Markets Are Not Random, They Are Hard to Predict: Instrumental Probability, the P–Q Wedge, and the Limits of Learnable Alpha

Battle Count: 73

Highly relevant to quantitative trading as a foundational conceptual framework. The paper directly addresses core questions: why alpha is hard to find, why backtests overfit, why signals decay, how costs and capacity limit strategies, and how to properly evaluate predictive signals. The P-Q wedge formalization, Doob decomposition, capacity constraints, reflexivity, and entropy-based evaluation metrics are directly applicable to strategy development, risk management, and signal evaluation. The falsification protocol provides a rigorous framework for distinguishing genuine alpha from statistical artifacts. However, it is a theoretical essay rather than a practical implementation guide.

The paper is primarily theoretical and does not propose a specific implementable algorithm. However, the concepts it unifies (GARCH modeling, entropy calculations, capacity-aware optimization, multiple-testing corrections, deflated Sharpe ratios) are individually implementable. The falsification protocol in Section 17 could be operationalized with moderate effort. The main complexity lies in the conceptual integration rather than computational implementation. The mathematical machinery (stochastic calculus, measure theory, information theory) requires advanced background but the results are standard.

This is a theoretical/conceptual essay with no empirical implementation or code. It provides a falsifiable empirical protocol (Section 17) but does not execute it. The mathematical derivations (Girsanov theorem, Doob decomposition, entropy calculations) are standard and reproducible from the literature. The illustrative calibration table (Table 1) uses simple closed-form formulas. No dataset, code repository, or computational experiment is provided.