# THE APPLICATION OF BENFORDâ€™S LAW IN DETECTING BANKING FRAUD IN THE BANKING SECTOR

#### PROJECT INFORMATION

**CHAPTER ONE**

**1. O INTRODUCTION**

**1.1 BACKGROUND OF STUDY**

As the banking activities increases in Nigeria with the advancement of technology the level of fraud in most of the Nigeria bank tend to increase respectively; this has had a lot of effect on the financial growth and position of most Nigerian banks. The role of auditors in most banks becomes irrelevant as they can no longer effectively detect bank fraud because of the complexity of the Nigeria banking sector or industry. It was due to the inability of the auditors and other fraud detectors to detect banking fraud in the banking sector that lead to the introduction of Benford’s law and digital analysis.

The Digital Analysis is the comparison of the difference between the expected and observed frequencies of the digits. The difference between the expected and observed frequencies indicates that the data includes systematic error (Nigrini and Mittermaier, 1997). This systematic error may arise from the measurement methods (Hales, Sridharan, Radhakrishnan, Chakravorty and Siha, 2008) or from the frauds and manipulations in the accounting records (Nigrini, 1996). On the other hand, although the Digital Analysis reveals the systematic errors, this is not a final evidence for a fraud or manipulation.

The Digital Analysis is a method that shows where to look in order to obtain the best result from the data (Nigrini, 1996; (Hales, Chakravorty and Sridharan, 2009). In other words, the Digital analysis is a method that reveals the doubtful data. This property of the Digital Analysis was first proposed by Varian (1972). According to Varian (1972), the fact that a data set complies with Benford Distribution does not confirm the realness and accurateness of that data set, however, the fact that a data set does not comply with Benford Distribution is enough to be suspicious about that data set.

Benford’s Law finding a wide application area in the social sciences started in 1881 and spread into a process that has constituted up to the present day. The first study basis to the Benford’s law was published by Simon Newcomb in the American Journal of Mathematics in 1881 with the headline “Note on the Frequency of Use of the Different Digits in Natural Numbers”. In this article, Newcomb, researched the probability of the ‘digits from “1” to “9” being found in the first digit of any number, and explained the Frequency Law stating that these probabilities are not equal. According to Newcomb (1881), the probability of the digits from “1” to “9” being found in the first digit of any number reduces as the digit grows. The first statistical evidence in the subject of the frequency law was provided by Frank Benford with the article called “The Law of Anomalous Numbers” published in the Proceedings of the American Philosophical Society in 1938. In the research he made by using 20.229 data from 20 different sources such as river lengths, population, temperature, atomic weights, Benford determined that the first digits of the numbers constituting four or more digits displayed a logarithmic distribution, and he reached the following the conclusion

Log (a) =log {(a+1)/a}

The “a” indicates the digits from “1” to “9”, and the “f(a)” indicates the probability of a digit taking place in the first digit of a number. According to this, the probability of the digit “1” to take place in the first digit of any number is,

Log(1)=log{(1+1)/1}

= 0.3010

The logarithmic relationship which Benford proposed is thoroughly supported by the results of the statistical study. According to the empirical results of the his study, while the digit “1” took place in the first digit in average 30,6% of the 20.229 data, in 4,7 of them, the digit “9” was reported Another important finding is related to which numbers complied with the law of logarithm more. Acting from the statistical results, Benford concluded that the irrelevant, natural and random numbers show more compliance to the law of logarithm compared to the formal or mathematical numbers. He stated the logarithmic relation as “The Law of Anomalous Numbers”. Pinkham (1961) showed that Benford’s Law was independent from scale. According to this, when a number sequence following the Benford distribution is multiplied by an constant which is not zero, the number sequence which has just been generated also complies with Benford’s Law. For example, when the lengths of the rivers on the earth are expressed by miles or km, they agree with Benford’s Law in both situations. Hill (1988) proved that when numbers were generated by human beings, they did not comply with Benford Distribution. In the study he made, he asked to 742 students to generate six-digit numbers. The sequence that was constituted according to the answers of the students doesn’t comply with the Benford distribution according to Chi-Square and Kolmohorov- Smirnoff Test. Carslaw (1988) applied Benford’s Law in the field of accounting. Carslaw (1988) stated that the managers generally round off the sales amounts to a higher sales amount in order to report more revenue when the corporation revenues remained under certain psychological limits. For example, the managers tend to report a sales amount such as 5.984.000 TRL to report as 6.000.000 TRL. As a result of the studies he made on the sales data of the firms in New Zealand, Carslaw (1988) found that there were more zero figures than the expected, and that fewer “9” figures than the expected in the second digit of the sales amounts due to the fact that the managers tended to round off their sales amounts. One year after Carslaw (1988), Thomas (1989) determined a surplus of zero in the second Digits of the data set constituting the net revenue data of the United States of America. Furthermore, he stated that there were fewer zero figures in the second Digits in the firms which reported loss. Nigrini (1994) demonstrated that Benford’s law could be used in fraud detection. On basis of Nigrini’s (1994) study, there is the opinion that the individuals will generate fraudulent numbers which are not compliant with the expected frequencies of the numbers (Benford Distribution) because of their unique psychological and limiting situations. By performing the first two Digit test over the fraudulent wage payments data, the compliance of the data set with Benford’s Distribution was checked. The fraudulent numbers in this 10- year data set which was known to be fraudulent displayed a great deviation according to Benford Distribution. Furthermore, when the data set was divided into two periods of five years, it was seen that the deviation from the Benford Distribution was more in the second five-year period. The reason of this was evaluated as the fact that the fraud realized by the employee was made more routinely. Nigrini (1996) performed the first and second digit test on the interest income according to the 200.000 tax statements given between 1985 and 1988. In spite of the fact that the data set displays a distribution compliant with Benford distribution, it was seen that the small numbers in the interest income were more than the expected and the big numbers were more than the expected in the interest payments.

