📈 economics

Historical-Memory Equity Selection: A Comparative Study of Retrieval, Neural Prediction, and Adaptive Mixing

This study evaluates a memory-centered framework for intermediate-horizon equity selection across six markets and finds that while the approach makes retrieval decomposable, similarity-based memory selection fails to outperform random precedents or historical benchmarks, ultimately showing no statistically significant improvement in portfolio performance compared to passive strategies.

Original authors: Rohil Gujarathi, Sangeeta Oswal, Vaibhav Goyal, Anjali Yeole

Published 2026-09-23

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Rohil Gujarathi, Sangeeta Oswal, Vaibhav Goyal, Anjali Yeole

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Investing in the stock market often feels like trying to predict the weather while standing in the middle of a storm. Investors look at past patterns, hoping that history will repeat itself, but the financial world is messy. Prices move in complex ways, influenced by global events, human emotion, and sudden shifts in how people feel about risk. For decades, financial experts have tried to build better tools to navigate this chaos. One promising idea has been to use powerful computer programs, specifically those designed to understand long sequences of data, to spot patterns that humans might miss. Another idea is to create a "memory" for these computers—a way to look back at specific past moments that look similar to today and see what happened next. The hope is that by combining these modern tools with a clear, inspectable record of past decisions, we can make smarter choices about which stocks to buy and hold for a few months.

A team of researchers set out to test whether this combination of advanced computer models and a strict historical memory actually works better than simpler, traditional methods. They built a system that could look at thousands of stocks across six different countries, including the United States, India, and the United Kingdom, over a six-year period from 2020 to 2025. Their goal was to see if a computer could pick a group of stocks that would grow in value better than a random selection or a basic strategy of buying everything equally. To do this, they created a framework where the computer could either make a prediction based on its own learning, look up twenty-five past examples that looked similar to the current situation, or mix the two approaches together. Crucially, they designed the "memory" part so that every single decision could be traced back to specific past records, making the process transparent and easy to check.

The researchers ran their system through a rigorous simulation involving more than one hundred stocks and over four million policy predictions. They compared sixteen different strategies, ranging from simple momentum rules to complex neural networks and their new memory-based system. They measured success not just by how well the computer guessed the future, but by how much money a portfolio would have actually made after accounting for trading costs and risks. The results were surprising and somewhat humbling. The strategy that performed the best was not the high-tech memory system, nor the advanced neural network. Instead, the simplest approach won: a passive strategy of buying an equal amount of every stock and holding them. This simple method achieved a higher return and a better risk-adjusted score than any of the complex models.

The specific memory system the researchers built, which tried to find the best past examples to guide future choices, actually performed worse than expected. It earned a lower return than a system that simply picked past examples at random. It also failed to beat a basic strategy that just used the average return of the entire market as a guide. The researchers found that the computer's attempt to find "similar" past situations did not lead to better investment decisions. In fact, every time they compared the memory system to a simpler control group, the memory system came out ahead in the wrong direction, showing a negative difference in performance. Even when they tried to let the computer decide when to use the memory and when to use its own predictions, the result was no better than just sticking with the simpler methods.

This study does not prove that computers cannot help with investing, but it does show that simply adding a historical memory or using complex pattern-matching tools does not automatically make a strategy more profitable. The researchers emphasized that while their system made the decision-making process very clear and easy to audit—allowing anyone to see exactly which past records were used to make a choice—this transparency did not translate into extra money. The "similar" past situations the computer found were not actually good predictors of what would happen next. The study suggests that the financial markets may be too complex or too changeable for these specific types of historical analogies to work, at least over the six-year period they tested.

Ultimately, the work serves as a careful check on the excitement surrounding artificial intelligence in finance. It demonstrates that having a tool that can look back at history and explain its reasoning is valuable for understanding how a model works, but it does not guarantee that the model will be right. The researchers concluded that their specific method of selecting stocks based on similar past records did not add any value compared to doing nothing special at all. For investors and developers alike, the lesson is that finding a pattern in the past is not the same as finding a path to future profit, and sometimes the simplest approach remains the most effective.

Technical Summary: Historical-Memory Equity Selection

1. Problem Statement

The study addresses two primary challenges in financial machine learning:

Intermediate-Horizon Forecasting: Can modern sequence models, specifically those capable of representing long contexts (e.g., Transformers), effectively support equity selection decisions held for intermediate periods (specifically 63 exchange sessions), rather than just high-frequency or very short-term horizons?
Inspectability of Decision Logic: Can a bounded, task-specific numerical memory be constructed to make the basis of a forecast inspectable and auditable without relying on open-ended language models or retrieval-augmented generation (RAG) layers?

The authors note that while sequence models have advanced, financial forecasting is complicated by slow outcome realization, regime changes, and the fact that forecast accuracy does not necessarily translate to profitable portfolio selection after accounting for trading costs and path-dependent exits.

2. Methodology

Data and Universe

Universe: A panel of 103 liquid equities across six markets (US, India, China, Brazil, France, UK), selected from 108 candidates based on continuity and venue criteria. The panel is survivorship-conditioned.
Timeframe: The evaluation spans six continuous years (2020–2025) using six annual walk-forward folds.
Features: 23 technical price-volume features (returns, momentum, volatility, volume, moving averages, drawdown, price location).
Input Representation: A "pooled-window" system constructs 42 non-overlapping six-session means from the 252-day lagged window, resulting in a 966-dimensional vector ( $42 \times 23$ ). This removes intra-patch daily order.
Target: A 63-session forward return ( $r_{63}$ ) calculated on model-adjusted prices (split/dividend adjusted), serving as a forecasting label and ranking proxy.

