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October 01, 2004

Relativity
by Adam Hamilton

Whenever the word Relativity is uttered, most people immediately think of last century's legendary physicist and genius Albert Einstein.

Ninety-nine years ago Einstein rocked the centuries-old foundation of Newtonian physics to its very core. His Special Theory of Relativity, published in 1905, claimed that Sir Isaac Newton's famous Three Laws of Motion were only approximately correct, that they started crumbling when velocities approached the speed of light. Einstein was right of course, but his unconventional ideas shocked the scientific world.

Interestingly, while the word relativity is inexorably linked to Einstein now, the principle bearing this name was actually introduced almost half a millennium ago in Florence, a city state in what is now modern Italy. Celebrated astronomer Galileo Galilei actually hatched the relativity idea during his extensive studies of the heavenly bodies. While observing planetary motion and celestial mechanics, Galileo pointed out that motion was only meaningful in relation to something else, a reference point.

In physics, all motion is relative. If you are observing a moving object from a platform that is also moving in the same direction and velocity, then there is no apparent motion between you and the object.

For example, if you are reading this essay near 40 degrees north or south latitude, like in the central US, then both you and your computer or paper are careening around near 800mph due to the Earth's rotation! Yet, since you and everything in your world are all moving at the exact same blistering 800mph speed, there is no apparent relative motion from your perspective. All motion is relative!

It is in the spirit of this pre-Einstein Galilean relativity that I would like to introduce my idea of Technical Relativity. Just as motion in the heavenly bodies is only relevant when considered in relative terms between the observer and the observed, in the financial markets short-term tradable price extremes are easiest to recognize relative to recent precedent.

This whole Technical Relativity thesis began gnawing at my skull about 18 months ago, as I studied the famous VIX implied volatility index in early 2003. As most speculators know, VIX extreme highs virtually always mark major tradable interim bottoms in the general stock markets. When a VIX extreme high is reached, traders have a very high probability of winning big if they immediately throw heavily long and buy index call options.

It all sounds simple, buy stocks when the VIX reaches an extreme high. After all, when the VIX is high and fear abounds stocks should be low, and the entire arts of investing and speculation can be summarized as Buy Low Sell High. Yet, just as Pontius Pilate rhetorically asked Jesus "What is truth?", speculators face similarly vexing questions. We constantly wonder "What is high?" and "What is low?". How do we know when a price is low enough for us to buy or high enough for us to sell?

Unfortunately it is impossible to emphatically answer these critical what-is-high and what-is-low questions. We mere mortals cannot know the future before it happens, and the markets are ultimately just a study in probabilities anyway. But perhaps Technical Relativity can enable us to swing these probabilities in our favor, to introduce trading discipline to help increase our chances of buying when prices are truly low and selling when prices are truly high.

Thus, this week I would like to formally introduce my thesis of Technical Relativity. Like Galilean relativity it is a simple idea that is easy to understand when laid out logically. In the past year I have written about relative studies countless times, but only tangentially in the context of analyzing something else. I hope to dispel the mystery and confusion surrounding Technical Relativity by fully explaining it in logical context this week.

When Galileo gazed through his ancient telescope at Jupiter, he realized that its apparent motion was a product of both its own orbit as well as the orbit of the very Earth on which he was standing. As you and I peer through our computers today to attempt to decipher the gyrations of the financial markets, we need to accept that our reference points for buying and selling should not be static. Like the Earth's motion relative to Jupiter, our vantage point for observing trading opportunities is dynamic.

Thus a particular market price may have been low or high in history, but that does not necessarily make it relevant today. The Dow Jones Industrial Average topped at the lofty height of 381.2 on September 3rd, 1929, a neck-snapping all-time-record high at the time. Since the Dow had traded under 100 for decades before the infamous 1920s bubble, 381 seemed stellar back in those days. Yet today with the Dow around 10k a level of 381 seems unthinkably low, not high.

As investors and speculators we can only decide that a particular market price is sufficiently low enough to buy or high enough to sell in the context of recent history. Lows and highs are not absolute, but totally relative. What was high a decade ago in a given market is most likely very different from what is considered high today or what will be considered high a decade in the future. It's not only our trading targets that are moving, like Jupiter's four largest moons which Galileo discovered, but our very reference points for trading, like Galileo's earthbound telescope.

