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This study presents an unsupervised machine learning approach for optimizingProfit and Loss (PnL) in quantitative finance. Our algorithm, akin to anunsupervised variant of linear regression, maximizes the Sharpe Ratio of PnLgenerated from signals constructed linearly from exogenous variables. Themethodology employs a linear relationship between exogenous variables and thetrading signal, with the objective of maximizing the Sharpe Ratio throughparameter optimization. Empirical application on an ETF representing U.S.Treasury bonds demonstrates the model's effectiveness, supported byregularization techniques to mitigate overfitting. The study concludes withpotential avenues for further development, including generalized time steps andenhanced corrective terms.

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