Loss Given Default Prediction Under Measurement-Induced Mixture Distributions: An Information-Theoretic Approach

TL;DR

This paper addresses the challenge of predicting Loss Given Default (LGD) with contaminated training data by applying information-theoretic methods, outperforming traditional recursive partitioning techniques in real-world bankruptcy data.

Contribution

It introduces an information-theoretic approach to LGD prediction that effectively handles mixture-contaminated data, providing practical guidance for financial modeling under data constraints.

Findings

Information-theoretic methods outperform recursive partitioning in contaminated data.

Leverage features contain more mutual information than size features.

Results generalize to other domains with mixture data structures.

Abstract

Loss Given Default (LGD) modeling faces a fundamental data quality constraint: 90% of available training data consists of proxy estimates based on pre-distress balance sheets rather than actual recovery outcomes from completed bankruptcy proceedings. We demonstrate that this mixture-contaminated training structure causes systematic failure of recursive partitioning methods, with Random Forest achieving negative r-squared (-0.664, worse than predicting the mean) on held-out test data. Information-theoretic approaches based on Shannon entropy and mutual information provide superior generalization, achieving r-squared of 0.191 and RMSE of 0.284 on 1,218 corporate bankruptcies (1980-2023). Analysis reveals that leverage-based features contain 1.510 bits of mutual information while size effects contribute only 0.086 bits, contradicting regulatory assumptions about scale-dependent recovery. These results establish practical guidance for financial institutions deploying LGD models under Basel III requirements when representative outcome data is unavailable at sufficient scale. The findings generalize to medical outcomes research, climate forecasting, and technology reliability-domains where extended observation periods create unavoidable mixture structure in training data.