The Power of Benford's Law in Finding Fraud

3/5/2014
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Copyright © FraudResourceNet LLC
The Power of Benford's Law
in Finding Fraud
Special Guest Presenter:
Donald E. Sparks, CIA, CISA, CRMA
March 5, 2014
About Peter Goldmann, MSc., CFE
• President and Founder of White Collar Crime 101
• Publisher of White-Collar Crime Fighter
• Developer of FraudAware® Anti-Fraud Training
• Monthly Columnist, The Fraud Examiner, ACFE
Newsletter
• Member of Editorial Advisory Board, ACFE
• Author of “Fraud in the Markets”
• Explains how fraud fueled the financial crisis.

3/5/2014
2
About Jim Kaplan, MSc, CIA, CFE
• President and Founder of
AuditNet®, the global resource for
auditors (now available on Apple
and Android devices)
• Auditor, Web Site Guru,
• Internet for Auditors Pioneer
• Recipient of the IIA’s 2007
Bradford Cadmus Memorial
Award.
• Author of “The Auditor’s Guide to
Internet Resources” 2nd Edition
About Don Sparks, CIA, CISA, CRMA,
CRMA, ARM
• Vice President Industry Relations -
Audimation Services, Inc.
• Property/casualty insurance internal
audit experience (12 yrs. as CAE)
• Risk Services firms
• The IIA – eLearning: GAIN, Flash
Surveys, & Role of Audit in SOX 2002
monthly 2 hour web tv broadcasts
• NAIC IT Working Papers Committee
• Co-Author of GTAG 13 & GTAG 16
• June 2011, Creator & Programmer
Auditchannel.tv
Don Sparks

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Copyright © FraudResourceNet LLC 6
Disclaimers
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Today’s Agenda
 Auditing for Fraud: Standards & Essentials
 Learning the logic/help explain it to others
 A user‐friendly introduction
 Help detect the red flags of fraud
 Best data to use
 Step‐by‐step demonstration of fraud audits
 Common software programs to facilitating use
 Demonstration on 492,000 P‐Card File
 Your Questions - Conclusion
Fraud Applications
 Forensic Auditing
 Tax Auditing
 Audit of Annual Financial Statements
 Internal Auditing
 Corporate Finance/Company Evaluation
 Controllers

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Using Statistics To Seek Out
Criminals
Feb. 26, 2013 – Discovery of banks’ efforts to
manipulate the London Interbank Offered Rate
(LIBOR) owes a lot to statistical techniques that
provide first indications of wrongdoing.
If regulators (and auditors) want to uncover more
misdeeds in the markets, they’ll have to use statistical
screening tools more actively than they do today.
Extending the analysis over a 30 year period revealed
Libor submissions followed Benford’s closely for about
20 years, but began to diverge sharply in the mid‐
2000’s.
Bernie Madoff Fraud
When it comes to Madoff, if it
is too good to be true chances
are it is not true.  This issue is
definitely a candidate for the
fraud of the century!

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Do Patterns in Data Mean
Anything?
Inventors and Innovators
 Simon Newcomb – 1881
 Frank Benford – 1938
 Roger Pinkham – 1961
 Mark Nigrini – 1992

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Benford’s Law Defined
On the right, you can see the
number 1 occurs as the leading digit
30.1% of the time, while larger
numbers occur in the first digit less
frequently.
For example, the number 3879
 3 ‐ first digit
 8 ‐ second digit
 7 ‐ third digit
 9 – fourth digit
Expected Frequencies Based
on Benford’s Law
Digit 1
st
Place 2
nd
Place 3
rd
Place 4
th
Place
0 0.11968 0.10178 0.10018
1 0.30103 0.11389 0.10138 0.10014
2 0.17609 0.19882 0.10097 0.1001
3 0.12494 0.10433 0.10057 0.10006
4 0.09691 0.10031 0.10018 0.10002
5 0.07918 0.09668 0.09979 0.09998
6 0.06695 0.09337 0.0994 0.09994
7 0.05799 0.0935 0.09902 0.0999
8 0.05115 0.08757 0.09864 0.09986
9 0.04576 0.085 0.09827 0.09982

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Polling Question 1
Benford’s Law is sometimes also called:
A. First‐Digit Law
B. First‐two Digits Law
C. Third‐Digit Law
D. Nigrini’s Law
Key Facts
 The number 1 predominates most progressions.
 Probabilities are scale invariant – works with
numbers denominated as dollars, yen, euros,
pesos, rubles, etc.
 Not all data sets are suitable for analysis.
 Not good for sampling – results in large
selection sizes.
 Good low cost entry into using continuous
auditing/monitoring.

