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The Wisdom of the Golden Ratio
And
Fibonacci Models Applied To HUI

"CAPTAINHOOK"

Fibonacci Principle of"1" (i.e. equality) will in all likelihood continue to be the mathematical framework in which gold will operate over the coming years.

This piece will simply be an extension of the same conceptual paradigm, as applied to the Gold Bugs Index (HUI). The purpose of this analysis is to establish a reasonably accurate conceptual road map, as it pertains to the future growth prospects of un-hedged gold and silver mining companies, which will enable the average investor to define his/her expectations as to an eventual long-term growth target for the HUI.

It is important for you to understand of the complexity of this mathematical model. The basis model known as the"Golden Ratio" has been the subject of extensive research among Fibonacci aficionados. The most applicable model that has been put forth to date, as it applies to what I have observed as the HUI's 'harmonic rhythm' comes from R. A. Dunlap. A basic overview of his work may be found at: http://www.mcs.surrey.ac.uk/Persona...bonacci/fibFormulae.html#basicgs

My purpose is to construct a basic mathematical model, which can be used to measure and project the harmonic characteristics of HUI, as it relates to price behaviour, based on a derivation of various premises found in Dunlap's model. In other words I am going to simplify a complex Fibonacci model into a much simpler and more easily understandable formula, which will make it more redilyfunctional to the average investor.

As you well know, one of my primary philosophies in life is to reduce complex matters to its simplest denominator. Certainly, applying the full spectrum of Fibonacci's genius to the task at hand would be outside the scope this essay. Consequently, I will limit the mathematical component of Fibonacci theory, and focus on what one may learn about the future growth prospects of HUI. I will do this by endeavouring to define it's past and future price patterns vis-à-vis Dunlap's underdstanding. That understanding is premised in the observation that certain dynamic phenomena within dynamic environments in nature, may behave within a definitional framework such that an action of certain phenomena, within certain dynamic environments, may be met with at least an equal reaction. A very straightforward example of this as it applies to a market would be the movement of a security's price from $5 to $10 over a 3 year period, and an ensuing correction from $10 right back down to $5, three years later. As you can see, this example is equal in all dimensions, including time, and will give you a basis to work from as we now delve into HUI's history and expected future price behaviour -- all per Fibonacci Theory.

Within the phrase 'price behaviour', the word behaviour should give one a clue to the fact that much of the price volatility within markets is a derivative of human emotion. In fact, the great gift that Fibonacci gave us in his observations and theories was a mathematical measure of human emotion, or the nature of human behaviour, as it applies to the dynamics of markets. The technical term for this phenomenon is 'harmonics' and when one is able to measure the rhythm a certain dynamic phenomenon displays within a certain dynamic environment, it is then possible to derive conclusions about expected future behaviour, based on previous rhythm patterns exhibited. Applying this to the HUI, if we can identify it's harmonic rhythm, in relation to price volatility, trend, and timing, or in other words it's frequency, pitch, and tempo, we can go a long way to being able to project probable future outcomes, going well down the road. In summation then, we are about to project the HUI's future growth path, by engaging Fibonacci's brilliant theory, described above.

As you will see in the following chart, it is imperative to exercise a flexible thinking process, even though the basic premise we are working with is for all intents and purposes quite straightforward. What do I mean? Charting markets is very much an art form in my opinion, and therefore one should not get stuck on absolutes, especially as it pertains to highs and lows. Let me show you what I mean, as it pertains to the subject matter below, in Figure 1.

Figure 1




Needless to say, there is a lot of information on the chart above, so let's deal with one item at a time. Firstly, one should notice that the price progressions in HUI since its bottom in November of 2000, are defined in two distinct stages, using a ratio of 1:1 as the increase interval. The exact calculations are denoted with the blue annotations. As you can see, viewing the HUI's price progression over the past couple of years on this basis, lends a high degree of logic and symmetrical appearance to it's overall characterization, just like a harmonic signature is suppose to do. That is because I believe what is displayed on the chart above IS the HUI's basic harmonic signature, and that absolute price peaks are not of primary concern.

