A New Perspective on Tax-Aware Investing: Optimal Trading in a Multi-Period Portfolio Optimization Model

Abstract

Long have portfolio managers, investors, and general market speculators focused on the performance of their assets, through the lens of a pre-tax world. There are several driving forces that go into the optimization of performance of a portfolio of assets, some have focused immensely on asset selection, others have focused their efforts on risk management and preventing drastic downward performance swings. In this paper, I decide to take a slightly different focus when it comes to portfolio performance, and rather than just consider the performance of portfolios on a pre-tax basis, I choose to innovate in a far more interesting, and realistic world, a world that aims to maximize after-tax portfolio performance. This is a relatively new area of portfolio optimization, and although there tends to be rather large uncertainty in calculating what one’s tax may be at a future date, since it is dependent on various market factors and the ultimate performance of assets through time, there is a tremendous opening for maximizing the wealth an individual entity ends up with once all is said and done. In saying this, much of the current tax-aware investing literature that exists is strictly single-period in nature. This means, optimizing the tax-aware return of a portfolio with a singular and non-varying time objective, which is typically completed on a monthly basis. Whilst this particular formulation and methodology has provided us with significant insights into optimal tax-aware investment strategies, and even been described as the most efficient way to formulate the problem, there inevitably seems to be a gap in the literature. Whilst single-period models capture much of the nuances required to efficiently invest on a tax-aware basis, one might wonder what additional inefficiencies could be cleaned up from a multi-period optimization. Many argue that multi-period formulations are challenging from a computational perspective, requiring significant computing power, time, and advanced optimization software which makes them challenging, and often intractable at times. In this paper, I aim to overcome this challenge by using multi-period optimization as a framework through which to draw broader, implementable conclusions from. In this paper, I develop a multi-period portfolio optimization model that is tax- aware. There have only been two prior papers that have even considered taxes in a multi-period setting ([1] & [2]), to my knowledge, however, they fail to capture some of the complexity that I wish to address in this paper. Firstly, it is unclear what an optimal decision-making process is constituted of in a multi-period structure. When developing the mathematical formulation for our tax-aware model, I was faced with a series of mathematical challenges, that make by-hand computation of an optimal asset allocation exceedingly difficult. I adopted a Markowitz mean-variance optimization, where I chose to maximize the expected after-tax liquidation value over a given investment horizon, relative to the portfolio variance. Traditional single-period Markowitz models have well-defined optimal strategies and mean-variance trade-offs; the ambiguity and non-obvious nature of a well-defined optimal strategy in a multi-period model even further motivated my extension to analyzing tax-aware investing in this framework. Additionally, prior multi-period tax-aware investing literature has not considered asset price projection and risk as combined input features, or considered a mean- variance approach to the problem. In this paper, I take a deep dive on input features, and analyze a range of portfolio metrics and their correlation to asset price projections (alpha), and our future belief of asset risk. It is my goal to demystify tax-aware investing through the lens of a multi-period framework, and compare our model optima with that of a multi-period tax-unaware portfolio. In my research, I find that there in fact are certain characteristics about an asset’s risk and return profile that make it increasingly tax-optimal in a multi-period framework. I discover that assets with relatively flat asset price linear regression gradients, and assets with increasing future asset standard deviation linear regression gradients perform substantially better than their tax-unaware counterparts in multi-period formulations. Additionally, I make a more significant contribution to the literature as I discover that there is a significant reduction in trading activity for our tax-aware model. On the surface, this may seem to represent a limitation of multi-period tax-aware investing, however, I expand on how this can generate improved portfolio-level returns and be used advantageously. This is made possible by the encouraging finding that the tax-aware model performs significantly better on a differential cost of returns basis, and evidently requires significantly less liquid cash invested, in order to generate the same portfolio-level returns as the tax-unaware model. I am enthusiastic about continuing to enhance the literature in this exciting area of finance, and hope that asset managers and academics can draw upon some of the conclusions in this paper to strengthen the power of their tax-aware investing regimes.