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Can You Use it To Win the
Lottery?
No. Outcome of the lottery is
truly random. This means
every lottery number has an
equal chance of occurring.
Is Benford’s Law in Your
Anti‐Fraud Program?

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See Red Flags ‐ Less Costly,
Better and Faster
 Technology is getting better all the time
 The need to find fraud faster to improve recovery
 Risk based audit planning
 Early warning sign past data patterns have changed
 Fraud Deterrence – fraudsters may not understand
the theory but know audit is always looking
 Identify Duplicates, Whole Numbers, Recurring
Expenses, other data pattern Anomalies
 Great analytic when coupled with high dollar and
stratified random sample techniques
Polling Question 2
Benford’s Law is a good tool for finding fraud
when just a few fraudulent transactions are
entered into the system.
A. True
B. False

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 CFE found a 6 year $860,000 AP fraud. I often
get a question could Benford’s have found this
sooner?
 CFE asked three questions:
 How many employees work in AP
 Longest tenure employee
 Can you pull 6 years of AP from AS400
 Imported AP into IDEA
 Ran Summarization
 Bank re‐imaged suspicious duplicate checks
selected by the CFO
Demo Real Fraud
Types of Data That Conform
Accounts Payable
(number sold * price)
Estimations in General
Ledger
Test of approval
violations under $2,500
Accounts Receivable
(number bought*price)
Inventories at many
locations
Purchase orders
Disbursements Computer System data
file conversions
Loan data
Sales Processing inefficiencies
due to high quantity
Customer balances
T&E Expenses New Combinations of
selling prices
Stock prices
Most sets of Accounting
Numbers with
Customer refunds Journal entries
Full year of transactions Credit card transactions

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Non‐Conforming Data Types
Situation Examples
Data set comprised of assigned
numbers
Checks, invoices, zip codes,
telephone, insurance policy
YYMM####
Numbers influenced by human
thought
Prices set at psychological thresholds
($1.99, ATM withdrawals)
Accounts with a large number of
firm-specific numbers
An account specifically set up to
record $100 refunds
Accounts with a built in minimum or
maximum
Assets must meet a threshold before
recorded
Airline passenger counts per plane Data sets with 500 or fewer
transactions
Where no transaction is recorded Theft, kickback, skimming, contract
rigging
Situation Examples
Data set comprised of assigned
numbers
Checks, invoices, zip codes,
telephone, insurance policy
YYMM####
Numbers influenced by human
thought
Prices set at psychological
thresholds ($1.99, ATM withdrawals)
Accounts with a large number of
firm‐specific numbers
An account specifically set up to
record $100 refunds
Accounts with a built in minimum or
maximum
Assets must meet a threshold before
recorded
Airline passenger counts per plane Data sets with 500 or fewer
transactions
Where no transaction is recorded Theft, kickback, skimming, contract
rigging
 First and Second Digit Analysis *
 First Two Digits Analysis*
 First Three Digits Analysis**
 Last Two Digits Analysis**
 Summation Test**
 Advanced Settings – Fuzzy Logic Setting #
 Rounded By Analysis #
 Duplication Analysis #
* =Primary **=Advanced #=Associated
Uses in Fraud Investigations

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Polling Question 3
Types of financial data that conform to use
in Benford’s Law testing (choose the best
answer(s)
A. Accounts Payable (number sold * price)
B. Accounts Receivable (number bought * price)
C. Disbursements
D. Sales
E. All of the above
F. All of the above
Check for Benford’s
Conformity

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First and Second Digit Analysis
First Two Digits Analysis
 Examines the frequency of the numerical
combinations 10 through 99 on the first two digits
of a series of numbers.
 In particular the output serves for the analysis of
avoided threshold values. Thus, these tests help to
clearly visualize when order or permission limits
have been systematically avoided.

