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  Date:14^th September 2010

 Compiled by: M Sathya Kumar  

Exploring Benford’s Audit Law

Greg is a financial frauds expert and consultant to large blue-chip conglomerates. Having worked with international intelligence bureaus on landmark and path-breaking investigations, he is a much sought after ‘Fraud Investigator’. Greg has the distinction of using specialised forensic tools on each of his engagements. Being techno-savvy he is a common face in all technical summits and symposiums on a wide range of topics from cutting-edge cyber security tools to old-age intuitive Sherlock Holme’s methods.

Greg was recently invited to a gathering of Internal Auditors to make a presentation on novel fraud investigation methods, tools and techniques. Having used CAATs for more than a decade he had mastered the art of using CAATs innovatively and making subtle interpretation of findings and patterns which were normally true. Greg decided to showcase a prominent General Audit Software (GAS).

GAS has strong and robust extraction and analytical capabilities. Being in the market for a decade and more, GAS has proved itself to be a worthy companion to fraud investigators.

Greg decided to make a presentation on the critically acclaimed Law of Digital Analysis — ‘Benford’s Law’.

Benford’s Law :

History of Benford’s Law :

Frank Benford was a physicist at the GE Research Laboratories in the 1920’s. He noted that the first parts of the log-table books were more worn than the back part. The first pages contain logs of numbers with low first digits. The fist digit is the left-most digit in a number.

Benford collected data from 20 lists of number totaling 20,229 observations. He found that the first digit of 1 occurred 31% of the time. Using integral calculus, he calculated the expected digit frequencies that are now known as ‘Benford’s Law’. It took Frank Benford 6 years to perform his analysis and develop his law of expected digit frequencies.

IDEA’s Benford’s Module can provide a valuable reasonableness test for large data sets. IDEA only test items with number 10.00. Number sets with less than 4-digits tend to have more skewed distributions and do not conform as well to Benford’s Law. Positive and negative numbers are analysed separately. This is due to the fact that abnormal behaviour patterns for positive numbers are very different from those for negative numbers.

Benford’s Law briefly :

Benford’s Law is a procedure of analysis within ‘Digital Analysis’ (DA). It is a procedure which analyses digits in numeric data. This procedure helps to identify ‘irregularities’ and ‘patterns’ in data sets. In this context, irregularities are defined as numbers, which, for example, may have been created through the (systematic) manipulation of data. An ‘irregularity’ is measured based on the scale of digit distribution in a natural population corresponding to the empirical legalities of Benford’s Law.

Pre-conditions for the application of Benford’s Law :

1. The data being investigated must describe the same phenomena. For example, the sales figures of companies listed on the Sensex.

2. The numbers being analysed should not intrinsically contain any artificial user-defined minimum or maximum limit. For example, the sale of items in a 49-99 Store will contain an owner-defined minimum price of 49 and a maximum price of 99.

3. The values being tested should not be formatted or pre-defined. For example, bank account numbers.

Application of Benford’s Law in real world investigations :

Greg went on to present Benford’s Law through a sample GAS — IDEA Data Analysis Software in an accounts payable scrutiny. Greg had been hired to identify possible systematic circumvention of payment threshold limits in an Accounts Payable function for an engineering major. There were allegations of bogus vendors being set up by certain colourful individuals from within the company. Payments to these bogus vendors were being split right below the threshold limit to accommodate the vendor. This was a classic vendor-employee nexus scam.

Greg went about the task meticulously with a careful eye for detail.

He conducted the preliminary First Digit Test in Benford’s Law.

The first digital analysis test is the test of first digit proportions. The first digit of a number is the left-most digit in the number. Zero can never be a first digit. This is a high-level test. Analysts will not usually spot anything unusual unless it is blatant. This is a test of goodness-of-fit to see if the first digit actual proportions conform to Benford’s Law. The First Digit Test is an overall test of reasonableness. The upper and lower bounds are merely guidelines for the auditor. The First Digit graph could show a high level of conformity, but the data set could still contain errors or biases.

He went on to generate the Digit Distributions.

Click the OK button to perform the analyse.

