What's the difference between logistic regression credit scoring and the Altman Z-score, and when would you use each?
I'm studying credit risk for FRM Part II and both logistic regression and the Altman Z-score are covered for default prediction. They seem to do similar things but in very different ways. Can someone compare them and explain which is more useful in modern practice?
Both methods predict default, but they come from different eras of credit risk modeling and have distinct strengths.
Altman Z-Score (1968):
A linear discriminant analysis model using five financial ratios:
Z = 1.2X1 + 1.4X2 + 3.3X3 + 0.6X4 + 1.0X5
Where:
- X1 = Working Capital / Total Assets (liquidity)
- X2 = Retained Earnings / Total Assets (cumulative profitability)
- X3 = EBIT / Total Assets (operating efficiency)
- X4 = Market Value of Equity / Book Value of Total Liabilities (leverage)
- X5 = Sales / Total Assets (asset utilization)
Interpretation:
- Z > 2.99: Safe zone (low default probability)
- 1.81 < Z < 2.99: Grey zone (ambiguous)
- Z < 1.81: Distress zone (high default probability)
Logistic Regression:
Models the probability of default directly:
P(Default) = 1 / (1 + e^(-[beta_0 + beta_1X1 + ... + beta_kXk]))
The output is a probability between 0 and 1, estimated via MLE.
Example — Oakmont Lending evaluates Bridgeport Manufacturing:
| Metric | Value |
|---|---|
| Working Capital/Assets | 0.15 |
| Retained Earnings/Assets | 0.22 |
| EBIT/Assets | 0.08 |
| Market Equity/Total Liabilities | 1.40 |
| Sales/Assets | 1.10 |
Z-Score = 1.2(0.15) + 1.4(0.22) + 3.3(0.08) + 0.6(1.40) + 1.0(1.10) = 0.18 + 0.31 + 0.26 + 0.84 + 1.10 = 2.69 (Grey zone)
Logistic model (different bank's proprietary model) assigns PD = 3.2%
Comparison:
| Feature | Altman Z-Score | Logistic Regression |
|---|---|---|
| Output | Score / zone | Probability (0-1) |
| Coefficients | Fixed (original sample) | Estimated from your data |
| Customization | None | Full flexibility |
| Variables | 5 financial ratios | Any relevant predictors |
| Interpretability | Very high | Moderate |
| Regulatory acceptance | Screening tool | Basel PD models |
| Accuracy | Moderate | Higher (if well-calibrated) |
Modern Practice:
- Z-score: Used as a quick screening tool, early warning indicator, or benchmark. Popular with credit analysts for fast assessment.
- Logistic regression: The backbone of internal ratings-based (IRB) models under Basel. Banks estimate PD using logistic regression calibrated on their own default data.
FRM Key Points:
- Z-score coefficients were estimated on 1960s US manufacturing firms — applying them to modern tech companies or non-US firms is questionable
- Logistic regression requires binary outcome data (default/no default) and can include macro variables
- Both suffer from multicollinearity when predictors are correlated
- Discriminant analysis assumes multivariate normality; logistic regression does not
Practice credit scoring models in our FRM Part II question bank.
Master Part II with our FRM Course
64 lessons · 120+ hours· Expert instruction
Related Questions
Why is DV01 so much smaller than dollar duration if both are supposed to measure rate risk?
When should I stop using modified duration and switch to effective duration?
How should I think about the relationship between Macaulay duration and modified duration instead of memorizing two separate definitions?
Why do hedge calculations often use dollar duration or DV01 instead of just modified duration?
When should I prefer historical simulation VaR over delta-normal VaR?
Join the Discussion
Ask questions and get expert answers.