THE BENNER CYCLE, FIBONACCINUMBERS

& THE NUMBER 56

David McMinn

MOON - SUN FINANCE

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

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

* cotton prices which moved in a cycle with peaks every11 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 yearperiod. Remarkably, he regarded this cycle as showing a gain -loss ratio of 45 to 1, which was “the most notable forecast ofprices in existence”.

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

Diagram 1 THE ORIGINAL BENNER CYCLE CHART ASPUBLISHED IN 1875.

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

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

Pig Iron Price Cycle Lows of his business cycle occurred orevery 11, 9, 7 years (bottom line Diagram 1) repeating every27 years. The low years were 1816, 1823, 1834, 1843, 1850,1861, 1870, 1877, 1888.

Benner's cycle worked well throughout the 20th century andwas a very good indicator of US crises and/or recessions(McMinn, 2004). The links between Benner's cycle and the9/56 year panic cycle have been covered extensively byMcMinn (2004) and thus will not be discussed in this paper.

Alas, Benner's cycle is surrounded by some confusion. EitherBenner is not given credit as the originator of the cycle or hisname is misspelt - Banner and Brenner are two variationsgiven 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 occurringevery 8-9-10 years and two additional 54 year cycles of historicDJIA lows based on cycles of 16 -18 -20 years. Mostimportantly, Diagram 2 is not an extrapolation of Benner'searlier work into the 20th century, but rather was based on histime cycles of 8-9-10 years and 16-18-20 years. These cycleswere aligned with observed chronological trends.

Diagram 2 THE BENNER - FIBONACCI CYCLE CHART1902 - 1987

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

Table 1 THE 54 YEAR CYCLE LOWS COMMENCINGIN 1903

Add A JFrost 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 MonthsLate

+ 16 1957 Recession 10/1957

+ 18 1975 1973-75 Crises 12/1974 - 1 MonthEarly

+ 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 didnot fall in the 9/56 year cycle (see Table B, Appendix 1).

Table 2 THE 54 YEAR CYCLE LOWS COMMENCINGIN 1913

Add A J Frost56 Yr

Sq36 ysc

S1US Event DJIA Bear

Market Low

1913 Sq 41 1913-14 Crises 7/1914 - 6Months Late

+ 20 1933 Sq 05 GreatDepression

7/1932 - 6Months Early

+ 16 1949 Sq 21 Recession 6/1949

+ 18 1967 1966 Crisis 10/1966 - 3Months Early

+ 20 1987 Sq 01 Black Monday 12/1987

+ 16 2003 After

GreenspanBubble

10/2002 - 3Months Early

The 16-18-20 year cycle in Tables 1 & 2 are artifacts of 9/56year patterns presented in Table B, Appendix 1 and Table 6.2McMinn (2004). Many such artifact sub-cycles can begenerated 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 inDJIA highs since 1902. There is a consistent pattern for peaksin the DJIA to take place every 8-9-10 years in line withBenner's findings. This cycle has persisted throughout the 20thcentury, with great accuracy. Only 1964 and 1983 weremarkedly out in the timing of major highs. For 1964, thesecular peak occurred somewhat later in February 1966,whereas the November 1983 record peak marked thebeginning of a DJIA correction market.

Table 3 THE 8-9-10 YEAR CYCLE OFDJIA MARKET HIGHS

Add A JFrost

Major DJIAHigh

DJIA BearMarket

1902 June 17, 1901* 7 months early

6/1901 -11/1903

+ 8 1910November 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 1964February 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 BearMarket

+ 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 thebeginning of a 14.89% correction market thatpersisted until 7/1984.

