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arxiv: 2606.09420 · v1 · pith:MAXC2WF3new · submitted 2026-06-08 · 🧮 math.OC · q-fin.PM

Benchmarking Deep Time Series Models for Equity Portfolios

Aoxin Zhang , Yuhan Cheng , Kwanting Leung This is my paper

Pith reviewed 2026-06-27 15:37 UTC · model grok-4.3

classification 🧮 math.OC q-fin.PM
keywords time series forecastingequity portfoliosbenchmarkingdeep learningstochastic multi-criteria analysisportfolio optimizationtransaction costsforecasting architectures
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The pith

No single time-series architecture dominates daily equity portfolio benchmarks after costs and constraints apply.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper constructs a CRSP daily-stock benchmark covering 15 deep and statistical time-series models from 2018 to 2024. It evaluates models through common-window decile portfolios followed by stochastic multi-criteria acceptability analysis and a constrained quadratic portfolio layer that enforces capacity, beta, industry, risk, leverage, and turnover limits. An entropic acceptability index derived from the SMAA prior downweights models that produce high portfolio regret. Results show no model exceeds a 0.36 rank-1 acceptability score, with TransEnc-8 highest at 0.352, while rankings shift across preferences, market states, features, and transaction costs. Constrained portfolios produce negative net Sharpe ratios at 20 basis points for every promoted model.

Core claim

Benchmarking forecasting architectures for daily equity portfolios is not just a prediction exercise. It also asks which model remains usable after preferences, costs, and portfolio constraints are imposed. We build a CRSP daily-stock benchmark for 15 deep and statistical time-series architectures over 2018--2024. The protocol combines common-window decile portfolios, stochastic multi-criteria acceptability analysis, a deployment-adjusted acceptability index defined as an entropic update from the SMAA prior, and a constrained quadratic portfolio layer with capacity, beta, industry, risk, leverage, and turnover controls. Empirically, no architecture dominates the raw benchmark: TransEnc-8 has

What carries the argument

The deployment-adjusted acceptability index as an entropic update from the SMAA prior, applied to decile portfolios before constrained quadratic optimization with capacity, beta, industry, risk, leverage, and turnover controls.

If this is right

  • Model rankings change with investor preferences, market state, feature universe, and transaction costs.
  • TransEnc-8 is selected in the five-model constrained-portfolio comparison under the full protocol.
  • Raw return-oriented rankings can instead favor TS-RIDGE.
  • Broad-universe decile signals survive costs in some configurations.
  • Net Sharpe ratios after 20 bps costs are negative for all models in the baseline constrained QP.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Model selection for portfolios should incorporate full construction pipelines rather than isolated accuracy metrics.
  • The entropic index could be tested on other multi-criteria problems such as credit or macro forecasting.
  • Extending the protocol to intraday data or international equities would reveal whether the no-dominance result holds outside daily U.S. stocks.

Load-bearing premise

The protocol of common-window decile portfolios, SMAA, entropic acceptability index, and constrained QP with the listed controls is sufficient to determine which models remain usable after preferences, costs, and constraints are imposed.

What would settle it

Finding one architecture that produces positive net Sharpe ratios in the constrained QP across multiple preference weightings and cost levels would show dominance where the paper reports none.

Figures

Figures reproduced from arXiv: 2606.09420 by Aoxin Zhang, Kwanting Leung, Yuhan Cheng.

