BENFORDSlide Number 1 Using Benford on Expense Reports ACL Users Group Wednesday, June 17, 2009...

BENFORD Slide Number 1

Using Benford on Expense Reports

ACL Users GroupWednesday, June 17, 2009

Richmond, VirginiaCharles R. Gauntt


Expense Report Audit

• Annual Audit Required by Board

• Now Conducted Quarterly

• Personnel notified by E-Mail of Exceptions

• Dramatic Improvement in Procedures during Early Stages

• Need Ground Rules for Complex or Sensitive Internal Control Situations


Expense Controls

• Corporate Reports• Retail Location Reports• Wholesale Location Reports• Expense Report Form• May be filed electronically via e-mail but signed

approved copy must be faxed.• All items require Receipt• Non Travel items often paid using Expense

Reports


Population

• Corporate and Field Support by Entity – includes more potential classification exceptions

• Feed, Farm & Home, Fertilizer, and Retail by entity and account number – fewer potential classification issues.

GEAC Accounts Payable

Corporate and Field Support

Feed Plants

Farm & Home

Retail Fertilizer


Sampling Strategy Using ACL• Benford• High Dollar Block• Excessive Frequency• Monetary Unit - Rejected• Random - Rejected• Stratified Random• Duplicates - Rejected• Excessive Frequency

More than 52• Whole Numbers -

Rejected


Why Benford?

• Identified Duplicates

• Identified Whole Numbers

• Identified Recurring Expenses

• Identified Anomalies

• Coupled with high dollar and stratified random sample


Benford Yields Interesting Information

• The focus is not just fraud, but identifying unusual trends in the transactions that might represent control weaknesses or savings opportunities.

• The Audit staff often finds that Benford items are more interesting to test.

• Large classes of items can be understood quickly and the test procedures adjusted.


Benford’s Law of Leading Digits

• Leading Digit Numbers do not occur randomly• Leading Digit Numbers do not occur normally• Leading Digits in multi-digit numbers resulting

from the same phenomenon appear in a distribution pattern where lower numbers are more likely to appear

• This distribution is closer to a logarithmic or Poisson distribution.


Which Distribution Fits Your Population?

0

0.05

0.1

0.15

0.2

0.25

0.3

0 1 2 3 4 5 6 7 8 9

Percent

0

0.05

0.1

0 2 4 6 8

Percent

00.10.20.30.4

0 2 4 6 8

Percent

Normal Uniform

Benford

• Inventory Variances – Normal

• Feed Tons Per Hour - Uniform

• Invoice Amounts – Benford


Benford Steps in ACL Presentation

• Stratify the Population• Analyze the Population Using Benford• Organize Population into groups by the number

of leading digits.• Analyze Groups Using Benford• Store Benford Analysis into a Table and then

extract high frequency digit combination using the z statistic and the variance between actual and expected occurrence. (exceptions)


Creating a Continuous Auditing Application

• Assign each Detailed record representing an expense report a Benford Index using the Integer Command

• Use Z Statistic or “Actual – Expected occurrences” to match leading digits from Benford Exceptions against the Benford index to extract detailed expense report for additional testing.

• Create a script for continuous execution.


Analysis ScriptOPEN expenserptpop2009STATISTICS ON Amount STD TO SCREEN NUMBER 5STRATIFY ON Amount SUBTOTAL Amount MINIMUM 0 MAXIMUM 10000

INTERVALS 20 TO PRINTBENFORD ON Amount LEADING 1 TO PRINTBENFORD ON Amount LEADING 2 TO PRINTBENFORD ON Amount LEADING 3 TO PRINTBENFORD ON Amount LEADING 4 TO Benford4OPEN benford4STRATIFY ON ZSTAT SUBTOTAL ACTUAL_COUNT MINIMUM 0 MAXIMUM

50 INTERVALS 50 TO PRINTOPEN expenserptpop2009BENFORD ON Amount LEADING 5 TO Benford5OPEN benford5STRATIFY ON ZSTAT SUBTOTAL ACTUAL_COUNT MINIMUM 0 MAXIMUM

50 INTERVALS 50 TO PRINT


Indices Script for 3 Digit MatchOPEN expenserptpop2009DELETE Digits3DELETE Bindex3DEFINE FIELD Digits3 COMPUTED

