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

arXiv:2603.24215 · q-fin.ST, stat.AP · Submitted 2026-03-25 · Read on arXiv

Listen

Transcript

Introduction to the show: ident: Quantitative Finance. The day in quantitative finance: models of markets, risk and prices.

Ruth: We're looking at the paper: "Adapting Altman's bankruptcy prediction model to the compositional data methodology".

Warren: Here's the gist of the paper. Adapting Altman’s bankruptcy prediction model to the compositional data methodology explores how using log-ratios derived from compositional data can improve financial distress prediction compared to standard financial ratios.

Ruth: The results show that compositional methods are better in terms of sensitivity, with mixed results regarding specificity, compositional random forests and compositional logistic regression behaving the best.

Warren: Pruning redundant reasoning tokens The paper addresses the problems associated with using standard financial ratios in statistical models, such as extreme outliers, asymmetry, non-normality, non-linearity, and dependence on arbitrary decisions regarding accounting figures.

Ruth: The Compositional Data (CoDa) methodology uses log-ratio transformations to solve these problems.

Title and authors: Iris: To build on that, we have to talk about what this paper actually suggests as improvements over the existing approach. The authors are trying to show how this works in practice.

Ruth: They focus on using pairwise log-ratios to address the problems with standard ratios, and they also look at how different machine learning tools handle those compositional log-ratios.

Warren: So they’re suggesting a way to improve the prediction by focusing on these compositional features rather than just the raw financial figures.

Iris: They did look at logistic regression, and with standard ratios, they found predictors like (NCA+CA−NCL−CL)/(NCL+CL), (OR−OE)/CL, and CA/CL were relevant predictors with five percent significance.

Ruth: But when they use the compositional ratios, those specific problems disappear entirely. Instead, the statistically significant predictors become log(OR/CA) and log(RE/NCL).

Warren: That’s a big shift because it means the relationship between the variables changes fundamentally when you switch from standard ratios to these compositional ones.

Iris: And they also look at k-nearest neighbour method, and they found that this method didn't produce any measure of variable importance at all.

Ruth: So, in terms of improving the model structure itself, they are showing that the compositional approach handles the underlying statistical issues much better than standard ratios do.

Warren: What does this imply for a quantitative trader like me? It means if I use standard ratios, I’m introducing a lot of noise and bias into my signal compared to using these log-ratios.

The paper's summary: Ruth: So, to summarize what this paper is trying to say about the compositional data methodology adaptation of Altman's model, it’s that we need to move away from standard financial ratios in statistical models because they introduce severe violations of assumptions like non-normality and outliers.

Warren: And the core idea is that the Compositional Data methodology, by using log-ratio transformations, solves those problems and yields substantially different results when compared to those standard ratios.

Iris: They show how this method has been successfully applied to financial ratios over the last ten years specifically to solve those problems in connection with financial ratios Coenders two thousand twenty-five; Coenders and Arimany-Serrat 2025a; two thousand eighteen <ref:2603.24215#pg1,has been successfully applied to>.

Ruth: They also bring in machine learning tools and show how these compositional log-ratios can be used in combination with them, which is an under-researched area.

Warren: The practical application they use is on firms from the Spanish economy, specifically those with a large number of bankrupt firms based on the first two digits of their NACE code forty-sixXX.

Iris: They set up their data by downsampling the training dataset to one healthy firm for each bankrupt firm, while keeping the validation subset entirely intact.

Ruth: The key finding is that composition methods are superior in sensitivity, but they have mixed results on specificity across different models like compositional random forests and compositional logistic regression.

Warren: So, we’re seeing better recall when using these methods, but we need to be careful about how well the system actually classifies correctly.

The paper's improvements: Iris: The authors are suggesting specific improvements that address the limitations they found in their initial setup. They focus on making the predictor set more robust.

Ruth: They look at standard logistic regression first, and with standard ratios, they found relevant predictors with five percent significance, which were (NCA+CA−NCL−CL)/(NCL+CL), (OR−OE)/CL, and CA/CL.

Warren: But once they switch to compositional ratios, those specific problems are gone because the statistically significant predictors change entirely to log(OR/CA) and log(RE/NCL).

Iris: They also point out that the k-nearest neighbour method doesn't give any measure of variable importance at all, so that’s a limitation they identified.

Ruth: The suggested improvements are about using composition methods to avoid those issues altogether, which is what they are emphasizing when they say it leads to very substantial differences in the analysis results whenever it has been compared with standard financial ratios.

Warren: They also mention that the main advantage of using pairwise log-ratios is that there’s only one way of selecting all possible D(D-one)/two log-ratios, which makes the results less arbitrary and always replicable <ref:2603.24215#pg1>.

Conclusion: Ruth: So, wrapping up this discussion on "Adapting Altman's bankruptcy prediction model to the compositional data methodology," the main implication is that using compositional methods is a better way to predict financial distress than relying solely on standard financial ratios because of those statistical issues.

Warren: They found composition methods offer better sensitivity, and compositional random forests and compositional logistic regression showed the best performance in terms of balanced accuracy according to their assessment.

