THE BENNER CYCLE, FIBONACCI NUMBERS
& THE NUMBER 56


David McMinn

MOON - SUN FINANCE


Samuel Benner, a prosperous farmer, was wiped out financially by the 1873 panic and a hog cholera epidemic. In retirement, he set about to establish the causes and timing of fluctuations in the economy. In 1875, he published business and commodity price forecasts for the period 1876 to 1904 (see Diagram 1). In his book, charts were produced giving;

*           an 11 year cycle in corn and pig prices with peaks alternating every 5 and 6 years.

*           cotton prices which moved in a cycle with peaks every 11 years.

*           a 27 year cycle in pig iron prices with lows every 11, 9, 7 years and peaks in the order 8, 9, 10 years.

Samuel Benner's book is available at Open Library.

E R Dewey, Director of the Foundation for the Study of Cycles, assessed Benner's pig iron price forecasts over a 60 year period. Remarkably, he regarded this cycle as showing a gain - loss ratio of 45 to 1, which was “the most notable forecast of prices in existence”.

Benner's pig iron price cycle may be broken down into three series, all of which were based on 9 years and its regular deviations (see Diagram 1). Those years listed by Kindleberger (Appendix B, 1996) as containing major financial crises have been presented in BOLD throughout the text.

Diagram 1      THE ORIGINAL BENNER CYCLE CHART AS PUBLISHED IN 1875.

   


The 54 Year Panic Cycle
arises from
panics every 16, 18, 20  years, with this series repeating every 54 years (see upper line Diagram 1). According to Benner, “it takes panics 54 years in their order to make a revolution or to return to the same order”. The key years were 1819, 1837, 1857, 1873 which were all found in the 36 ysc Series 1 of the 9/56 year cycle (see Table A, Appendix 1).

Pig Iron Price
Highs of good years took place every 8, 9, 10 years (middle line Diagram 1) repeating every 27 years. The high years were 1810, 1818, 1827, 1837, 1845, 1854, 1864, 1872, 1881, 1891

Pig Iron Price Cycle Lows of his business cycle occurred or every 11, 9, 7 years (bottom line Diagram 1) repeating every 27 years. The low years were 1816, 1823, 1834, 1843, 1850, 1861, 1870, 1877, 1888.

Benner's cycle worked well throughout the 20th century and was a very good indicator of US crises and/or recessions (McMinn, 2004). The links between Benner's cycle and the 9/56 year panic cycle have been covered extensively by McMinn (2004) and thus will not be discussed in this paper.

Alas, Benner's cycle is surrounded by some confusion. Either Benner is not given credit as the originator of the cycle or his name is misspelt - Banner and Brenner are two variations given by some sources. 

A J Frost's Adaptation

A J Frost presented a variation on Benner's theory (Prechter & Frost, 1978). This gave peaks in the US stock market occurring every 8-9-10 years and two additional 54 year cycles of historic DJIA lows based on cycles of 16 -18 -20 years. Most importantly, Diagram 2 is not an extrapolation of Benner's earlier work into the 20th century, but rather was based on his time cycles of 8-9-10 years and 16-18-20 years. These cycles were aligned with observed chronological trends. 

Diagram 2      THE BENNER - FIBONACCI CYCLE CHART 1902 - 1987 


The 54 year Cycle in Table 1 may be strongly linked to financial trends, as only the year 1995 did not align with a DJIA bear market low.  Importantly, the years 1903, 1921, 1941, 1957, 1975, 1995 all happen within the combined 36 ysc Series 3 & 4 (see Table 6.2, McMinn 2004). Taking this series and adding one year gives 1904, 1922, 1942, 1958, 1976, 1996 - all of which occurred in the 9/56 year cycles as presented in Table B, Appendix 1. The only year in Table 1 that cannot be linked to a bear market low was1995.

