Benford forensic screen
Benford’s law says that in most naturally occurring financial data, small first digits dominate: about 30% of numbers start with 1, only about 5% start with 9. Fabricated or heavily managed numbers tend to drift from that curve, which is why forensic accountants use the test. Here we run it in the open, on ourselves first: every tracked investor’s reported 13F position values, and every board name’s financial statements.
Read the limits before the table: deviation from Benford has many benign causes. Concentrated portfolios deviate mechanically (we measured a -0.79 rank correlation between book size and deviation, so the investor screen adjusts for book size and flags only residual outliers). Small samples are low power. Nothing here is an accusation of misreporting; it is a screen that says where a second look could start.
Tracked investors: 13F value conformity
| Investor | Positions filed | Benford MAD | Conformity (Nigrini bands) | Size-adjusted residual | Adjusted flag |
|---|---|---|---|---|---|
| mandel | 5,720 | 0.0337 | nonconforming | 0.0213 | residual outlier |
| starboard | 6,180 | 0.0295 | nonconforming | 0.0175 | residual outlier |
| ackman | 1,268 | 0.0405 | nonconforming | 0.0162 | residual outlier |
| burry | 1,343 | 0.0374 | nonconforming | 0.0136 | residual outlier |
| watsa | 7,072 | 0.0213 | nonconforming | 0.0100 | – |
First-digit Benford conformity of each tracked investor's reported 13F position values across all filed quarters (Nigrini MAD bands). Raw deviation mostly measures portfolio concentration (measured Spearman -0.79 between book size and deviation), so the screen adjusts for book size and flags only residual outliers. A statistical screen only: deviations have many benign causes and are never an accusation of misreporting.
Board names: financial-statement conformity
The classic forensic use of Benford: statement line items. Each board name’s income statement, balance sheet, and cash flow (annual and quarterly pooled), first digits against the curve.
| Ticker | Line items | Benford MAD | Conformity |
|---|---|---|---|
| USFD | 681 | 0.0300 | well above the n-matched null |
| UNM | 580 | 0.0291 | well above the n-matched null |
| GWW | 667 | 0.0280 | well above the n-matched null |
| MTCH | 937 | 0.0268 | well above the n-matched null |
| ESS | 887 | 0.0257 | well above the n-matched null |
First-digit Benford conformity of each board name's financial statement line items (income, balance sheet, cash flow; annual and quarterly pooled, duplicate values removed), each judged against a simulated null of its own sample size. THE HEADLINE IS THE BASE RATE: 101 of 150 large, liquid, heavily audited names exceed the null, because single-company statement pools are structurally non-Benford (subtotals, repeated scale, correlated line items). So this test, at this granularity, has weak discriminative power for manipulation, and we publish it partly to show that limit honestly. Only the handful of names far above the null merit even a curious second read, and a deviation is never an accusation.