The Fibonacci: Trend Charts, Retracement Analysis, and the "Holy Grail" of long term stock market trading and Mutual Fund investing. --Please scroll down to continue--           Ok , now getting back to those big DOW projections, from the beginning of the first page, for somewhere between 500,000 and one million (1,000,000) by the end of this century and which  have a probability of being correct that is nearly 95%, lets do some simple math to check this "outrageous claim." continued below>    Well, if you don't believe these numbers then just get yourself a financial calculator or find a web site that will calculate the "future value" (FV) of an existing investment (current or present value PV) based on compounding, which is used for a stock's retained earnings...like this one:    Financial Calculator   1) Select "compound interest MODE and then 2) enter 5,600 (Dow's current "mean in 2005") into "current principal $" (don't worry about the $ sign), then 3) "0"  addition, then 4) years as 10-20-30 or however far into the future  you want to estimate...from 2005, then 5) 5.5% for the rate, and then 6) click the calculate button.   As an example, using 10 years we get 9556 "as the future mean" for DOW in 2015.   To check an "extreme  high," use 11750 as PV, same 5.5% rate, and calculate years from 2000 to the future.  For example, for 2010 we get 20,000 IF another mania was to occur between now and then...even in the face of $89 oil (my estimate)?    For those who trust me to do the work for them, the answer is a "high" near 41,000 to 58,000 after 25 years (2030), 180,000-225,000  after 50 years (2055), and 1,315,012-3,247,000 after 100 years (2105).      As you can see, my claims, above, were a little conservative in relation to just a 5.5% return on investment (capital gains without cash dividends), and will, "most likely," be exceed unless companies start paying out 40%, 50% or even higher percentages of their earnings as "cash dividends," which is exactly what I think will happen, and is the reasons why I said the future value of the DOW "should be" these values, and not "will be" these values.      By the way, the Dow could also be at it's "mean" or even a low in those years we calculated, so for 2030 that could be only 21,000 or even an "extreme low" near 10,000...Ouch !    Ok, getting back to our typical stock analysis, lets not forget that a company who has annual earnings of 5% and pays out 50% of those earnings to share holders, as cash dividends, like a REIT (Real Estate Investment Trust), only grows "capital" at a 2.5% rate, which is, of course, 1/2 the earnings rate.      Furthermore, there are some companies that have low, very low, or no "free cash flow" because they need every penny of their "so called" earnings they make this year to fund next year's, and maybe even many more years, " future growth."      If a company has some "free cash," then they "could" pay a "cash dividend,"  whether they actually do or not, so they do have some "theoretical equity capital" to compound.  Of course, just the opposite is also true, in that a company with zero "free cash" has no "theoretical equity capital" to grow and would not be worth one penny more next year than it's worth today...on average.      Now, this is a "tricky" subject, but one that individual "value investors" need to get educated on a lot more than technical traders, since traders deal with the supply and demand of actual price movements rather that the expectations for that future movement.      Let me say that again, in simpler terms, and with an example.  Unlike an investment in say a rental house, where many times the rental income only pays all the bills and does not provide any actual present income until the property is eventually sold, investors in a company's stock do not invested with the assumption that the company will eventually be liquidated to free up "retained earnings," eventhough, that happens many times as the result of a "Buy Out," or when a company goes private.   We have an excellent article in the Fundamentals Section of the Review,  that was published by Credit Swiss-First Boston,  which explains this "free cash flow" concept very well.   As you can see, this DOW prediction is not a joke, and people need to "visualize" these "so-called" big numbers, that are not really big numbers at all ,  or you're going to get left behind.  The question is not even  whether or not this index will get there, because, unless the world comes to an end,  it will!   The key questions are "when is it most likely to get there" and "when is it most likely to start toward those targets...now or later"?   