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First Three Digits Analysis
 This test examines the frequency of the
numerical combinations 100 through 999 in the
first two digits of a series of numbers.
 The output serves for analysis after conspicuous
rounding off operations. Requires a large
amount of deviations with a population greater
than 10,000.
Last Two Digits Test:
The Last Two Digits test analyzes the frequency of the
last two digits and is useful in auditing election
results, inventory counts—any situation in which
padding or number invention is suspected.

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 This test is used to analyze the
relative increasing frequency of
rounded numbers.
 The determination comprises the
frequencies of the numbers that are
divisible by 10, 25, 100 and 1,000
(and any user‐defined values of
whole numbers) without
remainders.
Rounded By Analysis
The analysis of multiple duplicates includes all
number values in the entire database that occur
more than once.  This test helps the user to
recognize all existing duplicates in the data supply
whereas the result table presents the duplicates
sorted according to the descending frequency.  The
aim of the test is to identify certain numbers that
occur more than once (for example, possible
duplicate payments).
Difference from the other tests: Does not analyze
any numerical combinations, but the pure value of
a number.
Duplicates Analysis

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Summation Test
Second Order Test

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Advanced Settings
With most Benford’s Law tests in IDEA Version
Nine, you have the option of extracting
“suspicious” data whose digit frequencies do not
follow the digit frequencies of Benford’s Law.
With Advanced Settings, you can also refine this
output to limit the size of the output database.
Polling Question 4
Area(s) where Benford’s Law is not a good tool (choose all
that apply):
A. All the numbers in a series are at or below $9.99 or frauds
involving situations where nothing is recorded.
B. All of the numbers are positive.
C. All of the numbers are negative.
D. Very large data sets over 1 billion records.

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Benford’s Law Software
Integrated Tools Add‐In Component
CaseWare IDEA Excel
Arbutus Access
Active Data SAS
ACL
ESKORT Computer Audit
(SESAM)
Tableau
TopCAATs
Creating a Continuous
Auditing Application

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Demo P‐Card File ‐ Steps in
Presentation
 Stratify the Population
 Analyze the Population Using Benford
 Organize Population into groups by the number of
leading digits.
 Analyze Groups Using Benford
 Store Benford Analysis into a Table and then
extract high frequency digit combinations
 Make the analysis “repeatable and continuous”.
Polling Question 5
Mark Nigrini:
A. Invented Benford’s Law
B. Is a close relative of Benford
C. Is the only one to find fraud using Benford’s Law
D. Believes auditors should use it to detect fraud

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Improve Data Analysis Skills
Conclusion
Digital analysis tools like Benford’s Law enable auditors
and other data analysts to focus on possible anomalies
in large data sets. They do not prove that error or fraud
exist, but identify items that deserve further study on
statistical grounds. Digital analysis complements existing
analytical tools and techniques, and should not be used
in isolation from them.
Not necessarily fraud – many False positives
Certain types of fraud will not be detected
Useful tool, setting future auditing plans
Low Cost Entry into Digital continuous analysis

3/5/2014
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Questions?
Thank You!
• Peter Goldmann
• FraudResourceNet LLC
• 800-440-2261
• www.fraudresourcenet.com
• pgoldmann@fraudresourcenet.com
• Jim Kaplan
• FraudResourceNet LLC
• 800-385-1625
• www.fraudresourcenet.com
• jkaplan@fraudresourcenet.com
• Don Sparks
• 832‐327‐1877

3/5/2014
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Coming Up
March Anti‐Fraud Webinars…
 "Finding and Preventing Vendor
Procurement & P2P Fraud Using
Data Analytics”, March 12
 "How to Use Data Analytics to
Expose Fixed Asset and Inventory
Fraudsters”, March 19
Sign up at:
http://www.fraudresourcenet.com

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