Optimal two-parameter portfolio management strategy with transaction costs

ArXiv ID: 2411.07949 “View on arXiv”

Authors: Unknown

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.

Keywords: Transaction Costs, Signal Filtering, No-trade Zone, Autocorrelation, Portfolio Optimization, Single Asset (General)

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 2.5/10
• Quadrant: Lab Rats
• Why: The paper employs advanced stochastic calculus, AR(1) process modeling, and optimization theorems, indicating high mathematical complexity. However, the empirical evidence is purely theoretical, lacking backtests, real data, or implementation details, placing it in the Lab Rats quadrant.

  flowchart TD
    A["Research Goal: Minimize trades for fixed portfolio return<br>in single-asset strategy with transaction costs"] --> B["Model Inputs: Signal w/ Autocorrelation & Cross-Correlation"]
    B --> C["Methodology: Optimize 2-parameter controls"]
    C --> D{"Strategy Controls"}
    D --> E["Linear Filter: Adjusts Autocorrelation"]
    D --> F["Symmetric No-Trade Zone: Hysteresis"]
    E --> G["Optimization Objective: Minimize Trades"]
    F --> G
    G --> H["Findings: Remove Autocorrelation + Maintain No-Trade Zone = Locally Optimal Solution"]
    H --> I["Outcome: Maximizes Return & Quantifies Improvement Bound"]