On a fundamental statistical edge principle

TL;DR

This paper demonstrates that conditioning trading decisions on self-generated historical data is essential for achieving a statistical trading edge, and introduces a method to improve strategies by leveraging this information.

Contribution

It proves that strategies ignoring self-generated historical trading information can be systematically improved by incorporating it, under general practical conditions.

Findings

Strategies using self-generated HTI outperform those that do not.

Simulation results confirm the theoretical advantage of conditioning on HTI.

Real-world trading evidence supports the effectiveness of the proposed approach.

Abstract

This paper establishes that conditioning the probability of execution of new orders on the self-generated historical trading information (HTI) of a trading strategy is a necessary condition for a statistical trading edge. It is shown, in particular, that, given any trading strategy S that does not use its own HTI, it is always possible to construct a new strategy S* that yields a systematically increasing improvement over S in terms of profit and loss (PnL) by using the self-generated HTI. This holds true under rather general conditions that are frequently met in practice, and it is proven through a decision mechanism specifically designed to formally prove this idea. Simulations and real-world trading evidence are included for validation and illustration, respectively.