By the way, if you look at that old DOW longwave chart again, below, and just "think" about THE TIME it typically took DOW to move between those Deka Boundries, 100-1000-10,000, at about 25-60 years, and then visualize the TIME it should take for DOW to reach the next Deka Boundry, @ 100,000, or the one beyond that one, @ 1,000,000, THEN you see why I say 1/2 million to one million is a rational "target" for the end of the 21st century...SINCE this would merely be repeating history AND a very rational 5%-5.5% long term CAGR...NOW do you get it? <DOW LongWave again, 2nd looks at deka boundries and CAGR>   OUR work in this section provides the mountain of "strong circumstantial evidence" to back up our bullish "intermediate term" opinion (many months to the spring or late summer of 2008 maximum), our bearish "long" term bias (many years to a decade after 2007-8), and our "always bullish" bias for theLongWave (tm) trend starting after a series of small (cyclical) recessions in 2006, 2010, and 2014...or one monster recession-depression in 2010 through 2014.   FOR Mutual Fund investors with only an interest in reducing their  long term "RISK," by keeping a "casual connection" to the parallel universe of Technical and Wave Pattern Analysis, then you can learn as much about R.N. Elliott's and J.D. Collin's "Fibonacci methods" as you want,  from our massive educational material, or you can just use our MarketView Weekly's trend ratings and alerts.     Needless to say, while we do our best to leave few stones unturned for those aspects of complex pattern analysis that can have a significant influnece on the U.S. Stock Markets, including Mr. Elliott's Fibonacci work, there are no guarantees in this business, and we work in probabilities rather than absolute certainties.  While many of these complex and advanced methods are well know to apply to other types of markets, at PTR we deal ONLY in the analysis of the U.S. Stock market and to a few other World Stock Markets if they have the capacity to materially influence the U.S. markets, as many do.    Regardless of their origins, the Fibonacci numbers, series, and retracements have become a major "force" in the world's stocks markets, and every trader "must" (or should) obtain at least a good working concept of where and when this "force" is most likely to manifest itself.      By the way, the "curve," or "geometric pattern," for the common Fibonacci series (3-5-8-13-etc-etc) is a "perfect" exponential growth curve, and can be "perfectly" modeled by mathematical regression methods using the "exact" compound interest formula, or equation: a(1+b)^x.  Furthermore, if the time "step" (x or years) is one year (1y), exactly, then the "annually compounded rate of return" is 61.8, "exactly," per annum.  Say what?   Yep, that's  el correct-O,  and I'll bet you have never read that, or even heard that, anywhere else before...right?  Who says you can't get something for nothing?  You just got "something" for free that took me years, and mucho-denero, to find out.   Of course, giving away only part of the story is kind of like telling someone you will identify where the Pirate's treasure is buried and then telling them "it's in Virginia"!   If you know what I mean?        Below is a sample of our work with the Fibonacci Trends, and I think I better warn you that these graphics are big, 250k-300k, so if you have a dial up modem, be patient.  Also, please respect our copyrights. <SAMPLE FIBONACCI TREND-SPX  1926-5/2004   posted 5/27/04   THE word "Fibonacci" itself seems to have become some kind of magnet to draw in would be speculators to what must seem like the simplest aspects of Trading 101.      However, when I did a little informal survey, a few yeas ago (2003) on Silicon Investor, I found out that "about" seven out of ten new traders, with less than one year experience, knew little to nothing about the Fibonacci numbers beyond the retracement lines that popped up on their TradeStation, or whatever, software.  It also appears that many of those in-experienced traders still believed there is some validity to those "Fibonacci fans" and Fibonacci time segments, which are not based on reality, poorly supported, and, more likely than not, doomed to be exposed as someone's lame attempt to rewrite a simple mathematical concept.     NOW, I can understand how that happens, since there are a lot of people,  who obviously have little to no idea what the the actual basis of the Fibonacci numbers are, out writing books about them, and even otherwise credible software developers have included some "highly skeptical" Fibonacci  "tools" into their programs. Well, I'll tell you right here and now, with absolutely no doubts what so ever, there is no mathematical basis for any Fibonacci "fans," which are a total fallacy, or any so-called "Fibonacci time series." Now, that does not mean that these erroneous Fibonacci "new wave inventions" cannot "hit" from time to time, like those so-called price-time targets based on equally bogus theories that claim to be derived from W.D. Gann's work, but in reality have no actual basis in fact.   