INT(Amount*100) If Amount > .99 and Amount < 10INT(Amount*10) If Amount > 9.99 and Amount < 100INT(Amount/10) IF Amount > 999.99 and Amount < 10000INT(Amount/100) IF Amount > 9999.99 and Amount < 100000INT(Amount)DEFINE FIELD Bindex3 COMPUTED

STRING(DIGITS3,3)


Matching ScriptOPEN bendford3OPEN expenserptpop2009 SECONDARYJOIN PKEY DIGITS FIELDS ACTUAL_COUNT EXPECTED_COUNT

ZSTAT DIGITS SKEY Bindex3 WITH Amount Date newvendorname newvendorno PO Vendorloc TO "benford3sample" OPEN PRESORT MANY SECSORT IF ZSTAT > 5

OPEN "benford3sample"DUPLICATES ON newvendorname DIGITS OTHER ACTUAL_COUNT

Amount Date DIGITS EXPECTED_COUNT newvendorname newvendorno PO Vendorloc ZSTAT PRESORT OPEN TO "duplicatebendford.FIL"

CLASSIFY ON newvendorname SUBTOTAL Amount TO "benfordexceptions.FIL"

OPEN "benfordexceptions"


Issues in the Approach

• Benford on the whole population provided dramatic number groupings.

• The whole population did introduce noise. For example, $25, $250, and 2500 dollar transactions were grouped together. The $25 expense reports always shows up as exceptions due to association meetings. We do not test them in detail.

• However, make sure your alternate procedures give you comfort. We did try to review the $25 population to make sure an employee had no more more than 12 association meeting expenses.

• Benford creates a file with a character field “digits” as the key. A character index to match against digits had to be created in the expense report file

• Make sure you understand the logic of Benford and can explain it to Management. Benford sometimes is attacked as “Hocus Pocus”.


1 Digit

The Three Digit Analysis Provided the most Dramatic Variances

2 Digit

3 Digit

Variances


Benford Noise – Direct Versus Indirect

$25 and $250 mixed together

$25 turned out to be meeting dues


LEADING DIGITS

ACTUAL COUNT

EXPECTED COUNT

ZSTAT RATIO

240 39 31 1.417241 33 31 0.356242 26 30 0.709243 32 30 0.221244 33 30 0.427245 28 30 0.281246 22 30 1.357247 44 30 2.513248 25 30 0.767249 18 30 2.035250 134 29 19.197251 30 29 0.033252 33 29 0.611253 26 29 0.48254 21 29 1.39255 26 29 0.44256 34 29 0.887257 29 29 0.068258 35 29 1.12259 31 28 0.391260 54 28 4.739

Step 1 – Benford on 3 Digits for all Items Greater than 1.00

•Leading Digits – In this case 3

•Actual Count – Number of Expense reports for this combination of leading digits in the population

•Expected Count – Number of Expense Reports expected by Benford

•ZSTAT – Likelihood of the actual count occurring in population. Higher the number the less likely the count and the more likely this group is unusual. In this case 250 and 260 are potential exceptions.


Benford Index


Make sure you understand the logic of Benford and can explain it to Management. Benford sometimes is attacked

as “Hocus Pocus”. The following ACL Help Index is an example of the resources available.

Performing Benford digital analysis• The Benford command allows you to generate digital analysis using the Benford

formula.• This command counts the number of times each leading digit or digit combination

occurs in a data set, and compares the actual count to the expected count. The expected count is calculated using the Benford formula. The command output can be sent to a graph.

• To help you evaluate the significance of deviations between actual and expected counts, the command output includes the Z-statistic for each count. You can also use the Bounds option to help you identify digit frequencies that are significantly outside expectations. When more than one count column falls outside the bounds, the data represented by these columns may be anomalous.

• For more information about digital analysis, see Digital Analysis Using Benford’s Law: Tests & Statistics for Auditors by Mark J. Nigrini, Ph.D., published by Global Audit Publications.

• Digital analysis tools like the Benford command enable auditors and other data analysts to focus on possible anomalies in large data sets. They do not prove that error or fraud exist, but identify items that deserve further study on statistical grounds. Digital analysis complements existing analytical tools and techniques, and should not be used in isolation from them.

BENFORDSlide Number 1 Using Benford on Expense Reports ACL Users Group Wednesday, June 17, 2009...

Documents

Transcript of BENFORDSlide Number 1 Using Benford on Expense Reports ACL Users Group Wednesday, June 17, 2009...