Table 1     THE 54 YEAR CYCLE LOWS COMMENCING IN 1903
Add A J Frost US Event DJIA Bear Market Low
  1903 1903-04 Crises 11/1903 
+ 18 1921 1920-21 Panic 7/1921 
+ 20 1941 1942 WW II 4/1942 - 4 Months Late
+ 16 1957 Recession 10/1957
+ 18 1975 1973-75 Crises 12/1974 - 1 Month Early 
+ 20 1995 No Event No Major Low


Table 2 gives the second 54 year cycle of major trough years - 1913, 1933, 1949, 1967, 1987, 2003  - only the latter year did not fall in the 9/56 year cycle  (see Table B, Appendix 1).

Table 2        THE 54 YEAR CYCLE LOWS COMMENCING IN 1913
Add A J Frost 56 Yr Sq
36 ysc S1
US Event DJIA Bear Market Low
  1913 Sq 41 1913-14 Crises 7/1914 - 6 Months Late 
+ 20 1933 Sq 05 Great Depression 7/1932 - 6 Months Early
+ 16 1949 Sq 21 Recession 6/1949
+ 18 1967    1966 Crisis 10/1966 - 3 Months Early
+ 20 1987 Sq 01 Black Monday 12/1987
+ 16 2003   After Greenspan Bubble 10/2002 - 3 Months Early


The 16-18-20 year cycle in Tables 1 & 2 are artifacts of 9/56 year patterns presented in Table B, Appendix 1 and Table 6.2 McMinn (2004). Many such artifact sub-cycles can be generated from the 9/56 year cycle (Section 2.4 & Chapter 6, McMinn, 2004).

8-9-10 Year Cycle of DJIA Highs

Diagram 2 by A J Frost also gives the 8-9-10 year trends in DJIA highs since 1902. There is a consistent pattern for peaks in the DJIA to take place every 8-9-10 years in line with Benner's findings. This cycle has persisted throughout the 20th century, with great accuracy. Only 1964 and 1983 were markedly out in the timing of major highs.  For 1964, the secular peak occurred somewhat later in February 1966, whereas the November 1983 record peak marked the beginning of a DJIA correction market. 

       Table 3       THE 8-9-10 YEAR CYCLE OF DJIA MARKET HIGHS

Add

A J Frost

Major DJIA High

DJIA Bear Market

  1902 June 17, 1901* 
7 months early
6/1901 - 11/1903
+ 8 1910 November 19, 1909 
2 months early
11/1909 - 9/1911
+ 9 1919 November 3, 1919* 11/1919 - 8/1921
+ 10 1929 September 3, 1929* 9/1929 - 7/1932
+ 8 1937 March 10, 1937 3/1937 - 3/1938
+ 9 1946 May 29, 1946 5/1946 - 6/1949
+ 10 1956 April 6, 1956* 4/1956 - 10/1957
+ 8 1964 February 9, 1966* 
14 months late
2/1966 - 10/1966
+ 9 1973 January 11, 1973* 1/1973 - 12/1974
+ 10 1983 No High (a) No DJIA Bear Market
+ 8 1991 July 16, 1990*
6 months early
7/1990 - 10/1990
+ 9 2000 January 14, 2000* 1/2000 -  10/2002
+ 10 2010 High ???? Bear Market ????

(a) 11/1983 marked a record high and the beginning of a 14.89% correction market that persisted until 7/1984.


11-10-7 Year Cycle of DJIA Lows ????

The 11-9-7 year cycle of market troughs was not mentioned in A J Frost's assessment on market cycles, even though it was a key element of Benner's original cycle. No series of DJIA bear market lows could be established based on 11-9-7 years, even though it was extensively assessed.  

