Opening-Price Shortcut in Stock Prediction: A Conditional Opening Prior-and-Evidence Framework

1 Introduction

• The target-day opening price is the first concentrated realization of overnight information and is naturally correlated with the eventual adjusted-close direction.The supplied passage also notes that it is already observable at market open.Source: §1 · p. 1
• The opening-price shortcut is copying the opening direction to predict closing direction; naively adding opening features can raise apparent accuracy without better historical-state understanding.Underpowered models such as LSTM may fail to exploit the shortcut and remain at chance-level accuracy.Source: §1 · p. 2
• COPE formalizes the shortcut risk with SDR, the share of predictions matching opening direction, and ρ, which measures that agreement relative to above-chance accuracy gains.These metrics distinguish genuine predictive improvement from opening-direction copying.Source: §1 · p. 2
• COPE reparameterizes closing-direction prediction as continuation/reversal discrimination conditioned on the opening state, then judges whether current trading evidence corrects the opening move.It extracts residual evidence relative to the opening-conditioned prior and recovers the closing direction from the opening condition and reversal prediction.Source: §1 · p. 2
• The paper presents the opening-price shortcut as a measurable, reproducible risk in closing-direction prediction and proposes compatible diagnostic metrics.The introduction positions this as a first direct analysis of the risk under the target-day opening state.Source: §1 · p. 2
• COPE is evaluated on four real-market datasets for predictive performance, shortcut suppression, and trading application value, with reported significant advantages.The introduction identifies these as the evaluation aims, without giving specific result values.Source: §1 · p. 3

2.1 Unimodal Price-Sequence Prediction

• Unimodal price-sequence methods use recurrent networks, attention, and other sequence or structural modules, but generally treat OHLCV inputs homogeneously rather than modeling their microstructural roles.Examples include ALSTM [21], Adv-ALSTM [7], DTML, and StockMixer.Source: §2.1 · p. 3

2.2 Multimodal and Relation-Enhanced Stock Prediction

• Multimodal and relation-enhanced methods add news, social media, announcements, earnings, cross-stock relations, or language-model features; this paper returns to price data to study opening-state evidence.The related work describes these additions as expanding cross-stock and cross-modal modeling capacity.Source: §2.2 · p. 3

2.3 Overnight Information and Opening-State Modeling

• Prior overnight and opening-state studies treat opening information as a signal to predict or exploit, but do not analyze the opening-price shortcut as a measurable model-degradation risk.Examples include overnight-return and price-discovery research, opening-state modeling, and timezone-based spillover work.Source: §2.3 · p. 3

3 Problem Definition

• Each stock-day sample uses a historical-window observation limited to price features available before the previous day's close, alongside the target-day opening state in raw-price terms.The target-day opening direction is defined by comparing its raw opening price with the previous day's raw closing price.Source: §3 · p. 3
• The task predicts the direction of the target-day adjusted close conditioned on the historical window and the observable target-day opening state.The figure caption describes the framework's final output as the adjusted-close direction recovered from opening condition and reversal discrimination.Source: §3 · p. 4, Figure 2 · p. 4

4.1 Conditional Reparameterization under the Opening State

• COPE predicts continuation or reversal conditioned on the observed opening state, then recovers the final direction without changing the label information.The opening condition supplies the background, while the evidence helps judge whether the opening move continues or reverses.Source: §4.1 · p. 4

4.2 Structured Evidence Decomposition

• The model separates the opening condition from historical evidence about an individual stock and contextual support or divergence from the opening move.The opening representation includes direction and standardized gap strength; historical features include prior return, amplitude, relative volume, and historical-window reversal frequency.Source: §4.2 · pp. 4–5

4.3 Conditional Latent Residual Modeling

• A latent variable T aggregates posterior corrections from historical and contextual evidence under the opening condition, approximated with a variational posterior.The opening-conditioned prior represents the latent decision center from the opening state alone, while the posterior captures sample-level correction from structured evidence.Source: §4.3 · p. 5

4.4 Reliability-Gated Evidence Tokens

• The model estimates each historical or contextual evidence group's reliability from summary statistics and gates its token before conditional attention aggregation.The statistics include nonzero ratio, mean absolute magnitude, standard deviation, and evidence dimensionality.Source: §4.4 · p. 5

4.5 K-conditioned residual attention

• K-conditioned residual attention uses the opening condition to shape evidence-group interactions and residualizes transmitted values against that condition.The resulting representations are aggregated to produce the variational posterior parameters.Source: §4.5 · p. 6

4.6 Training Objective and Inference

• Training samples a residual state for reversal discrimination, subtracts an opening-conditioned baseline tendency, and optimizes a KL-plus-BCE objective; inference uses the posterior mean.The KL term keeps the residual state close to the opening-conditioned prior; free bits address early KL collapse, and reversal class weights mitigate scarce reversal samples.Source: §4.6 · p. 6

5.1 Experimental Setup

• Experiments use four datasets and five random seeds under a unified split, label definition, and sample-filtering protocol.ACC and MCC are the primary metrics; shortcut analyses use SDR and ρ.Source: §5.1 · p. 7

5.2 Main Results

• COPE achieves the best ACC and MCC across all four datasets, with stable cross-market predictive capability.The comparison includes unimodal price models and multimodal or relation-modeling methods; the concurrent MCC improvement indicates more reliable directional discrimination rather than class bias.Source: §5.2 · p. 8

5.3 Ablation Study

• Removing contextual support causes the largest ACC degradation, while removing the conditional prior, reliability gating, or K-conditioned residual attention generally increases ρ.The direct-opening-input variant can achieve moderate ACC on some datasets but has much stronger shortcut dependence.Source: §5.3 · p. 8, Table 2 · p. 8

