BENNER CYCLE & FIBONACCI NUMBERS

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 establish the causes and timing timing of of fluctuati fluctuations ons in the economy. In 1875, he published business and commodity price forecasts for the period 1876 to 1904 (see Diagram Diagram 1). In his book, char ts ts were produced produced giving; * an 11 year cycle in corn and pig prices 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. Library . E R Dewey, Director of the Foundation Foundation for the Study of Cycles, assessed Benner's pig iron price forecasts over a 60 year  period. Remarkably, Remarkably, he regarded this th is 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, series, all of which were based on 9 years and its regular  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 AJ 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

Add

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

Add

THE 54 YEAR CYCLE LOWS COMMENCING IN 1913 56 Yr  Sq A J Frost 36 ysc S1

US Event

DJIA Bear  Market Low

7/1914 - 6 Months Late

1913

Sq 41 1913-14 Crises

+ 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

+ 16

Sq 01 Black Monday

2003

After  Greenspan Bubble

12/1987 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 AJ 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

+9

1946

May 29, 1946

5/1946 - 6/1949

+ 10

1956

April 6, 1956*

4/1956 10/1957

Add

March 10, 1937 3/1937 - 3/1938

+8

1964

February 9, 1966* 14 months late

+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 ?? ??

2/1966 10/1966

(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

Add

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

11-10-7  Year Cycle 1893

US Event

DJIA Bear Market Lows

1893 Panic 7/1893

+ 11

1904

1903-04 Crises

+ 10

1914

WW 1

11/1903 Two Months Early 7/1914

Crises

+7

1921

6/1921

+ 11

1932

+ 10

1942

+7

1949

+ 11

1960 (a)

+ 10

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

Great 7/1932 Depression WW 11

4/1942

Recession 6/1949 Recession

6/1962 18 Months Late

Recession 6/1970

(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

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

1901

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

1932 7/1932 Low

+ 34

+ 21 x 2 1974 12/1974 Low

2008 - ????

1966 - 2/1966 High

+ 34

+ 21 + 13

1987 12/1987 High

+ 13

1966 - 10/1966 Low +8

2000 - 1/200 High

1974 - 12/1974 Low

2000 1/2000 High

+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 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 16-1820 year cycles will predict trends 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. Moon Sun Finance