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
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