Detect Financial Fraud with Benford's Law

Benford's Law:
How to Use it to Detect
Fraud in Financial Data
August 7, 2013
Special Guest Presenter:
Don Sparks
CIA, CISA, CRMA
Vice President
Audimation Services Inc
Partner with CaseWare IDEA

Copyright © 2013 FraudResourceNet™ LLC

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.


About Jim Kaplan, MSc, CIA, CFE
 President and Founder of AuditNet®,
the global resource for auditors
 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


Don Sparks, CIA, CISA, ARM
 Vice President Industry Relations 







Audimation Services, Inc.
24-years property/casualty insurance
internal auditing experience (12 as
the CAE)
ISACA International Education &
Dissemination Committee
Former senior staff member of the IIA
– GAIN, Flash Surveys, Role of Audit
in SOX 2002 video conferences
Co-Author of GTAG 13 & GTAG 16
Creator/Programmer Auditchannel.tv


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5

Today’s Agenda
 Auditing for Fraud: Standards & Essentials
 Assist in learning the logic and help explain it to
others as sometimes it is attacked as “Hocus Pocus”.
 A user‐friendly introduction
 Help detect the red flags of fraud
 Best data to use
 Step‐by‐step demonstration to fraud audits
 Common software programs to facilitating use
 Demonstration on 492,000 P Card File

The Auditor’s Role

 IPPF Standard 1210.A3
 Internal auditors must have
sufficient knowledge of…available
technology based audit techniques
to perform their assigned work


IIA Guidance – GTAG 13
Internal auditors require appropriate
skills and should use available
technological tools to help them
maintain a successful fraud
management program that covers
prevention, detection, and
investigation. As such, all audit
professionals — not just IT audit
specialists — are expected to be
increasingly proficient in areas such as
data analysis and the use of
technology to help them meet the
demands of the job.


Professional Guidance


Using Statistics To Seek Out
Criminals

Feb. 26, 2013 – The 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
If you took the annual returns of all
possible investments, you would
find that the population matches
Benford’s Law very closely.
However, the returns that Madoff
was reporting don’t. They nearly all
have a 1 as a leading digit, as he
consistently reported returns
between 10%-20%. This would
have been a clear indication that
his returns were being made up.

Do Patterns in Data Mean Anything

Statistics students are asked to
perform a simple task.  Create a
matrix of heads and tails by
recording the results of 200
coin flips.  The professor
reviews the results and easily
identifies the students that just
made up the results without
flipping a coin.  How did he
know?


Inventors and Innovators

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Simon Newcomb – 1881
Frank Benford – 1938
Roger Pinkham – 1961
Mark Nigrini – 1992


Benford’s Law Defined
Often called the first‐digit law, refers to
the frequency distribution of digits in
many (not all) real‐life data sources. 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

st

1 Place

0

nd

2 Place

rd

3 Place

th

4 Place

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


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


Simple Facts
 The number 1 predominates most
progressions.
 Probabilities are scale invariant – works with
numbers denominated as dollars, yen, euros,
pesos, rubels, 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.

Can You Use it To Win the
Lottery?

No. The outcome of the lottery
is truly random. This means
every lottery number has an
equal chance of occurring. The
leading‐digit frequencies
should, in the long run, be in
exact proportion to the number
of lottery numbers starting with
that digit.

Where Does Benford’s Fit into
Your Anti‐Fraud Program?


The Red Flags of Fraud

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

As technology matures, finding fraud will increase.
Best use today is to prioritize audit planning.
Early warning sign past data patterns have changed.
Fraud Deterrence – Potential Fraudsters may not
understand the theory of Benford’s but know audit is
regularly running data analysis.
 Identify Duplicates, Whole Numbers, Recurring
Expenses, other data pattern Anomalies
 Coupled with high dollar and stratified random sample
techniques (use with other analytical tools)


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


Demo Real Fraud
 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

Types of Data That Conform
Accounts Payable
(number sold * price)

Estimations in General
Ledger

Test of approval
violations say 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

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 firmspecific numbers

An account specifically set up to record
$100 refunds

Accounts with a built in minimum or
maximum
Airline passenger counts per plane

Assets must meet a threshold before
recorded

Where no transaction is recorded

Theft, kickback, skimming, contract
rigging

Data sets with 500 or fewer
transactions


Uses in Fraud Investigations

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

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


Polling Question 3
Types of financial data that conform to use in Benford’s
Law testing (choose the best answer(s)
A.
B.
C.
D.
E.

Accounts Payable (number sold * price)
Accounts Receivable (number bought * price)
Disbursements
Sales
All of the above


First and Second Digit Analysis
The designated first or second
digits in a number series will be
analyzed. The expected output
serves as a rough check of the
actual numerical distribution in
the population and is used to
determine level of compliance
with the Benford’s Law.


First Two Digits Analysis
 This test 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.


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.


Rounded By Analysis
 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.


Duplicates 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.

Summation Test
The Summation test is similar to the traditional
Benford’s Law test, but instead of calculating
the number of occurrences for each first two
digits, it sums each amount.
Advantage: Allows you to identify clearly
significant amounts that do not follow the
expected results of Benford’s Law.


Second Order Test
The Second Order test is based on the digits
of the differences between amounts that
have been sorted from smallest to largest
(ordered). The first two digits of the
differences should follow the digit
frequencies of Benford’s Law. This test is
particularly useful in indicating data integrity
issues.


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.


Check for Benford’s
Conformity


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.


Benford’s Law Software
Integrated Tools

CaseWare IDEA

Add-In
Component

Excel

Arbutus
Access
Active Data
SAS
ACL
ESKORT Computer Audit (SESAM)
Tableau
TopCAATs

Creating a Continuous
Auditing Application

Source: July 2011 ISACA


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 (use the z
statistic and the variance between actual and
expected occurrence).
 Make the analysis “repeatable and continuous”.


BENFORD
Slide Number 40

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


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

Questions?
 Any Questions?
Don’t be Shy!


Coming Up This Month
 1. When Law Enforcement Comes
Knocking on August 14, 2013 1:00 PM
 2. Best Practices in Detecting
Accounts Payable Fraud Using Data
Analysis on August 21, 2013 11:00 AM


Thank You!
Website: http://www.fraudresourcenet.com
Jim Kaplan
FraudResourceNet™
800-385-1625
jkaplan@fraudresourcenet.com
Peter Goldmann
FraudResourceNet™
800-440-2261
pgoldmann@fraudresourcenet.com
Don Sparks
dons@audimation.com
832-327-1877

Detect Financial Fraud with Benford's Law

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