Figure 1
Figure 1. Figure 1: Equal-weighted and value-weighted Sharpe ratios for the fifteen retained models [PITH_FULL_IMAGE:figures/full_fig_p011_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: SMAA rank acceptability over 15 models and 15 possible ranks. The full rank distribution in [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: SMAA top-3 acceptability probabilities. Top-3 acceptability concentrates around the lower-turnover transformer-encoder and recurrent configurations ( [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Rank-1 SMAA acceptability bands for the leading models. gross sharpe net20 sharpe vw sharpe abs ff5 alpha t minus turnover minus max drawdown bootstrap significance TS-RIDGE SMAA Central Weight Vectors 0.0 0.2 0.4 0.6 0.8 1.0 Weight LSTM TransEnc-8 [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Central SMAA weight vectors for selected leading models [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: SMAA preference-space geometry and turnover-weight acceptability frontier [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Ranking sensitivity across transaction cost levels. bps; as the cost schedule tightens, cost-sensitive preferences move acceptability toward architectures whose rankings rotate more slowly [PITH_FULL_IMAGE:figures/full_fig_p016_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: SMAA rank acceptability by market-volatility state [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Robust net Sharpe under ellipsoidal score ambiguity [PITH_FULL_IMAGE:figures/full_fig_p018_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Net Sharpe ratios under wider constrained-portfolio designs [PITH_FULL_IMAGE:figures/full_fig_p019_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Predict-then-optimize rank association between raw SMAA expected ranks and constrained-QP ranks across transaction cost levels [PITH_FULL_IMAGE:figures/full_fig_p020_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Deployment regret in net Sharpe units under constrained-portfolio designs. 20 [PITH_FULL_IMAGE:figures/full_fig_p020_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Raw 15-model decile SMAA, restricted to promoted models, and optimized five-model portfolio SMAA [PITH_FULL_IMAGE:figures/full_fig_p021_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Raw and deployment-adjusted rank-1 acceptability for promoted models. rows use the same full-universe forecast files as the confirmatory headline benchmark, so the shared F3 cells match [PITH_FULL_IMAGE:figures/full_fig_p022_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: TS-RIDGE regularization path across nested feature universes. that information becomes valuable only when coefficient discipline prevents overreaction to unstable high-dimensional variation. 0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 Average absolute coefficient mktcap_log rev_5 mom_5 ret_l1 mom_21 rsi_14 ret_l2 gap_open log_dollar_vol spread_hilo range_1 ma_21_ratio ma_5_ratio excess_sp_l1 excess_ew… view at source ↗
Figure 16
Figure 16. Figure 16: Average absolute TS-RIDGE coefficient by feature [PITH_FULL_IMAGE:figures/full_fig_p023_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Feature-block ablation heatmap for the five promoted models under the common forecast protocol. The feature-block ablation reinforces the same mechanism. Because F2 is F3 without the size, beta, and market-relative block, removing the price block weakens the nonlinear price-path channel and removing activity variables tests whether trading intensity carries the ranking. Restoring the full structured stack… view at source ↗
Figure 18
Figure 18. Figure 18: Average daily cross-sectional Spearman rank correlations among retained model prediction signals. RIDGE long–short. TS-RIDGE supplies the stable full-signal linear anchor, and LSTM supplies the price-sensitive nonlinear contrast [PITH_FULL_IMAGE:figures/full_fig_p025_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Promoted-set pairwise rolling-combination net Sharpe matrix. 9 Deployment Boundaries Daily stock sorting draws strength from universe breadth, so restricting capacity changes the ranking [PITH_FULL_IMAGE:figures/full_fig_p026_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Capacity frontier for promoted models [PITH_FULL_IMAGE:figures/full_fig_p027_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: Breakeven transaction-cost diagnostics for promoted models. Curves report net Sharpe under one-way cost schedules for the broad decile layer and the baseline constrained-QP layer; vertical reference lines mark 0.8, 20, and 50 bps [PITH_FULL_IMAGE:figures/full_fig_p027_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: Design sensitivity and aggregate prediction boundary. The aggregate boundary test is sharper than the state comparison. None of the market-plus￾signal specifications produces positive aggregate out-of-sample R2 , so strong stock-level sorting does not automatically become market-timing ability. Adjacent forecasting targets impose different con￾straints once the target, aggregation level, and portfolio rul… view at source ↗
Figure 23
Figure 23. Figure 23: F3 neural-model decile-return profiles used to audit the negative RankIC and positive long–short Sharpe cases. 2021-01 2021-07 2022-01 2022-07 2023-01 2023-07 2024-01 2024-07 2025-01 Date 0.2 0.0 0.2 0.4 0.6 0.8 1.0 Cumulative D10-D1 F3 LSTM long-short cumulative (a) LSTM 2021-01 2021-07 2022-01 2022-07 2023-01 2023-07 2024-01 2024-07 2025-01 Date 0.4 0.2 0.0 0.2 0.4 Cumulative D10-D1 F3 TransEnc-8 long-s… view at source ↗
Figure 24
Figure 24. Figure 24: F3 cumulative long–short returns under the same score direction as the RankIC calculation. non-monotonicity effect rather than a long–short direction or label convention error. 36 [PITH_FULL_IMAGE:figures/full_fig_p036_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: SMAA rank-1 Monte Carlo convergence for leading models [PITH_FULL_IMAGE:figures/full_fig_p038_25.png] view at source ↗
Figure 26
Figure 26. Figure 26: Deployment-adjusted rank-1 sensitivity across dimensionless regret-discount multipliers c. −2.0 −1.5 −1.0 −0.5 0.0 0.5 Net Sharpe TS-OLS TS-RIDGE Linear 20 bps LSTM Calibrated sqrt TransEnc-8 TransEnc-10 [PITH_FULL_IMAGE:figures/full_fig_p039_26.png] view at source ↗
Figure 27
Figure 27. Figure 27: Linear and square-root transaction-cost robustness for promoted common-window portfolios [PITH_FULL_IMAGE:figures/full_fig_p039_27.png] view at source ↗
Figure 28
Figure 28. Figure 28: Net Sharpe ratios under daily and weekly rebalancing. nonlinear models have lower turnover under both rules, so the weekly change is smaller for them. The ranking under weekly rebalancing is led by TS-RIDGE, TS-OLS, and TransEnc-8. 42 [PITH_FULL_IMAGE:figures/full_fig_p042_28.png] view at source ↗
read the original abstract

