Zmijewski Score X-Score
A three-ratio statistical model from 1984 that turns profitability, leverage, and liquidity into a model probability that a company is financially distressed.
What it is
The Zmijewski Score is a bankruptcy-risk model published by Mark Zmijewski in 1984 in the Journal of Accounting Research (volume 22, supplement). It is a probit model built on just three ratios: return on assets, total liabilities to total assets, and the current ratio. It produces a raw score X, which is then converted into a probability of distress by running it through the standard normal cumulative distribution function — not the logistic function used by logit models like Ohlson's O-Score. Zmijewski estimated it on 40 bankrupt and 800 non-bankrupt NYSE and AMEX industrial firms, and a resulting probability above 0.5 is the model's classification cutoff for distressed. Its appeal is simplicity: three inputs, all available from a single balance sheet and income statement.
Why it matters
The score compresses a company's financial condition into one number that is easy to compare across a large universe, which makes it useful as a first-pass screen rather than a conclusion. Because leverage carries the largest positive coefficient (+5.679) and profitability the largest negative one (-4.513), the model essentially asks whether a company earns enough on its assets to carry the liabilities it has piled on them. Reading it alongside models built on different information — Altman's Z, Ohlson's O, or a market-based measure like Merton distance-to-default — is more informative than any single score, since they disagree in revealing ways. A pitfall is that the model is calibrated to a 1980s sample of NYSE and AMEX industrial firms with a deliberately oversampled bankrupt group, so its absolute probabilities travel poorly to modern asset-light, financial, or non-US companies; the liquidity coefficient of +0.004 was also statistically insignificant in the original estimation and is transcribed inconsistently across secondary sources. Treat the output as a model probability describing what the ratios look like, not a forecast that a company will fail.
How it's calculated
The score needs three ratios from one set of financial statements: return on assets (net income divided by total assets), leverage (total liabilities divided by total assets), and liquidity (current assets divided by current liabilities). Each ratio is multiplied by its probit coefficient — minus 4.513 on ROA, plus 5.679 on leverage, plus 0.004 on liquidity — and the three products are added to the constant of -4.336. That sum is X, which is not itself a probability; it is fed through Phi, the standard normal cumulative distribution function, to convert it into a probability between 0 and 1. Note that Zmijewski used a probit link, so the conversion is the normal CDF and not the logistic function used by Ohlson's O-Score. A probability above 0.5 places the firm on the distressed side of the model's own classification cutoff.
How Quintarthai uses it
The screener's Quant Scores category carries a Zmijewski PD % filter, so you can narrow a universe by where names fall on the model's probability scale — it sits alongside the Piotroski F-Score (0-9) and the Sloan accrual ratio % in that same category. The deep-analysis risk block on /app/ does not carry Zmijewski: it shows Altman Z, Ohlson O-Score, Merton distance-to-default (banded remote/watch/stressed), the CHS 12-month failure hazard, and the Economic-Profit spread (ROIC - WACC), each n/m-gated for banks, insurers, and missing inputs. Every score on the platform is shown with its methodology and caveats as a research signal — the platform never turns a score into advice.