Unexpectedly, a 11-10-7 year cycle of DJIA bear market lows fits much more precisely (see Table 5). During the first half of the 20th century, most  important historic lows fall within this cycle - 1893, 1904, 1914, 1921, 1932, 1942 & 1949. The record for the latter half of the century was not as good because the major bear markets of 1974 and 1982 did not take place within the cycle. The accuracy of the 11-10-7 year cycle was amazing as only there was one notable exception - 1960, which was followed by a major low in June 1962 some 18 months overdue. All other lows fell within the cycle or or one or two months before or after. Those lows exactly within the cycle occurred in the months April to August.
 

Table 5    11-10-7 YEAR CYCLE OF DJIA BEAR MARKET LOWS

Add

11-10-7 Year Cycle

US Event

DJIA Bear Market Lows
  1893 1893 Panic 7/1893
+ 11 1904 1903-04 Crises 11/1903    Two Months Early
+ 10 1914 WW 1 7/1914
+ 7 1921 1920-21 Crises 6/1921
+ 11 1932 Great Depression 7/1932
+ 10 1942 WW 11 4/1942
+ 7 1949 Recession 6/1949
+ 11 1960 (a) Recession 6/1962   18 Months Late
+ 10 1970 Recession 6/1970
+ 7 1977 No Event 2/1978   Two Months Late
+ 11 1988 1987 Panic 12/1987  One Month Early
+ 10 1998 1997-98 Crises 8/1998 (b)
+ 7 2005 No event No Bear Market Low

(a) 10/1960 was the low of a 17.4% correction market, which commenced in 1/1960. 
(b) This was a near bear market low, as a drop of 19.6% was recorded. (A bear market is commonly defined as a 20% market fall.)


Why this 11-10-7 year cycle is so important remains unknown, although 28 multiplied by two gives 56 a key number in cycle theory. 

Carolan's 16-20 Year Cycles

Chris Carolan found four 36 year sub-cycles persisted in US market trends during the 20th century as follows:

1901  1917 1910 1930
+ 36 + 36 + 36 + 36
1937 1953 1946 1966
+ 36 + 36 + 36 + 36
1973 1989 1982 2002


These four 36 year cycles were presented in terms of two series of 16-20 year cycles, based on the timing of major market turns or financial panics. The interval between these two series is 29 years or one Inex eclipse cycle (David McMinn). Most of these years fall in the 9/56 year cycle patterns as shown in Table C Appendix 1 - only the exceptions being 1953 and 1989

        1910 Nov 19, 1909   DJIA High
  1901 May 9  US Panic + 20 1930 Sep 03, 1929  DJIA High
+ 16 1917 Dec 19  DJIA Low + 16 1946 May 29   DJIA Peak
+ 20 1937 Mar 10  DJIA Peak + 20 1966 Feb 9   DJIA Peak
+ 16 1953 No Major Market Turn + 16 1982 Aug 12  DJIA Low
+ 20 1973 Jan 11  DJIA Peak +20 2002 Oct 9   DJIA Low
+ 16 1989 Oct 13  Near Panic      


Fibonacci Numbers & Market Activity

The Fibonacci numbers, based on the tropical year, have been linked by various sources to financial activity. For example, beginning with the secular low of 1877:

  1877 - 1877 Secular Low
+ 55 1932 - 8/1932 Secular Low
+ 34 1966 - 2/1966 Secular High
+ 21 1987 - 8/1987 High
+ 13 2000 - 1/2000 Secular High
+ 8 2008 - ????

 

1932 - 7/1932 Low + 34 1966 - 2/1966 High + 34 2000 - 1/200 High

+ 21  x 2

 

+ 21

 

-

1974 - 12/1974 Low + 13 1987 - 12/1987 High + 13 2000 - 1/2000 High

 

  1966 - 10/1966 Low
+ 8 1974 - 12/1974 Low
+ 8 1982 - 8/1982 Low
+ 8 1990 - 10/1990 Low
+ 8 1998 - 8/1998 Low
+ 8 2006 - ????



Adding Fibonacci numbers to the high of September 1929 (Sq 01) produced a reasonably accurate trend of DJIA Highs/Lows through to 1942 with declining accuracy after that.