As all this relativity stuff percolated relentlessly between my ears early last year, I was struggling with how we can use dynamic reference points as traders. Without dynamic reference points, we get stuck using absolute highs and lows that quickly become outdated as the markets evolve. Yet, as soon as we get into relative reference points to define tradable lows and highs, how do we remain objective? This paradox sorely vexed me.

After far too much thought about this puzzle a potential solution emerged, praise God! What is a trading reference point that is not static, that moves gradually over time to reflect new market realities, yet that is totally objective and well defined? One answer is the 200-day moving average of any price series! 200dmas are the perfect happy medium between static reference points prone to obsolescence and totally arbitrary dynamic reference points sans objectivity.

A 200dma is calculated by taking today's closing price, adding the closing prices of the previous 199 trading days, and dividing by 200. Tomorrow, and on each subsequent day, one new day's data is added while the oldest day's close is dropped off. Thus this constantly rolling 200dma provides an ideal objective dynamic reference point that only considers the last 200 trading days' action, roughly 10 calendar months.

Now calculating 200dmas way back in Galileo's time would have been a hideous exercise in self torment. Can you imagine writing out 200 closing prices in longhand, adding them up, dividing by 200, and then repeating this exercise over and over every single trading day? Ouch, I think I would have fallen on my sword first before manually calculating 200dmas!

Thankfully though in our modern computer age common spreadsheet software like Excel can effortlessly calculate endless 200dmas in a fraction of a second. Hence this analysis is easily accessible and replicable by everyone today.

200dmas have long been considered one of the most important lines in all of technical analysis, largely for two reasons. First, 200dmas tend to run parallel with the secular, or long-term, trend in force in any market. Thus a 200dma is like a big arrow pointing in the direction that a market is heading. Second, 200dmas tend to form the most foundational bull-market support or bear-market resistance of a secular trend. Short countertrend pullbacks (in a bull) or bear-market rallies (in a bear) tend to end at the 200dma.

This tendency is very easy to see in any graph of a secular trend. While my Technical Relativity thesis is totally neutral and can be applied to any market, I chose to use gold in these particular examples. Gold is a market near and dear to my own heart that I have written extensively about in recent years, so I am intimately familiar with it. In addition, its current secular bull market is textbook perfect for illustrating the magic of the mighty 200-day moving average.

Thus our first graph shows gold's current secular bull to date, as well as its 200dma.

Way back in April 2001, which feels about as ancient as Galileo these days, gold stealthily carved a long-term bottom just above $250. In the subsequent three years it marched relentlessly higher to achieve its current bull-to-date highs just above $425. As such, after more than three years gold is indisputably in a secular bull market.

Gold's black 200dma above, just like it ought to, acts as a big arrow running parallel with gold's primary trend. If you drew a simple linear trend channel to envelope the gold price in the last few years, gold's 200dma would run along with it roughly parallel like a third railroad track.  Because 200dmas distill about 10 months worth of trading action they deftly filter out all the short-term market noise and point out the true underlying trend of any price.

The whole thesis of Technical Relativity rests on the second great attribute of 200dmas though, their tendency to act as the major support in a bull market or major resistance in a bear market. If you carefully examine the price data above, you will note that gold's inevitable countertrend pullbacks and corrections tend to bounce higher right near its 200dma. This is why investors and speculators have often viewed the 200dma as the most important technical line.

Why is this phenomenon universal across all markets? The very mathematical nature of a 200dma makes it so. Since the 200dma considers today's close along with the preceding 199 days' closes, it tends to lag actual prices. 200dmas are constantly struggling to catch up with secular trends. In a very real sense, it is not the price reverting to the 200dma that is the noteworthy technical event, but the price moving countertrend long enough to give the 200dma time to catch up.

Stated another way, the mathematical interaction of an ongoing secular trend and its 200dma is a constant duel between convergence and divergence. When speculators get excited and bid up prices, a price pulls away and diverges from its 200dma. At some point though, greed waxes too extreme and a countertrend reversion is due. At this point a price pulls back and converges with its 200dma. Like a giant sine wave, a trending market constantly sprints away from and then returns to revisit its trailing 200dma.