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

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

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

Table 5 11-10-7 YEAR CYCLE OF DJIA BEARMARKET LOWS

Add 11-10-7Year Cycle US Event DJIA Bear Market

Lows 1893 1893 Panic 7/1893

+ 11 1904 1903-04Crises

11/1903 TwoMonths Early

+ 10 1914 WW 1 7/19141920-21

+ 7 1921 1920-21Crises 6/1921

+ 11 1932 GreatDepression 7/1932

+ 10 1942 WW 11 4/1942+ 7 1949 Recession 6/1949

+ 11 1960 (a) Recession 6/1962 18 MonthsLate

+ 10 1970 Recession 6/1970

+ 7 1977 No Event 2/1978 TwoMonths Late

+ 11 1988 1987 Panic 12/1987 OneMonth Early

+ 10 1998 1997-98Crises 8/1998 (b)

+ 7 2005 No event No Bear MarketLow

(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 a20% 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 USmarket 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 twoseries of 16-20 year cycles, based on the timing of majormarket turns or financial panics. The interval between thesetwo series is 29 years or one Inex eclipse cycle (DavidMcMinn). Most of these years fall in the 9/56 year cyclepatterns as shown in Table C Appendix 1 - only the exceptionsbeing 1953 and 1989

1910 Nov 19, 1909 DJIA High

1901 May 9 USPanic + 20 1930 Sep 03, 1929

DJIA High

+ 16 1917 Dec 19 DJIALow + 16 1946 May 29 DJIA

Peak

+ 20 1937 Mar 10 DJIAPeak + 20 1966 Feb 9 DJIA

Peak

+ 16 1953 No MajorMarket Turn + 16 1982 Aug 12 DJIA

Low

+ 20 1973 Jan 11 DJIAPeak +20 2002 Oct 9 DJIA Low

+ 16 1989 Oct 13 NearPanic

Fibonacci Numbers & Market Activity

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

1877 - 1877 SecularLow

+ 55 1932 - 8/1932Secular Low

+ 34 1966 - 2/1966Secular High

+ 21 1987 - 8/1987 High

+ 13 2000 - 1/2000Secular High

+ 8 2008 - ????

1932 -7/1932 Low + 34 1966 - 2/1966

High + 34 2000 - 1/200High

+ 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 (Sq01) produced a reasonably accurate trend of DJIA Highs/Lowsthrough 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 7months early

1929 + 34 1963 - 6/1962 Low 7months early

1929 + 55 1984 - 8/1982 Low 20months early.

However, something similar could not be repeated for theAugust 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 DJIAHigh/Low

1987 + 8 1995 - No DJIAHigh/Low

1987 + 13 2000 - 1/2000 High

The secular high of 1966 produced better results.

Sq 03 - 10/1966High + 3 1969 - 12/1968 High - One

Month Early

1966 + 5 1971 - 6/1970 Low - 7Months early

1966 + 8 1974 - 12/1974 Low

1966 + 13 1979 - 2/1980 High - 2Months Late

1966 + 13 Months Late1966 + 21 1987 - 8/1987 High1966 + 34 2000 - 1/2000 High

Walter E White, in his Elliott Wave Principle (1968), believedthat "the next important low may be in 1970". This correct

forecast was derived by using Fibonacci numbers.

6/1949Low 1949 + 21 1970

10/1957Low 1957 + 13 1970

6/1962Low 1962 + 8 1970

2/1966High 1965 + 5 1970

Prechter (2000) predicted a bear market low for 2003-2004,based on various technical forecasting techniques, includingthe Fibonacci numbers. The following has been derived from

his work with only one year that was clearly amiss - 1995 whichproduced no major market turns. The 10/2002 market low wasthe nadir of the 2000-02 bear market and thus be a little earlier

than forecasted.

1857 Secular Low - 14months early 1859 + 144 2003

07/1914 Low 1914 + 89 20036/1949 Low - 6

Months Late 1948 + 55 2003

6/1970 Low - 6 MonthsLate 1969 + 34 2003

8/1982 Low 1982 + 21 200310/1990 Low 1990 + 13 2003No High/Low 1995 + 8 2003

8/1998 Near BearMarket Low 1998 + 5 2003

01/2000 Record DJIAHigh 2000 + 3 2003

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

have been simply ignored.

