1 / 33

# It s All in the Numbers -Benford s Law - PowerPoint PPT Presentation

It’s All in the Numbers - Benford’s Law. Ed Tobias, CISA, CIA May 12, 2010. Topics. Expectations Background Why it works Real-world examples How do I use it? Questions. Expectations. How many have heard of it? All over the professional journals J. of Accountancy – 2003, 2007

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'It s All in the Numbers -Benford s Law' - nonnie

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### It’s All in the Numbers -Benford’s Law

Ed Tobias, CISA, CIA

May 12, 2010

• Expectations

• Background

• Why it works

• Real-world examples

• How do I use it?

• Questions

• 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

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

• 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

• 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

• Tested random #s and random categories

• Areas of rivers

• Baseball stats

• #s in magazine articles

• Street addresses - first 342 people listed in “American Men of Science”

• Utility Bills in Solomon Islands

• 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%

• What are “random numbers”?

• Non-manipulated numbers

• Population stats, utility bills,

• Areas of rivers

• NOT human-selected #s

• Zip codes, SSN, Employee ID

• 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

• “Random data” = non-manipulated numbers

• AP txns, company purchases

• NOT human-selected #s

• Expense limits (< \$25)

• Approval limits (No sig < \$500)

• Hourly wage rates

• How will it help me with non-random data?

• Aid in detection of unusual patterns

• Circumventing controls

• Potential fraud

• 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” ...

• At \$500M … First digit is “5”

• Takes 1.9 yr to increase \$100MM

• Although time is decreasing, there are more years that start with lower digits

• Eventually, we will reach \$1B

• First digit is “1”

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

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

• 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

• \$2M Check Fraud in AZ

• \$4.8M Procurement fraud in NC

• Check fraud in AZ

• #s appear random to untrained eyes

• Suspicious under Benford’s Law

• Counter-intuitive to human nature

• Wrote 23 checks (approx. \$2M)

• Many amts < \$100K

• Tried to circumvent a control that required a human signature

• Mgr tried to conceal fraud

• Human choices are not random

• Avoided common indicators:

• No duplicate amounts

• No round #s – all included cents

• 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

• Benford’s Law can be extended to first 2 digits

• Allow examiner to focus on specific areas

• High-level test of data authenticity

• 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 …

See any suspicious areas?

Drilling down in the “51” txns

• 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

• Built-in Excel Functions

• Expectations

• Background

• Why it works

• Real-world examples

• How do I use it?

• 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

• 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.

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