As investors and speculators, we want to consider trading when these price and 200dma convergences and divergences grow extreme. In a bull market we want to buy near 200dma convergences and sell near 200dma divergences. In a bear market the opposite approach is in order, selling near 200dma convergences and buying near 200dma divergences. The gold chart above beautifully illustrates this timeless principle.

So far in this gold bull to date, there have been five interim lows that were ideal points to buy and four interim highs that were ideal points to sell. All these buy-low convergence points are labeled in green while the sell-high divergence points are labeled in red. Notice that all of the green buy-low points are at or near the black 200dma line, while all of the red sell-high points are far away from the 200dma.

So if you are a speculator who wants to buy low and sell high, all you need to do in a secular bull market is buy when a price nears its 200dma and prepare to sell when it stretches too far away from its 200dma. If you are an investor who wants to buy low and hold, you should only consider buying when a price nears its 200dma. If you buy when a price diverges from its 200dma, then odds are you are not getting the best possible price.

Thus the perpetual interaction between a price in a secular trend and its 200dma is of paramount importance for both investors and speculators to monitor. We can better gauge opportunities to buy low and sell high by observing a price relative to its 200dma. The 200dma provides a relative reference point that gradually follows any market price yet remains perfectly objective since it is a mathematical construct totally devoid of emotional bias.

Now that the immense power of the 200dmas is apparent, another problem arises. While hindsight is 20/20 and eyeballing a graph illustrates the principle of 200dma convergences and divergences as opportune moments to trade, we need a tool to help us recognize these in real-time. After all, when we hit one of these interim lows and highs like the ones shown above we need to be trading right now, not waiting a few months while the great opportunity passes us by.

In addition, we need a precise way to quantify these 200dma convergences and divergences. Due to the nature of graphs and price percentage changes off of varying bases, what our eye sees is often deceiving. To illustrate this, please check out points 2, 6, and 8 above. At which point do you think gold is farthest above its 200dma? Visually, my eyes tell me that point 2 is the least far above its 200dma while point 8 is the most far above its 200dma. But my eyes deceive me.

The true answer is revealed by the black numbers above, which quantify where gold hit an interim top or bottom relative to its 200dma. At point 2 gold topped $38 above its 200dma, $38 again at point 6, and $41 at point 8. Thus these distances, in absolute terms, are essentially the same! If we can only rely on visual cues on a graph, we are stuck with distortions due to changing bases (a rising 200dma) and true distances are tough to gauge.

When the power of trading on 200dma convergence-and-divergence extremes is combined with the problem of precisely quantifying and recognizing these very extremes, the Technical Relativity thesis is born. Relativity creates a simple objective tool that empowers traders to recognize tradable 200dma extremes while totally eliminating the visual distortions and emotional bias inherent in chart analysis.

Rather than relying on absolute prices such as gold's graphed above, Technical Relativity considers prices in relation to their 200dma. The 200dma becomes the gradually moving reference point, like the Earth was for Galileo's telescope. Thus we no longer care that gold is $20, $40, or $60 above its 200dma. Instead we are concerned of at what multiple of its 200dma that gold happens to be trading at the moment.

Computing a Technical Relativity number is exceedingly easy. The simple formula is closing price divided by its current 200dma. So if gold was trading at $440 and its 200dma was hovering near $400, then Relative Gold, or rGold in shorthand, would be $440 divided by $400, or 1.1. An rGold reading of 1.1 tells us that gold is currently trading at 1.1x, or 110% of, its 200dma.

Thinking of a market price in terms of a multiple to its 200dma deftly kills multiple technical problems with one stone. Because we are now talking in multiples and percentages, the base level no longer matters. Whether gold is trading $20 above its 200dma at $220 or $100 above its 200dma at $1100, it still has the same relative level of 1.1 in both cases. Technical Relativity eliminates the distortion inherent in using absolute numbers as compared to a constantly changing base over time.

In order to visualize why a relativity graph looks like it does, imagine if the black 200dma line above was flattened into a horizontal axis, and gold was flattened as appropriate right along with it. Rather than rising, the 200dma would always be constant at 1.0, a perfectly flat horizontal line regardless of gold's absolute price. And oscillating around this 1.0 line representing gold trading at a multiple of its 200dma, the rGold number would meander.

When gold was trading above its 200dma, the relativity reading would be greater than 1.0. When gold was trading below its 200dma, the relativity reading would be less than 1.0. And when gold hit its 200dma, the rGold reading would be exactly 1.0. Simple, yet powerful, stuff.

