APEX Methodology

0. System overview

APEX is organised as a pipeline where one online posterior over the current market regime feeds several downstream decisions simultaneously — factor weighting, covariance shaping, prediction-interval width, and confidence scaling. The same posterior powers all of them, so the outputs are coherent rather than independently averaged.

Twelve academic factor families are composed into a per-ticker 0–100 score. A confluence engine then applies literature-backed multi-factor pattern overrides (e.g. Sloan + gross-margin crack; Asquith short-squeeze setup). Every override carries a published effect size and is conditionally fired only when the participating factors show genuine joint tail-dependence — not merely high average correlation.

The engine is Bayesian end-to-end: priors come from the literature, posteriors update from live residuals (once forward returns accumulate), and uncertainty is reported alongside every point estimate as a conformal interval.

1. Twelve factor families

Each factor returns a 0–100 score per ticker per day; higher is more bullish. Factor scorers are self-normalising against the live universe so a 70 means "top-quintile today", not against a stale literature baseline.

Twelve factors is a headline number; the effective breadth after removing redundancy is lower. We report that explicitly — the composite optimiser penalises correlated signals rather than double-counting them.

2. Tail-dependence layer

Linear correlation describes average co-movement; in crises what matters is what factors do together specifically in the tails. A Gaussian copula with ρ = 0.5 has zero tail-dependence; a Student-t copula at the same ρ has meaningful joint-crash probability. We estimate lower- and upper-tail dependence non-parametrically for every factor pair, per regime, and shrink toward an independence prior so thin-sample pairs do not dominate.

The Confluence Engine uses this directly: a pattern's confidence is amplified when its participating factors also show genuine tail-alignment in history, and damped when the alignment is weak. This prevents "textbook pattern, no real co-movement" overrides.

Method: Schmidt & Stadtmüller 2006; Frahm, Junker & Schmidt 2005; Embrechts, McNeil & Straumann 2002.

3. Regime-aware risk model

Standard mean-variance (Markowitz) optimisation solves for weights that minimise factor-score variance for a given information-coefficient vector. Using Spearman ρ as the covariance input under-estimates correlated crash risk — exactly the risk that matters for sizing. APEX blends the correlation matrix with the tail-dependence matrix, with the blend weight determined by the current regime posterior: crash-dominated in risk-off, squeeze-dominated in risk-on, unbiased in calm regimes.

A Tikhonov ridge auto-tunes to guarantee positive-definiteness even when the empirical tail-dependence matrix is near-singular on thin samples. The same regime posterior that decides the blend also supplies the factor weights themselves — one posterior, two coherent uses.

Method: Grinold & Kahn 1999; Embrechts, McNeil & Straumann 2002; Higham 2002 on nearest-correlation projection.

4. Online regime detection

Hidden Markov Models give discrete regime labels that flip abruptly. APEX uses a Bayesian online changepoint detector that maintains a full posterior over how long the current regime has been running. From the run-length posterior we derive a probability vector across three market regimes — risk-on, transition, risk-off — so the engine is honest about uncertainty near turning points rather than forcing a binary decision.

Fresh regime (low expected run-length) ⇒ the engine admits ignorance and leans on transition priors. Mature regime ⇒ directional bias takes over. The same posterior powers factor-weight blending, covariance blending, interval width, and dynamic exposure updates (sections 3, 5, 6). One posterior, four coherent decisions.

Method: Adams & MacKay 2007; Hamilton 1989 for baseline hazard rate.

5. Bin-conditional prediction intervals

Marginal conformal intervals guarantee coverage on AVERAGE across the universe — over-covering easy tickers and under-covering hard ones. APEX uses a bin-conditional (Mondrian) variant that partitions tickers by tail-alignment strength and regime, then calibrates one width per partition. The result: the stated 90% interval is close to 90% inside each bin, not only on average.

Until enough forward-return observations accumulate per partition, APEX falls back to a marginal interval inflated by average tail-dependence. This is the single place where the engine publicly admits the difference between "calibrated" and "prior" — every ticker page shows it.

Method: Vovk, Lindsay, Mammen & Vovk 2003 (Mondrian Confidence Machine); Angelopoulos & Bates 2021 for introduction.

6. Dynamic factor exposures

Static factor weights lag regime shifts. APEX tracks factor exposures as a Kalman dynamic linear model where the per-state random walk is accelerated on days the regime detector signals a change-point. Process noise is driven directly by the change-point posterior, so exposures pivot fastest on precisely the days they need to — again the same posterior powering yet another decision.

The DLM output is blended with the regime-aware Markowitz solution. Early in calibration the blend leans on Markowitz priors; as the DLM accumulates observations it takes over. Both are reported; the blend is transparent.

Method: Kalman 1960; West & Harrison 1986, 1997 on Bayesian forecasting and dynamic models.

7. Factor attribution

When the Confluence Engine overrides the linear composite (e.g. a value-trap pattern pulls a superficially-cheap ticker down), which factor deserves the credit? The naïve linear answer is misleading — overrides fire only under joint conditions, so part of each factor's contribution comes from its role in enabling the pattern, not from its standalone score.

APEX uses a Shapley decomposition of the score attributable to each factor. Every contribution splits cleanly into a linear share (the coefficient-style piece) and an interaction share (the pattern-enabling non-linearity). The four uniqueness axioms guarantee a consistent story across tickers. Per-ticker attribution is available in the authenticated research API.

Method: Shapley 1953; Štrumbelj & Kononenko 2014 for ML interpretability.

References