Algometrics: Forecasting Under Algorithmic Feedback

Battle Count: 75

Highly relevant to quantitative trading. The paper directly addresses a fundamental problem in financial ML: models that perform well in backtesting may fail in live deployment because their actions change the market. The non-identifiability result (Theorem 1) warns that passive backtests cannot reveal deployment risk. The ranking inversion result (Theorem 2) explains why historically best signals decay under crowding (e.g., August 2007 quant crisis). The instrumented evaluation result (Theorem 3) provides a path to measuring true deployment risk. The framework directly informs benchmark design, strategy selection, and risk management in algorithmic trading. The paper is complementary to the 'virtue of complexity' literature in financial ML.

The paper is purely theoretical with no implementation required. The mathematical framework involves standard linear algebra, probability theory, and econometric identification arguments. The closed-form examples are trivially implementable (linear models with Gaussian noise). The practical value lies in the conceptual framework and evaluation diagnostics (Table 2) rather than in any specific algorithm to implement. Implementing the suggested diagnostics (crowding curves, impact perturbation, action randomization) would require integration with existing trading infrastructure and market simulators.

The paper is purely theoretical with complete mathematical proofs provided in the appendix. All theorems (non-identifiability, ranking inversion, finite-sample estimation) are proven rigorously. Closed-form illustrations (Figures 1 and 2) are fully specified with parameters. However, there is no code repository or empirical dataset to reproduce. The theoretical results are self-contained and verifiable from the proofs alone.