Our next graph this week undertakes this flattening operation just described. The absolute gold numbers from the first graph above are moved to the right axis, while the left axis notes relative gold. The black 200dma line slaved to the right axis evolves into the flat 1.0 rGold centerline on the left axis. And the wildly oscillating blue gold line on the right axis becomes the flattened red multiple of gold's 200dma on the left axis.

Behold Technical Relativity! I hope Galileo can forgive me for shamelessly appropriating his wonderful term.

Just like this Relative Gold graph, a Technical Relativity indicator effectively flattens a price's 200dma along the 1.0 line and then shows the price as a multiple of that 200dma. This simple conversion calculated by dividing a price by its 200dma eliminates the distortion and skew always inherent in using absolute prices to make buying and selling decisions over time.

Now, regardless of the absolute level of gold, we have a constant-percentage comparison of it relative to its key 200dma support over time. Whether gold is trading at $400 or $4000 makes no difference in a relativity graph, if rGold is at 1.10 then gold is trading at 110% of its 200dma regardless of its 200dma's base. This tool provides an outstanding relative reference point for us to consider in determining whether the gold price happens to be low or high on any particular day.

All nine points labeled above correspond with the first graph, but this time they include the rGold reading. The second number below rGold is the number of days between rGold's top or bottom and the actual top and bottom in gold. In only two cases above did the rGold turning point vary from that of gold itself.

Interestingly, however, the gold price only moved by 2.7% in the first case at point 3 and 0.2% in the second case at point 8 between the rGold interim extreme and the actual gold interim extreme. Thus, even in peculiar situations where a Relativity extreme doesn't coincide exactly with an actual price extreme, the percentage difference over this period of time is usually trivial. In general, relativity extremes mark true price extremes very accurately.

The beauty of a relative indicator is it gives us a range of interest over time to guide our actual trades, and this range is generally fairly consistent. A couple examples really help illustrate this key point.

First, please consider points 5 and 9 on the buy side. As the first graph showed, gold traded at $323 and $374 at these points respectively. Both points marked fantastic moments to buy gold, but the actual gold price at which these buy opportunities triggered varied dramatically. At what gold price should traders buy in the future? Technical Relativity solves this puzzle as it considers gold as a constant multiple of its 200dma.

At point 5 rGold traded down to 0.981, under 1.0 which marks gold's 200dma. At point 9 rGold traded even lower, down to 0.953. Both of these rGold buying opportunities, even though gold itself was at very different levels, witnessed sub-1.0 rGold readings. In fact, if you look at all five odd-numbered buying opportunities above, you will note that rGold was always right around 1.0 or so to mark all of the greatest buying opportunities in this entire bull market to date. So why not buy next time rGold trades around 1.0 or so?

The sell signals on top work the same way. The gold sell at point 2 happened at $327 but the gold sell at point 8 happened at $427. While a vast gulf separates these actual prices, the relative levels of gold were 1.130 and 1.156 respectively during both of these ideal moments to sell. Gold had advanced too far away from its 200dma so a divergence was in order to bring this ratio back into line in both cases. So why not sell next time rGold heads north of 1.14ish or so?

Technical Relativity helps precisely quantify a price's typical extremes relative to its 200dma over time, and as investors and speculators we can use these past extremes to help us identify future trading opportunities in real-time. We don't have to worry about whether a price is absolutely low or high when we can view prices as relatively low or high as compared to their key 200dmas.

Now after a trend has been running for a couple years, like gold's above, we can even use the previous extremes to define a potential trading range to watch for in the future. There are a couple steps to take in finding and defining one of these relative trading ranges.

First, it is useful to consider an entire relative range in percentage terms. To start, build a graph like this one running back two or three years. In general I think relativity ranges should encompass two to three years of data, but not too much more. We want our relativity indicators to stay current and reflect today's market conditions, so it is important to drop off old data periodically when considering extremes. Two to three years is just about right.

With these few years of data, find the highest and lowest relative readings. In gold's case above the highest the Ancient Metal of Kings has climbed relative to its 200dma was to 1.184x at point 4 in early 2003. The lowest gold has traded since its bull market began in April 2001 occurred just this past May at an rGold reading of 0.953. If we subtract this low from this high we get a max relative range to date of 0.231.

