Uncovering Financial Shenanigans: Benford’s Law as a Computer Assisted Analytical Procedure

PricewaterhouseCoopers (2020) has reported the highest level of economic crime in their comprehensive annual survey of the issue since it launched more than twenty years ago. Two thirds of respondents indicated that the costs of fraud can reach up to a million dollars each, amounting to approximately ten percent of their annual turnover. Inside perpetrators such as employees commit about 37 percent of these frauds. In this context, a technique known as Benford’s Law can be cost-effectively applied to detect financial fraud which can be invaluable to auditors and other financial professionals. Benford’s technique is founded on the mathematical distribution of integers found in nature and has been shown to be particularly efficient and cost-effective in financial fraud detection. The technique can swiftly flag suspicious transactions from lists of numbers that comprise millions of records when employed as a computer assisted auditing procedure. Despite this, Benford’s Law is not widely used in accounting and finance. One of the key reasons for its limited use is because fraud investigators are often incognizant and unfamiliar with the method, and how it can be implemented in a fraud detection workflow. This paper set forth a concise and organised approach for implementing Benford’s technique as an analytical procedure through the well-known IDEA generalised audit software to flag suspicious transactions, which can then be further investigated. Both the application of the method and its interpretation in situations of both compliance and non-compliance is discussed. The methodology proposed in this paper can be an indispensable aid for fraud investigators in view of the considerable costs associated with economic crime.


Introduction
PricewaterhouseCoopers (PwC) in their latest Global Economic Crime Survey 2020 reports that 51% of identified frauds exceeded US$100,000, and the costs from fraud over the past 24 months exceeded US$42 billion (PricewaterhouseCoopers, 2020). Crow Clark and Whitehall, an accountancy firm based in the UK also reports the high cost of fraud, stating that about ten percent of corporate revenues are wiped out by economic crime (Gee, 2018). In a similar vein, Lavion (2018) report a survey in the US where sixty four percent of participants indicated that their most significant fraud incident could see damages in the vicinity of US$1 million.
The global impact of fraud is colossal. This is reported as being close to $3 trillion dollars (Sweet, 2018). In this environment, a notable yet novel advancement is the identification of the usefulness of the Benford technique in detecting fraud. Benford's Law is established on the mathematically proven distribution of naturally existing integers, such as those found in accounting and finance. Prior studies have acknowledged its usefulness as a method that can assist investigators uncover fraud in accounting numbers (Kuruppu, 2019).
While most frauds (55%) are committed by external parties, a significant proportion (37%) are committed by internal perpetrators (PricewaterhouseCoopers, 2020). This represents a 5% year on year increase over PwC's earlier fraud survey. In this context, external auditors and other investigators can immensely benefit from techniques that can assist in efficiently identifying situations where fraud may have occurred. Corporate management and internal auditors will benefit by having an efficient technique that can quickly identify potential internal occurrences of fraud, which can be the starting point for further detailed investigation (Kuruppu, 2019). journal entries. For instance, this might be by creating and recording non-existent purchases of inventory. Similarly, false expense claims may be used to hide the misappropriation of assets (Amouzegar & Moshirvaziri, 2018;Pomykacz et al., 2017). When fraudsters succeed in merging fabricated entries among real journal entries, investigators face an uphill task (Nigrini, 2019;Simkin, 2010). This is a real issue for fraud investigators as the fraudulent entries may be hidden amongst millions of legitimate transactions, which makes accounting frauds very difficult to detect (Kuruppu, 2019;PricewaterhouseCoopers, 2020).
What is promising in this context is the fact that Benford's Law can "see through" these spurious accounting entries with little effort from the fraud investigator. This enables suspicious entries to be quickly identified and looked into more thoroughly (Collins, 2017;Singleton, 2011). Because the rates of naturally occurring integers differ from unnaturally formulated distributions such as when accounts are manipulated to commit fraud, the Benford technique can flag the latter as anomalies. For instance, an artificial distribution arises when a fraudster attempts to understate a series of expenses so that they do not exceed a particular threshold value (Kuruppu, 2019;Nigrini, 2019). These types of artificial distributions are effortlessly identified by the Benford technique.
