The Occurrence of Fibonacci Numbers in Time Series of Financial Accounting Ratios: Anomalies or Indicators of Firm Survival, Bankruptcy and Fraud? An Exploratory Study
16 Pages Posted: 30 Jul 2008 Last revised: 20 Feb 2018
Date Written: 2000
Although there have been conjectures about possible occurrences of Fibonacci numbers and golden means and ratios in financial statements (Feroz 1992), it is intriguing as to why managers should be reporting these rather stylized series of numbers the occurrences of which have hitherto been documented mostly in the biological sciences (Davis 1989). One possible explanation is that these numbers are merely random occurrences and are not part of any systematic financial reporting patterns. Still other conjectures are that these numbers are generated by a process of skillful manipulation of accounting rules which has been documented in empirical accounting literature.
The purpose of this study is to empirically verify the null hypothesis that the occurrence of Fibonacci numbers, golden ratios and means in financial ratios, is merely a random occurrence without any statistical significance. We constructed two samples: a random sample of 200 companies, and another sample of 200 companies that have survived 20 years or more. We find that (1) there is an infinity of distributions under which the null hypothesis cannot be rejected for either sample, and (2) there is an infinity of distributions under which the null hypothesis cannot be rejected for the sample of 200 surviving companies but can be rejected for the random sample. The latter result is particularly important because it shows that it is possible to discriminate between surviving companies and randomly selected companies based on golden mean in total debt/total invested capital ratio.
Keywords: Fibonacci Numbers, Golden Ratio, Golden Mean, Time Series, Debt to Toal Invested Capital Ratio, Capital structure, Firm survival, Bankruptcy, Fraud, Number theory, Political Economy
JEL Classification: C6, G1, G2, G3, M4
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