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

 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, 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

 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

 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

 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., 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 suspicio us

 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 ◦ 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 ◦ Add-Ons ◦ Built-in Excel Functions

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

 Ed Tobias  ◦ LinkedIn 

 Benford’s Law Overview. n.d. Retrieved March 10, 2010 from  Browne, M. Following Benford’s Law, or Looking Out for No. 1. n.d. Retrieved March 10, 2010 from  Durtschi, C., Hillison, W., and Pacini, C. The Effective Use of Benford’s Law to Assist in Detecting Fraud in Accounting Data Journal of Forensic Accounting. Vol. V. Retrieved March 10, 2010 from  Managing the Business Risk of Fraud. EZ-R Stats, LLC Retrieved March 10, 2010 from  Kyd, C. Use Benford’s Law with Excel to Improve Business Planning Retrieved March 10, 2010 from

 Lehman, M., Weidenmeier, M, and Jones, T. Here’s how to pump up the detective power of Benford’s Law. Journal of Accountancy Retrieved March 10, 2010 from  Lynch, A. and Xiaoyuan, Z. Putting Benford’s Law to Work Internal Auditor. Retrieved March 10, 2010 from  Nigrini, M. Adding Value with Digital Analysis. Internal Auditor Retrieved March 10, 2010 from  Nigrini, M. I’ve Got Your Number. Journal of Accountancy Retrieved March 10, 2010 from  Rose, A. and Rose, J. Turn Excel Into a Financial Sleuth Journal of Accountancy. Retrieved March 10, 2010 from  Simkin, M. Using Spreadsheets and Benford’s Law to Test Accounting Data. ISACA Journal. 2010, Vol. 1. Pp

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