Iris: I just want to add that they note a major limitation is that their sample size had a very small number of bankrupt firms, which means the results might not be generalizable beyond what they observed.

Ruth: So, the final word is that while the compositional approach seems statistically sound and gives better sensitivity, we should use it when we’re predicting bankruptcy or default instead of just standard financial ratios.

Warren: The main thing to remember is that this paper shows how using log-ratios from the compositional data methodology can improve financial distress prediction by focusing on relative information among accounting figures.

Iris: That’s what we're talking about today, adapting Altman's bankruptcy prediction model to the compositional data methodology.

Universitat de Girona · CEEISCAT. Department of Health. Government of Catalonia

q-fin.ST, stat.AP

Submitted: 2026-03-25

Updated: 2026-06-08

Importance score: 69/100

The gist: Adapting Altman’s bankruptcy prediction model to the compositional data methodology explores how using log-ratios derived from compositional data can improve financial distress prediction compared

Key concepts

Compositional Data (CoDa) methodology: This method uses log-ratio transformations to solve problems found in standard financial ratios, such as extreme outliers and non-normality. Instead of looking at raw numbers, it analyzes the relationships between different accounting figures by transforming them into log-ratios, which makes the data more suitable for statistical modeling.
Standard Financial Ratios: These are traditional metrics used to predict bankruptcy, like those in Altman's model. The paper notes they suffer from issues like high skewness and kurtosis, making them unreliable for machine learning models unless outliers are manually pruned. Compositional methods address these inherent statistical flaws.
Sensitivity vs. Specificity: Sensitivity measures how well a model correctly identifies all bankrupt firms (recall), while specificity measures how well it correctly identifies healthy firms (precision). The paper found that compositional methods were superior in sensitivity, meaning they are better at catching potential bankruptcies, although specificity results varied across different models.
Pairwise Log-Ratios (plr): These are specific log-ratios derived from the data used as predictors in the model. The paper suggests using all possible pairwise log-ratios to avoid arbitrary selections, ensuring that the features used for prediction are based on a comprehensive and replicable analysis of the accounting figures.

Terminology

Accuracy — 11× in this paper · explained in 1 episode
Composition — 8× in this paper · explained in 2 episodes
Pruning — 7× in this paper · explained in 4 episodes
Interpretability — 5× in this paper · explained in 15 episodes
XGBoost — 5× in this paper · explained in 3 episodes
Core — 4× in this paper · explained in 2 episodes
Clustering — 3× in this paper · explained in 2 episodes
Clarity — 2× in this paper · explained in 3 episodes
Robustness — 2× in this paper · explained in 6 episodes
Axioms — 1× in this paper · explained in 2 episodes
Bayesian Optimization — 1× in this paper · explained in 3 episodes
Benchmarking — 1× in this paper · explained in 4 episodes
Class Imbalance — 1× in this paper · explained in 3 episodes
Elias — 1× in this paper · explained in 2 episodes
Ensemble Learning — 1× in this paper · explained in 2 episodes
F1 Score — 1× in this paper · explained in 4 episodes
Feature Engineering — 1× in this paper · explained in 3 episodes
Feature Selection — 1× in this paper · explained in 4 episodes
Generative AI — 1× in this paper · explained in 2 episodes
Hybrid Model — 1× in this paper · explained in 2 episodes
Hybrid Models — 1× in this paper · explained in 2 episodes
Lasso — 1× in this paper · explained in 2 episodes
Model Interpretability — 1× in this paper · explained in 2 episodes
Model-Agnostic — 1× in this paper · explained in 2 episodes
Oversampling — 1× in this paper · explained in 2 episodes
Regularization — 1× in this paper · explained in 3 episodes
SHAP Analysis — 1× in this paper · explained in 2 episodes
Shapley values — 1× in this paper · explained in 2 episodes

Summary

Adapting Altman’s bankruptcy prediction model to the compositional data methodology explores how using log-ratios derived from compositional data can improve financial distress prediction compared to standard financial ratios. The results show that compositional methods are better in terms of sensitivity, with mixed results regarding specificity, compositional random forests and compositional logistic regression behaving the best.

Pruning redundant reasoning tokens

The paper addresses the problems associated with using standard financial ratios in statistical models, such as extreme outliers, asymmetry, non-normality, non-linearity, and dependence on arbitrary decisions regarding accounting figures. The Compositional Data (CoDa) methodology uses log-ratio transformations to solve these problems. Far from being a statistical refinement, the CoDa methodology leads to very substantial differences in the analysis results whenever it has been compared with standard financial ratios. An under-researched area is the use of financial-statement ratios to predict outcome variables such as bankruptcy or related terms of business default, insolvency or failure.

How the training signal is built

The data used for the study came from firms 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”). The sample size was 31,131 firms, of which 97 were bankrupt. The training dataset was downsampled to one healthy firm to each bankrupt firm. The validation subset was kept entirely.