Now, as a general principle, a price cannot be extreme very often. If we consider a one-hundred percent range, it is probably not a problem to only consider the top 10% and bottom 10% as "extreme". This leaves the middle 80% to be considered as "normal" price movements. We are only interested in these relativity indicators when they approach the top or bottom 10% or so of their ranges.

In gold's case 10% of its 0.231 relative range is 0.0231. This 10% added to the bottom of the range (0.953) and subtracted from the top (1.184) yields us an initial relativity range of 0.976 to 1.161. Now if you look at the graph above, rGold only traded out of this range twice, once to the upside and once to the downside. With 9 major turning points and 2 extremes, this works pretty well as considered in the lower 10% extreme, 80% normal, and upper 10% extreme paradigm.

This brings us to our second step in defining these relative trading ranges. In some cases, there can be an outlier that skews this range. This has happened a little bit in gold, with the high and low readings above both a bit higher and lower than its general high and low relative readings. If you draw two lines in the graph above intersecting the rGold levels of 0.976 and 1.161, they only have one real-world intercept each. I believe this is insufficient for a trading indicator.

In these cases where there is only one intercept on the top and bottom with the 10%, 80%, 10% model, it is best to rein in the relativity range so there are at least two intercepts each on the top and bottom. This helps prevent outliers from skewing the relativity range beyond what we might expect to see in the future. Using this farther refinement, I defined an rGold range of interest of <0.990 to >1.140 based on the data above. These buy and sell zones are shaded in this graph.

When gold approaches a relative reading of 0.990 or less on the low side, it is time to consider buying with reckless abandon as long as you think its secular bull market remains in force. Similarly, if you are a speculator, whenever rGold gets near or above 1.140 it is time to consider selling, going neutral, or even shorting. Gold has intersected these levels twice at both the top and bottom of its relative band in recent years, so this range looks pretty solid.

An important caveat to consider when using relativity ranges as trading tools is that the old warnings that the markets are nothing more than a game of probabilities definitely applies. The farther away from its 200dma a price stretches, the more likely it is to revert back dramatically. But there are no magic levels. A price can easily turn around before or after a relativity band is reached. Relativity is another valuable tool to help us understand when high-probability-for-success trades are possible, but it cannot forecast the future. It is no crystal ball.

And while I chose to use gold in this example today, Technical Relativity is a generic tool that can be applied to any trending market. At Zeal, between our published work and unpublished internal research, we have run relativity analyses on all of the major US stock indices, stock ETFs, the implied volatility indices, a bunch of commodities, various currencies, sector indices, and even individual stocks. Any trending price is a potential candidate for relativity analysis.

In fact in the brand new October Zeal Intelligence monthly newsletter just published for our subscribers, we totally revamped our various trading indicators including all the relativity ones. New indicators have been added and existing indicators have been totally recalibrated. While our primary focus continues to be on the immensely profitable precious-metals arena for most of our investments and speculations these days, we continue to watch other markets as well and are ready to strike fast when great opportunities arise.

Please subscribe today to see these 17 new and updated trading indicators and learn how we use them to launch high-probability-for-success trades as appropriate in the coming months.

Just like Galileo Galilei declaring that all planetary motion was only relevant on a relative basis, that there were no absolute celestial reference points, I believe that investing and speculation can benefit greatly from a similar relative focus. Observing prices relative to their 200dmas provides a sound measuring point for our modern financial explorations today.

Technical Relativity combines the timeless principle of 200dma convergences and divergences as major trading opportunities with an absolutely objective way to measure and compare these extremes over time. After a trending market establishes an effective range, investors and speculators would do well to monitor and heed these relativity signals.

Adam Hamilton, CPA
Zeal LLC.com

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If you have questions I would be more than happy to address them through my private consulting business. Please visit www.zealllc.com/financial.htm for more information.

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Mr. Hamilton, a private investor and contrarian analyst, publishes Zeal Intelligence, an in-depth monthly strategic and tactical analysis of markets, geopolitics, economics, finance, and investing delivered from an explicitly pro-free market and laissez faire perspective. Please visit www.ZealLLC.com for more information, www.zealllc.com/samples.htm for a free sample, and www.zealllc.com/subscribe.htm to subscribe.

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