Our base model then may be defined as follows. The basic price progression sequence of the HUI may be mathematically defined by the ratio of 1:1, in that subsequent progression sequences are likely to equal the sum of the previous advance. It is of importance to note that when the basic ratio of 1:1 is exceeded, this will indicate that the future trend path for the HUI remains higher. That being the case, notice the most recent closing price peak put in on the HUI is 151.91 (Figure 1), but that the basic Fibonacci progression, or harmonic impulse was only up to 143.96. Therefore, it is likely that the HUI is going to rally in another progression sequence. It will be interesting to monitor whether the HUI can make it up to 287.92 on a closing basis once it begins the next leg higher, due to commence in mid-April, as measured by the 14.5 month, or 300 day cycle, which seems to be the timing component, or time cells that define each successive progression sequence, denoted in charcoal in Figure 1. If it can, and perhaps even exceed the 1:1 ratio mark, that will indicate that the primary harmonic rhythm that the HUI has been advancing within over the past three years would still be alive and well.

So then, what can we expect out of the HUI's price progression in it's next sequence, as defined by the harmonic impulse pattern of adding an equal amount of the previous point gain in the sequence to the price high of that same sequence? Well, we know that based on the previous two sequences, that starting some time in mid-April of this year, the HUI should embark on it's next leg higher, which may include the following characteristics.

The price impulse higher may attain a level of no less than 287.92 (143.96 + 143.96), and possibly exceed this level, to signal the HUI's bullish intentions.
The rally sequence high should be attained within four to six months of cycle initiation, as defined by the previous time sequences, and denoted by the red dashed vertical rails in Figure 1 above.
The full time interval of the sequence should last 14.5 months, or 300 trading days, and be characterized by a 'five wave affair' higher (denoted in the pink annotations), coming off of an ABC flat corrective sequence, which looks to have ended in March at 114.35 on a closing basis.
Sound like fun? The fun using this method of projecting the HUI's future growth path is just beginning if you embrace the full depth of the model's construct. For example, as you know, the HUI is not going to go straight up. There are likely going to be corrections along the way. So, for you traders out there, how can we use the logic stream we have now established to our advantage? Certainly on of the best answers I can think of is trading the big corrective swings that will come upon us, as we advance through the staged sequences that lay ahead in the HUI's harmonic progression. Figure 2 gives us the benefit of hindsight and tactical observation within the parameters of this Fibonacci model, which will enable the educated investor to make potentially profitable trading decisions in the future, by avoiding the next substantial correction, and substantial it will be.

Figure 2




Although I have only shown the last corrective phase in relation to the entire move, it should be noted that both Fibonacci sequences experienced 50% pullbacks (a Fibonacci retracement number which when added to itself equals"1") in relation to the full extent of their respective advances on a closing price basis, so you don't have to be a mathematician to hypothesize that it is likely that this condition will persist into the future. Also, it should be noted that with the HUI attaining ever-higher nominal values, the shear magnitude of the corrections will increase dramatically, as we work through the next three progression sequences which should comprise the characterization of the HUI's harmonic advance. For example, if the next progression sequence takes the HUI to 287.92 on a 1:1 ratio basis, comprising a total point gain of 251.93, a 50% correction from the high point, assuming it's restricted to that level, would take the HUI all the way back down to a bone jarring nadir of 161.95, wiping 125.96 points off the index in as little time as several months. Pretty scary, huh? I have been trading for a long time and my preferred method for taking profits on long-term positions is the one that has been defined here for you today, as trading swings of this magnitude can be justified on an after-tax basis, especially when you consider opportunity cost on other trading possibilities, if you are nimble enough to take advantage of them. What have we learned from the above then?

