Note on pre-taxation reported data by UK FTSE-listed companies. A search for Benford’s laws compatibility

ArXiv ID: 2509.09415 “View on arXiv”

Authors: Marcel Ausloos, Probowo Erawan Sastroredjo, Polina Khrennikova

Abstract

Pre-taxation analysis plays a crucial role in ensuring the fairness of public revenue collection. It can also serve as a tool to reduce the risk of tax avoidance, one of the UK government’s concerns. Our report utilises pre-tax income ($PI$) and total assets ($TA$) data from 567 companies listed on the FTSE All-Share index, gathered from the Refinitiv EIKON database, covering 14 years, i.e., the period from 2009 to 2022. We also derive the $PI/TA$ ratio, and distinguish between positive and negative $PI$ cases. We test the conformity of such data to Benford’s Laws,- specifically studying the first significant digit ($Fd$), the second significant digit ($Sd$), and the first and second significant digits ($FSd$). We use and justify two pertinent tests, the $χ^2$ and the Mean Absolute Deviation (MAD). We find that both tests are not leading to conclusions in complete agreement with each other, - in particular the MAD test entirely rejects the Benford’s Laws conformity of the reported financial data. From the mere accounting point of view, we conclude that the findings not only cast some doubt on the reported financial data, but also suggest that many more investigations be envisaged on closely related matters. On the other hand, the study of a ratio, like $PI/TA$, of variables which are (or not) Benford’s Laws compliant add to the literature debating whether such indirect variables should (or not) be Benford’s Laws compliant.

Keywords: Benford’s Law, Financial Statement Analysis, Tax Avoidance, FTSE All-Share Index, Accounting Fraud Detection

Complexity vs Empirical Score

• Math Complexity: 3.0/10
• Empirical Rigor: 7.0/10
• Quadrant: Street Traders
• Why: The paper applies standard statistical tests (χ² and MAD) to real financial data from a specific database, but the mathematics is relatively simple and descriptive rather than advanced or novel.

  flowchart TD
    A["Research Goal: Test conformity of FTSE-listed companies' financial data<br>to Benford's Law to assess data integrity and tax avoidance risk"] --> B["Data Collection &amp; Preparation"]
    
    B --> C["Key Inputs: 567 FTSE All-Share companies<br>2009-2022 (14 years)<br>Refinitiv EIKON Database"]
    
    C --> D["Variables Derived"]
    D --> D1["Pre-tax Income PI"]
    D --> D2["Total Assets TA"]
    D --> D3["Ratio PI/TA"]
    
    D --> E["Computational Process"]
    E --> E1["Statistical Tests Applied"]
    E1 --> E1a["Chi-square test χ²"]
    E1 --> E1b["Mean Absolute Deviation MAD"]
    E1 --> E1c["Focused on Digits: Fd, Sd, FSd"]
    
    E1a --> F["Key Findings &amp; Outcomes"]
    E1b --> F
    
    F --> F1["Inconsistent Results: χ² and MAD tests disagree<br>MAD test completely rejects Benford conformity"]
    F --> F2["Accounting Implications: Raises doubts about<br>reported financial data integrity"]
    F --> F3["Research Contribution: Adds to literature debate<br>on compliance of ratio variables to Benford's Law"]