Abstract
Hierarchical trading separates broad portfolio decisions from the implementation of positions, but evidence about one layer cannot automatically validate the other. This article examines that boundary using a reproducible secondary analysis of ten public industry return portfolios. For January 2000 through December 2025, monthly cross-industry dispersion averages 3.550 percentage points. A first-order autoregression estimates a persistence coefficient of 0.360, with a heteroskedasticity and autocorrelation consistent 95 percent confidence interval of 0.251 to 0.468. These estimates describe an observable market state; they do not measure trading profitability, stock selection quality, or execution efficiency. The analysis uses the Hierarchical Reinforced Trader as a motivating architecture and identifies the additional observations required to evaluate its decision layers. Efficient adaptation methods can support text-based state construction, provided that information timing and adaptation costs enter the evaluation. A useful trading claim must connect a documented state to an implementable decision and then to an outcome net of the costs of obtaining and executing that decision. Keywords: hierarchical trading; industry dispersion; public return data; temporal dependence; execution costs; reproducibility.
References
Zhao, Zijie, and Roy E. Welsch. “Hierarchical Reinforced Trader (HRT): A Bi-Level Approach for Optimizing Stock Selection and Execution.” arXiv, 2024, arXiv:2410.14927, version 2 revised 11 May 2026. https://arxiv.org/abs/2410.14927v2.
Tong, H., Xu, G., & Chen, Y. (2026, May). Hadamard Tensor Ring for Efficient Low-Rank Fine-Tuning. In ICASSP 2026-2026 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
French, Kenneth R. “10 Industry Portfolios.” Kenneth R. French Data Library, downloaded 22 Oct. 2026. https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/Data_Library/det_10_ind_port.html.
Newey, Whitney K., and Kenneth D. West. “A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix.” Econometrica, vol. 55, no. 3, 1987, pp. 703–708. https://doi.org/10.2307/1913610.
White, Halbert. “A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity.” Econometrica, vol. 48, no. 4, 1980, pp. 817–838. https://doi.org/10.2307/1912934.
Fama, Eugene F. and Kenneth R. French. “Common risk factors in the returns on stocks and bonds.” Journal of Financial Economics, vol. 33, no. 1, 1993, pp. 3-56. https://doi.org/10.1016/0304-405x(93)90023-5.
Almgren, Robert and Neil Chriss. “Optimal execution of portfolio transactions.” The Journal of Risk, vol. 3, no. 2, 2001, pp. 5-39. https://doi.org/10.21314/jor.2001.041.
Lo, Andrew W. “The Statistics of Sharpe Ratios.” Financial Analysts Journal, vol. 58, no. 4, 2002, pp. 36-52. https://doi.org/10.2469/faj.v58.n4.2453.
Bailey, David, Jonathan Borwein, Marcos López de Prado, and Qiji Jim Zhu. “The probability of backtest overfitting.” The Journal of Computational Finance, 2017. https://doi.org/10.21314/jcf.2016.322.
Hu, Edward J., et al. “LoRA: Low-Rank Adaptation of Large Language Models.” International Conference on Learning Representations, 2022. https://openreview.net/forum?id=nZeVKeeFYf9.
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Copyright (c) 2026 Adrian Wells, Gavin Russell, Tyler Sullivan (Author)