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The S.M.A.R.T. Silver Equation (reloaded)

By: Rock Gale

-- Posted 3 November, 2006 | |

Ottawa, Canada

October 31, 2006


A bit more than two years ago - September 2004 it was - I studied the trajectory of the Silver Rocket in an article called "The SMART Silver Equation". Many readers liked the idea, and made me promise to update the regression analysis at a later date. I never promised to write the sequel before a set date, or update it every year, but I have felt that it was about time to undertake the process again, even though my original work had been partially lost due to a break-in at my residence. Some of the final programming had been done on a brand new Pentium 4 computer that was stolen. Luckily, I still had much of the original work on an ancient 266MHz Pentium 2 that is still running to this day, and on which I have scribed this report.


It's interesting to think that this program took about 3 or 4  days in total to write/modify on either machine, but the program ran in about 5 seconds - around 25 seconds faster - on the new Pentium 4 model, and I really only have to run it once or twice! That's all I have to say about the US government's hedonistic computer-efficiency-based productivity numbers…and no wonder my productivity is so low since the break-in.


The premise of the SMART Silver Equation is that if the Price of Silver really is like a rocket, then it should adhere to Newton's Laws of Motion, and I should be able to calculate the rocket's trajectory and show that the Silver Price, has gobs of measurable acceleration! No one really objected strenuously to the premise on the first pass, and I think we got a pretty good handle on the rocket's path in that first article. Whether or not many people actually understood the theory, I don't know. The piece had better jokes than this one and a pretty chart that showed the SMART equation, and the path that silver might take, if it stayed on trajectory, so everyone seemed to be fairly happy. But now comes the true test! How well did the equation predict the flight of the silver rocket over the last two years?  Did the Price of Silver double in those two years as was suggested? As a matter of fact, we came pretty close.  But before we get into the comparisons, for the benefit of new young Silver Rocket Scientists, we should review the Silver Equation a bit.


An equation does one simple thing. It tells us an object's Position at any given Time.  A Mathie would say that Position is a function of Time, or P = F(T). The function is just a whole bunch of things that we already know or can measure.


1. POSITION - When we measure rockets, we measure altitude. When we measure silver, we measure the Price in US dollars to buy one once.


2. VELOCITY - Velocity is a measure of position (in this case Price) over time. Seven years ago, the Silver Rocket had a bad thruster problem. It was falling out of the sky and had negative Velocity. It took two years and seven months from our first point on the chart, to finally reach it's average monthly low of $4.17. At this point, the POS velocity was zero. The Silver Rocket was gong sideways, which meant that from its negative initial velocity, some force must have been acting on the POS to slow down its decent.  That force, in the Newtonian sense, caused Velocity to change. Another measurable quantity.


3. ACCELERATION - This is simply the rate of change of velocity.  When you apply a constant force to a moveable object, the object changes it's velocity proportionally to the force exerted. It accelerates. If you maintain the force on the Silver Rocket, It's price-velocity changes and changes and changes, faster and faster - until the Force is removed. The same thing happens when you toggle the jets of a Rocket. Some time back more than 7 years ago, a positive force (demand), was applied to Silver- for now, let's call it the SMART Force. That force has not only continued to this day, but as you will see, Acceleration has been continually INCREASING over the last 7 years!. Like a Rocket, fighting against the earth's gravity, the higher Silver flies, the lighter it becomes, as the Stored Fuel Supply (silver in warehouses), is burned. The negative forces of friction and the pull of gravity (negative public sentiment and dollar strength) also decrease; therefore, the net force causing Acceleration - the change in Silver Price Velocity - increases. Is the Silver Price Acceleration still increasing after 7 years? Why don't you just read on and find out instead of asking all these silly questions?


The SMART Silver Equation - (reloaded)


Assume that the Price Position of Silver, like the vertical height of a rocket above the earth, can be expressed by an equation. The Price Position (P) in any Month (m) depends upon five factors - the equation parameters:

1.      The Initial position (I).

2.      The initial Velocity (V).

3.      The Acceleration (A).

4.      The rate of change in acceleration (Q).

5.      The month (m), starting with month 1 which is November, 1999.


This then, is the SMART Equation, that we will try to fit to the Kitco silver data:

Price  = ( I ) + (V * m) + (A * m * m) + (Q * m * m * m).


The following chart shows the results of the regression analysis on Kitco monthly silver averages.




Initial Price ($)



Velocity ($ per m)

- .052

- .049

Acceleration ($ per mm)



Change in A ($ per mmm)





I = $ 5.25 - This is the initial Silver price my program calculated at m=0, about 83 months ago, based on average monthly Kitco silver data I downloaded.


V =  - $ 0.049 per month - This is Silver's initial price Velocity at Time=0. The minus sign says that the price was moving down initially, at an approximate average rate of 4.9 cents per month.  Like North Korea's next A-bomb - falling from the sky.


A = $ .00028 per month per month - An initial SMART Force is acting to push the price positively and is changing the velocity faster by this rate every month. This is a small initial acceleration, although it is much larger than the 2004 value which was negligable!  But that small number gets multiplied by the square of the month (m), and so the Velocity begins to change more quickly as the month (m) increases.!


Q = $ .000017 per month per month per month. The SMART Acceleration may start tiny, but it's increasing at a rate that is four orders of magnitude (powers of ten) larger than the Initial Acceleration. The Acceleration is changing by this rate every month. Thus, the $ Velocity changes faster and faster every month. Notice that this Q parameter becomes increasingly more important with time!  The cube of month 10 = 1,000, but the cube of month 100 = 1,000,000! So Q grows one thousand times more important at month 100 than it is at month ten.