Upon performing the test within IDEA, he arrived at the Benford Curve.

The curve displayed a clear and apparent spike at Digit 7. Upon further investigation he viewed the Benford Result.

This result warrants further investigation as the CFO has indicated that any items in excess of $ 80,000 require additional approval. This spike could be indicating an abnormal level of items being processed just below the additional approval level.

Given the nature of the finding, Greg proceeded to undertake the First Two Digits Test which was more revealing.

Conclusion of Greg’s Investigation :

Greg had identified clear red flags and systematic approval patterns for payables clerk ‘HMV’. These payments were questionable. Greg set about investigating HMV’s motives and dealings through trained cross-examination and process of elimination. His investigation revealed that ‘HMV’ was a disgruntled employee of the company with acute money spending personal habits like wagering and gambling. HMV’s activities had caused financial losses to the company over the last 3 years to the tune of INR 5 Million. Necessary criminal action was initiated against HMV, based on the evidence gathered by Greg.

Some of Greg’s Landmark investigations using Benford’s Law :

Check fraud on the basis of refund claims for medical costs :

In 1995, a digital analysis was conducted for an American company, on the reimbursement of medical costs to employees for the year 1994. It was suspected that cases of fraud had occurred connected to this because employees charged the costs they had first borne themselves, to the company, although they were not justified. The company’s controls connected to the reimbursements of costs were extremely poor. Basically, it depended on the head of the department, who had been working with the company for 10 years.

Due to the suspected fraud, all claims for reimbursement exceeding USD 1,500 were analysed using digital analysis. (For processing reasons and in order to reduce the amount of data to be processed, only reimbursements of more than USD 1,500 were registered, as it was assumed that the reimbursements from any fraud would exceed this amount.)

The analysis showed that the starting digits ‘10’ to ‘14’ occurred relatively rarely. This could basically be referred back to the erasing of all reimbursements from USD 1,000 to USD 1,500. In addition, statistically significant deviations in the section with digits starting from ‘15’ to ‘31’ could be observed in relation to the expected values according to Benford. The reason for this is that the majority of numbers begin with low digits and because the starting digits from ‘10’ to ‘14’ were eliminated, the starting digits ‘15’ to ‘31’ occurred relatively frequently.

A different deviation, which was classified as an anomaly, resulted for the frequency of the starting digits ‘65’ (thus, USD 65, 650 to 659, USD 6,500 to 6.599, etc.). After a thorough analysis it was found out that 13 of the supervised checks and incidents of fraud were for 13 bottle/slay rides. Through the analysis it was found that these 13 cases were prepared and processed directly by the head of the department for the reimbursement of the rent and heating.

Errors in the valuation of inventories :

The assigned auditing company examined the valuation of the inventories of a company in the consumer goods sector. As the company had a wide range of products, with great differences in value and extremely different quantities of stock, it was assumed that the values of the inventory followed the natural distribution of Benford’s Law. Hence the inventory was analysed to determine whether the starting digits of the inventories corresponded with the expected frequency distribution. Greg conducted a digital analysis based on a data file with inventory data for all locations of the company. Based on the analysis, it was realised that the numerical combination ‘10’ occurred relatively often as a leading figure. The analysis of the first three digits showed as well, that the numerical combination ‘100’ had an extraordinarily high frequency.

Except for these distinctive features all other digits remained within the framework of expected frequencies. Further analysis of the deviations showed that an increasing number of articles, which were planned for advertising purposes, had been recorded in the inventory list with a wrong value of INR 0.01. According to the system of Benford’s Law they were assigned to the groups of the starting digits ‘1’, ‘10’ and ‘100’, as soon as the user chose the option (‘include digits after the decimal point’). If these articles had been valued correctly, their value would have been INR 200,000.

Conclusion :

Greg’s use of Benford’s Law and the CAATs tool led to uncovering of a fraud. The management appreciated this new knowledge skill to be used in internal auditing and encouraged the setting up of a one-member team for using CAATs and Benford’s Law on various data being generated from the company for any red flags.

Article by Deepjee Singhal Manish Pipalia Chartered Accountants

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