The Power of Benford's Law in Finding Fraud

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Copyright © FraudResourceNet LLC

ThePowerofBenford'sLawinFindingFraud

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.

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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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Disclaimers

• The views expressed by the presenters do not necessarily represent the views, positions, or opinions of FraudResourceNet LLC (FRN) or the presenters’ respective organizations. These materials, and the oral presentation accompanying them, are for educational purposes only and do not constitute accounting or legal advice or create an accountant‐client relationship.

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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 1st

Place 2nd

Place 3rd

Place 4th

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 LawB. First‐two Digits LawC. Third‐Digit LawD. 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. TrueB. 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 inefficienciesdue 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. DisbursementsD. SalesE. All of the aboveF. 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 LawB. Is a close relative of BenfordC. Is the only one to find fraud using Benford’s LawD. 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

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Questions?


Thank You!

• Peter Goldmann

• FraudResourceNet LLC

• 800-440-2261

• www.fraudresourcenet.com

• [email protected]

• Jim Kaplan

• FraudResourceNet LLC

• 800-385-1625

• www.fraudresourcenet.com

• [email protected]

• Don Sparks

• 832‐327‐1877

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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

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