A multitude of number distributions in accounting and finance comply with Benford's Law. Examples of these are number distributions from sales transactions, depreciation expenses and accounts receivables data (Kuruppu, 2019). The latter examples can be considered to be naturally occurring as long as the numerals are not restricted to particular values (Pomykacz et al., 2017). These types of number distributions are ideal candidates in fraud detection using the Benford method (Kruger & Yadavalli, 2017;Kuruppu, 2019).
One of the main benefits of the Benford method is its efficacy and cost effectiveness. The method can be effortlessly implemented by a fraud examiner through a spreadsheet program or through generalised audit software (Kuruppu, 2019;Kyd, 2017;Pomykacz et al., 2017). This allows an investigator to determine if the numbers under examination needs to be looked at more thoroughly (Nigrini, 2018). Courts of law have also recognised Benford's analysis as admissible evidence (Pomykacz et al., 2017;Nigrini, 2019).
Several studies have shown the effectiveness of Benford's Law. For instance, both Collins (2017) and Kuruppu (2019) demonstrate in detail how the technique can be applied through Microsoft Excel to carry out the requisite analysis to detect suspicious transactions. Although the method can be implemented through a spreadsheet program, it is tedious and more prone to error due the number of intermediate steps involved. Using a spreadsheet for carrying out Benford's analysis requires specialist skill, which to a great extent can be eliminated by using one of the commonly available Generalised Audit Software.
Many audit software packages recognise the Benford method for uncovering accounting anomalies by integrating modules into the software. Two of the popular audit software on the market is IDEA™ and ACL™. Both these packages are able to report if transactions comply with Benford's distribution and isolate any anomalies for further investigation (Oregon Audit, 2016;Pomykacz et al., 2017). The main issue, however, is that many accounting professionals are unaware of the Benford method. Many investigators who are acquainted with the method lack a clear understanding of how to operationalize the technique to swiftly detect anomalies in accounting numbers that can be a starting point for more thorough investigation (Kuruppu, 2019). This paper introduces a succinct approach that will permit accounting professionals to implement Bedford's Law as a computer assisted auditing procedure to flag suspicious amounts. A cost effective and swift method that can detect accounting anomalies can be of significant benefit to professional accountants, auditors and fraud examiners.
The paper is structured in the following manner. The next section examines Benford's Law, with a discussion on its usefulness for uncovering fraud. The relevance of the method as a computer assisted audit technique is also discussed. Section three presents a succinct approach for applying Benford's technique using two real world data sets. Both the compliance to Benford's Law indicating no anomalies is examined with instances of noncompliance indicating the presence of suspect amounts that need further investigation. Section four concludes the paper with implications for uncovering fraud and presents additional research opportunities.

Background to Benford's Law
The origins of Benford's Law date back to 1881, when Simon Newcomb, a Professor of Mathematics in the U.S. Navy observed the first pages of logarithm books were far more worn than later pages (Bhattacharya et al., 2011;Singleton, 2011). Lower level numbers occur in the first pages of logarithm books used at the time to aid in computations. This led Newcomb to postulate that earlier integers were used more than later numerals in the natural world, and he developed an ingenuous yet simple equation to summarise this fact. (Newcomb, 1881;Nigrini, 2019). This equation was: The potential of Benford's Law in identifying tax fraud was examined by Cho & Gaines (2007), Watrin et al., (2008) and Nigrini (1999Nigrini ( , 2019. The overarching conclusion from these studies was that Benford's Law can be used to identify number patterns indicative of manipulation in payable tax amounts. This can be the foundation for more detailed examination. From an auditing perspective, Nigrini and Mittermaier (1997) developed six numerical tests based on Benford' Law that were subsequently used by Ernst & Young to discover irregularities in different audit areas (IDEA, 2018). This study was instrumental in applying Benford's distribution in the form of a reasonableness check.
Later, Weinberg and Busta (1998) demonstrated the method's efficacy as an audit tool. More recently, Carreira & Silva (2016) demonstrated the real-world applicability of the method when used as part of a continuous audit program.
