Optimal Linear Signal: An Unsupervised Machine Learning Framework to Optimize PnL with Linear Signals

ArXiv ID: 2401.05337 “View on arXiv”

Authors: Unknown

Abstract

This study presents an unsupervised machine learning approach for optimizing Profit and Loss (PnL) in quantitative finance. Our algorithm, akin to an unsupervised variant of linear regression, maximizes the Sharpe Ratio of PnL generated from signals constructed linearly from exogenous variables. The methodology employs a linear relationship between exogenous variables and the trading signal, with the objective of maximizing the Sharpe Ratio through parameter optimization. Empirical application on an ETF representing U.S. Treasury bonds demonstrates the model’s effectiveness, supported by regularization techniques to mitigate overfitting. The study concludes with potential avenues for further development, including generalized time steps and enhanced corrective terms.

Keywords: Unsupervised Machine Learning, Sharpe Ratio, Optimization, ETF, Bonds

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematical derivations including linear algebra (matrix notation), closed-form optimization solutions, and statistical measures like Sharpe Ratio maximization. It also demonstrates empirical rigor with a 20-year backtest on a specific ETF (IEF), mentions regularization techniques to prevent overfitting, and provides code availability on GitHub.

  flowchart TD
    A["Research Goal:<br>Optimize PnL via Linear Signals"] --> B["Input: U.S. Treasury Bond ETF Data"]
    B --> C["Method: Unsupervised ML<br>(Linear Signal Construction)"]
    C --> D["Objective Function:<br>Maximize Sharpe Ratio"]
    D --> E{"Parameter Optimization"}
    E -- Overfitting Risk --> F["Regularization<br>Applied"]
    F --> G["Outcome: Effective PnL Optimization<br>with Generalizable Time Steps"]