After the initial advance in the HUI as it enters a new 14.5 month cycle, investors should expect at least a 50% corrective adjustment, which could occur in as little as several months, which may need to be further tested within the 300-day cycle, and may very well act as a stopping point within the advance, until a new cycle begins.
You may be asking yourself,"How does the above examination of the corrective process within the advance sequence of the Fibonacci model we have constructed fit into the definitional framework of our model, or the ratio of 1:1, as it pertains to the price volatility patterns in the HUI, within the dynamic environment known as the precious metals market?" A very good question, because the answer to this question is going to help us statistically verify the validity of the hypothesis of this essay, in that the harmonic rhythm of the HUI is centred around the ratio of 1:1, and the concept of equality.

As mentioned above in brackets above, when you add the two halves of the corrective phase back together, you obviously come back to the whole of the move, or the integer of"1". Without getting into too much detail, some Fibonacci practitioners define this process as a Phi calculation (.5 /.5 =1). The most commonly understood Phi value within the Fibonacci universe is known as the"Golden Ratio", which is best expressed as a ratio of 1:1.618 for our purposes. Why? Because we are going to use the"Golden Ratio" within the construct of our model, in order to test the validity of our model mathematically, within an acceptable variance.

Although you may think that because of its name the"Golden Ratio", that this relationship is centred around gold itself. In actuality, the coefficient factor of 1.618 is arrived at by dividing a Fibonacci number by the previous Fibonacci number in the sequence, averaged over the full extent of the sequence, and applies to far more dynamic phenomena in nature, than just gold. I find it fascinating however, that it does happen to occur as a coefficient value within the character of the gold market's movements, none the less. I find it more fascinating yet, that it actually does validate the construct of the Phi calculation that is the basis of our model. Per that definition the ratio value of 1.618 is understood by Fiboinacci practitioners to be Phi. And when used as a coefficient to project a point gain in HUI based on the previous progression sequence, we get values that are within an acceptable variance to our model's construction. Before I go any further with this explanation then, let me show what I came up with regard to verifying our model below, in Figure 3.

Figure 3




In examining the chart above, one should first notice that basic character of the entire move can be separated into two sequences, and that they are relatively equal in proportion, as it pertains dimensions and time. The more important aspect of the above chart however, is based in the understanding that we arrived at the values denoted in blue annotations using a Fibonacci coefficient projection method, using the"Golden Ratio" value of 1.618. Please note how very close these projections are compared to the calculations in Figure 1, and the price progression itself. Based on this exercise, it certainly appears that we are indeed on the right track.

Further, if we take the same method of arriving at the" Golden Ratio" coefficient of 1.618 and apply it to our model, we come up with a coefficient for the HUI of"2" (2 / 1 = 2). And as you can see above, 76.58 X 2 = 153.16, again further cementing the validity of the model, in that we arrive at essentially the same high values for the entire move in the HUI by adding the previous progression sequence high to itself, performed at a ratio of 1:1. Going back to the corrective sequence displayed in Figure 2, we can also calculate the HUI's phi (notice the first letter in the term is not capitalized) to define the corrective coefficient as.5 (1 /2). Of course it is far too early to say for sure, but future price progression sequences may be characterized by the HUI's phi, and retracements by phi, and if this so, the next price progression may take us to 303.83, over the next 300 trading days. Let's summarize what we have learned as it pertains to verifying our model, as follows.

The HUI appears to be advancing in sequential progression cycles, which are symmetrical in all dimensions, and can be quantified by engaging a Fibonacci projection calculation method using a factor of 1.618, commonly known as the"Golden Ratio".
We have learned that at a minimum, the HUI's projection coefficient factor is 1.618, but may more likely be a Phi of 2, in that if you multiply a previous progression sequence total point gain by 2, the product you derive equals the total point gain for the bull run so far, within an acceptable variance. If this proves to be the case in further progression sequences, it will be statistically acceptable to label the coefficient factor of 2 as Phi, as it pertains to the HUI, therein making it the HUI's"Golden Ratio". (See Figures 1 and 3)
It appears that the phi coefficient for corrective sequences in the HUI is.5 (1 / 2), in that it has exhibited this behaviour in two successive corrective sequences within both of the sequential progression cycles thus far.
What other relationships could we possibly look at to help us statistically verify the harmonic model we have hypothesized is central to the HUI's price sequential price progression characteristics? Well, the most obvious one has got to be it's relationship to gold, so why don't we look at how gold is relating to the HUI within the character of it's progression sequences. That would of course involve a look at the HUI/Gold Ratio, presented for you in Figure 4 below.