**1.2 STATEMENT OF PROBLEM**

What instigated the application of Benford’s law in the banking sector was due to high level of bank fraud in the banking sector. The auditor’s role in the reduction of fraud was no longer effective. The level of fraud in the banking sector has significant effect on their performance and profitability; the inability of banks to determine the root cause of the continuous bank fraud is the major problem. According to (Olorunsegun, 2010) states that fraud is a major challenge faced by the entire banking industry; he also stated that no bank is has resistance over the issue of fraud.

Adeyemo (2012) states that bank fraud can only be possible with the corroboration of an insider; banks are suppose to deliver and carry out their various responsibilities with all sincerity which is devoid of fraudulent practices.

Another problem faced by banks is the inability of the federal government of Nigeria and its agencies to put in the control and prevention of bank fraud in Nigeria. The position and location of banks matters a lot; most banks tries to establish in remote area in order to serve the people living in such area but at the end of the day, such bank might be robbed; a fraudster will comfortably carry out his or her activities without pressure.

Another cause of bank fraud is the desire to get rich and poor salary scheme; it could also be as a result in the level of competition among staff, peer group pressure, social and family expectations.

**1.3 AIMS AND OBJECTIVES OF STUDY**

The main aim of the study is to apply the Benford’s law in the detection and prevention of bank fraud in the banking sector of Nigeria. The specific aims of the research work are stated below as follows:

1. To examine the efficiency of Benford’s law in the detection of fraud

2. To determine the root causes of bank fraud in the Nigeria banking sector

3. To elicit information on the relationship between benford’s law and fraud detection in Nigeria banks

4. To apply the Benford’s law in the detection and prevention of fraud in the banking sector

5. To make recommendation for improvement in policy and decision making in the Nigeria banking sector

**1.4 RESEARCH QUESTION**

To ascertain the above stated objectives the study came up with the following research questions. The research questions are stated below as:

1. Is application of the Benford’s law more efficient than use of auditors?

2. What are the root causes of bank fraud in the banking sector

3. Is there any relationship between Benford’s law and fraud in the Nigeria banking sector

4. Will the application of Benford’s law be the solution to bank fraud in the Nigeria banking sector?

**1.5 RESEARCH HYPOTHESIS**

H0: The application of Benford’s law is ineffective in detecting bank fraud in the banking sector

H1: The application of Benford’s law is very effective in detecting bank fraud in the banking sector

**1.6 SIGNIFICANCE OF STUDY**

The study will be of immense benefit to the banking sector of Nigeria, the state and the federal government of Nigeria, in decision making; the study will also be of great importance to the students, and other researchers that wishes to carry out a further study on the application of Benford’s law in other financial sectors in Nigeria.

**1.7 SCOPE OF STUDY**

The study the application of Benford’s law in the detecting of bank fraud in the banking sector will cover the level of fraud in some selected banks for a period of two (2) years.

**1.8 LIMITATION OF STUDY**

**FINANCIAL CONSTRAINTS**: financial constraints tend to impede the researcher speed in getting information and other materials that is needed for the research work. But the researcher managed in getting the information from the available materials to carry out his or her research.

**TIME CONSTRAINTS**: the researcher being a student will be involved in other departmental activities like submission of assignment, attending lectures, presenting seminars etc. but the researcher was able to meet up with the time allocated for the submission of the research work.

**1.9 DEFINITION OF TERMS:**

**BANK FRAUD**: Bank fraud is the use of potentially illegal means to obtain money, assets, or other property owned or held by a financial institution, or to obtain money from depositors by fraudulently posing as a bank or other financial institution. In many instances, bank fraud is a criminal offence.

**BENFORD’S LAW**: Benford's law, also called the first-digit law, is an observation about the frequency distribution of leading digits in many real-life sets of numerical data. The law states that in many naturally occurring collections of numbers, the leading significant digit is likely to be small

**REFERENCES**

*Can Auditors Detect Fraud: A review of the research evidence. The Journal of Forensich Accounting* Albrecht, C., Albrecht, W. S., & et al. (2001).

*The Law of anomalous numbers. *Proceedings American Philsophical

Society, Benford, F. (1938).

*Analitical review: A guide to analytical procedures *(2nd ed)*. *Colorado: Shepard’s/McGraw-Hill, Blocher, E., & Willingham, J. J. (1988).

Applying Business Intelligence Concepts to Medicaid Claim Fraud, Copeland, L. (2012).

*Competing on Analytics: New Science of Winning, *Boston: Harvard Business Scol Press, Davenport, T. H., & Harris, J. G. (2007).

The Effective Use of Benford’s Law to Assist in Detecting Fraud in Accounting Data, Durtschi, C. (2004).

*Neural network detection of management fraud using*

*published financial data. International Journal of Intelligent Systems in Accounting, Finance*

*& Management, 7*, 21-24, Fanning, K., & Cogger, K. (1998).

Detection of management fraud: a neural network approach, Fanning, K., Cogger, K., & Srivastava, R. (1995).

Forecasting Fraudulent Financial Statements Using Data Mining.Kotsiantis, K., & Tzelepis, T. (2006).

A Hybrid Knowledge-Statistical-Based System for the Detection of Fraud.Major, J., Riedinger, D. (2002).