Checking financial markets via Benford’s law: the S&amp;P 500 case

Corazza, Marco; Ellero, Andrea; Zorzi, Alberto

doi:10.1007/978-88-470-1481-7_10

Cited by 20 publications

(15 citation statements)

References 7 publications

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“…In both cases, [24] and [26], Benford's law is claimed to be valid. Closely connected to our research, [25] checked whether financial markets like the S&P 500 case, from August 14, 1995, to October 17, 2007, thus 3067 data points, obeyed BL1 [25]. The authors also found some reasonable agreement, except that they claim the presence of anomalous times, like market crashes or special events.…”

Section: State Of the Artsupporting

confidence: 72%

Benford’s laws tests on S&P500 daily closing values and the corresponding daily log-returns both point to huge non-conformity

Ausloos

Ficcadenti

Dhesi

et al. 2021

Physica A: Statistical Mechanics and its Applications

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The so-called Benford's laws are of frequent use to detect anomalies and regularities in data sets, particularly in election results and financial statements. However, primary financial market indices have not been much studied, if studied at all, within such a perspective.This paper presents features in the distributions of S&P500 daily closing values and the corresponding daily log-returns over a long time interval, [03/01/1950 -22/08/2014], amounting to 16265 data points. We address the frequencies of the first, second, and first two significant digits and explore the conformance to Benford's laws of these distributions at five different (equal size) levels of disaggregation. The log-returns are studied for either positive or negative cases. The results for the S&P500 daily closing values are showing a remarkable lack of conformity, whatever the different levels of disaggregation. The causes of this non-conformity are discussed, pointing to the danger in taking Benford's laws for granted in large databases, whence drawing ''definite conclusions''. The agreements with Benford's laws are much better for the log-returns. Such a disparity in agreements finds an explanation in the data set itself: the index's inherent trends. To further validate this, daily returns have been simulated via the Geometric Brownian Motion and calibrating the simulations with the observed data averages and testing against Benford's laws when the log-returns distribution's standard deviation changes. One finds that the trend and the standard deviation of the distributions are relevant parameters in concluding about conformity with Benford's laws.

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Section: State Of the Artsupporting

confidence: 72%

Benford’s laws tests on S&P500 daily closing values and the corresponding daily log-returns both point to huge non-conformity

Ausloos

Ficcadenti

Dhesi

et al. 2021

Physica A: Statistical Mechanics and its Applications

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“…Among previous studies on fraud detection, Corazza et al (2010) examined the frequency distribution of the first digit of the price and daily returns of the index. The results of the Chi-square test at two significant levels of 1% and 5% indicated that the research data did not follow Benford's law.…”

Section: Research Backgroundmentioning

confidence: 99%

Predictability of financial statements fraud-risk using Benford’s Law

Rad

Amiri

Ranjbar

et al. 2021

Cogent Economics & Finance

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The main objective of this research is to investigate the Predictability of Financial Statements Fraud-Risk Using Benford's Law on the Tehran Stock Exchange. Therefore, based on financial fraud detection criteria, a sample of 50 companies was extracted that 25 companies had fraud-risk in financial statements (experimental group) and 25 did not have fraud-risk (control group). Next, the frequency distribution of the first left digit of the numbers in the financial statements as well as the financial ratios of both groups was extracted, and their conformity with Benford's distribution was evaluated through the chi-square test to test the research hypotheses. The comparison between the mentioned frequency distribution and Benford's distribution showed a significant difference. The result indicates that Benford's law cannot predict the financial statements fraud-risk of companies, in other words, Benford's law cannot separate companies with fraud-risk from those without fraud-risk in financial statements.

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“…Benford's Law was also applied in finance literature by De Ceuster, Dhaene, and Schatteman (), Dorfleitner and Klein () and Shawn and Kalaichelvan (), which explored stock index data. Corazza et al () studied the stock prices of and returns on assets in the S&P 500 Index. Perhaps not surprisingly, they found that the first digits of the prices and returns followed the expectations of Benford's Law, providing evidence that markets, at least in the short term, are truly unbiased and that their data are distributed randomly (Ley, ).…”

Section: Studying Ceo Pay Using Benford's Lawmentioning

confidence: 99%

“…Counterintuitively, however, Benford ()—and before him Newcomb ()—found that first digit values are not as equally distributed as one might expect. In a randomly distributed unbiased dataset of stock prices, for example, “1” is the first digit almost 30.1 percent of the time, whereas “9” occurs only 5 percent of the time (Corazza, Ellero, & Zorzi, ; Ley, ). This statistical phenomenon has been found in all unbiased datasets; studies have confirmed its existence on the basis of data from disparate fields (Abrantes‐Metz, Kraten, Metz, & Seow, ; Benford, ; Leemann & Bochsler, ; Mir, ; Nigrini, ; Nigrini & Mittermaier, ).…”

Section: Introductionmentioning

confidence: 99%

Can Benford's Law explain CEO pay?

Mukherjee

2017

Corporate Governance

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Manuscript Type Empirical Research Question/Issue This study applies the statistical properties of Benford's Law to CEO pay. Benford's “Law” states that in an unbiased dataset, the first digit values are usually unequally allocated when considering the logical expectations of equal distribution. In this study we question whether the striking empirical properties of Benford's Law could be used to analyze the negotiating power and preferences of CEOs. We argue that performance‐based or market‐determined compensations should follow Benford's Law, demonstrating no direct negotiation by the CEOs. Conversely, deviation from Benford's Law could reveal CEO negotiating power or even preference. Research Findings/Insights Our analysis shows that market‐determined “Option Fair Value” (the dollar value of stock options when exercised) conforms closely to Benford's Law, as opposed to “Salary”, which is fully negotiated. “Bonus”, “Option Award”, and “Total Compensation” are generally also largely consistent with Benford's Law, but with some exceptions. We interpret these exceptions as negotiation by the CEOs. Surprisingly, we found that CEOs prefer to be paid in round figure values, especially “5”. We use Benford's Law to study the negotiating powers of CEOs vs. that of other executives. Finally, we compare the negotiating tactics of CEOs before and after SOX and analyze the impact of firm size on their compensation. Theoretical/Academic Implications This study introduces Benford's Law and its applications within the corporate governance literature. Practitioner/Policy Implications This method could be used by academics, industry and regulators to uncover compensation patterns within large business departments and/or organizations or even entire industry segments.

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Checking financial markets via Benford’s law: the S&P 500 case

Cited by 20 publications

References 7 publications

Benford’s laws tests on S&P500 daily closing values and the corresponding daily log-returns both point to huge non-conformity

Benford’s laws tests on S&P500 daily closing values and the corresponding daily log-returns both point to huge non-conformity

Predictability of financial statements fraud-risk using Benford’s Law

Can Benford's Law explain CEO pay?

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