Figure 4




Throughout my transgressions associated with this study, the one comment I would have to make in relation to the model's construct to centre not only around the HUI sequential progressions itself, but all of the relationships involved as well, is amazing. Notice in the above chart, the symmetrical apportioning of this ratio's advance, inalterably being drawn towards the ratio of 1:1, in what appears to be a series of staged sequences, one built upon the other in equal proportions, in terms of it's previous progression, again at a ratio of 1:1, and a Phi of 2. As you can see, we are actually right in the middle of a progression sequence at present, which suggests that the impending advance in the gold complex will be characterized by the continued out performance of the HUI over the price of gold, and that the rally will extend itself until this ratio hits at least.542. Well, that is certainly worth knowing, and in the bigger picture, it is equally rewarding to observe that this understanding was derived using our model construct, as it applies to the harmonic rhythm of the HUI itself. I find this occurrence truly fascinating. Let us see if we can find more.

Why don't we look at the inverse of the HUI/Gold Ratio, to see if this can help us establish the model's validity, and predictive capabilities. After all, bottom line what I am attempting to do here is define a model with statistical integrity, that can be used as a tool well into the future, so we had better test it thoroughly. Once you see the uncanny commonality of the HUI's rhythm characteristics centred around it's propensity to flux and pulse in a direction that ultimately draws it to a state of equality in terms of it's previous sequential progressions, the verification process is engendered with a higher degree of certainty. In Figure 5 below, this goal is accomplished with crystal clear imagery, as it appears that the Gold/HUI Ratio is pulsing it's way down to a ratio of 1:1, as well.

Figure 5




Isn't this just the previous chart flipped upside down? The answer to that question is yes. What then, is the significance of doing so? The answer to that question will become apparent once we delve into the more detailed workings of the Gold/HUI Ratio's sequential progressions over the past couple of years, as I can assure you it will aid our efforts at further verifying that the construct of the model is valid, but before we do so, lets see if we can do a simple comparison to Figure 4. Upon taking a cursory glance at Figure 5, you should be able to readily discern that indeed, our model construct is present within the sequential progressions of the two large sequential progressions that began in November of 2000. Further, it should noted that it appears we have made the turn in what appears to be the final sequence of this cycle, and that once the bottom rail in the current consolidation flag is taken out, this ratio should pulse down to the ~1.5 area, according to the construct of our model [applying HUI's Phi coefficient to the above you derive a product of ~1.5 (.5 X 3 = 1.5).

You may be saying to yourself,"~1.5 is not"1", so this leaves part of the comparison suspect." To address that concern, I have included a small diagram in the top left hand corner of the above figure, which represents the larger sequential progressions that the Gold/HUI Ratio should trace out into the future, potentially taking as long as 18 years, assuming gold itself will adhere to the same model construct as the HUI. Even though we may not make it all the way down to equality this time around, I believe that this ratio will eventually do so, as we progress through the larger cycle. The larger cycle should be characterized by a 'five wave affair' and involve minimum 50% retracements within the corrective sequences, as well. Notice that the impending wave structure is identical to that of gold itself, which ended a 21-year bear market coiling process in 2001, and for that reason it is possible that the larger cycle in the HUI could last until the year 2021. Certainly that is the prospective for gold itself, with it's larger cycle likely to end in the year 2022, in order to fit the equality criterion of our model's ratio of 1:1, with a start date in 2001.

