### Amershi, AH and Feroz, EH (2000)

#### The occurrence of Fibanocci numbers in time series of financial accounting ratios: Anomalies or indicators of firm survival, bankruptcy and fraud? An exploratory study

Managerial Finance 26(11), pp. 5-20.

**ISSN/ISBN:** Not available at this time.
**DOI:** 10.1108/03074350010766954

**Abstract:** Although there have been conjectures about the 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 a part
of any systematic financial reporting pattern. Still other conjectures are that these numbers
are generated by a process of skilful manipulation of accounting rules (e.g. smoothing)
which has been documented in the empirical accounting literature (Healy, 1985). The purpose
of this study is to empirically verify the null hypothesis that the occurrence of Fibonacci
numbers, golden ratio and means in financial accounting 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 i) there is an infinity of distributions under which the null hypothesis
(Ho) cannot be rejected for either sample; and ii) there is an infinity of distributions
under whichH0 cannot be rejected for the sample of 200 surviving companies but can be rejected
for 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 the golden mean in total debt/total invested capital ratio.

**Bibtex:**

```
@article{,
AUTHOR = {Amershi, Amin H. and Feroz, Ehsan H.},
TITLE = {The occurrence of Finobacci numbers in time series of financial accounting ratios: Anomalies or indicators of firm survival, bankruptcy and fraud? An exploratory study},
JOURNAL = {Managerial Finance},
YEAR = {2000},
VOLUME = {26},
NUMBER = {11},
PAGES = {5--20},
DOI = {10.1108/03074350010766954},
URL = {http://dx.doi.org/10.1108/03074350010766954},
}
```

**Reference Type:** Journal Article

**Subject Area(s):** Accounting