In the simplest of terms, the Fibonacci numbers are mathematically associated to the "price" of individual stocks and the index value of stock market proxies, but there is no mathematical association to the Fibonacci numbers when applied to time, in days, weeks, months, or whatever.     However, do to some assertions made by R.N. Elliott in his Elliott Wave Theory, many waves or wave patterns will be "related to" prior waves and/or wave patterns by either the 1:1 "unity" ratio, or a ratio based on the mathematical "limit" of the Fibonacci sequence's growth curve, which is 1.618, or it's inverse at .618, which is commonly referred to as "Phi and it's inverse."     Therefore, some of these new, and "highly skeptical," Fibonacci methods have become a lot like those so-called new, and highly skeptical, Gann theories that merely "project" so many "changes in trend" (CIT) targets forward that price would have a lot harder time missing one of them then hitting it.  Unfortunately, that is exactly what is now going on with the Fibonacci.  Of course, if you can convince enough people to believe in the smoke and mirrors then the smoke and mirrors may actually become a self-fulfilling prophesy, for at least the length of time it takes for those believers to find out the truth.  Needless to say, do to the financial gains that can be milked from those bogus Gann methods, bogus Fibonacci fans, and now these bogus Fibonacci time segments to replace Periodic Cycles, that revelation could take a lot longer then a reasonable person would expect.    IN PTR's Fibonacci introduction, I explain why the Fibonacci numbers, series, and retracements are based on mathematical fact, and why no Fibonacci time sequence in conjunction with a Fibonacci number sequence will work, and why a linear periodic progression in time with price advancing along the Fibonacci number series will.    In addition to that, in the introduction I show you why there is actually only three "real" Fibonacci retracements, and three extension ratios, with 50%, 78%, 87% and 76.4% not being one of them.  Of course, the 50% retracement does works very well, and the other two will "work out" from time to time, but that has a lot more to do with W.D. Gann's "rule of eighths" then R.N. Elliott's, and C.J. Collin's, work with the Fibonacci numbers.     In that introduction, I will also show you way there is no such thing as a 3.618 "extension," or any .276 reciprocal of that nonexistent extension, and why there is no real "mathematical association" to the "roots" any Fibonacci number.  For those who want to keep on sticking their heads in the sand, then all I can say is "have at it"...and keep those dice rolling!   AT PTR, we have "absolutely no doubt" that most stocks, and most stock indexes, follow a long term rising trend (centered mean) that is represented by a simple mathematical function, whose underlying basis is a simple mathematical formula, or equation.  No! It is not a linear function based on a simple linear equation, like W.D. Gann's y=x (one point per day-week-or month), or y=x+1...y=a*x...y=aX+b, or even Mr. Gann's "parabolic" Square of Nine, which is 4x^2+/-b.   THE stock market, and many debt markets (but not necessarily commodities) follow the exponential growth function (ae^bx), which has as it's basis, in the case of the stock market anyway, the compound interest formula: y= a (b+1)^x or Fv=Pv (1+i)^t.    Furthermore, since the exponential growth curve is the basis of most plant and animal reproduction functions, then it can be said with absolute clarity that this mathematical "compounding" function is part of Natures Law , which had been alluded to by many master stock traders during the 20th century, including W.D. Gann, R.N. Elliott, and Robert Prechter.  <Natures Law and the Fibonacci>     Since most long term trends (over five years), and a majority of intermediate term trends (two to five years), or even many short term trends (less then two years), have a "strong tendency" to follow an exponential growth curve, their charts will only have "straight" trend lines (regression mean, minimum, or maximum) in logarithmic scale.  In stock analysis, this "log scale" is is actually a log-linear scale, which is commonly refereed to as "semi-log" scale.  In the "semi-log" scale for long term charts, the vertical "price" (or index value) axis is scaled as the common log (base 10) of the actual price, and the horizontal "time" axis is linear (every time period with the same span always has the same distance on the chart).   