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

See all articles by Amin H. Amershi

Amin H. Amershi

McMaster University

Ehsan H. Feroz

University of Washington Tacoma, Milgard School of Business-Accounting ; University of Illinois at Urbana-Champaign; Government of the United States of America - US GAO Advisory Council; University of Minnesota Duluth, Labovitz School of Business-Department of Accounting; University of Minnesota, Carlson School of Management-Department of Accounting; American Accounting Association

Date Written: 2000

Abstract

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

Suggested Citation

Amershi, Amin H. and Feroz, Ehsan H., The Occurrence of Fibonacci Numbers in Time Series of Financial Accounting Ratios: Anomalies or Indicators of Firm Survival, Bankruptcy and Fraud? An Exploratory Study (2000). Managerial Finance, Vol. 26, No. 11, pp. 5-20, 2000 , Available at SSRN: https://ssrn.com/abstract=1180582

Amin H. Amershi

McMaster University ( email )

1280 Main Street West
Hamilton, Ontario L8S 4M4
Canada

Ehsan H. Feroz (Contact Author)

University of Washington Tacoma, Milgard School of Business-Accounting ( email )

1900 Commerce Street, Campus Box 358420
Tacoma, WA 98402-3100
United States
(253) 692 4728 (Phone)
253 692 4523 (Fax)

HOME PAGE: http://www.tacoma.washington.edu/business

University of Illinois at Urbana-Champaign ( email )

515 East Gregory Drive# 2307
Champaign, IL 61820
United States

Government of the United States of America - US GAO Advisory Council ( email )

441 G Street NW
Washington, DC 20548-0001
United States

University of Minnesota Duluth, Labovitz School of Business-Department of Accounting ( email )

10 University Drive
Labovitz School of Business
Duluth, MN 55812
United States
218-726-6988 (Phone)
218-726-8510 (Fax)

University of Minnesota, Carlson School of Management-Department of Accounting ( email )

420 Delaware St. SE
Minneapolis, MN 55455
United States

American Accounting Association ( email )

5717 Bessie Drive
Sarasota, FL 34233-2399
United States

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