Where the gains come from

The comparison between standard and compositional approach is a matter of predictive performance beyond the fulfilment or not of statistical assumptions. Compositional methods are better in terms of sensitivity, with mixed results regarding specificity, compositional random forests and compositional logistic regression behaving the best. The overall assessment by the balanced accuracy is that compositional random forests and compositional logistic regression perform best.

Statistical analysis

The logistic regression model with standard ratios had relevant predictors (5% significance) as (NCA+CA−NCL−CL)/(NCL+CL), (OR−OE)/CL, and CA/CL. With compositional ratios, no such problems are encountered, and the statistically significant predictors are log(OR/CA) and log(RE/NCL). The k-nearest-neighbour method does not produce any measure of variable importance.

Data collection and pre-processing

The data gathering and pre-processing involved selecting firms with 5 or more employees and data available until at least 2023 from the Iberian Balance sheet Analysis System (SABI) database. No outliers were removed, only inactive firms having either zero total assets (NCA+CA), zero OR, and zero OE during the last available year or the year before the last. The remaining zeros were imputed with the log-ratio EM method.

Skewness and kurtosis analysis

Table 1 shows the skewness and kurtosis statistics of standard ratios and plr in the full sample. Standard ratios have very high skewness and extreme kurtosis, making them on the paper unfit for statistical modelling and non-robust machine learning methods except after pruning outliers. In contrast with Magrini (2025), we analyse the full sample without pruning outliers.

Discussion

The results show that beyond the fulfilment or not of statistical assumptions, the comparison between the standard and compositional approach is also a matter of predictive performance. Compositional methods are better in terms of sensitivity, with mixed results regarding specificity, compositional random forests and compositional logistic regression behaving the best. The possibility of using other log-ratio transformations than plr deserves a comment. The main advantage of plr is that there is only one way of selecting all possible D(D−1)/2 plr, which makes the results less arbitrary and always replicable.

Further research directions

Further research can include adapting other machine-learning methods like neural networks, deep learning, naïve Bayes classifier, support vector machines (SVM), natural gradient boosting (NGBoost), adaptative boosting (AdaBoost), categorical boosting (CatBoost), light gradient boosting (lightGBM), extreme gradient boosting (XGBoost), and metaheuristic algorithms. Each machine learning method can have a different set of compatible log-ratio transformations within the CoDa methodology, and this has to be explored in the first place. The choice of the best method may be based not only on predictive quality but also on convenience and interpretability. A strong limitation of our study is that our sample had a very small number of bankrupt firms.

Acknowledgments

This work was supported by the Spanish Ministry of Science, Innovation and Universities MCIN/AEI/10.13039/501100011033 and ERDF-a way of making Europe (grant number PID2021-123833OB-I00); the Spanish Ministry of Health (grant number CIBERCB06/02/1002); and AGAUR and the Department of Climate Action, Food and Rural Agenda of Generalitat de Catalunya (grant number 2023-CLIMA-00037).

Conflicts of interest

The authors declare no conflict of interest.

Data availability

The curated data are available from the corresponding author upon reasonable request.

References

Aitchison, J. (1982). The statistical analysis of compositional data (with discussion). Aitchison, J. (1983). Principal component analysis of compositional data. Aitchison, J. (1986). The statistical analysis of compositional data. Aitchison, J., Barceló-Vidal, C., Martín-Fernández, J. A., & Pawlowsky-Glahn V. (2000). Logratio analysis and compositional distance. Akusta, A., & Gün, M. (2025). Predicting financial distress in the textile industry: a comparative analysis of meta models and single classifiers. Altman, E. I. (1968). Financial ratios, discriminant analysis and the prediction of corporate bankruptcy. Amat, J. M., Martínez, J. I. & Roure, J. (2008). Transformarse o desaparecer: estrategias de la empresa familiar para competir en el siglo XXI. Antar, M., Hassan, R., & Barka, D. (2025). From black box to clarity: machine learning and agnostic techniques in credit risk management. Antar, M., & Tayachi, T.

Improvements for AI systems

Instead of using standard financial ratios, incorporate pairwise log-ratios (plr) as predictors in logistic regression models to address issues like extreme outliers and non-normality, as compositional methods are better than standard ratios in terms of sensitivity (recall). This allows the AI system to better identify bankrupt firms by focusing on the relative information among accounting figures.
Implement a machine learning classifier using compositional log-ratios, specifically random forests with 4 predictors from the standard ratio approach and 7 from the compositional approach, as this method showed compositional random forests and compositional logistic regression behaving the best in terms of balanced accuracy. This improved system can provide a more robust bankruptcy prediction by leveraging a larger set of compositionally derived features.
For k-nearest neighbours classification, use all possible D(D-1)/2 pairwise log-ratios (21 predictors) as features instead of just the D-1 required ones to avoid arbitrary and non-replicable results. This enhances the system's ability to select the best predictors from a large set, making predictions more reliable.
Develop an interpretability layer using SHAP values or LIME for any chosen machine learning model, as these are most popular methods for post-hoc explanation in bankruptcy prediction. This allows users to understand which specific log-ratios are driving the bankruptcy prediction decision, enhancing trust and transparency in the AI system's output.