Optimal two-parameter portfolio management strategy with transaction costs

TL;DR

This paper develops an optimal two-parameter portfolio management strategy considering transaction costs, autocorrelation, and a no-trade zone, demonstrating how to maximize returns while minimizing trading frequency.

Contribution

It introduces a novel approach combining signal filtering and hysteresis control to optimize single-asset portfolios with transaction costs.

Findings

Removing autocorrelation optimally reduces trading frequency.

A no-trade zone can be combined with signal filtering for better performance.

Derived bounds on return improvements based on autocorrelation removal.

Abstract

We consider a simplified model for optimizing a single-asset portfolio in the presence of transaction costs given a signal with a certain autocorrelation and cross-correlation structure. In our setup, the portfolio manager is given two one-parameter controls to influence the construction of the portfolio. The first is a linear filtering parameter that may increase or decrease the level of autocorrelation in the signal. The second is a numerical threshold that determines a symmetric "no-trade" zone. Portfolio positions are constrained to a single unit long or a single unit short. These constraints allow us to focus on the interplay between the signal filtering mechanism and the hysteresis introduced by the "no-trade" zone. We then formulate an optimization problem where we aim to minimize the frequency of trades subject to a fixed return level of the portfolio. We show that maintaining a no-trade zone while removing autocorrelation entirely from the signal yields a locally optimal solution. For any given "no-trade" zone threshold, this locally optimal solution also achieves the maximum attainable return level, and we derive a quantitative lower bound for the amount of improvement in terms of the given threshold and the amount of autocorrelation removed.