Source-linked AI summary
DisclosureBeta: A Measurement-Channel Theory for Regime-Conditioned Betas from LLM-Read Risk Disclosures
Ping Kuen Wong
TL;DR
The paper addresses beta estimation when firms lack trustworthy price histories and prior text-based work lacks identification theory and an explicit error budget. It models LLM features as noisy measurements in a regime-conditioned FF5 framework, proves identification and consistency, derives a matching lower bound, and develops disclosure-incentive and adaptive-blending results. The empirical evaluation is forthcoming, with a frozen panel and design pre-registered before outcomes are read.
Problem
Beta estimation is difficult for S-1 filers, recent listings, and firms just past regime breaks, while prior text-based work lacks identification theory, an error budget, and a lower bound.
Method
The paper models LLM-extracted risk features as noisy measurements of latent characteristics in a piecewise-stationary Fama–French five-factor model with inferred regimes.
Results
The paper proves identification and consistency of regime-conditional loadings, establishes a matching lower bound, and shows disclosure incentives sharpen estimation while adaptive blending is never worse than either estimator.
Takeaways & Limitations
Text-based beta estimation is given a formal measurement-error budget, with precision linked to disclosure incentives and text weighted more when price history is weak or stale.
Takeaways & Limitations
The empirical evaluation is forthcoming; the current preprint records theory and a pre-registered design, and the disclosure-clarity result depends on specified channel assumptions.
Abstract
from arXiv · showhide
The problem is the beta a desk needs when a firm's price history is too short to trust: an S-1 filer, a recent listing, or a name just past a regime break. The state of the art collapses to a comparable-firm peer beta with no error budget, and the recent text-based competitor Breitung (2025) reports strong empirical IPO accuracy but no identification theory, no error budget, and no lower bound. We fill that gap. We model a large language model as a noisy measurement channel on a firm's latent risk characteristics and write its channel noise into the asset-pricing error budget. In a piecewise-stationary Fama-French five-factor model the loadings are a function of latent risk characteristics and an inferred regime. We prove identification and consistency of the regime-conditional loading function under explicit assumptions on the channel, the detector, and within-regime sampling, and give a matching lower bound showing that the disclosure-noise and detector-misclassification terms are unavoidable for any estimator that observes only returns, factors, LLM features, and a regime estimate. A disclosure-incentive corollary makes estimation precision monotone in a firm-level disclosure-incentive measure (DIM). An adaptive convex combination of the text-based and rolling-window estimators is never worse than either component and shifts its weight toward text exactly when price history is short, stale, or straddles a detected regime break. The empirical evaluation on a frozen, pre-registered panel of price-history-thin firms is forthcoming; this preprint records the theory and the pre-registered design so priority is established independently of the empirical outcome.
1 Introduction
The paper addresses beta estimation when return histories are short, stale, or regime-inconsistent by treating LLM-read disclosures as noisy measurements with an explicit error budget. It develops identification theory, unavoidable-error bounds, disclosure-incentive implications, and a never-worse blend with rolling estimates, while reserving empirical evaluation for a pre-registered study.
- Problem: Short, stale, or regime-breaking price histories leave practitioners relying on peer betas and judgement, motivating disclosure-based beta estimation with an explicit measurement-error budget.The target cases include S-1 filers, recent listings, and mature firms entering new regimes.
- Motivation: Corporate disclosures contain systematic-risk information, affect cost of capital through forward-looking beta, and can be read at scale by LLMs.
- Contributions: The paper’s measurement-channel theory identifies regime-conditional factor loadings and decomposes error into sampling error, detector misclassification, and channel noise.
- Contributions: Disclosure noise and detector error are unavoidable for estimators observing only returns, factors, LLM features, and estimated regimes.The matching lower bound establishes that the error budget is tight rather than merely an upper bound.
- Contributions: Estimation precision is monotone in a firm-level disclosure-incentive measure, while a variance-weighted text–rolling blend is never worse than either component.The blend shifts toward text when price history is short, stale, or straddles a detected regime break.
- Empirical program: A frozen, balanced panel of IPO and recent-listing events is pre-registered before outcomes are read; its empirical evaluation is forthcoming.
2 Model
The model links latent firm risk characteristics and market regimes to conditional Fama–French five-factor loadings, while LLM-extracted features observe those characteristics with measurement noise. It also defines DIM and allows the static FF5 model as a special case.
- Model: Returns follow a conditional Fama–French five-factor structure whose loadings depend on latent firm risk characteristics and the market regime.
- Measurement channel: LLM-extracted risk features are observable measurements of latent characteristics, with η_i,t representing measurement noise.
- Disclosure incentives: DIM_i,t is an LLM-scored index of management’s disclosure propensity based on guidance, Q&A responsiveness, and segment granularity.
- Special cases and detection: The static FF5 model is nested when fβ(z, s) ≡ β_i, while regime estimates come from the AdaptiveCMDP detector.
Assumptions
The theory assumes a conditional FF5 structure, regular and ergodic factors, smooth loading functions, an identifiable LLM measurement channel, mixing, within-regime sampling, and a disclosure-clarity noise link. These assumptions are presented as empirically checkable, with attribute-level heterogeneity reported separately.
- Core assumptions: The conditional FF5 structure assumes mean-zero pricing errors conditional on factors, latent characteristics, and regime, with finite conditional variance.
- Core assumptions: Factors are strictly stationary and ergodic with finite fourth moments, and within-regime factor covariance is non-singular.
