Theories of periodicity (cycles) in the stock market are as intriguing as they are controversial. The subject of equity market cycles has been discussed at length over the past 60 years with precious little in the way of agreement among cyclists as to what exactly constitutes a cycle, let alone which cycles are key.

Unfortunately, one of the major attempts at advancing the understanding of cycle theory, namely the Foundation for the Study of Cycles, was marked by internecine strife and fell by the wayside in the mid-1990s despite the pioneering work of its founder, Edward Dewey. In recent years, much credit must be given to Samuel "Bud" Kress for discovering the remarkable rhythms that define the series of yearly cycles that compose the K-wave long-term series. The K-wave has been traditionally defined as a 60-year rhythm as formulated by the Russian economist Nikolai Kondratiev.

Breaking down the yearly cycles there are only four of any consequence. They are: the 2-year, the 6-year, the 10-year and the 30-year cycles. The other cycles can be chalked up to merely the products of the "Rule of Alternation" or to a composite of the four cycles under discussion.

It's not uncommon for cycle analysts to mix cycles of various compositions and assume they've arrived at a definite single rhythm. For instance, you will sometimes hear cyclists talk of a 36-year cycle. That such a rhythm exists at all, in and of itself, is questionable. What these analysts are probably seeing is just the 6-year cycle which may (or may not) happen to bottom with extra emphasis after six consecutive bottoms. This is one of the problems with any given cycle since sometimes the cycles - even the ones which bottom with definite regularity - don't seem to have all that much of an impact on market prices.

Cycles should never be viewed as anything more than a rough guideline, or road map if you will, for navigating the markets. They can rarely be used to great success as a standalone trading tool with long-term consistency. For optimum success, cycle theory should always be combined with a comprehensive study of market internals (i.e., technical analysis) as well as fundamental analysis, market psychology analysis, and an analysis of market liquidity.

Returning to the cycles, the Kress long-term cycle series as originally conceived was based on the 60-year cycle and its double, the 120-year cycle. This is roughly analogous to the 60-year K-wave. It has been historically divided in the following manner:

120-year
60-year
40-year
30-year
24-year
20-year
12-year
10-year
8-year
6-year
4-year
2-year

The above cyclical series, which is interrelated, will come under question for reasons that will be explained in this and in future commentaries.

Each cycle of course contains a point of origin as well as a definite peak, which is always exactly half the cycle's duration (e.g., half a 10-year cycle is 5 years). Like all true cycles, the dominant yearly cycles all have a fixed peak and a fixed trough.

There has been some debate among cycle enthusiasts recently as to whether or not the famed 4-year cycle has bottomed. But one observation that has been lacking in this debate is that a cycle, by its very definition, has a fixed point of origin and a fixed ending before the cycle begins anew. This means that a 4-year cycle (if such a cycle exists at all) *must* bottom at exact four year intervals without fail, otherwise it's not a pure cycle. For a cycle such as the 4-year rhythm to be artificially extended beyond 4 years (as some cycle theorists assume) is either ignorance of what constitutes a cycle or else an intellectual excuse for the purported cycle's failure to produce the desired effect on the market.

As the Kress theory holds, not only should a cycle be fixed in duration and absolutely immovable -- and not only should a cycle be evenly divided between its origin and completion by a peak at the halfway point -- but a true cycle is ideally comprised of a Fibonacci number which can be multiplied by the number 2. For instance, the starting point of Kress cycle theory is the number two. This basic number can be divided evenly into all the various components of the 60-year cycle series.

But the most profound cycles; that is, the ones that exert the greatest influence on the stock market over time, are the cycles that can be divided by the number 2 and which also have a Fibonacci component based on the numbers 3 and/or 5.

For instance, the 10-year cycle can be derived by multiplying the 2-year cycle by 5 years. The mid-point, or peak, of the 10-year cycle is thus 5 years. The 30-year cycle is essentially 10 times 3 (with 3 being a Fibonacci number). The 30-year cycle can also be derived by multiplying the Fibonacci number 5 by the number 6 (which in turn can be derived by multiplying the Fibonacci number 3 by the number 2).

Based on this observation the most basic and "pure" cycles in the Kress cycle theory are the following:

2-year
6-year
10-year
30-year

These are the essential cycles and the remaining cycles mentioned earlier in this commentary are really nothing more than doubles, triples or quadruples of the above mentioned cycles. The 2-year cycle is pure because its peak is 1-year (with the number 1 being a Fibonacci number). The 6-year cycle has a peak of 3 years (3 also being a Fibonacci number). The 10-year cycle has a peak of 5 years (Fibonacci), and the 30-year cycle has a half-life of 15 years (15 = 5 x 3, both Fibonacci numbers).

It boils down to this: The essential cycles in the stock market are always even numbered, but their half-cycle components are always odd numbered. We can also observe the following rule for the cycles: The mid-point of any given cycle is *never* a cycle in and of itself. For instance, the mid-point of the 2-year cycle is 1 year but there is no 1-year cycle. The mid-point of a 6-year cycle is 3 years but there is not 3-year cycle. The mid-point of a 10-year cycle is 5 years but there is no 5-year cycle. The mid-point of a 30-year cycle is 15 years but there is no 15-year cycle.

Now if we go back to the original cycles in the Kress series we find several that are merely duplicates of the four cycles mentioned above (2, 6, 10 and 30). Moreover, most of the other cycles referred to by popular cycle theories don't fit the definition of a cycle provided in the above paragraph. Taking the 4-year cycle as an example, the half-cycle component of the 4-year cycle is obviously the 2-year cycle. But how can there be a legitimate 4-year cycle if the mid-point of a 4-year cycle coincides with a 2-year cycle bottom? Are we to assume that the 4-year cycle "peaks" simultaneous with the 2-year cycle bottom?