This "strong tendency" for long term stock trends to "regress" to their exponential growth curves mean says that the likelihood of the  "long term" linear regression trend lines having any "real" value is low; eventhough, one should always consider them as support or resistance because of what I call the Rabbit's Foot Effect.  That is to say, many traders are like gamblers and even a totally bogus idea like rubbing a Rabbits Foot for luck can come into play if enough gamblers are doing it, and in the case of "rubbing" the linear regression lines, there are a lot of them "doing it."   As for the short-term trends that make up the long term and intermediate trends, these can be linear, quadratic, or exponential.   It's these short-term trends (days to a few years max.) where W.D. Gann's (famous market trader and author) "angles," "squares of price to time," or his "circular calculator" (square of nine) comes into play. The "square of nine" can return either a "predicted point on the curve" of a quadratic function (ax^2+bx+c), or a point on the curve of X^2, by using the mathematical function: y= (SQRT a+/-x) ^2, were "a" is a high or low, and "x" is a time "factor" related to the angles of rotation within a cycle (and I mean cycle and not circle).  All of this is explained in the Gann, Longwave, and other sections of the review.    Now, this may all sound to technical or mathematical for a few of you, but I can assure that most of our service is based on "visual" charts and graphics.  Furthermore, most of the supporting comments and opinions are not highly technical or mathematical.   However, for those who want to learn all the "dirty details,"  then we have an extensive educational "introduction" to each section of the review that is light years ahead of most other web sites.    Need less to say, at times our educational material may get very technical, but we have managed to avoid, so far, using very little Calculus and other higher level mathematics, and for those minor applications where we do have to go full blown technical the subscriber can either use them if they have the training or discarded then without loosing too much, but a little, "overview" meaning of the presentation.    Like I was saying, there is little doubt that stock markets have a "very strong tendency" to follow this exponential function, mostly in the long-term trends, and for a very good reason.   That very good reason for the  "Stock Market” to  follow this function is that compounding interest, profits, or earnings as capital gains is exactly what stocks are meant to do.   That is to say, they compound interest (as a percentage of company profits) made on an investors original capital (purchase of stock), quarter after quarter and year after year, for as long as the investment remains and the company behind the stock makes profits (as earnings).  These earnings are "added" as payments every reporting period (a 13 week "cycle") on a   "percentage  basis" to the current "average" stock price, and a mathematical function where values are periodically added as a percentage of the existing value (capital or equity) is called an exponential growth function.    While there are a number of different mathematical equations for these exponential growth functions, only the basic equations, of Ae^Bx or AB^x, apply because this is the "regression model" for the compound interest formula.  This is all explained in detail within the introduction to the Longwave Regression section of the Review.  By the way, for a "linear" equation to be the mathematical basis of stocks, these stocks would have to have the "same," or materially the same, earnings added each period (say a fixed $1 every quarter) for as long as the trend remains in force, which is the case only with stocks that have 100% fixed dividends and nearly flat chart prices over time. Ok, now do you "get it"?  IF so, then please don't forget where you "got it" from...The Price-Time Review.    IN many stocks, or actually most stocks, the compounding is not on interest, but on "retained earnings" in the form of capital gains.  While it doesn't matter much to most investors whether a company pays out any of it's earnings (profits) as cash dividends, or they "retain" all the profits to reinvest in the business, it's the ratio between cash dividend pay outs and retained earnings that is one of the major factors in determining the rate of growth (ROC) of the stock's price; and therefore, the slope of the exponential curve and which Fibonacci summation series a stock's trend will have a "strong tendency" to follow...if any.   While most stocks like to "get onto" a "common Fibonacci summation series" (which has integer "yearly time steps" between each Fibonacci price line), that is not the only "exponential growth curve" that they can "get onto," by any means.   