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REVIEW 5 major objections 6 minor 59 references

Directly Learning Stock Trading Strategies Through Profit Guided Loss Functions

T0 review · 5 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read A set of profit-based loss functions lets time-series networks output daily long/short portfolio weights directly, and the best configuration reports 48 to 53 percent backtested annual returns on 50 S&P 500 stocks over 2021 to 2023.

desk verdict A useful idea undercut by a misdefined objective: the 'profit' losses do not actually measure trading P&L, and the headline returns are not grounded. read the letter →

arxiv 2507.19639 v1 pith:2QVNCGWB submitted 2025-07-25 cs.LG cs.NE

Devroop Kar , Zimeng Lyu , Sheeraja Rajakrishnan , Hao Zhang , Alex Ororbia , Travis Desell , Daniel Krutz This is my paper
classification cs.LGcs.NE
keywords tradingfunctionslossstocklearningprofitsstocksbest
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Most stock-forecasting models are trained to predict tomorrow's price, and a separate system turns those predictions into trades. The authors instead train the network directly on the profit of the trades it would make. They add one output neuron per stock plus a 'hold' neuron, convert the outputs into long or short portfolio weights, and define four loss functions that equal the negative of the next-day portfolio return. To keep gradients well behaved, they replace the sharp sign function with a smooth approximation.

They attach these losses to several time-series models, including Crossformer, DeformTime, DLinear, TimesNet, P-sLSTM, and Autoformer, and test on a 50-stock S&P 500 portfolio with 2021, 2022, and 2023 held out. The best configurations, especially Crossformer with the L3 loss using prices, report annual returns around 48 to 53 percent, above the best reinforcement-learning baselines and above buy-and-hold for those years.

Two caveats matter. The profit calculation shown in the paper includes no transaction costs, shorting costs, or slippage, which are large for a daily trading strategy over 50 stocks. Also, the headline numbers are chosen from many models, losses, and settings by looking at validation performance, so part of the reported edge may come from selection rather than from a single stable strategy. The code is available, but the CRSP data is private.

Extended reading notes

Core claim

The paper's load-bearing claim is stated as: 'The results from these loss functions outperform the RL strategies as well, and in some cases quite significantly as in the bear market year of 2022,' with the headline example being Crossformer with StockLoss-L2 and price inputs returning 51.42%, 51.04%, and 48.62% for 2021, 2022, and 2023. If correct, training a time-series network with a profit-based loss produces a long/short strategy that is profitable across three test years and beats RL baselines and buy-and-hold on a 50-stock S&P 500 portfolio.

Load-bearing premise

The evaluation assumes that profits can be measured directly from daily return differences with no transaction costs, shorting costs, or slippage. Equations 1 through 4 and Tables 3, 5 through 12 contain no cost term, yet the strategy rebalances long and short positions across 50 stocks daily. If realistic costs are applied, the reported 48 to 53 percent annual returns would be substantially reduced, possibly below the RL baselines. A second load-bearing choice is selecting the best model/loss per test year on validation data from many configurations, which makes the headline a product of selection rather than a single pre-specified strategy.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 6 minor

Summary. The paper proposes four loss functions intended to let any time-series forecasting network output a direct trading strategy (buy/short/hold weights) by training on a 'profit' signal. The method is evaluated on 50 S&P 500 stocks across three test years (2021, 2022, 2023) and compared against five RL baselines and buy-and-hold, with headline annual profits of 51.42%, 51.04%, and 48.62% for Crossformer with the StockLoss-L2 variant and price inputs. The authors claim that the loss functions 'account for the potential profits or losses' of the suggested positions and that the resulting strategies outperform RL and buy-and-hold.