While the potential usefulness of Benford's Law to identify accounting anomalies has been recognised, it is only lately that its applicability to fraud detection has been thoroughly considered (Wells, 2013;Moolman, 2017). The assertion made by Chou (2018, p.2) that "Benford's law is widely applicable but not widely known…" is an apt depiction of the scope of its usage among accounting professionals. Nevertheless, it is promising that the technique's applicability is being increasingly recognised in accounting and finance (Kuruppu, 2019;Nigrini, 2019;Wells, 2013) With the reported high levels of economic crime and fraud, a reliable and systematic implementation of Benford's technique has the potential to be immensely beneficial to accounting professionals such as auditors and fraud examiners (IDEA, 2018;Kruger & Yadavalli, 2017;Kuruppu, 2019). ACL™ and IDEA®, which are two of the noted generalised audit software on the market both implement Benford's Law. This can allow auditors and fraud examiners to examine millions of number records almost instantaneously for non-conformity with Benford's distribution indicating specific transactions that require more detailed examination.
With audit firms facing considerable pressure to reduce costs and increase efficiency, audit techniques based on information technology can significantly expedite audit efforts. Despite the increasing interest in such technologies, not many auditors are conversant with Benford's Law in the form of a computer based analytical procedure (Baker, 2009;IIARF, 2009;Kuruppu, 2019). Others recognise the usefulness of generalised audit software, but perceive features such as Benford's Law as difficult to use (Kim et al., 2009). The latter is a misconception as the method can be deployed in minutes to flag questionable transactions. Auditors' unfamiliarity with the technique means that they are not using an effective tool in the fraud fighting toolkit to its full potential. The current Global Economic Crime and Fraud Survey refer to various fraud fighting technologies as part of a rounded corporate anti-fraud programme (PricewaterhouseCoopers, 2020).
The objective of this paper is to present a systematic methodology to allow for a more pervasive use of Benford's Law as a computer assisted analytical procedure through IDEA®. The methodology delineated here can be swiftly implemented to identify accounting anomalies that may warrant more detailed examination to eliminate the possibility of fraud. This can be invaluable to fraud investigators in light of the substantial increase in economic crimes in recent times. The following section presents this methodology.

Applying Benford's Law in IDEA®
Benford's Law holds for numbers occurring naturally such as in corporate sales or accounts receivables, if the amounts are not restricted by set boundaries. Amounts within a given number distribution that do not meet Benford's distribution such as when they are artificially created or manipulated will be flagged as anomalies. As such, it is important to utilise real world data to examine the efficacy of Benford's Law as an analytical technique.
IBM Watson Analytics provides several real-world corporate datasets that are ideal for this purpose and are in the public domain. Two of these datasets were utilised in this paper to show how Benford's Law can be applied through IDEA® to detect accounting anomalies. Moreover, the availability of the data on the IBM Watson website is helpful for reproducing the presented methodology. For clarity and conciseness, the methodology is summarised in three main steps as follows:  No. 7; amined to shown in t accounts ore detail, spect bars orm of an during the ord's Law.
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This paper put forward a consistent and concise approach for accounting professionals to operationalise Benford's Law through IDEA. The methodology was demonstrated on two real-world datasets in the public domain comprising of several thousand instances. It examined transactions complying with Benford's distribution, and transactions that did not fit Benford's expected pattern which signifies possible anomalies. The method described in this paper can be cost effectively implemented by accounting professionals on whole populations of interest rather than resorting to sampling. This can also serve as an effective reasonableness check for auditors in identifying high risk areas that can enable more extensive audit coverage corresponding to the established risk. If properly implemented, Benford's Law can be a valuable aid for accounting professionals in light of the considerable costs associated with economic crime. Future research should explore accounting professionals' perceptions and attitudes towards the practical utility of Benford's Law in identifying suspect transactions. If the extent of implementing Benford's Law in practice is found to be lacking, professional bodies should promote its value given its proven ability to identify anomalies in accounting numbers.