Causal Mechanisms

According to Benner, "the cause producing the periodicity andlength of these cycles may be found in our solar system". "Itmay be a meteorological fact that Jupiter is the ruling elementin our price cycles of natural productions; while also it may besuggested that Saturn exerts an influence regulating the cyclesin manufacture and trade". Additionally, Uranus and Neptune"may send forth an electric influence affecting Jupiter, Saturnand, in turn, the Earth". "When certain combinations areascertained which produce one legitimate invariablemanifestation from an analysis of the operations of thecombined solar system, we may be enabled to discover thecause producing our price cycles, and the length of theirduration. 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 byJevons, Herschel and others.

The Sun, The Moon & The Number 56 showed that the 9/56year panic cycle arises from cycles of the Moon and Sun.Given the links between the Benner and the 9/56 year cycles, itcould be reasonably postulated that both are based onlunisolar cycles. Hard evidence of a sunspot or planetaryinfluence in financial markets has failed to be established,despite a tremendous level of research. Thus, Benner's view ofsunspots and/or planets influencing the timing of his cyclescannot be supported.

The 11-9-7 Year Cycle of market troughs was not mentioned intA J Frost's assessment on market cycles, although it was akey component of the Benner Cycle. It may be more than acoincidence that 7, 11 and 18 are all Lucas numbers. Theseare similar to the Fibonacci numbers except they commencewith 1, 3 instead of 1, 1 as for the Fibonacci numbers. TheLucas 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 11-9-7can be broken down into various eclipse cycles of the 7 yearTzolkinex, 9 Year Half Saros and 11 Year Tritos. The 8-9-10year cycle of market highs is much more difficult to explain interms of know eclipse cycles.

Conclusions

The 8-9-10 year and the 16-18-20 year cycles are based onthe interval of 9 years and its regular deviations. This is quiteamazing as they have been so relevant in stock market trendsduring the 20th century. The three 54 year cycles, proposed byboth Benner and Frost, may be directly linked to the 9/56 year

both Benner and Frost, may be directly linked to the 9/56 yearpanic cycle (see Tables A & B, Appendix 1). As noted byDavid McMinn (2004), the 9/56 year cycle only correlated withthe timing of financial crises. Something similar could not beconfirmed for the timing of peaks and troughs in financialactivity. Thus these findings on the 8-9-10 year cycle are veryinteresting, as they may provide clues on the timing of peaksand troughs in financial markets. If the Benner - Fibonaccicycle holds up to critical assessment, it may offer theoreticalsupport for the use of these numbers in financial forecasting.

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

* The findings are presented selectively and thus areheavily biased. Those series that do not support the Fibonaccihypothesis are ignored. Thus, the Fibonacci series could ariseby coincidence alone and thus may not have any truerelevance in market trends.

* Both highs and lows may appear in a given series, but noexplanation can be offered as to why this is so. One couldreasonably expect a series to consist of all highs or all lows.Why the peaks and troughs are interchangeable in a particularseries cannot be accounted for.

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

It remains to be seen how accurately these 8-9-10 and 16-18-20 year cycles will predict trends into the 21st century. The9/56 year cycle and presumably the Benner Cycle mustchange over very long time frames rather remaining fixed.Furthermore, the business cycle has profoundly altered sinceWorld War II (Zarnowitz, 1992), with much longer growthperiods and brief shallow recessions. With the abandonment ofthe gold standard in the 1930's, the US Government has beenable to increase money supply continuously over the past 65years. This has resulted in almost perpetual inflation andaltered the periodicity of recessions, which now occur as rareevents. A looming financial crisis is also now countered bylowering interest rates and flooding the financial system withmoney. Even so, the Benner Cycles of 8-9-10 and 16-18-20years remain of great interest, especially given Dewey'scomments on their forecasting accuracy.

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

References

Benner, S. Benner's Prophecies of Future Ups & Downs inPrices. Robert Clark Co.1875.

Prices. Robert Clark Co.1875.McMinn, David. Market Timing By The Number 56. TwinPalms Publishing. 2002. Revised 2004.Mogey, Richard. The Mystery of the Forecast of an EarlierGeneration. Cycles. p 199-202. July - August 1991.Prechter, Robert. A Major Stock Market Low Is Still Due in2003-2004. The Elliott Wave Theorist. July 2000.Prechter, Robert & Frost A J. Elliott Wave Principle: Key toStock 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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