What about the 12-year cycle? The mid-point of 12 years is 6 years. How can there be a true 12-year cycle peak when it's basically just the 6-year cycle bottoming at the midway point? This calls into question whether there actually is a 12-year cycle. It also calls into question whether there is a 4-year cycle, an 8-year, a 20-year, a 24-year, a 40-year or even a 60-year cycle. These numbers just mentioned are merely extensions or duplicates of the four primary cycles: the 2-year, 6-year, 10-year and 30-year cycles. As such, they are extraneous.

In order to prove the existence of the 4-year cycle, for example, one would not only have to show a marked tendency for the stock market to bottom at precise 4 year internals over an extended period of time, but one would also have to demonstrate a definite peak at the 2-year point of the cycle. Going back just over the past 30 years of stock market history makes this an arduous task. The existence and effects of the 2-year cycle are fairly easy to establish. But arriving at a definite 4-year cycle that peaks and bottoms with reliability is vexing to say the least.

Another common mistake made by cycle analysts is the failure to take into account the interplay among the various cycles. In some years, the 2-year cycle bottom can be greatly mitigated by the peaking of, say, the 6-year cycle (as happened in 2004). Or the 2-year cycle bottom can be cushioned by the freshly rising 10-year cycle (as happened in 2006).

Another folly commonly committed by cycle theorists is the assumption that cyclical factors are the sole determinants, or even the primary determinants, of stock market prices. Cycles should always be viewed as basic outline, or skeleton, of what to expect from the markets. The details, or "flesh and blood" if you will, are always provided by other factors such as market internals, supply and demand, market psychology, liquidity factors, et al. To rely exclusively on cycles to predict market moves would be foolish and many a cyclist has been waylayed by the vagaries of the market in such attempts.

One high-profile instance of how cycle theory is misused to explain market occurrences is the stock market crash of 1929. Cycle theorists have assigned the primary blame for this crash on cycles ranging from the 4-year cycle bottom to the 40-year cycle bottom. The 4-year cycle supposedly bottomed in 1930 but, as elsewhere discussed in this commentary, the 2-year cycle was what actually bottomed in 1930 (not the supposed 4-year cycle). The 2-year cycle also peaked in 1929 around the time of the crash. Anything as small as the 2-year cycle, however, can hardly be blamed for causing something as magnificent as the Great Crash of '29. The 2-year cycle was likely just a small factor in the crash; it almost certainly was not a primary cause.

For that matter, the 10-year cycle, which always bottoms in the fourth year of every decade, was peaking in 1929 around the time of the crash. While this may have added some pressure against the equities market, this influence alone couldn't have been expected to exert as much downward pressure as was required to crash the market in 1929. The more likely culprits in causing the '29 crash were a combination of factors ranging from massive over-valuation of stocks and oversupply of shares against an ever-shrinking demand; overly exuberant investor psychology; and, most importantly, a conspicuous shrinkage in monetary liquidity courtesy of the Federal Reserve.

This observation can be extended to any number of financial market panics and bear markets that have occurred in the years since 1929. The tendency of the die-hard cycle theorists is to assign blame for virtually every market movement to some cycle or combination of cycles. There is also a tendency to overlook the other factors mentioned in the above paragraph in accounting for market movements. But it is these "flesh and blood" factors that normally account for conspicuous market volatility in any given year.

By this point a cycle theorists is likely to ask: If we assume the 4-year, 12-year, 20-year, 40-year, 60-year, etc., cycles don't really exist but are instead multiples of the more basic 2-year, 6-year, 10-year and 30-year cycles, how does one account for the observable 4-year phenomenon known as the "Presidential Cycle?" And what about the famous 60-year "K-wave" cycle itself?

The answer to the first question is that the 4-year phenomenon is probably nothing more than the 2-year cycle bottoming with extra emphasis. This is probably due to the well-known "Rule of Alternation" as discussed by Elliott Wave Theory among other theories of technical analysis. This rule states that market cycles, much like everyday swings in stock prices, tend to balance out over time by alternating from one extremity to the other (i.e., overbought to oversold). We've all observed that a runaway bull market in stock prices always eventually "corrects" itself by reversing and retracing some, or even most, of its previous gains. Likewise, bear markets always reverse and give way to bull markets. The 2-year cycle assures that in most years, the even-numbered year tends to be relatively lackadaisical for the stock market, whereas in the odd-numbered years, stocks tend to fare better. This is the Rule of Alternation at work.

Some K-wave theorists maintain that every other K-wave cycle bottom is less pronounced than the previous one (or put another way, you can expect a hard bottom to the K-wave every other time). This is also an extension of the Rule of Alternation. This rule can be used to explain that what is commonly assumed to be a K-wave of 60 years is really just the 30-year cycle bottoming with extra emphasis the second time around.

Equity market cycles are important but should never be used as a panacea to solve major problems in stock market trading methodologies. By concentrating primarily on the 2-year, 6-year, 10-year and 30-year cycles to the exclusion of the others noted here, and by observing the interrelations between them, the cycle analyst will greatly simplify his approach to the stock market. This makes the proverbial market "road map" a hundred times more readable than it used to be.

One of the main detriments in the science of prediction is using too many variables. Using too many inputs in market analysis has ruined the calculations of countless would-be prognosticators. Occam's razor (a.k.a., the Principle of Parsimony) states that entities shouldn't be multiplied needlessly and this rule can and should be applied to the science of cycle research. When it comes to following the cycles, simplicity is the key.