Well, that is certainly taking it far enough out into the future. Lets come back to a more timely perspective, and see if we can't continue the model construct verification process by examining in more detail, the sequential progressions of the Gold/HUI Ratio since it started it's decent in the year 2000, to see exactly what we can learn from performing this exercise. (See Figure 6)

Figure 6




As you can see above, we can learn quite a bit, from performing this exercise. First and foremost, the basic underpinnings of our model's construct are unquestionably verified, with the Gold/HUI Ratio's relentless decent over the past 25 months within exacting values as it pertains to phi, which is of course the reciprocal coefficient factor of Phi, and a ratio of 1:1 when measured in terms of the preceding sequential progression. The other significant observation that can be made in the above chart is the presence of time cells indicated by the dashed vertical lines. Note that represent six month time blocks, and that they both encompass and separate intermediate term cycles, and that a new cell is about to commence in late May, after running two consecutive cell blocks in a row, defining the corrective phase the HUI has experienced since the end of May/beginning of June, last year. In referencing our model construct, this opens up the possibility of a one-year rally sequence, which may begin in earnest, at the end of May, as the ratio looks set to penetrate the bear flag defined it's movements over this time. When one integrates this knowledge with the timing cells identified in Figure 1, the conclusion is suggestive of a rally in the HUI commencing anytime now, but perhaps not putting in disproportionate gains until we get closer to the end of May, and once the bottom rail on the most recent bear flag identified above in Figure 6 is taken out.

To reiterate then, what we have accomplished in the examination of the HUI as it relates to gold within the construction of our model is as follows.

First and foremost, the basic underpinnings of our model's construct are unquestionably verified, with the relentless ascent/decent of the HUI/Gold ratio / Gold/HUI Ratio over the past 25 months within exacting values as it pertains to Phi / phi, which also confirm the basic construct of model in that a ratio of 1:1 is established, when an advance is measured in terms of the preceding sequential progression.
We have also learned that because these respective ratios are advancing in this fashion, that it is likely they will attain an ultimate factor of"1" (1 / 1), and we are likely to see this occurrence sometime, and perhaps repeatedly, over the next 18 years.
Based on the timing cells identified in Figure 6, it is possible, if not likely, that a substantial rally in the HUI will commence in late May, and could possibly last up to a full year, based on the need for our model to attain a 1:1 ratio.
The one thing the above exercise doesn't do is delineate exact numerical targets for the HUI and gold, so lets do that now. It will be necessary to look at gold now, in terms of our model construct, in order to perform a reasonably accurate projection of just what kind of progression targets we should be looking for in the HUI, as we progress into another sequence. A view of the gold chart using our model construct can now be seen below.

Figure 7




As you can see, once we have the model's construct in place, the task of putting the pieces of this puzzle together get a lot easier. From the above chart, using the basic Fibonacci formula of 1 / 1 to arrive at a coefficient of 1, and then taking that value and adding it to itself to arrive at the projection target of $499, we accomplish the first step in our model construct. Then, by multiplying the then known product of the first step by the a coefficient factor of 2 (2 /1), which has proven itself to be a reliable product within the gold complex through our examination of the HUI against gold already, we verify that our first calculation is reasonably accurate, by comparing the product we get from the Phi computation. And voila, you have a variance of $4 (503 - 499), between the two.

Based on the observation that Phi, as defined as a coefficient factor of 2 (2 /1), has proved as an accurate verifier to our basic model's construct, it is now possible to label the coefficient 2 as Phi, as it pertains to the entire gold complex, and as it applies to the advance of this gold bull market. Notice that it is also possible to identify the coefficient of.5 (1 / 2) as phi as the possible template to characterize the corrective phases of HUI's sequential advance, with the recent correction in gold attaining an almost perfect 50 % retracement off of the highs, against the entire gold move to date.
Based on the observation that gold seems to work into higher progression sequences in 15-month time cells, I do not expect it will take out the previous highs in the three and a half months left in this cycle. However, once gold commences a new 15-month progression sequence in August of this year, I would expect it to pulse through the previous highs not long after it begins, if our work with gold's relationship to the HUI above has any predictive value. In fact, if we look at Figure 6, and note that the HUI has run two successive six-month time cells in the current consolidation, in order to attain a ratio of 1:1, we would then have to run two time cells in rally mode, beginning in late May. When we put these two above observations together, along with the fact that within the last progression sequence in the gold complex we saw the HUI hit it's initial high values in May of '02, and gold did not hit it's high values until February of '03, the task becomes slightly more daunting, but doable never the less.

