These are the slides for a 5-minute lightning talk at the Bloomberg Quant Seminar on September 6, 2016. The talk provided a brief introduction to Benford's Law and its use in fraud detection to an audience of quantitative finance professionals.

1. Benford’s Law
and
Fraud Detection
Ozan Gurel
Certified Fraud Examiner
Bloomberg Quant Seminar
September 6, 2016

2. If you have a large set of numbers, what would you expect the
frequencies of the possible first digits of all the numbers to be?

3. If you have a large set of numbers, what would you expect the
frequencies of the possible first digits of all the numbers to be?
With the first digit being one of nine numbers (1-9), would you expect
the probability of each to be 0.1111 (1/9, 11.11%)?

4. If you have a large set of numbers, what would you expect the
frequencies of the possible first digits of all the numbers to be?
With the first digit being one of nine numbers (1-9), would you expect
the probability of each to be 0.1111 (1/9, 11.11%)?

5. What became known as Benford’s Law was observed at General
Electric by Frank Benford in the 1930s and published as
Benford, Frank, “The Law of Anomalous Numbers,” Proceedings of the American
Philosophical Society, 78 (4), Mar. 31, 1938, pp. 551-572,
but was first reported in 1881 by Simon Newcomb of the National
Almanac Office in
Newcomb, Simon, “Note on the Frequency of Use of the Different Digits in Natural
Numbers,” American Journal of Mathematics, 4 (1), 1881, pp. 39-40.

6. Benford’s Law
The expected proportion of numbers beginning with the
leading digit n is:
log10((n + 1)/n)

8. Intuition
The percentage increase of a number required to get it to the next
first-digit level decreases as the first digit increases from 1 to 9.
100 to 200 - 100%
200 to 300 - 50%
300 to 400 - 33.33%
400 to 500 - 25%
500 to 600 - 20%
600 to 700 - 16.67%
700 to 800 - 14.29%
800 to 900 - 12.5%
900 to 1000 - 10%

9. Miller-Nigrini Excel Benford Tester
France - Populations légales en quartiers de la politique de la ville - 2013

11. Comparison of First Digits of Returns of Madoff and Apple
Source: http://www.nigrini.com/benfordslaw.htm
Madoff Apple

12. Benford’s Law and Enron

13. Disbursement Fraud in Oregon
Unusually high percentage of disbursements beginning with 1 found in
audit conducted by Audits Division, Secretary of State, State of Oregon.
Further analysis found a large number of $100 transactions, most of which
were fraudulent.
Source: https://oregonaudits.org/category/fraud-investigation/

14. Source: Durtschi, Cindy, William Hillson, and Carl Pacini, “The Effective Use of Benford’s Law to
Assist in Detecting Fraud in Accounting Data,” Journal of Forensic Accounting, 5, 2004, pp. 17-34.

15. Commercial Applications
• ACL – Vancouver, BC – Internal Audit
• AQRM – Accounting Quality + Risk Matrix by Ives Group – Sutton, MA
(Bloomberg Terminal App)
• IDEA by CaseWare Analytics – Ottawa, ON