1. Ed Tobias, CISA, CIA May 12, 2010

2.  Expectations  Background  Why it works  Real-world examples  How do I use it?  Questions

3.  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

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

5.  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

6.  1938 – Frank Benford, P hysicist 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

7.  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

8.  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%

9.  What are “random numbers”? ◦ Non-manipulated numbers  Population stats, utility bills,  Areas of rivers ◦ NOT human-selected #s  Zip codes, SSN, Employee ID

10.  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

11.  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

12.  How will it help me with non- random data? ◦ Aid in detection of unusual patterns  Circumventing controls  Potential fraud

13.  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”...

14.  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”

15.  Seems reasonable that the lower digits (1-3) occur more frequently ◦ These 3 digits make up approx. 60% of naturally-occurring digits

16.  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

17.  $2M Check Fraud in AZ  $4.8M Procurement fraud in NC

18.  Check fraud in AZ ◦ #s appear random to untrained eyes ◦ Suspicious under Benford’s Law ◦ Counter-intuitive to human nature

19.  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

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

21.  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 suspicio us

22.  Benford’s Law can be extended to first 2 digits ◦ Allow examiner to focus on specific areas ◦ High-level test of data authenticity

23.  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 …

24. See any suspicious areas?

25. Drilling down in the “51” txns

26.  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.

27.  Data Analytics software ◦ ACL / IDEA  Excel ◦ Add-Ons ◦ Built-in Excel Functions

29.  Expectations  Background  Why it works  Real-world examples  How do I use it?

30.  Ed Tobias  ed.tobias@hillsclerk.com ed.tobias@hillsclerk.com ◦ LinkedIn  http://www.linkedin.com/in/ed3200 http://www.linkedin.com/in/ed3200

31.  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 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 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 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 http://www.exceluser.com/tools/benford_xl11.htm

32.  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 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/ 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/ 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 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 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.

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