Credit Analysis & Solvency Lab

Ohlson O-Score Bankruptcy Probability Lab

Estimate 2-year logistic bankruptcy probability, 9-factor econometric distress terms, and leverage risk thresholds.

Company Archetypes:

Sensitivity Matrix: Total Debt Load vs. Net Profitability

Simulated 2-year default probability (%) across varied liabilities and bottom-line earnings.

Liabilities \ Net Income	-$500M NI	-$250M NI	Base NI	+$250M NI	+$500M NI

Theoretical Foundations & Econometric Formulation

1. The Logistic Probability Function

Unlike linear scoring models, Ohlson maps multi-factor corporate attributes onto a sigmoid curve to produce an exact probability of bankruptcy between 0 and 1:

P = \frac{1}{1 + e^{-T}} = \frac{e^T}{1 + e^T}

Where $T$ is the linear composite O-Score. When $T = 0$, $P = 0.50$ (50% default probability).

2. The 9-Variable Logit Equation

James Ohlson estimated the following maximum likelihood parameters on a sample of 105 bankrupt and 2,058 non-bankrupt industrial firms (Model 1):

\begin{aligned} T = &-1.32 - 0.407 \times \text{SIZE} + 6.03 \times \text{TLTA} \\ &- 1.43 \times \text{WCTA} + 0.0757 \times \text{CLCA} - 1.72 \times \text{OENEG} \\ &- 2.37 \times \text{NITA} - 1.83 \times \text{FUTL} + 0.285 \times \text{INTWO} \\ &- 0.521 \times \text{CHIN} \end{aligned}

3. Altman Z-Score vs. Ohlson O-Score

While Edward Altman's 1968 Z-score is an industry benchmark, Ohlson's 1980 O-score resolves several structural limitations:

No Normality Assumption: Multiple discriminant analysis requires financial ratios to be jointly normally distributed with identical covariance matrices across groups—assumptions frequently violated by skewed accounting data. Logit models require no such distribution assumptions.
Firm Size Inclusion: Incorporates $\ln(\text{Assets} / \text{GNP Price Index})$, capturing the empirical reality that large enterprises have superior access to credit markets during downturns.
Cash Flow Integration: Incorporates Funds from Operations (FFO) to measure cash-generating capacity directly.

4. Solvency Risk Tiers

Safe Zone ($P < 20\%$, $T < -1.38$): High solvency cushion, robust cash coverage, low credit default risk.
Watchlist / Grey Zone ($20\% \le P \le 50\%$): Moderate leverage strain or cyclical profit decline requiring close monitoring.
High Distress Zone ($P > 50\%$, $T > 0.00$): Elevated statistical likelihood of technical default, restructuring, or Chapter 11 insolvency within 24 months.

Interactive Self-Assessment Quiz

Test your mastery of Ohlson O-Score logit modeling, default probabilities, and corporate solvency diagnostics.

1. What is the fundamental mathematical distinction between the Ohlson O-Score and the Altman Z-Score?

Ohlson only applies to financial institutions and commercial banks

Altman uses machine learning neural networks while Ohlson uses discounted cash flows

Ohlson uses logistic (logit) regression yielding a direct default probability (0 to 1), avoiding normality assumptions

Altman includes price-to-earnings multiples while Ohlson ignores liabilities

2. What predicted default probability threshold (P) typically triggers the "High Bankruptcy Risk" classification?

P > 1.0%

P ≥ 50% (corresponding to an O-Score T ≥ 0.00, or historically 0.38 / 38% cutoff)

P = 0%

P > 99.9%

3. Which of the 9 variables has the largest positive coefficient (+6.03), indicating the strongest driver of bankruptcy risk?

Net Income / Total Assets (NITA)

Funds from Operations / Total Liabilities (FUTL)

Working Capital / Total Assets (WCTA)

Total Liabilities / Total Assets (TLTA)

4. What does the indicator variable INTWO represent in the Ohlson model?

1 if Net Income was negative for the last two consecutive fiscal years, 0 otherwise

Interest expense divided by total long-term debt

The company operates in more than two geographic jurisdictions

Times Interest Earned is less than 2.0x

Frequently Asked Questions

What is the Ohlson O-Score in credit analysis and corporate finance?

Developed by Professor James Ohlson in 1980, the O-Score is an econometric logit model designed to predict the probability of a company entering bankruptcy within two years. Unlike the linear discriminant Altman Z-Score, the Ohlson model uses a logistic function yielding a direct default probability between 0% and 100% across nine financial statement variables.

How is default probability calculated from the Ohlson O-Score (T)?

The O-Score (T) is transformed into a default probability (P) using the standard logistic sigmoid function: P = 1 / [1 + exp(-T)]. A score of T = 0 corresponds to a 50% probability of default, with scores above 0 indicating high distress risk and scores below -1.38 corresponding to default probabilities below 20%.

Why is Ohlson's O-Score often preferred over the Altman Z-Score?

Ohlson's model overcomes key econometric limitations of Altman's multiple discriminant analysis (MDA): it does not assume normally distributed financial ratios, incorporates company size and cash flow from operations, and directly outputs a bounded probability of default rather than an ordinal index.

Which financial variable has the largest influence in the Ohlson O-Score?

The ratio of Total Liabilities to Total Assets (TLTA) has the largest positive coefficient (+6.03), meaning excessive financial leverage is the primary mathematical driver increasing a company's predicted default probability.

Can I export the Ohlson 9-variable breakdown and sensitivity matrix to CSV?

Yes. You can export complete balance sheet metrics, 9-factor model terms, default probability calculations, and the 5x5 leverage vs. profitability sensitivity table as a formula-protected CSV spreadsheet.

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