Benchmarking forecasting architectures for daily equity portfolios is not just a prediction exercise. It also asks which model remains usable after preferences, costs, and portfolio constraints are imposed. We build a CRSP daily-stock benchmark for 15 deep and statistical time-series architectures over 2018--2024. The protocol combines common-window decile portfolios, stochastic multi-criteria acceptability analysis, a deployment-adjusted acceptability index, and a constrained quadratic portfolio layer with capacity, beta, industry, risk, leverage, and turnover controls. The index starts from the SMAA rank-acceptability distribution and downweights models whose criteria-level wins produce high portfolio regret; its Gibbs form is characterized as an entropic update from the SMAA prior. Empirically, no architecture dominates the raw benchmark: TransEnc-8 has the largest rank-1 acceptability, 0.352, and no model exceeds about 0.36. Rankings vary with preferences, market state, feature universe, and transaction costs. In the promoted five-model constrained-portfolio comparison, TransEnc-8 is selected throughout, while return-oriented raw rankings can favor TS-RIDGE. Broad-universe decile signals can survive costs, but the baseline constrained-QP net Sharpe at 20 bps is negative for every promoted model. The benchmark supports model selection and diagnosis rather than a standalone trading-strategy claim.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The paper benchmarks 15 deep and statistical time-series architectures for daily equity portfolio construction on CRSP data (2018–2024). It deploys a multi-stage protocol that constructs common-window decile portfolios, applies stochastic multi-criteria acceptability analysis (SMAA), defines a deployment-adjusted acceptability index via an entropic (Gibbs) update from the SMAA prior, and solves a constrained quadratic program incorporating capacity, beta, industry, risk, leverage, and turnover limits. The central empirical claims are that no architecture dominates (TransEnc-8 attains the highest rank-1 acceptability of 0.352; no model exceeds ~0.36), that rankings are sensitive to preferences, market state, feature universe, and transaction costs, that TransEnc-8 is selected in the five-model constrained comparison while return-oriented rankings can favor TS-RIDGE, and that broad-universe decile signals can survive costs yet the baseline constrained-QP net Sharpe at 20 bps remains negative for every promoted model.

Significance. If the protocol and implementation details hold, the work supplies a reproducible, preference-aware evaluation framework that moves beyond raw forecast accuracy to usability under realistic portfolio constraints. It credits the use of standard CRSP data, explicit multi-criteria SMAA, the explicit entropic characterization of the acceptability index, and the full set of QP controls. The negative net-Sharpe finding and the observation that no model dominates are falsifiable, policy-relevant results that caution against over-reliance on any single architecture.

minor comments (3)
  1. Abstract and §4: the exact functional form of the entropic update (Gibbs distribution) from the SMAA rank-acceptability vector to the deployment-adjusted index should be written explicitly, including the temperature parameter and any normalization, so that the index can be reproduced from the reported acceptability numbers alone.
  2. §3.3 and Table 2: the precise definition of the five-model constrained-QP comparison (which models are included, how the capacity and turnover limits are set, and whether the same random seeds are used across architectures) needs a dedicated paragraph or pseudocode block to eliminate ambiguity in the reported selection of TransEnc-8.
  3. Figure 3 and §5.2: the market-state and transaction-cost sensitivity plots would benefit from error bars or bootstrap intervals on the acceptability values so that the claim “rankings vary” can be assessed for statistical significance rather than visual inspection alone.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the careful summary of the manuscript, the positive evaluation of its significance, and the recommendation of minor revision. No major comments appear in the report, so we provide no point-by-point rebuttals below. Any minor suggestions will be incorporated in the revised version.

Circularity Check

0 steps flagged

No significant circularity; empirical claims rest on external data and stated definitions

full rationale

The paper is an empirical benchmarking exercise on CRSP data using common-window decile portfolios, SMAA rank-acceptability, a defined entropic deployment-adjusted index (explicitly characterized as an update from the SMAA prior), and constrained QP optimization with explicit controls. No derivation reduces by construction to fitted parameters or self-citations; the index form is stated rather than derived from the target results, and all performance numbers (e.g., rank-1 acceptability 0.352) are computed from external market data and standard portfolio layers. The protocol is presented as a composite method whose outputs are falsifiable against the data rather than tautological.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract was available for review; no explicit free parameters, axioms, or invented entities are identifiable beyond standard domain assumptions of portfolio theory. The 20 bps transaction cost level and any internal weights inside the entropic index are not detailed.

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discussion (0)

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