Lesson 6 of 9
What a fitted score was fitted on
A score is one sample compressed into one number. Using it outside that sample is not an approximation, it is a category error.
By Javier Sanz
Founder of ValueScreener. Built Ninety Nine, a securities services provider, and sold it to a tier-one global bank; ran operations and internationalization at Alpaca, the brokerage API.
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In one minute
- A model fitted on one sample carries that sample's industry mix and time period with it, whether or not the published threshold says so.
- Altman's zones, fitted on manufacturers, read an ordinary utility's heavy plant and borrowing as distress.
- Even an accurate screen for a rare event can flag mostly companies that are not the thing it looks for.
A fitted score is one sample compressed into one number. The sample had an industry mix, a period and a definition, and none of that travels with the published thresholds. Using a score outside the conditions it was fitted on is not an approximation of the right answer. It is a different question wearing the same arithmetic.
What an accurate screen still gets wrong, when the target is rare
- Flagged, and really the case · 80 percent of 100 real cases, out of 10,000 companies80
- Flagged, but not the case · 5 percent of the other 9,900495
What fitting does
A discriminant model is handed two groups of companies and asked to find the weighted combination of ratios that best separates them. The weights are not a theory of how businesses fail. They are the numbers that happened to separate those particular companies over that particular period.
Everything about the sample is baked into the weights: which industries were in it, how those industries finance themselves, and how common the outcome being predicted was. The published score arrives with none of that attached, which is exactly why it travels so well and exactly why it should not.
Altman's zones, off their sample
Altman's 1968 Z-Score was fitted on public manufacturers: five ratios weighted to separate the ones that went bankrupt from the ones that did not. The zones commonly quoted put a score below 1.81 in the distressed range and above 2.99 in the safe one.
Across the 74 US utility companies with a computed Z-Score on 2026-09-07, from prices last stored on 2026-08-26, the median was 0.98. That is well inside the zone the published thresholds call distressed. Three of the model's five terms explain why, without looking at a single company. The largest is sales against total assets: a utility's plant is huge next to its yearly revenue, so it scores a fraction of what a manufacturer scores on it. Market value against total liabilities is low for a company funded mostly by debt. Thin working capital is normal for a business that bills monthly and holds little stock. All three terms work exactly as fitted. They were fitted on manufacturers.
Why even an accurate screen misfires
The figure above is not specific to any one score. When the event a screen looks for is rare, misclassifying a small share of the much larger group can produce more false alarms than real ones. An 80 percent catch rate and a 5 percent false-positive rate are both respectable properties. The result above is still a list where fewer than one flagged company in seven is doing anything wrong.
The same caution reaches the other two scores by different routes. Beneish fitted his M-Score's weights on his own sample, by a different method, so its cutoff carries that sample. Piotroski fitted nothing: each of his nine tests scores one point. His evidence came from one cohort, the cheapest fifth of the market by book to market, so running the tests on every company is a different exercise.
Read any of these numbers as a rank against a group you chose, not as the zone its paper published. A rank keeps only the ordering, a weaker claim that travels further, though the weights still came from the original sample. A zone came out of one sample, and it travels exactly as far as that sample does.
Check yourself
Altman's Z-Score zones were fitted on which companies?
- Every public company
- Public manufacturers
- US utilities
Show the answer
Answer: B.
The 1968 paper fitted the model on manufacturers. Applying its zones to a different industry is a different question with the same arithmetic.Why do US utilities score low on the Altman Z-Score even when they are not in distress?
- Utilities hold too much inventory
- The model rewards fast asset turnover, low debt and ample working capital, which a utility's ordinary structure lacks
- Utilities are excluded from the model entirely
Show the answer
Answer: B.
Three of the model's five terms were fitted on manufacturers. A utility's heavy, long-lived plant, its debt funding and its thin working capital score low on all three for reasons unrelated to its condition.One company in 100 has the problem. A screen catches 80 percent of those and wrongly flags 5 percent of the rest. What share of its flagged list really has the problem?
- About 80 percent
- About 95 percent
- Well under half
Show the answer
Answer: C.
When the event is rare, the much larger group of false alarms outweighs the smaller group of real cases, even at these respectable catch and false-positive rates.Sources
- Altman, Journal of Finance, 1968, "Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy": the Z-Score, fitted on public manufacturers.
- Piotroski, Journal of Accounting Research, 2000, "Value Investing: The Use of Historical Financial Statement Information to Separate Winners from Losers": the F-Score, tested inside a high book to market cohort.
- Beneish, Financial Analysts Journal, 1999, "The Detection of Earnings Manipulation": the M-Score, covered in full elsewhere in this course.
- The Altman Z-Score distribution published on the open research pages of ValueScreener, built 2026-09-07: 2,773 US companies, with banks, capital markets firms, equity REITs, insurers, mortgage REITs and specialty finance companies excluded.
What this leaves out
- The utilities figure was computed on 2026-09-07 and the distribution is rebuilt on a schedule, so a later reader will see a different number for the same cohort.
- ValueScreener withholds the Z-Score for banks, capital markets firms, equity REITs, insurers, mortgage REITs and specialty finance companies, and the other two scores for the same list less specialty finance.
- A score flags a company for reading. It is not a verdict on any company.
- Nothing here is advice about any security.