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