Sq 01 - 9/1929  High + 3 1932 - 7/1932 Low 
1929 + 5 1934 - 7/1934 Low 
1929 + 8 1937 - 3/1937 High 
1929 + 13 1942 - 4/1942 Low 
1929 + 21 1950 - 6/1949 Low 7 months early
1929 + 34 1963 - 6/1962 Low 7 months early
1929 + 55 1984 - 8/1982 Low 20 months early.

However, something similar could not be repeated for the August 1987 record high (Sq 03). 

Sq 03 - 8/1987 High   + 2 1989 - No DJIA High/Low
1987 + 3 1990 - 7/1990 High & 10/1990 Low
1987 + 5 1992 - No DJIA High/Low
1987 + 8 1995 - No DJIA High/Low
1987 + 13 2000 - 1/2000 High


The secular high of 1966 produced better results.

Sq 03 - 10/1966 High   + 3 1969 - 12/1968 High - One Month Early 
1966 + 5 1971 - 6/1970 Low - 7 Months early
1966 + 8 1974 - 12/1974 Low
1966 + 13 1979 - 2/1980 High - 2 Months Late
1966 + 21 1987 -  8/1987 High
1966 + 34 2000 - 1/2000 High


Walter E White, in his Elliott Wave Principle (1968), believed that "the next important low may be in 1970". This correct forecast was derived by using Fibonacci numbers.

6/1949 Low 1949 + 21 1970
10/1957 Low  1957 + 13 1970
 6/1962 Low 1962 + 8 1970
2/1966 High  1965 + 5 1970


Prechter (2000) predicted a bear market low for 2003-2004, based on various technical forecasting techniques, including the Fibonacci numbers. The following has been derived from his work with only one year that was clearly amiss - 1995 which produced no major market turns. The 10/2002 market low was the nadir of the 2000-02 bear market and thus be a little earlier than forecasted.

1857 Secular  Low - 14 months early 1859 + 144 2003
07/1914  Low 1914 + 89 2003
6/1949  Low  - 6 Months Late 1948 + 55 2003
6/1970  Low - 6 Months Late 1969 + 34 2003
8/1982  Low 1982 + 21 2003
10/1990  Low 1990 + 13 2003
No High/Low 1995 + 8 2003
8/1998  Near Bear Market Low  1998 + 5 2003
01/2000 Record DJIA High 2000 + 3 2003


These findings on the Fibonacci numbers are certainly interesting, but they can be justifiably criticised. Such market patterns may arise by selecting the data that confirms the Fibonacci hypothesis. Contrary examples, which do not fit, have been simply ignored.


Causal Mechanisms
 


According to Benner, "the cause producing the periodicity and length of these cycles may be found in our solar system". "It may be a meteorological fact that Jupiter is the ruling element in our price cycles of natural productions; while also it may be suggested that Saturn exerts an influence regulating the cycles in manufacture and trade". Additionally, Uranus and Neptune "may send forth an electric influence affecting Jupiter, Saturn and, in turn, the Earth". "When certain combinations are ascertained which produce one legitimate invariable manifestation from an analysis of the operations of the combined solar system, we may be enabled to discover the cause producing our price cycles, and the length of their duration. Benner never fully explained the basis of his cycle, but he did make a connection through the weather and climate, suggesting he was aware of the earlier work on sunspots by Jevons, Herschel and others.
 

The Sun, The Moon & The Number 56 showed that the 9/56 year panic cycle arises from cycles of the Moon and Sun. Given the links between the Benner and the 9/56 year cycles, it could be reasonably postulated that both are based on lunisolar cycles. Hard evidence of a sunspot or planetary influence in financial markets has failed to be established, despite a tremendous level of research. Thus, Benner's view of sunspots and/or planets influencing the timing of his cycles cannot be supported.

