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Benford's Law to the rescue: extending the logarithmic analysis from two to three or more digits using Excel

  • February 2011
Authors:
Christopher C Kelly at Kelly Partners LLP
Christopher C Kelly
  • Kelly Partners LLP
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Abstract

The full article is appended below. Scroll down and click the blue button 'View full text". If it helps your research, please give it a ‘Recommend’. Benford’s Law does not provide a final answer as to whether irregularities have occurred, but it is useful in leading the auditor to discrepancies for further investigation (Nigrini 1995). What makes Benford’s Law particularly useful for this kind of forensic audit is that it simultaneously allows both systematic and deep analysis of a large number of transactions. Analyzing the leading two digits is a minimum requirement. Analyzing to three digits increases the sensitivity of the test and can highlight repeated transactions as dramatic spikes. Specialist software is not essential. This can be done in Microsoft Excel. Publication Name: Internal Auditor (ISBN 0020-2745) Journal of the US Institute of Internal Auditors CITATION REF: Kelly, CC (2011), 'Benford's Law to the rescue', (Internal Auditor), 68(1): 25-27
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2011 02 01 Benfords law to the rescue USI
IA.pdf
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All content in this area was uploaded by Christopher C Kelly on Oct 30, 2014
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








10











DRILLING GREENFIELD’s DATA





2011 






n



















A DEEPER VIEW OF DATA







































expected frequency = log(n+1) - log(n).





WHAT BENFORD’s LAW REVEALED







n





n



n





















HOW THE LOGs WORK
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2011 
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0.301 0.176 0.125 0.097 0.079 0.046
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An analytical tool to aid the reflective selection of equity investments
Thesis
Full-text available
  • Mar 2013
If the full article linked below helps your research, please give it a ‘Recommend’. The full thesis can be viewed and downloaded free of charge from the Middlesex University research repository at this link: http://eprints.mdx.ac.uk/10714/ -----PURPOSE----- The problem the allocator of financial capital has to deal with is that asset selection decisions need to be made today based on uncertain future expectations derived from accounting measurements and estimations produced in the past which are vulnerable to error and creative accounting. The research looks at how this problem has been dealt with in the academic and professional literature and develops a new tool leveraging both quantitative methods and the reflective practitioner’s experiential intuition. -----METHODOLOGY DESIGN----- A qualitative methodology based on real-world case study (Flyvbjerg 2011) and microanalysis (Strauss and Corbin 1998) is used to develop customised reflexive research tools to assess management success in allocating capital, and audit metrics to illuminate techniques used to conceal poor returns. -----FINDINGS----- Returns which failed to reach market indices or inflation were observed in the UK investment trust sector over the past ten years suggesting their customers’ capital lost value in real terms. Although Modern Portfolio Theory has useful insights, strong form Efficient Market Hypothesis is rejected as is the over-reliance on mathematical models most of which have been developed under non-realistic assumptions. Monte Carlo simulation was examined and used alongside experiential intuition (Burke and Miller 1999, Dane and Pratt 2007) to generate insights into future risk management priorities and also as a way of optimising portfolio weighting options. The use of Monte Carlo for risk analysis, while not new in the financial services industry, is less common in industry, which in turn served to generate client work and publication of findings during the research. In carrying out the research, data inquiry limitations and in some cases data, design and formulaic errors were found in the publicly available research databases. Therefore a customised accounting database was designed with which to carry out the real-world case studies, which in turn exposed usage of modified accounting bases, creative accounting (Griffiths 1992) and concealment of earnings fluctuations in the statement of comprehensive income (Athanasakou et al 2011). -----CONCLUSIONS----- A customised accounting research database (CARD) is developed to provide a basis for conducting structured quantitative analysis based on DuPont (Brealey et al 2006), Graham (1976) and my own experientially derived metrics. This quantitative analysis is further supported with experiential intuitive unstructured inquiries in such areas as the likelihood of future returns, debt structuring risks, management orientation and so forth. Monte Carlo is used for estimating probable future outcome distributions and in optimising portfolio weighting. To further reduce the risk of incorrect decisions, a capital allocation policy is developed drawing from both the literature review (mainly Hertz 1964, Modigliani and Miller 1958, Buffett 1977 – 2012, Stiglitz 2010) and my own experiences. At each step in the analysis the practitioner has the opportunity to reflect on the data gathered and to formulate questions needed to address the knowledge gaps arising. The findings expose the care needed when analysing corporate financial data due to the vulnerabilities of financial databases to error as well as the vulnerabilities of published financial data to earnings management (Nelson et al 2002). The tools developed in the project place particular emphasis on data integrity through the use of both existing and new analytical and triangulation formulae.
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