We know that once the Gold/HUI Ratio breaks the bear flag that is currently restraining it's decent, that it is likely that the HUI will hit it's high value range sometime within the first 4 to 6 months, but gold will not. Gold peaked in May of '02 at $325, which was14.2 lower than the eventual $379 top. Using the same variance off of our projected topping value of ~$500, we get an initial high value for gold's first pulse higher into the new progression sequence of $429, which should occur in coordination with the HUI's first run at high values for the sequence sometime in October, or at the latest, November of this year, before we go into a phi retracement sequence. Using a 1.5 value in the Gold/HUI Ratio then, we arrive at a projection high for the HUI this year of 286 (429 / 1.5).

I'm fairly confident that the above objective(s) for the HUI and gold will be attained this year, and I am certainly hoping that the full potential of these relationships is released next year, if gold puts in a pulse towards $500, sometime in and around July of '04, we could be looking at the high value on the HUI attaining 333 (500 / 1.5), with a double bottom forming on the Gold/HUI Ratio, before it begins it's corrective ascent higher.

Using our model construct, I have projected some targets for HUI into the future. You should note, that I used the conservative projection model, not the Phi coefficient factor of 2 multiplied by the absolute price peaks in each progression sequence. If I had shown that, the ultimate peak would have been in the 3,000 range. Who knows, maybe Richard Russell is right.

Figure 8




Russell is professing that the Dow and gold are going to reach a ratio of 1:1 again sometime in the future, at or about 3,000. Well, if our model is correct, so will HUI against the Dow and gold, as well. And it will happen sometime between 2013 and 2021 either 13 or 21 years (both Fibonacci numbers) from the start of the HUI's bull market, in the year 2000. Note that because the HUI was established as an index in 1996, we do not have a record of it ever attaining a ratio of 1:1 with gold, however I believe there is a strong possibility of this potentially occurring sometime over the next 18-years. We sure have a record of the Dow/Gold Ratio hitting a 1:1 value however, and here is how it's progressing this time around.

Figure 9




Do you think it's unlikely that the Dow, Gold, and the HUI can all reach the same levels, at the same approximate times? Well, after you view the following chart, you may change your mind, as it appears that just as the Dow/Gold Ratio is progressing towards a value of 1:1 within the construct of our model, the Dow/HUI Ratio is doing exactly the same thing. And if I had to pick a number that would characterize where the three are going to meet, I would have to go with a value closer to 2,000, because of the high degree of integrity we have established in this model's construct.

Figure 10




However, I must tell you, I wouldn't a bit disappointed if the HUI 's absolute price highs maintain the character of Phi (2) factored into the HUI's sequential high value, as that would indeed put it closer to the 3,000 mark, as it's ultimate peak. Whether we peak at 2,000 or 3,000, one thing is for sure, our model's validation process has now been extended to markets outside of the gold complex and it is still holing up nicely. There's only one conclusion you can come to after observing that fact. Must be the human element in the markets, and isn't Fibonacci's work truly brilliant.

After a cerebral excursion like the one we've just been through, it's always a good idea to summarize our findings, so here it goes.

