Adapting Altman's bankruptcy prediction model to the compositional data methodology

Paper: arXiv 2603.24215

Authors: Fatemeh Keivani, Germà Coenders, Geòrgia Escaramís

Abstract

Using standard financial ratios as variables in statistical analyses has been related to several serious problems, such as extreme outliers, asymmetry, non-normality, and non-linearity. The compositional-data methodology has been successfully applied to solve these problems and has always yielded substantially different results when compared to standard financial ratios. An under-researched area is the use of financial log-ratios computed with the compositional-data methodology to predict bankruptcy or the related terms of business default, insolvency or failure. Another under-researched area is the use of machine learning methods in combination with compositional log-ratios. The present article adapts the classical Altman bankruptcy prediction model and some of its extensions to the compositional methodology with pairwise log-ratios and three common statistical and machine learning tools: logistic regression models, k-nearest neighbours, and random forests, and compares the results with standard financial ratios. Data from the sector in the Spanish economy with the largest number of bankrupt firms according to the first two digits of the NACE code (46XX “wholesale trade, except of motor vehicles and motorcycles”) were obtained from the Iberian Balance sheet Analysis System. The sample size (31,131 firms, of which 97 were bankrupt) was divided into a training and a validation dataset. The training data set was downsampled to one healthy firm to each bankrupt firm. No outliers were removed. Focusing on predictive performance, the results show that compositional methods are better than standard ratios in terms of sensitivity, with mixed results regarding specificity, compositional random forests and compositional logistic regression behaving the best.

Complexity vs Empirical Score

• Math Complexity: 5.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents an innovative application of compositional data analysis (CoDa) and log-ratio transformations to credit risk and bankruptcy prediction models like Altman’s Z-score. It combines sound statistical theory with solid empirical evaluation on a large dataset of Spanish wholesale firms using machine learning methods.

Research Flowchart

  flowchart TD
    A["Research Goal:<br>Adapt Altman Bankruptcy Model to Compositional Data Methodology"] --> B["Data Extraction & Preprocessing:<br>31,131 Spanish Wholesale Firms from SABI<br><i>(Downsampled Training Set & Validation Set)</i>"]
    
    B --> C["Feature Engineering:<br>Standard Financial Ratios vs.<br>Compositional Pairwise Log-Ratios"]
    
    C --> D["Model Training & Classification:<br>1. Logistic Regression<br>2. k-Nearest Neighbours<br>3. Random Forests"]
    
    D --> E["Model Evaluation:<br>Predictive Performance Comparison<br><i>(Sensitivity & Specificity)</i>"]
    
    E --> F["Key Findings:<br>Compositional Log-Ratios outperform Standard Ratios in Sensitivity<br><i>(Compositional Random Forest & Logistic Regression perform best)</i>"]

Cited References (111)

1. Addressing class imbalance in bankruptcy prediction: a cost-aware and explainable machine learning approach (2026) — link
2. Predicting firm bankruptcy using macroeconomic and uncertainty variables: an ensemble machine learning study of the French market (2026) — link
3. Bankruptcy prediction using cost-sensitive multi-objective feature selection and imbalance-XGBoost (2026) — link
4. Hybrid bankruptcy forecasting for Indian firms: Integrating financial ratios, macroeconomic indicators, and random forest (2026) — link
5. Leveraging Multiview Data Through Discrete and Regularized Deep Learning for Dynamic Financial Risk Prediction (2026) — link
6. The Mechanism analysis of Corporate Financial Risk Influences via BiLSTM-MAttention Model (2026) — link
7. Hierarchical Fuzzy Cognitive Maps for Financial Risk Monitoring Using Aggregated Financial Concepts (2026) — link
8. A thinking innovation strategy based Northern goshawk optimizer enhanced extreme learning machine for bankruptcy prediction problems (2026) — link

2 of 111 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.