Transcript Slide 1
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
What
about financial txns?
◦“Random data” = nonmanipulated 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 nonrandom 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
◦ Add-Ons
◦ Built-in Excel Functions
Expectations
Background
Why
it works
Real-world examples
How do I use it?
Ed
Tobias
[email protected]
◦ LinkedIn
http://www.linkedin.com/in/ed3200
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.