Rather than try to explain individually how these differences affect the trajectory in 2006 compared to 2004, it is much simpler to show the graph at this point. You can be the judge.



SMART Discussion


In general the new 2006 "best fit curve" clearly shows that Silver is still following a similar trajectory compared to 5 years ago; however, the curve has flattened slightly as a result of the extended price correction in 2004. Technically, the strongest and most imortant part of the equation, the Q component (rate of $ acceleration), has been reduced. I've a theory about that later…


What else does the SMART Curve tell us?

1.      In general, the good news is that the curve still increases strongly and exponentially upward. This 2006 curve predicts that the POS will again double from about  $12 this month (82), October 2006, to $24 in month 107, (November 2008, 25 months from now) - if it stays upon the path. 

2.      Price Position - The current Price of Silver is only about a dollar less than the 2006 SMART curve prediction, and we have been in a "normal" correction for about 6 months now already, and are coming up on the seasonally strongest time of the year for precious metals. The silver Prices are obviously quite cyclical and appear to be oscillating above and below the curve in a kind of sine wave. In my opinion, we should exceed the predicted values in the very NEAR future as Prices swing back to the other extreme.

3.      Price Velocity - Price Velocity is still increasing dramatically.

4.      Price Acceleration - Notice that the current Price levels are about 8 months behind the predicted 2004 Price values. It seems that there was some huge change in Price Pressure (the force that causes Price Acceleration - the force of Demand upon Supply) brought to bear on the Silver market which was above and beyond the normal cyclical nature of the rest of the curve. What could have caused the large change in $ pressure in 2004-2005?   This is only speculation, but I wonder if the change in Price Pressure (supply/demand balance) was a result of Warren Buffet, when he (?was forced to?) put his 130 million ounces of silver back into circulation quite suddenly and unexpectedly!  This added supply pressure in a fairly short period of time, would have caused just such a Price Deceleration. If so, then the effects would only be temporary, as the REAL overall world supply/demand has not changed. Short-term supply dumping of this nature would merely delay the immediate Silver supply problem by about 8 or 9 months until the excess supply was naturally digested by the market. Could this kind of dumping happen again? Yes. In my opinion, it could happen, but only if someone else has another 100 million ounces of silver to disinvest in a sudden random manner. Other than that, we might expect to eventually resume the HIGHER Silver Price Velocity and Price Acceleration of the 2004 curve. We will KNOW in only a couple more years!


In Conclusion


I will not try to speculate in this report what is coming next, and whether I think Silver is due to run into supply problems - like copper and zinc - causing it to explode in price. There are many rumours that real supply problems exist and manifest themselves already as delivery delays. There are some who think otherwise. It would be wise however, for all  investors to research the Silver supply/demand fundamentals for themselves, and especially to assess the possibility of supply problems or outright contract defaults, related to the unnaturally large Commercial Traders short positions as written about for many years by Ted Butler and others.


Note also several other interesting new Price Pressures that Silver Demand will make on Silver Supply in the next year or two:

1.      Renewed investor interest as Asia expands and the world commodity war heats up.

2.      As a result of environmental laws, changes to world electronics manufacturing which used over 100 million ounces of lead annually as a major component in solder, now will cause silver to be used instead for at least some applications. I don't know what percentage of the new solders used will be silver, only that it is a preferred alloy, and a potentially large demand situation.

3.      Silver threads are now being woven into cloth for anti-bacterial clothing. I purchased such a shirt for myself several months ago from LuluLemon, a growing yoga and sports clothing supply chain. I expect this application to grow even more quickly in coming years, as the odour fighting qualities of the cloth become more widely known and marketed.

4.      Silver use in all types of bacteria fighting is on the increase, including silver coatings in refrigerators and washing machines as well as hospital applications such as wound dressings for burn victims.

5.      Silver usage is growing in power transmission systems, where it is used as a low loss electrical super-conductor.

6.      Silver Exchange Traded Funds or ETFs are sprouting up like Hedge Funds, all over the world. A new one started yesterday in Shanghai I believe.

7.      New Silver-Zinc batteries for laptops that don't explode!


All of the above and more are already represented in the curve to some extent. These new forces of Silver demand, and many others, are causing the Silver Price Acceleration which will cause the SMART Curve to continue to rise exponentially until higher prices eventually choke off demand. This will only happen at much higher prices in my opinion, as silver prices are currently trading at VERY low historical ratios compared to all other metals, both base and precious. The amount of silver in any of these new products (except the ETF) amounts to only pennies per item. There is MUCH more room to fly for this rocket.


To those potential investors who are worried about government intervention in the silver market, remember these little-known corollaries of Newton's Laws of Motion:

1.      A Silver Rocket in motion will stay in motion, and cannot be stopped by any external force from the FED - because their force is spent.

2.      Silver Projectiles cause Negative Acceleration to Government Vampirism!


Rock on!

October 31, 2006


Disclosure Statement: 

I currently own lots of lovely, shiny Silver Coins, as well as myriad Silver and Gold Mining Shares…My Precioussss!...Do not believe anything I say, (don't even believe this), because in spite of my scientific genius, I am a mere human; therefore, I am highly biased, overly emotional, and probably legally insane.  (I am not!)  Are too…

-- Posted 3 November, 2006 | |

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