IN this section of the Review (Fibonacci Trend Charts),  we also explain that the Fibonacci Series of numbers, not the numbers  themselves, form a near perfect exponential growth curve , which can be used, and obviously has been used for many years, to visualize and predict where a stock's price is "most likely heading" in the next few years, or less.    Now, while the exponential mathematical function is most strongly connected with the long term trends, the Fibonacci Series can "many times" locate the near term trends as well, which typically take from a few months to a few years to develop. In this section, we explain why the Fibonacci "summation series" yields a ratio called Phi (=1.61:1 and not Pi or 3.1412), and why that ratio is so common in the stock market.  No, it's not black magic or voodoo, it's a simple mathematical ratio very common to exponential growth curves, the compounding interest formula, many stock trends, and most summation series...including, you got it, the Fibonacci series! <Example: Fibonacci Trend method at PTR...DOW long wave.>    Since exponential growth is one of the most common mathematical functions found in nature, like just about all population growth, and since the Fibonacci series also forms an exponential growth curve, then it can be inferred that a Fibonacci series is part of  'Natures Law," which was a phrase used by both R.N. Elliott and W.D. Gann to describe an association between the natural laws of nature and the stock market.    While this association may or may not be true, I have no doubt that both W.D. Gann's and R.N. Elliott's methods do have a "strong influence" on the U.S. stock markets, and any investor or trader that disregards them will be essentially going to into a bull-bear fight with one hand tied behind their back...so to speak. <Natures Law and the Fibo----same chart as above! >    In this area, we will show the true mathematical function of the Dow Jones Industrial Average (DJIA), a common exponential growth function, from 1896 to 2004. We then project that function forward in time so you can see where the index is "most likely" headed in the next twenty to one-hundred years. Dow 36,000 you say? Try Dow 17,711 as a near certainty by 2030, and "possibility" a DOW as high as 28,756 by then!  Don't think so? Well, try a Dow Industrial Average between 500,000 and one million (1,000,000) by the end of this century that has a probability of being correct that is nearly 95%, with that 5% error in the "projection" being a discount factor for the end of the world...just kidding of course.   This is not a joke, and people need to "visualize" these big numbers, "that are not really big numbers at all," or you're going to get left behind.      OK , before anyone thinks I'm a big time Perma Bull, I can assure you that I'm currently bearish (60%-40% probability) until late 2006 minimum, and most likely until 2010 to 2014. After the "actual bottom" of this big Bear Market is seen, most likely during those times (and even more likely at all three of them), I'm looking for a "modest" new bull charge. J.M. Hurst, W.D. Gann, and Charles Dow all stated that Bull Markets "spring" from the pent-up energy "built-up" during Bear Market consolidations. They are exactly right, and there has been no base building from this last decline, and the valuations never became "undervalued to the long term trend," the way they did in 1932, 1942, 1952, 1982, or 1974. Therefore, the logical "assumption" is, until proven wrong, that the current rally is a 1966-1970-1973 style Bear Market rally, which you can see for yourself in the example chart of the DOW that was "linked" above.    OF course, nothing is cast in stone, and the Dow could actually make new highs in this Bear Market rally, or even make one more new high to the old Bull Market, that began in 1974, here in 2004 or as late as 5/2005; eventhough, we think that is unlikely (see 1966-1973).  As for the other indexes, the Nasdaq has little to zero chance of being in anything other then a Bear Market rally, but could easily make a counter trend top that reaches 1990-2080-2584-2645 (key), or even 3120 (Compx) before heading back down in a big way. The SPX is unlikely to make new highs, but that is not as nearly as clear-cut as it is for the Nasdaq.  The Transports will be another area for an all out jam job, because the big speculators wouldn't want anyone-"else"- to have a DOW THEORY reason not to get long at that top, whether it's a final bull high or a bear rally high. One thing is a virtual certainty; all markets are likely to have a lot of "intimate contact" with 10,000 and 1,000 for the rest of this decade.  Ok, what do I mean by that one?    