- Core assumptions: The regime-specific loading function is Lipschitz in latent risk characteristics, or twice continuously differentiable for the second-order rate.
- Measurement and sampling: The LLM channel requires a known or estimable, strictly monotone measurement map, while observations satisfy mixing and within-regime sampling conditions.
- Disclosure channel: The disclosure-clarity channel assumes reader noise is non-increasing in DIM, while risk-feature channels may be heterogeneous by attribute and are reported separately.
- Empirical checks: The noisy-sensor and disclosure-incentive assumptions are empirically checkable through human coding, DIM ensemble disagreement, and per-feature diagnostics.
3 Theorems
The paper develops theory for regime-conditioned beta estimation from noisy LLM-read disclosures, including identification, disclosure-linked error bounds, and an adaptive blend with rolling-window estimates.
- Identification and consistency hold for the regime-conditional loading function under assumptions on the channel, detector, and within-regime sampling.
- As sample sizes grow, the induced conditional pricing errors vanish uniformly under the plug-in estimator’s convergence.
- Disclosure incentives: Theorem 2 makes disclosure-related beta-estimation error non-increasing in disclosure incentives, with strict decreases where channel noise falls strictly.The monotonicity is cleanest for disclosure clarity, while risk-feature ambiguity is attribute-dependent.
- Disclosure incentives: Higher disclosure quality tightens the investor-disagreement component carried by a channel and weakly lowers cross-investor variance when the channel satisfies A7.Channels whose ambiguity reflects newly revealed complexity are measured and reported separately.
- Disclosure incentives: The DIM proposition separates between-firm composition effects from within-firm precision effects, implying disclosure-policy evaluations should compare variation within issuers.Firm-level disclosure incentives can covary positively with realized beta drift because structurally unstable firms disclose more.
- Adaptive combination: The adaptive convex combination is never worse than either rolling or text-based estimation when component errors are conditionally uncorrelated.Its minimum MSE is V M/(V + M), which is no greater than min(V, M). Correlated errors add a bounded cross term.
- Adaptive combination: The blend shifts toward rolling estimates for long-history stable firms and toward text estimates when history is short, volatile, stale, or straddles a detected regime break.The blend’s diagnostic weight incorporates the text estimator’s disclosure and detector error budget.
4 Text-spanned factors: extending the basis (FF5+T)
The paper extends the factor basis with LLM-measured characteristics while treating reading noise as an estimable source of attenuation and estimation error. Ensemble reads reduce idiosyncratic noise, and disclosure quality determines both beta-estimation precision and the detectability of text-factor premia.
- Basis extension: LLM-measured firm characteristics define candidate long–short factors that augment the FF5 basis when per-regime second moments exist.The augmented model replaces the factor vector with (f, g) and preserves the identification results under the stated moment condition.
- Noisy-sort attenuation: Noisy reading attenuates a measured text-factor premium by exactly its score reliability ρ.Poor disclosure can therefore make a genuine factor fail a spanning test, while Proposition 8 permits de-attenuation because it measures reading noise.
- Noisy-sort attenuation: Improving disclosure for channels satisfying (A7) can make previously invisible premia detectable by reducing the disclosure-noise term.The paper presents this as a market-level channel complementing the disclosure-incentive result.
- Worked implication: At K = 3 reads, the DMD factor loses only ≈4% of its premium to reading noise, versus ≈34% for a single-read pipeline.The comparison uses the reported ensemble reliability and the weakest-feature cross-model disagreement as the single-read benchmark.
- Identification limits: The lower bound shows disclosure noise and detector misclassification cannot be removed by changing estimators within the stated observation class.The proof uses a Le Cam two-point argument, yielding unavoidable τ^2 and πT risk-floor terms.
- Measurement channel: Ensemble reads reduce idiosyncratic noise variance to τ^2/K up to a common-bias floor and make the error budget and blend weight estimable per observation.Within-document cross-read variance cancels common reading bias and provides a direct noise diagnostic.
- Measurement channel: The workflow records evidence quotes, rationales, K scores, medians, and dispersion so readings can be audited and re-scored.The paper also argues that disclosure incentives should be measured within issuer because raw DIM and firm-demeaned DIM have opposite cross-firm and theory-consistent signs.
Proof sketches
The paper states that proof sketches for the main theorems and propositions appear inline, while complete proofs and extensions are included in the source module and will be expanded in the full paper.
- Proof sketches: Proof sketches for Theorems 1–7, Corollary 3, Propositions 4 and 8, and Theorem 5 are given inline.Complete proofs, the text-spanned-factor extension, and noisy-sort attenuation theorem are included in the source module.
Pre-registered empirical program (design frozen; outcome forthcoming)
The empirical program targets firms whose price histories are too short to trust using a frozen, pre-registered design. Its outcome is forthcoming, and the paper distinguishes this planned evaluation from concurrent empirical work.
- Design: The study pre-registers a frozen, balanced panel of IPO and recent-listing events before reading outcomes.The registered estimator, comparators, winzone rule, and block-bootstrap confidence-interval analysis are fixed.
- Comparators: The planned evaluation compares the proposed approach with peer beta, Vasicek shrinkage, peer-history shrinkage, and cheap-text benchmarks.The analysis focuses on the population where the theory predicts text should matter most: firms with insufficiently trustworthy price histories.
- Relation to concurrent work: Breitung (2025) reports strong empirical IPO accuracy from aggregated cluster embeddings but does not provide identification theory, an error budget, a lower bound, or a disclosure-incentive channel.The paper presents its own contribution as complementary and does not claim the concurrent empirical accuracy result as its own.