Our base model then, can be defined as follows. The basic price progression sequence of the HUI can be mathematically defined by the ratio of 1:1, in that subsequent progression sequences are likely to equal the sum of the previous advance.
Accordingly, the next progression sequence in the HUI should contain these characteristics, as follows:

The price impulse higher may attain a level of no less than 287.92 (143.96 + 143.96), and possibly exceed this level, to signal HUI's bullish intentions.
The rally sequence high should be attained within four to six months of cycle initiation, as defined by the previous time sequences, and denoted by the red dashed vertical rails in Figure 1 above.
The full time interval of the sequence should last 14.5 months, or 300 trading days, and be characterized by a 'five wave affair' higher (denoted in the pink annotations in Figure 1), coming off of an ABC flat corrective sequence, which looks to have ended in March at 114.35 on a closing basis
After the initial advance in the HUI as it enters a new 14.5 month cycle, investors should expect at least a 50% corrective adjustment, which could occur in as little as several months, which may need to be further tested within the 300 day cycle, and may very well act as a stopping point within the advance, until a new cycle begins.
The HUI appears to be advancing in sequential progression cycles, which are symmetrical in all dimensions, and can be quantified by engaging a Fibonacci projection calculation method using a factor of 1.618, commonly known as the"Golden Ratio", verifying our model construct.
We have learned that at a minimum, the HUI's projection coefficient factor is 1.618, but may more likely be a Phi of 2, in that if you multiply a previous progression sequence total point gain by 2, the product you derive equals the total point gain for the bull run to that point, within an acceptable variance. If this proves to be the case in further progression sequences, it will be statistically acceptable to label the coefficient factor of 2 as Phi, as it pertains to the HUI, therein making it the HUI's"Golden Ratio". (See Figures 1 and 3)
It appears that the phi coefficient for corrective sequences in the HUI is.5 (1 / 2), in that it has exhibited this behaviour in two successive corrective sequences within both of the sequential progression cycles thus far.
What we have accomplished in the examination of HUI as it relates to gold within the construct of our model is as follows:

First and foremost, the basic underpinnings of our model's construct are unquestionably verified, with the relentless ascent/decent of the HUI/Gold ratio / Gold/HUI Ratio over the past 25 months within exacting values as it pertains to Phi / phi, the HUI's dominant coefficient factors.
We have also learned that because these respective ratios are advancing in this fashion, that it is likely they will attain an ultimate factor of"1" (1 / 1), and we are likely to see this occurrence sometime, and perhaps repeatedly, over the next 18 years.
Based on the timing cells identified in Figure 6, it is possible, if not likely, that a substantial rally in the HUI will commence in late May, and could possibly last up to a full year, based on the need for our model to attain a 1:1 ratio.
Further, we have learned that with the projected target of ~1.5 for the Gold/HUI Ratio in this progression sequence, and gold forecast to attain $429 and then ~$500 using our model, we would expect see the HUI trading at the high values of 286 in October of this year, and potentially as high as 333 by July of next year, assuming our constructs are valid.
Based on the observation that Phi, as defined as a coefficient factor of 2 (2 /1), has proved as an accurate verifier to our basic model's construct, it is now possible to label the coefficient 2 as Phi, as it pertains to the entire gold complex, and as it applies to the advance of this gold bull market. Notice that it is also possible to identify the coefficient of.5 (1 / 2) as phi as the possible template to characterize the corrective phases of the HUI's sequential advance, with the recent correction in gold attaining an almost perfect 50 % retracement off of the highs, against the entire gold move to date.
The validity of our model's overall construct is enhanced considerably, above that which has already been established with our examination of the HUI's relation to gold itself, by further testing the operational constructs of Phi and phi using inter-market relationships as a verifier. As a product of this exercise, we have learned it is likely the Dow, gold, and the HUI will all meet at a ratio of 1:1, sometime between the years 2013 and 2021, and the level they will attain equality at will in all likelihood be very close to 2,000, with the possibility of a value closer to 3,000, if the more aggressive derivation of our model proves to be the dominant force.
Overall then, what we have accomplished in this essay is the design of a functional model as it applies to the harmonic rhythm of HUI, as defined by the brilliant principles of Fibonacci. We have discovered the base dimensions, tempo, and timing of the HUI's advance to date, and constructed a template from those findings with which we can project future price trajectories for HUI.

I hope it is a template that you will put to good use.



CAPTAINHOOK
16 April 2003


<ul> ~ Original-Seite</ul>