Lesson 8 of 8
The limits of detection
Dechow and colleagues put the rate of misstatement at about 0.35 percent of firm-years. Work that through a flag and most flags are false ones.
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
- In Dechow, Ge, Larson and Sloan's own worked calculation, the unconditional probability of misstatement is 498 firms out of 143,988, about 0.35 percent.
- The Beneish M-Score's commonly quoted threshold of minus 1.78 sits between the 75th and 90th percentile of the US cohort this product computes, so it flags a meaningful share of ordinary companies.
- Put those two together and almost every flag is a false positive, which makes a flag a reason to read a filing and never a finding on its own.
Every method in this course produces flags. The last thing to learn is what a flag is worth, and the answer is arithmetic rather than judgement.
The M-Score threshold against the US market
The commonly quoted threshold, minus 1.78: between the 75th percentile (−2.08) and the 90th percentile (−0.60).As a floor it admits between a tenth and a quarter of the cohort.
- 5th percentile: −4.19
- 10th percentile: −3.36
- 25th percentile: −2.82
- median: −2.51
- 75th percentile: −2.08
- 90th percentile: −0.60
- 95th percentile: 2.10
The base rate, from the paper that built the database
Dechow, Ge, Larson and Sloan examined 2,190 enforcement releases issued between 1982 and 2005 and drew 677 misstating firms from them. In the worked example they publish for their own model, the denominator is written out: the unconditional probability of misstatement is 498 divided by 143,490 plus 498, which is 0.00345.
About one firm-year in 290. That is the number every detection method has to be evaluated against, and it is the number people leave out.
What a threshold catches
The M-Score is built from eight indices, including days sales in receivables, gross margin, asset quality, sales growth, depreciation rate, selling and administrative expense, leverage and total accruals to total assets. A score above minus 1.78 is commonly quoted as the flag.
Across the 3,459 US companies with a computed M-Score on 2026-09-12, minus 1.78 falls between the 75th percentile of minus 2.08 and the 90th of minus 0.60. So the threshold flags somewhere between one company in ten and one in four, on a base rate of roughly one in 290.
The arithmetic, done once
Take 1,000 companies. On the base rate, between three and four of them are misstating. Suppose the flag catches most of those, and separately flags 15 percent of the 996 or so that are not.
That is about 3 true flags and about 149 false ones. Roughly 2 percent of the flagged group is a real misstatement, and 98 percent is a company whose receivables grew, whose margin moved, or which is simply growing fast.
Nothing in that arithmetic is a criticism of the score. It was fitted to separate manipulators from non-manipulators in a sample, and it does that. What it cannot do is overcome a base rate of one in 290 with any realistic accuracy, and no score can.
What a flag is actually for
Not a verdict. A queue. A score that flags 15 percent of a market is useful only if the 15 percent is a better place to spend an hour of reading than a random 15 percent, and on the evidence it is.
So the honest claim a flag supports is narrow and worth saying in full: this company's reported figures have a property that has been more common among companies later found to have misstated, in a sample from a different period, and the filing is therefore worth opening. Anything stronger than that is not supported by the arithmetic, and about a company that has not been the subject of an action it is also a statement no reader should make.
Check yourself
What unconditional probability of misstatement do Dechow, Ge, Larson and Sloan use in their own worked example?
- About 3.5 percent of firm-years
- 498 divided by 143,988, about 0.35 percent of firm-years
- About 12 percent of firm-years
Show the answer
Answer: B.
The paper writes the denominator out: 498 misstatement firms over 143,490 plus 498, which is 0.00345.Where does the threshold of minus 1.78 sit in the US cohort computed on 2026-09-12?
- Above the 95th percentile
- Between the 75th percentile at minus 2.08 and the 90th at minus 0.60
- Below the median
Show the answer
Answer: B.
It flags roughly between one company in ten and one in four of the 3,459 companies with a computed score, which is far above the base rate of misstatement.A company's M-Score is above the threshold. What does that support?
- A conclusion that the accounts are being manipulated
- A decision to read the filing, because the flagged group is a better use of an hour than a random group
- Nothing at all: the score is meaningless
Show the answer
Answer: B.
With a base rate near one in 290, almost every flag is a false positive. The value of a flag is in ordering what to read, not in reaching a conclusion.Sources
- Dechow, Ge, Larson and Sloan, "Predicting Material Accounting Misstatements": 2,190 enforcement releases issued 1982 to 2005, 677 misstating firms, and the unconditional probability used in the paper's worked example.
- Beneish, "The Detection of Earnings Manipulation," Financial Analysts Journal, 1999: the eight indices and the commonly quoted threshold of minus 1.78.
GET /api/public/distribution/beneish_mon the production API, coverage tier VERIFIED.
What this leaves out
- The distribution was computed on 2026-09-12 across 3,459 US companies with one row per company, excluding exact zeros as coerced missing data and 774 companies as not applicable because they are banks, capital markets firms, equity REITs, insurers or mortgage REITs. It is rebuilt on a cadence, so a reader checking later will see different numbers.
- The base rate comes from a sample of enforcement actions between 1982 and 2005. Detection and enforcement rates change, and an undetected misstatement is absent from the numerator by construction, so the true rate is not knowable from this source.
- The two-by-two table uses an illustrative 15 percent false-positive assumption. It is an assumption, stated so it can be disagreed with.
- A flag is a property of reported figures. It is not a finding about any company, and nothing here is advice about any security.