Just go look at a long term chart of the DOW or the SPX for the last 75-100 years, like this one <deka/deca boundary-Dow> , or go back to that first example, above, and you will see how the Deka (deca) Frame Boundaries (10-100-1000-10000) held these indexes up for many years until the index value (price) was actually "undervalued" to it's long term trend...and it's underlying mathematical function.  It is "unlikely" that history will not repeat that action and spawn another Bull Market from here, or at least from here and now!  For example, the DOW launched its 30's-40's-50's-60's Bull Market from a 1.88% rate line up from 1896, and then launched it's 70's-80's-90's-00's Bull Market from a 4.32% rate line up from 1896. Yet now, many expect the Dow to launch a new Bull from a 6.4% rate line. Well, anything is possible, but I'll stay will the higher probability until I see evidence to the contrary.    BY the way, the reason that 10,000 and 1,000 are big time support and resistance is not because of just the psychological value, and the actual battle line is not even those "Deka Numbers." Say what? Ok, I'll give you a hint!  The next battle "should be" for DOW 10,946, not 10,000. This is all explained, in more detail, in the introduction to the Fibonacci Trend section of the review, which is only available to subscribers. I cannot express strongly enough that this section alone is worth many times the price of a subscription.  Of course, I may be a tad bit biased in that opinion...ha-ha. 1  ALSO in this Fibonacci section of the Review, we explain why a Fibonacci "time step" between Fibonacci number lines that is between eight (8) and (9) years "fits" the long term "mean" trend line of the SPX index, with the DOW's trend not being far away at "about" nine (9) to ten (10) years per step.    These time "steps" between Fibonacci number lines represent an exponential growth trend of "about" 6% for the SPX index and "about" 5% to 5.5% rate for the DOW.  While it is still a little early  to "project" a mean trend for the Nasdaq index since it has only completed one major "spur" trend up, and has, "most likely," has not shown it's true long term mean or even a node on that mean trendline.    Never the less, from what we seen so far, we can "roughly estimate" that the Fibonacci time "step" for Nasdaq could be either 5, 6, or 7 years.  That would yield a long term trend "rate" that would be either 12.9% (4y), 10% (5y), or 8.3% (6y), with something between five (5) and six (6) years looking to be the most likely time step. Furthermore, we don't want to forget that when the next leg of the main long term trend does start up, most likely after 2010 or 2014, then it "should" also start a new, and "only moderately steep," upward sloping spur trendline, at least for the Nasdaq.  THIS new and long developing upward slope to "retest" the 2000 highs will be a final wave five (V), of Super-Cycle degree, and the final wave ((I)), of Grand Super-Cycle degree, in Elliott Wave Theory terms...with wave (IV) down and sideways now in progress since 2000's top of (III).       Like I just said, In Elliott Wave Theory terms that new spur trend will be the beginning of a wave five (V) of Super-Cycle degree, FOR THE NASDAQ ONLY, and in lay terms that means this spur trend will be the beginning of a strong and long bull market for those stocks that "fit' the Nasdaq long term model. On the other hand, the SPX and DJIA indexes will also be starting a wave five (V) of Super-Cycle degree, and would also be expected to have a ROC about the same as Nasdaq; except for the fact that, the DOW will be working (5) of ((III) up from 1932 or 1896, AND Nasdaq will be working a (V) of ((I)) up from 1971.   While I do not know what the new technology will be that propels this final bull market forward (after 2010-2014 to?), the pattern and length should look a lot like the DOW and SPX indexs looked moving from 1942-1942 to 1966.  However, this Nasdaq index "should have" a Fibonacci time step,  for the "mean," that is closer to four or five years than the eight or nine years that the Dow and SPX indexes have delivered over that fifty to seventy year time period.  Don't foget, we would also expect to see all indexs make multi year "consolidations" at their deka (deca) boundaries (100-1000-10,000), which is also explained in the Fibonacci and Longwave sections of the Review, and the current one at DOW 10,000 could, and even "should," last for many more years, eventhough,  peaks both well above and well below that line can be expected to occur as the battle along it continues. For the Price -Time Review Andrew J. Quiggly   B.Bonfoey Co-Editors The Price-Time Review and Into The looking Glass (1999) Goto the PriceTime-Review Home page         Subscribe now:  $19/m--cancel anytime