Significance. If the claims were correct, the paper would offer a simple, architecture-agnostic way to convert forecasting models into profitable long/short strategies, with code provided and experiments spanning multiple models, years, and portfolios. However, the central technical premise is invalid: the loss functions defined in Section 3 do not measure portfolio profit. This undermines the headline numbers regardless of the breadth of the experimental setup. The comparison to RL baselines is further weakened by the absence of transaction costs and by post-hoc model selection.

major comments (5)
  1. [Section 3.1, Eq. (1) (also Eqs. (2)–(4))] The term V_i·(Ret_{i,t+1}−Ret_{i,t})·sign(O_i) is not the profit of the trade implied by O_i. For a dollar position V_i opened at time t and closed at t+1, the per-dollar P&L is V_i·Ret_{i,t+1}·sign(O_i); the subtracted Ret_{i,t} is the previous day's return and is unrelated to that trade. A correct long on a stock with equal +1% returns on days t and t+1 therefore receives zero reward. The loss is a first-difference/momentum objective, not a profit objective, so the central claim that the loss functions are 'profit guided' is not supported.
  2. [Section 3.5] Replacing the return difference with (P RC_{i,t+1}−P RC_{i,t}) does not make the loss 'a more direct measure of the actual profit' because positions are dollar-weighted, not share-denominated. The P&L per dollar invested in stock i is (P_{i,t+1}−P_{i,t})/P_{i,t}; a raw price difference is not comparable across stocks with different price levels. This affects all PRC-based results in Tables 3, 6, 8, 10, and 12.
  3. [Section 6, Tables 3–12] The manuscript never states the formula used to compute 'Profit %'. If the backtest accumulates the training loss expression, the reported percentages are not portfolio returns; if it uses a standard long/short P&L based on daily returns, then training and evaluation optimize different objectives. Either way, the headline returns of 51.42%, 51.04%, and 48.62% do not demonstrate that the proposed loss functions directly maximize profit. The backtest procedure must be specified precisely.
  4. [Sections 5 and 6] The reported strategy rebalances long and short positions across 50 stocks daily, but no transaction costs, shorting costs, or slippage appear in Eqs. (1)–(4) or in the profit calculations. The stated 48–54% annual returns are therefore not investable, and the comparison with the RL baselines and Buy-and-Hold is not meaningful without a cost model or at least a breakeven transaction-cost analysis.
  5. [Section 5 (training configuration and results)] All results are selected from 10 repeated runs by best validation performance, and the headline model is additionally chosen across six architectures, four losses, two input types, and two hold settings. This post hoc selection makes the reported profits a product of multiple comparisons rather than a pre-specified strategy; no correction or nested evaluation is provided, so the expected out-of-sample performance is overstated.
minor comments (6)
  1. [Abstract and Table 3] The stated best RL profits 'around 41%, 2.81% and 41.58%' do not match the table maximums (SAC 43.00% in 2021, PPO 2.81% in 2022, TD3 40.96% in 2023); please align the abstract with the table.
  2. [Section 5] The text lists '8 numerical features' but enumerates nine items (price, return, bid-ask, spread, turn over, volume change, illiquidity, shares outstanding, market capitalization); please correct.
  3. [Section 3.3 heading] The heading 'LoST III' should be 'StockLoss-L2'.
  4. [Section 3.2] 'Subtracting this from Equation 1' is misleading; Eq. (2) is not Eq. (1) minus the normalized term but a new expression starting from 1.
  5. [Eq. (4)] The numerator uses |O_i| and the denominator uses |O_j| while Eq. (1) uses V_i; the relationship between O and V is defined in Section 3, but the notation should be made consistent in all four losses.
  6. [Tables 1–12] Several entries are exactly 0.00 or 0, which the authors attribute to the model learning not to trade; a brief explanation or confidence interval would help the reader distinguish zero from a failed run.

Circularity Check

0 steps flagged · score 1.0 of 10

No circularity: the profit-based losses are the training objective by design, but the reported headline results are out-of-sample evaluations on held-out years; the only self-citations are in related work and are not load-bearing.

full rationale

The paper's derivation chain is: define losses (Equations 1–4) that reward positions based on return or price differences, train time-series models with these losses, and then measure the resulting trading strategy's profit on held-out test years (2021, 2022, 2023). Minimizing a profit-based loss maximizes that same training objective at train time, which is tautological, but that is the intended design of a loss function and is not circular. The empirical claim—that the resulting strategies generate positive out-of-sample returns and outperform RL baselines—is evaluated on data not used for training, with validation taken from the year prior to each test year. Selecting the best model on validation data is standard model selection, not a fitted-input-called-prediction step, because the test labels are not used for selection. The paper's self-citations (Kar et al. [16] and Lyu et al. [27]) appear only in related-work discussions of bandit and RNN forecasting methods and are not load-bearing for the proposed loss functions or the evaluation. Concerns that the reported 'Profit %' may not correspond to a realistic portfolio return—for example, because no transaction costs or shorting costs are modeled, or because Equations 1–4 use one-day changes in returns rather than exact per-trade P&L—are correctness and validity concerns, not circularity. Since the backtest computation is not specified in the paper, one cannot exhibit a specific equation-level reduction showing that the reported profits equal the loss expression by construction. Therefore, no circular step can be identified from the manuscript text, and the circularity score is low.