5.4 Shortcut-Sensitivity Analysis

• Across four datasets, COPE maintains the highest ACC while keeping ρ substantially lower than direct-opening-input models.LSTM+Opening remains near chance on several datasets, so a low SDR alone does not establish robustness.Source: §5.4 · pp. 8–9, Table 3 · p. 8

5.5 Attention Visualization

• Correct reversal predictions emphasize the H → C cross-evidence path, while correct continuation predictions emphasize H → H historical self-attention; incorrect predictions are more dispersed.The visualization analyzes high-confidence correct and incorrect predictions in the ACL18 test set, partitioned by (K, R).Source: §5.5 · p. 9, Figure 3 · p. 9

5.6 Simulated Investment and Backtesting

• In the low-open reversal backtest, COPE outperforms History-only in annualized return, Sharpe ratio, and maximum drawdown.The strategy retains low-open stocks after the open, ranks them by reversal confidence, and holds them to the close.Source: §5.6 · p. 9

6 Conclusion

• COPE formalizes the opening-price shortcut as a measurable risk and models closing direction through continuation/reversal discrimination conditioned on the observed opening state.It models residual evidence relative to the opening-conditioned prior, using reliability gating, K-conditioned residual attention, and a conditional information bottleneck.Source: §6 · p. 9
• Across four datasets, COPE consistently improves predictive performance, suppresses opening-direction copying, and shows application value in opening-decision backtests.The low-open reversal long-only backtest reports annualized return, Sharpe ratio, and maximum drawdown.Source: §6 · p. 9, Table 4 · p. 9

A.1 Label Equivalence of Conditional Reversal Reparameterization

• Defining R = Y ⊕ K makes recovery exact: K ⊕ R = Y, so predicting reversal and recovering direction preserves the original label.This is the label-equivalence argument for conditional reversal reparameterization.Source: §A.1 · p. 10

A.2 Conditional Distribution Equivalence

• The conditional distribution of Y given X and K equals that of R = Y ⊕ K given X and K, so reversal likelihood changes parameterization, not the prediction target.The target remains closing direction.Source: §A.2 · p. 10

A.3 Shortcut Risk of Directly Inputting the Opening Direction

• When P(Y = K) > 0.5, predicting K achieves accuracy P(Y = K), allowing a low-complexity opening-direction shortcut to deliver strong surface performance.Such reliance can reduce use of evidence that distinguishes continuation from reversal.Source: §A.3 · p. 10

A.4 Validity of SDR and ρ

• SDR measures prediction agreement with the opening direction, while ρ compares above-chance opening agreement with above-chance accuracy and should be read alongside ACC and MCC.A higher ρ indicates stronger association between above-chance performance and opening-direction copying.Source: §A.4 · p. 10

B Baseline Details

• Baselines cover historical-price models and multimodal or relation-modeling methods, while direct-opening variants diagnose whether adding opening features induces direction copying.All baselines are re-reported under a unified split, label definition, and sample-filtering protocol.Source: B Baseline Details · p. 10

C Metric Definitions

• ACC measures overall accuracy; MCC uses all four confusion-matrix entries and is more suitable for binary classification with imbalanced classes.ACC/MCC evaluate direction prediction, whereas SDR/ρ diagnose reliance on opening-direction copying.Source: C Metric Definitions · pp. 10–11

D Dataset Details

• Four public datasets—ACL18, CMIN-US, CMIN-CN, and KDD17—cover market environments including the US and China.Data are split chronologically into training, validation, and test sets; the target is adjusted-close direction relative to the previous day’s adjusted close.Source: D Dataset Details · p. 11
• Samples are excluded when the previous close is missing or the absolute adjusted-close change is below 0.003; standardization uses training-set statistics only.The target-day opening direction is based on raw opening price relative to the previous day’s raw close.Source: D Dataset Details · p. 11

• Main comparison results report means and standard deviations over 5 random seeds.Source: E Implementation Details · p. 11
• Continuous features are standardized with training-set statistics, and the same transformation is applied during validation and testing.Source: E Implementation Details · p. 11
• Training jointly optimizes binary cross-entropy and the conditional information bottleneck term, with reversal class weights, free bits, and supervised warmup addressing imbalance and early KL strength.Source: E Implementation Details · p. 11
• Checkpoint selection uses a composite validation score with Abal = min(Acont, Arev), solely for model selection and not as a method objective or test-set evaluation measure.Source: E Implementation Details · p. 11

F Investment Simulation Protocol

• The simulation tests economic consistency rather than constructing a complete trading system, and reports only the low-open reversal protocol because it aligns the prediction, candidate pool, and return calculation.Source: F Investment Simulation Protocol · pp. 11–12
• On each test day, methods rank low-open stocks; COPE uses reversal probability and History-only uses historical features, selecting the top 20% equally weighted and liquidating at the close.Source: F Investment Simulation Protocol · p. 11
• COPE and History-only share the pool, dates, candidate set, transaction cost, and portfolio rule; selection and standardization use training/validation data, while closing prices only determine realized returns.Source: F Investment Simulation Protocol · pp. 11–12

G Societal Impact

• The backtest omits slippage, liquidity constraints, market impact, and capacity limits, so it is a signal-consistency test rather than a deployable strategy; the authors frame the method as predictive modeling, not investment advice.Source: F Investment Simulation Protocol · p. 12, G Societal Impact · p. 12

• The study focuses on price-data microstructure rather than multimodal features; adding news or other overnight information would require fine-grained timestamps and strict control of information availability.Source: H Limitations · p. 12
• Evaluation is limited to daily-frequency direction prediction and historical backtests, whose returns should not be read as executable because real trading also faces slippage, market impact, liquidity, regulation, capacity, and risk-management constraints.Source: H Limitations · p. 12