The 11-9-7 Year Cycle of market troughs was not mentioned in tA J Frost's assessment on market cycles, although it was a key component of the Benner Cycle. It may be more than a coincidence that 7, 11 and 18 are all Lucas numbers. These are similar to the Fibonacci numbers except they commence with 1, 3 instead of 1, 1 as for the Fibonacci numbers. The Lucas series is as follows:

                      1, 3, 4, 7, 11, 18, 29, 47, 76,  123, 199...............

These numbers have been linked to lunisolar cycles (McMinn, 2004). Additionally, Benner's cycles of 16-18-20 and 11-9-7 can be broken down into various eclipse cycles of the 7 year Tzolkinex, 9 Year Half Saros and 11 Year Tritos. The 8-9-10 year cycle of market highs is much more difficult to explain in terms of know eclipse cycles. 

Conclusions

The 8-9-10 year and the 16-18-20 year cycles are based on the interval of 9 years and its regular deviations. This is quite amazing as they have been so relevant in stock market trends during the 20th century. The three 54 year cycles, proposed by both Benner and Frost, may be directly linked to the 9/56 year panic cycle (see Tables A & B, Appendix 1). As noted by David McMinn (2004), the 9/56 year cycle only correlated with the timing of financial crises. Something similar could not be confirmed for the timing of peaks and troughs in financial activity. Thus these findings on the 8-9-10 year cycle are very interesting, as they may provide clues on the timing of peaks and troughs in financial markets. If the Benner - Fibonacci cycle holds up to critical assessment, it may offer theoretical support for the use of these numbers in financial forecasting.

It is debatable whether the Fibonacci numbers can be found in markets patterns, as suggested in this paper. This work can be criticised for two reasons:

*         The findings are presented selectively and thus are heavily biased. Those series that do not support the Fibonacci hypothesis are ignored. Thus, the Fibonacci series could arise by coincidence alone and thus may not have any true relevance in market trends.

*         Both highs and lows may appear in a given series, but no explanation can be offered as to why this is so. One could reasonably expect a series to consist of all highs or all lows. Why the peaks and troughs are interchangeable in a particular series cannot be accounted for.

Whether Fibonacci numbers are actually valid in market trends is debatable and more research is required before any firm answer may be given.


It remains to be seen how accurately these 8-9-10 and 16-18-20 year cycles will predict tren
ds into the 21st century. The 9/56 year cycle and presumably the Benner Cycle must change over very long time frames rather remaining fixed. Furthermore, the business cycle has profoundly altered since World War II (Zarnowitz, 1992), with much longer growth periods and brief shallow recessions. With the abandonment of the gold standard in the 1930's, the US Government has been able to increase money supply continuously over the past 65 years. This has resulted in almost perpetual inflation and altered the periodicity of recessions, which now occur as rare events. A looming financial crisis is also now countered by lowering interest rates and flooding the financial system with money. Even so, the Benner Cycles of 8-9-10 and 16-18-20 years remain of great interest, especially  given Dewey's comments on their forecasting accuracy.

Copyright. ©  2003. David McMinn. All rights reserved.


References

Benner, S. Benner's Prophecies of Future Ups & Downs in Prices. Robert Clark Co.1875.
McMinn, David. Market Timing By The Number 56. Twin Palms Publishing. 2002. Revised 2004.
Mogey, Richard. The Mystery of the Forecast of an Earlier Generation. Cycles. p 199-202. July - August 1991.
Prechter, Robert.
A Major Stock Market Low Is Still Due in 2003-2004. The Elliott Wave Theorist. July 2000.
Prechter, Robert & Frost  A J. Elliott Wave Principle: Key to Stock Market Profits. New Classics Library. 1978.
Tsing.com Elliott Wave Principle. www.tsing.com/theory/lesson25.htm 

Zarnowitz, Victor. Business Cycles: Theory, History, Indicators and Forecasting. The University of Chicago Press. 1992.

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