ed tobias, cisa, cia may 12, 2010. expectations background why it works real-world examples how...

It’s All in the Numbers -Benford’s

LawEd Tobias, CISA, CIA

May 12, 2010

ExpectationsBackgroundWhy it worksReal-world examplesHow do I use it?Questions

Topics

How many have heard of it?◦All over the professional journals

J. of Accountancy – 2003, 2007 J. of Forensic Accounting – 2004 Internal Auditor – 2008 ISACA Journal – 2010 Fraud Magazine - 2010

Expectations

As of 2004, over 150 articles have been written about Benford’s Law

Expectations

1881 – Simon Newcomb, astronomer / mathematician

Noticed that front part of logarithm books was more used

Inferred that scientists were multiplying more #s with lower digits

Background

1938 – Frank Benford, Physicist at GE Research labs

Front part of the log book was more worn out than the back

Analyzed 20 sets of “random numbers” – 20,299 #s in all

Background

Tested random #s and random categoriesAreas of riversBaseball stats#s in magazine articlesStreet addresses - first 342 people listed in “American Men of Science”

Utility Bills in Solomon Islands

Background

Benford’s Law:◦Random #s are not random

◦Lower #s (1-3) occur more frequently as a first digit than higher numbers (7-9)

In a sample of random numbers: #1 occurs 33% #9 occurs 5%

Background

What are “random numbers”?◦Non-manipulated numbersPopulation stats, utility bills,Areas of rivers

◦NOT human-selected #sZip codes, SSN, Employee ID

Background

What’s the practical use?◦1990s – Dr. Mark Nigrini, college professor Tested insurance costs (reim. claims), sales

figures Performed studies detecting under/overstmts

of financial figures Published results in J. of Accountancy (1990)

and ACFE’s The White Paper (1994)

◦Useful for CFEs and auditors

Background

What about financial txns?◦“Random data” = non-manipulated numbers AP txns, company purchases

◦NOT human-selected #s Expense limits (< $25) Approval limits (No sig < $500) Hourly wage rates

Background

How will it help me with non-random data?

◦Aid in detection of unusual patterns

Circumventing controls Potential fraud

Background

You won the lottery – invest $100M in a mutual fund compounding at 10% annually◦First digit is “1”◦Takes 7.3 yr to double your $

◦At $200M, first digit is “2” ...

Why it works

At $500M … First digit is “5”◦Takes 1.9 yr to increase $100MMAlthough time is decreasing, there are more years that start with lower digits

◦Eventually, we will reach $1BFirst digit is “1”

Why it works

Seems reasonable that the lower digits (1-3) occur more frequently

◦These 3 digits make up approx. 60% of naturally-occurring digits

Why it works

Scale invariant◦1961-Roger Pinkham◦If you multiply the numbers by the same non-zero constant (i.e., 22.04 or 0.323) New set of #s still follows Benford’s Law

Works with different currencies

Why it works

$2M Check Fraud in AZ$4.8M Procurement fraud in NC

Examples

Check fraud in AZ◦#s appear random to untrained eyes

◦Suspicious under Benford’s Law◦Counter-intuitive to human nature

Example #1

Wrote 23 checks (approx. $2M)Many amts < $100K

◦Tried to circumvent a control that required a human signature

Mgr tried to conceal fraudHuman choices are not random

Example #1

Avoided common indicators:◦No duplicate amounts◦No round #s – all included cents

Example #1

Mistakes:◦Repeated some digits / digit combinations

◦Tended towards higher digits (7-9) Count of the leading digit showed high

tendency toward larger digits (7-9) Anyone familiar with Benford’s Law would

have recognized the larger digit trend as suspicious

Example #1

Benford’s Law can be extended to first 2 digits◦Allow examiner to focus on specific areas

◦High-level test of data authenticity

Example #2

Procurement fraud in NC◦660 invoices from a vendor◦Years 2002-2005◦Total of $4.8M submitted for payment

Run the 660 txns through Benford’s Law …

Example #2

Example #2

See any suspicious areas?

Example #2

Drilling down in the “51” txns

Example #2

Over a 3-year period, at least $3.8M in fraudulent invoices for school bus and automobile parts were submitted.

The investigation recovered $4.8M from the vendor and former school employees.

Data Analytics software◦ACL / IDEA

Excel◦Add-Ons◦Built-in Excel Functions

How do I use it?

Questions

ExpectationsBackgroundWhy it worksReal-world examplesHow do I use it?

Summary

Ed Tobias ed.tobias@hillsclerk.com

◦LinkedIn http://www.linkedin.com/in/ed3200

Contact Information

Benford’s Law Overview. n.d. Retrieved March 10, 2010 from http://www.acl.com/supportcenter/ol/courses/course.aspx?cid=010&ver=9&mod=1&nodeKey=3

Browne, M. Following Benford’s Law, or Looking Out for No. 1. n.d. Retrieved March 10, 2010 from http://www.rexswain.com/benford.html

Durtschi, C., Hillison, W., and Pacini, C. The Effective Use of Benford’s Law to Assist in Detecting Fraud in Accounting Data. 2004. Journal of Forensic Accounting. Vol. V. Retrieved March 10, 2010 from http://www.auditnet.org/articles/JFA-V-1-17-34.pdf

Managing the Business Risk of Fraud. EZ-R Stats, LLC. 2009. Retrieved March 10, 2010 from http://www.ezrstats.com/CS/Case_Studies.htm

Kyd, C. Use Benford’s Law with Excel to Improve Business Planning. 2007. Retrieved March 10, 2010 from http://www.exceluser.com/tools/benford_xl11.htm

References

Lehman, M., Weidenmeier, M, and Jones, T. Here’s how to pump up the detective power of Benford’s Law. Journal of Accountancy. 2007. Retrieved March 10, 2010 from http://www.journalofaccountancy.com/Issues/2007/Jun/FlexingYourSuperFinancialSleuthPower.htm

Lynch, A. and Xiaoyuan, Z. Putting Benford’s Law to Work. 2008. Internal Auditor. Retrieved March 10, 2010 from http://www.theiia.org/intAuditor/itaudit/archives/2008/february/putting-benfords-law-to-work/

Nigrini, M. Adding Value with Digital Analysis. Internal Auditor. 1999. Retrieved March 10, 2010 from http://findarticles.com/p/articles/mi_m4153/is_1_56/ai_54141370/

Nigrini, M. I’ve Got Your Number. Journal of Accountancy. 1999. Retrieved March 10, 2010 from http://www.journalofaccountancy.com/Issues/1999/May/nigrini.htm

Rose, A. and Rose, J. Turn Excel Into a Financial Sleuth. 2003. Journal of Accountancy. Retrieved March 10, 2010 from http://www.systrust.us/pubs/jofa/aug2003/rose.htm

Simkin, M. Using Spreadsheets and Benford’s Law to Test Accounting Data. ISACA Journal. 2010, Vol. 1. Pp. 47-51.

References

Stalcup, K. Benford’s Law. Fraud Magazine. 2010, Jan/Feb. Pp 57-58.

References