation of exact tax-basis problems are much easier to solve than the corresponding primal problems. Indeed, we can easily solve dual problem instances where the number of securities and time periods is much larger than 20. We also note, however, that while the average tax-basis problem is relatively easier to solve in general, its corresponding dual problem instances are non-convex and more difficult to solve. We therefore propose convex relaxations for the average tax-basis dual problem so that valid dual bounds may still be obtained.

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