The Axiomatic Trader: Latent Regularity, Information Budgets, and the Canonical Form of a Quantitative Investment System

Battle Count: 50

This paper is directly and fundamentally about the architecture of quantitative trading systems. It derives from first principles (five axioms) the complete design of a systematic trading pipeline: what to optimize (CVaR 1/Lambda), how to evaluate (contiguous purged blocks), how complex models may be (capacity ceiling), how many strategies may be tested (search budget), how much robustness is affordable (price of the tail), and how large bets may be (fractional Kelly). It unifies and derives from axioms virtually every practice in quantitative finance: purged k-fold, embargo, deflated Sharpe ratio, fractional Kelly, stationarizing transforms, combinatorial purged CV, meta-labeling, and structural break tests. The impossibility theorem (Theorem 5.1) proves that without a recurrence bound, no estimator can guarantee anything. The information budget (Theorem 7.5) provides a single accounting for model capacity, search effort, and representation selection. The paper is essentially a theory of what a correct quantitative trading system must look like, derived from the minimal assumptions about market behavior.

The theoretical framework is extremely dense, requiring understanding of: axiomatic systems, PAC-Bayes bounds under dependence, CVaR duality (Rockafellar-Uryasev), density-ratio sensitivity models, beta-mixing processes, Fano's inequality, McDiarmid's inequality, Berbee's coupling lemma, information-theoretic generalization bounds, Kelly criterion with shrinkage, and regime-switching models. The five-stage canonical form requires: declaring five constants before seeing data (Lambda, epsilon_0, coherence times, rho, kappa), computing effective sample sizes with regime-dependent charges, implementing contiguous purged block evaluation with CVaR aggregation, maintaining an explicit search budget in nats, and sizing positions with robust fractional Kelly. The budget computation (Section 11) requires converting model complexity to effective degrees of freedom, tracking search size N, and computing c(Lambda) from block scores. The framework is conceptually complete but practically demanding: many constants are declared rather than estimated, and the paper itself shows (Experiment 5) that a real configuration may fail to produce any position.

The paper states all experiments run as committed scripts with fixed seeds, outputs in RESULTS.txt, and designs in module docstrings. Seven experiments on real market series are described with full panel-by-panel narratives. The French Data Library (CRSP) is referenced for cross-sectional data. However, the theoretical framework requires declaring constants (Lambda, epsilon_0, coherence times, rho, kappa) that are not estimable, making exact reproduction of the axiomatic declarations dependent on researcher judgment. The rule libraries were written once and not tuned. Earlier Monte Carlo audits were retired.