- 1998: Volume 7, No. 2 Will the Bull Market Ever End? A Kondratieff Perspective

Perhaps the business cycle has been repealed. Perhaps long waves are not as viable for studying the markets as for studying social trends. If the latter is the case, then I may be the last proponent of using any long wave for anticipating market movement.

Before being exiled to Siberia, Soviet economist Nikolai Kondratieff suggested a model (i.e., the Kondratieff Wave) to explain the 55-year boom-bust cycle which capitalist economies appeared to undergo as a product of capital accumulation, consumption, replacement, and so on. Kondratieff Wave enthusiasts believe that a peak in the cycle came around 1987.

While many embrace the Kondratieff Wave for analyzing socio-economic trends, there is no doubt that market technicians who were proponents of both Kondratieff and Elliott Wave have been disappointed by the markets' continued rise since their calculated wave climaxes. However, when adjustments are made to the Kondratieff Wave parameters and the cycle undergoes wave deformation, a calculable terminus ad quem (or, climax) occurs during the first quarter of 1998.

Parameter Adjustments

Some have tried to clarify the movement of capital as a product of demographic fluctuations. Some believe that the Fed is doing such a good job of managing the nation's money supply that the business cycle has been repealed. My analysis suggests that a Kondratieff-type Wave is a modification of "cycles of war." That is, the end of a war is a terminus which is a trigger for a new "bull" cycle. My earliest attempts to clarify the cycle concentrated on the Franco-Prussian War as a terminus. The Franco-Prussian War may be viable for some analysis in the cycles of war, but was abandoned for this one. In the end, I settled for the end of the American Revolution, the end of the American Civil War, and the surrender of Japan to America at the end of the Second World War as termini.

Wave Deformation

My "wave deformation" hypothesis may trouble mathematicians and physicists, alike. Whereas most wave analysis relies on the period (length) of the wave remaining the same, my hypothesis anticipates wave deformation via a constant factor. How can a mathematical "wave" that does not have a constant period be considered viable? As a real world example, I would like you to envision a stretch of roadway with a telephone line strung along side. When you are looking at the telephone line from a perpendicular perspective, the distance between the poles is the same, and the "wave" will be the same between the poles. However, when you look at the poles from the roadway, for example, you will see the same "waves" with periods being diminished (or deformed) by a constant factor. Wave deformations also exist as repeating major and minor cycles.

Also, logarithms are an example of a diminishing cycle.

The Numbers

My earlier analysis of shorter waves uses an observed diminishment factor of approximately 0.80. The observed factor between the first and second long wave is approximately 0.8126; and, the observed factor is used to calculate the third (current) wave. The duration between Cornwallis' surrender and the bombardment of Fort Sumter is 78 years, five months, six days (78.5.6) or 28,991 days. The duration between Lee's surrender and the stock market collapse is 64 years, six months, 22 days (64.6.22) or 23,560 days. Using the same multiplication factor, the duration of the current wave which begins with the Japan's surrender is 52 years, five months, 16 days (52.5.16) or 19146 days (see Figure 1).

Triggering Event	Trigger	Lambda	Climax
Cornwallis surrenders	1781.10.19	79.5.6	1861.03.25
Lee surrenders	1865.4.9	64.6.22	1929.10.29
Japan surrenders	1945.9.2	52.5.16	1998.2.18

A year of 365 days and months of 30 days were used in the calculations. Leap years are not accounted for in the primary calculations. Estimating for leap years extends the cycle length (lambda) and the duration of the current wave is approximately 52 years six months zero days (52.6.0) or 19160 days (see Figure 2).

Triggering Event	Trigger	Lambda	Climax
Japan surrenders	1945.9.2	52.6.0	1998.3.2

The Margin of Error

Both calculations presume a constant factor in the wave deformation which may not exist. Such precision may not be calculable; but, any imprecision can be resolved after the climax actually occurs. Other variables exist (for example, bank holidays) and using rounded off values for years and months introduces imprecision. Although a statistical analysis was not performed, one may wish to allow a margin of error (sigma) within the parameters normally associated with statistical analysis of between one and three per cent. A "sigma" for a wave of 52.5 years is: 1% = 0.53 years, 2% = 1.05 years, 3% = 1.58 years. A minimal margin of error of one percent means that anytime from now until the end of August is a vulnerable time with the September-October 1999 time-frame being the outside period for a climax if a Kondratieff-type wave is viable.

Possible Flaws

There is inherent folly in trying to predict market movement, and I am aware of limitations and possible flaws in my analysis which subordinates either the business cycle or a Kondratieff-type wave to cycles of war. The following are some possible complaints: 1) The several monetary crises of the 19th Century (and therefore, stock market recessions) are simply absorbed within the presumed long wave as lesser economic fluctuations. 2) As noted, the foregoing calculations do not take into account the "bear" phase, and only considers economic growth as a reflection of presumed post-war expansion. Additionally, the analysis presumes the financial markets are measurable barometers for the wave's expansion phase and minor aspects such as the day count excludes real or de facto closures from bank holidays or other causes.

Conclusion

Two calculable climax dates were generated by the foregoing analysis: February 18th and March 2 of 1998. Allowing for a reasonable margin of error broadens the time frame to encompass the current (1998) calendar year and much of 1999. Regardless of whether some may consider the analysis to be simplistic at best or foolish manipulation of numbers in the worst case, I believe that it is based on a sound mathematical conjecture that waves can be deformed. If you believe that long waves are viable, and that waves can be deformed, you will know what the underlying reason is if a market climax occurs anytime in the next year and a half while you hear the pundits suggest that other factors-Asia, Bosnia, Iraq, whatever-had been at play. Time will tell.

Al Feng is an independent investor who formerly worked for several firms on the Chicago Mercantile Exchange trading floor. His analysis of the Kondratieff Wave as a modification of the cycles of war is coincident with attempts to clarify other ineffable subjects which include both the basis for the ordering of the alphabetic characters and the decipherment of the Etruscan language. He can be reached at alfeng@juno.com.