Framework Components

The study implements a framework where forecasts are constructed from eligible historical records, their completed returns, and an explicit aggregation rule. The memory operates alongside or independently of neural predictors.

Historical Memory (Similarity Retrieval):
- Eligibility: Records must have a completed 126-session outcome window. Exact same-ticker matches are excluded. Selected precedents from the same ticker must be at least 21 sessions apart, with a cap of three per ticker.
- Retrieval: For a query, the system selects $k=25$ precedents based on Euclidean distance between standardized pooled feature windows.
- Aggregation: The forecast is the arithmetic mean of the 25 selected precedents' 63-session returns.
- Auditability: The process is fully decomposable into eligibility checks, selected IDs, distances, and returns, providing a "citation-like" audit trail.
Neural Predictors:
- Temporal Transformer: Accepts the (42, 23) pooled windows, projects patches to width 64, and uses two encoder layers (4 heads, feed-forward width 128) with attention pooling and a scalar head.
- MLP: Consumes the flattened 966-dimensional vector through layers (966 → 64 → 128 → 1) with LayerNorm and GELU activations.
- Both use deterministic checkpoints (seeds 7, 17, 37).
Mixing and Gating:
- Fixed Mixtures: Linear combinations of the neural forecast ( $\hat{r}_{base}$ ) and memory forecast ( $\hat{r}_{mem}$ ) using a coefficient $\lambda$ selected via grid search (MSE or Sharpe objectives) on development data.
- Adaptive Gates: A logistic gate ( $g = \text{sigmoid}(a^T z + b)$ ) dynamically weights the two forecasts based on magnitude and disagreement diagnostics ( $| \hat{r}_{base} |$ , $| \hat{r}_{base} - \hat{r}_{mem} |$ , $| \hat{r}_{mem} |$ ).
Portfolio Execution:
- Allocation: Scores are volatility-scaled ( $S = \hat{r} / (v_{21} + 10^{-4})$ ).
- Constraints: Long-only, maximum three positions per account, executed at the next open.
- Exit Rules: Trailing stop (Chandelier style) based on ATR, with a 63-session holding ceiling.
- Costs: 10 bps commission + 5 bps modeled slippage per side.

Controls and Baselines

The study compares 16 policies, including:

Memory Controls: Random eligible retrieval, unconditional historical mean (historical prior), and plain KNN (without the 3-per-ticker/21-session constraints).
Neural Controls: Direct MLP, Direct Transformer, and their mixtures/gates.
Financial Benchmarks: 21-session momentum, volatility-scaled momentum, and passive equal-weight buy-and-hold.

3. Key Results

Performance Metrics (2020–2025)

The primary metric is the mean-market Sharpe ratio, calculated across 204 continuous market/run accounts.

Passive Equal Weight: Achieved the highest mean-market Sharpe (0.636) and annualized return (11.91%).
Neural Baselines: Annual Ridge regression followed with a Sharpe of 0.444. Direct MLP and Transformer models ranged between 0.274 and 0.383.
Memory Performance:
- Similarity Memory (Retrieval): Sharpe of 0.245 and annualized return of 2.99%.
- Comparison: Similarity memory underperformed Random Memory (Sharpe 0.423) and the Historical Prior (Sharpe 0.352).
- Statistical Significance: All six primary contrasts comparing similarity memory against controls (Random, Prior, KNN, Ridge, MLP, Transformer) yielded negative point estimates. After Holm adjustment, none of the differences were statistically significant at the 5% level (Holm-adjusted p-values ranged from 0.7487 to 1.0000).

Specific Findings

No Incremental Value: The implemented similarity selection rule did not add portfolio value over simpler alternatives (random retrieval, historical mean) or neural baselines.
Gate vs. Mixture: Adaptive gating did not statistically outperform fixed Sharpe-selected mixtures.
Market Heterogeneity: Similarity memory showed positive Sharpe ratios in Brazil, India, UK, and US, but negative ratios in China and France. However, these were not benchmark wins.
Reversal of Evidence: The results contradicted earlier single-year (2024) development evidence, where memory-based approaches had shown promise. The authors attribute this reversal to factors like broader regime coverage, the pooled representation, or the Euclidean distance metric, though no single cause was isolated.

4. Contributions and Significance

Primary Contributions

Specified Interface: The paper defines a rigorous interface between memory construction, neighbor selection, forecast aggregation, and portfolio execution. This allows the retrieval mechanism to be audited separately from the neural predictor.
Matched Comparison: It provides a matched comparison of 16 policies with paired inference for the same mean-market Sharpe statistic, controlling for the eligible information set.
Inspectability: The framework demonstrates that a bounded numerical memory can make the retrieval calculation decomposable and reviewable at the case level without requiring a language model.

Modest Claims and Limitations

The authors explicitly state that:

The study does not claim that the memory layer guarantees reliability, correctness, or regulatory compliance.
The results represent negative evidence regarding the specific implemented similarity rule (Euclidean distance on pooled technical features) rather than a general rejection of historical memory concepts.
The evaluation period (2020–2025) was inspected during development, and the universe is survivorship-conditioned; thus, the results are research simulations with data-vintage and corporate-action limitations.
The framework makes the retrieval contribution identifiable, but the multi-year evidence does not show that similarity selection improves portfolio performance in this specific configuration.

Conclusion

The central lesson is that an inspectable memory mechanism and a profitable similarity signal are distinct achievements. While the framework successfully links historical evidence to forecasts in a transparent way, the current multi-year results provide no incremental portfolio advantage for the implemented analogue rule or adaptive gates over passive equal-weight or simple neural baselines. Future work should focus on testing alternative state representations and distance measures under the same matched-control design.