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	1,269	0.0403	nonconforming	0.0159	residual outlier
burry	1,343	0.0374	nonconforming	0.0136	residual outlier
watsa	7,072	0.0213	nonconforming	0.0100	–
ubben	355	0.0533	nonconforming	0.0089	–
semper	5,073	0.0209	nonconforming	0.0078	–
abrams	2,583	0.0253	nonconforming	0.0076	–
greenblatt	127,598	0.0090	acceptable conformity	0.0049	–
egerton	4,888	0.0168	nonconforming	0.0035	–
oakmark	26,039	0.0101	acceptable conformity	0.0033	–
ainslie	36,116	0.0091	acceptable conformity	0.0030	–
loeb	7,509	0.0134	marginal	0.0023	–
sachem_head	2,219	0.0207	nonconforming	0.0018	–
hound	6,351	0.0137	marginal	0.0018	–
spier	595	0.0363	nonconforming	0.0016	–
bridgewater	64,287	0.0065	acceptable conformity	0.0015	–
tci	1,473	0.0240	nonconforming	0.0013	–
viking	11,672	0.0106	acceptable conformity	0.0013	–
de_shaw	447,714	0.0043	close conformity	0.0013	–
citadel	1,110,903	0.0037	close conformity	0.0011	–
two_sigma	308,535	0.0036	close conformity	0.0003	–
druckenmiller	7,477	0.0113	acceptable conformity	0.0002	–
valueact	2,339	0.0185	nonconforming	0.0001	–
coatue	17,198	0.0080	acceptable conformity	0.0001	–
kantesaria	1,044	0.0266	nonconforming	-0.0001	–
russo	15,142	0.0080	acceptable conformity	-0.0003	–
millennium	468,791	0.0026	close conformity	-0.0004	–
whale_rock	6,005	0.0111	acceptable conformity	-0.0010	–
soros	30,531	0.0051	close conformity	-0.0013	–
ariel	24,602	0.0055	close conformity	-0.0015	–
southeastern	7,280	0.0097	acceptable conformity	-0.0016	–
renaissance	367,460	0.0014	close conformity	-0.0018	–
rochon	6,644	0.0095	acceptable conformity	-0.0021	–
tepper	4,863	0.0112	acceptable conformity	-0.0022	–
point72	134,583	0.0017	close conformity	-0.0023	–
light_street	4,882	0.0109	acceptable conformity	-0.0024	–
himalaya	588	0.0323	nonconforming	-0.0026	–
marks	34,518	0.0034	close conformity	-0.0027	–
robbins	8,693	0.0076	acceptable conformity	-0.0028	–
icahn	3,442	0.0125	marginal	-0.0030	–
corvex	5,322	0.0097	acceptable conformity	-0.0032	–
tiger_global	9,684	0.0065	acceptable conformity	-0.0035	–
hosking	19,082	0.0039	close conformity	-0.0037	–
polen	12,083	0.0049	close conformity	-0.0043	–
einhorn	8,393	0.0060	acceptable conformity	-0.0045	–
peltz	1,492	0.0176	nonconforming	-0.0050	–
akre	4,393	0.0087	acceptable conformity	-0.0052	–
sundheim	3,514	0.0100	acceptable conformity	-0.0053	–
altimeter	3,685	0.0093	acceptable conformity	-0.0057	–
buffett	12,534	0.0031	close conformity	-0.0059	–
singer	3,694	0.0090	acceptable conformity	-0.0060	–
klarman	5,433	0.0065	acceptable conformity	-0.0062	–
pabrai	681	0.0263	nonconforming	-0.0063	–
fairholme	2,181	0.0114	acceptable conformity	-0.0076	–
jana	3,427	0.0075	acceptable conformity	-0.0081	–
punchcard	549	0.0253	nonconforming	-0.0108	–
engaged	1,700	0.0085	acceptable conformity	-0.0127	–

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
EWTX	473	0.0254	above the n-matched null
TRGP	972	0.0253	well above the n-matched null
BNY	807	0.0238	above the n-matched null
BLDR	817	0.0237	above the n-matched null
KSS	587	0.0236	above the n-matched null
MKL	622	0.0231	above the n-matched null
MKSI	609	0.0229	above the n-matched null
HBAN	749	0.0229	above the n-matched null
OKE	755	0.0221	above the n-matched null
SPG	923	0.0217	above the n-matched null
GLW	875	0.0213	above the n-matched null
ELV	675	0.0211	above the n-matched null
BNS	848	0.0210	above the n-matched null
ACHC	957	0.0207	above the n-matched null
VNO	936	0.0206	above the n-matched null
SMG	890	0.0205	above the n-matched null
WCN	951	0.0204	above the n-matched null
PRU	659	0.0203	above the n-matched null
HUM	667	0.0201	above the n-matched null
L	585	0.0200	above the n-matched null
RTX	915	0.0199	above the n-matched null
MSCI	945	0.0199	above the n-matched null
MTN	1013	0.0199	above the n-matched null
PRMB	850	0.0197	above the n-matched null
SNDK	529	0.0197	above the n-matched null
BBIO	912	0.0196	above the n-matched null
ADP	955	0.0194	above the n-matched null
ON	953	0.0194	above the n-matched null
FITB	732	0.0192	above the n-matched null
FDS	877	0.0192	above the n-matched null
CM	834	0.0192	above the n-matched null
SPGI	814	0.0188	above the n-matched null
HRL	997	0.0187	above the n-matched null
SYF	529	0.0186	above the n-matched null
MU	893	0.0181	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.