Assumptions & free parameters 1 free parameters · 3 assumptions · 0 invented entities

The central claim rests less on fitted constants than on the evaluation protocol. The only hand-set parameter reported is gamma=10 for smoothing sign(x). The load-bearing assumptions are a cost-free daily profit model, the use of next-day realized returns as training targets, and validation-based selection of the best configuration. No invented entities are introduced.

free parameters (1)
  • smoothing coefficient gamma = 10
    Hand-chosen in Section 4 to approximate sign(x); all experiments use gamma=10. The reported results depend on this choice, though it is not fitted per dataset.
assumptions (3)
  • domain assumption Portfolio profit equals the sum of daily weighted return differences, with no transaction costs, shorting costs, or slippage.
    Equations 1-4 define the objective from return differences only, and Tables 3 and 5-12 report profits from that objective. No cost model is specified in the paper.
  • domain assumption Next-day realized returns are valid training targets and the train/validation/test year split preserves temporal causality.
    The loss functions use (Ret_{i,t+1}-Ret_{i,t}) or price equivalents; the paper states that the year before each test period is validation and everything before that is training.
  • ad hoc to paper Selecting the best model/loss/hold configuration on validation is an acceptable way to report method performance.
    Section 5 and Table 3 choose the best of many configurations per test year; multiple comparisons are not adjusted, so headline returns may be inflated by selection.

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Pith. "Pith review of Directly Learning Stock Trading Strategies Through Profit Guided Loss Functions." pith.science (2026). https://pith.science/paper/2QVNCGWB

@misc{pith2026250719639,
  author       = {Pith},
  title        = {Pith review of: Directly Learning Stock Trading Strategies Through Profit Guided Loss Functions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2QVNCGWB}},
  note         = {Machine review of arXiv:2507.19639}
}
read the original abstract

Stock trading has always been a challenging task due to the highly volatile nature of the stock market. Making sound trading decisions to generate profit is particularly difficult under such conditions. To address this, we propose four novel loss functions to drive decision-making for a portfolio of stocks. These functions account for the potential profits or losses based with respect to buying or shorting respective stocks, enabling potentially any artificial neural network to directly learn an effective trading strategy. Despite the high volatility in stock market fluctuations over time, training time-series models such as transformers on these loss functions resulted in trading strategies that generated significant profits on a portfolio of 50 different S&P 500 company stocks as compared to a benchmark reinforcment learning techniques and a baseline buy and hold method. As an example, using 2021, 2022 and 2023 as three test periods, the Crossformer model adapted with our best loss function was most consistent, resulting in returns of 51.42%, 51.04% and 48.62% respectively. In comparison, the best performing state-of-the-art reinforcement learning methods, PPO and DDPG, only delivered maximum profits of around 41%, 2.81% and 41.58% for the same periods. The code is available at https://anonymous.4open.science/r/bandit-stock-trading-58C8/README.md.

Figures

Figures reproduced from arXiv: 2507.19639 by the authors.

Figure 1
Figure 1. Modifying the final layer of any neural network to capture trading decisions for the present [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 3
Figure 3. Comparison between sign(x) and tanh(γx) for different γ. To overcome the above discontinuity issue, we utilized a smoothing operation to approximate sign(x). Specifically, we employed the sig￾moidal function tanh(γx) in place of sign(x) as the tanh() function is smooth and defined at 0 (and γ is a coefficient that controls the sharpness/steepness of the sigmoidal funciton’s slope). Furthermore, by increasing the val… view at source ↗

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    Also, the results with the loss functions are overall higher than any of the RL strategies for each of the testing years, and even the Buy & Hold strategy (Refer Table 3)

    For 2021, DLinear performed the best with an annual profit of 50.94% followed by TimesNet with a profit of 46.82%. Also, the results with the loss functions are overall higher than any of the RL strategies for each of the testing years, and even the Buy & Hold strategy (Refer ...

    2021

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