 Trading HUI Parabolas
Adam Hamilton
Archives
October 16, 2004
One of the first cognitive
skills babies learn is to identify certain shapes, like circles,
squares, and triangles. It is kind of funny, but technically-oriented
traders follow in these very infant footsteps when we examine
charts. A big part of technical analysis involves identifying
certain recurring shapes on price charts.
While I have pretty much outgrown
circles, squares, and triangles, one shape that endlessly fascinates
me today is the mighty parabola. My 4î thick Webster's
dictionary has a complicated definition for a parabola that only
a mathematician would love, but I like to think of them as just
plain old constantly accelerating slopes.
The proper definition of a
slope is equally convoluted unless you have a doctorate in applied
math, but the no-nonsense carpenters' definition is easy to understand,
rise over run. If you are laying piping or installing a roof,
the slope is critical. A roof that rises one vertical foot for
every ten feet of its horizontal distance has a slope of 1/10,
a rise of one over a run of ten.
Parabolas, or constantly accelerating
slopes, are ubiquitous in the financial markets. Once you start
looking for them they start to pop up everywhere, kind
of like Elvis sightings.
The most famous example I am
aware of today is the enormous NASDAQ bubble of the late 1990s.
If you examine a
graph of the entire decade, you will note that the NASDAQ
was barely climbing in the early 1990s, it started accelerating
in the mid-1990s, and by the late 1990s it was shooting vertical
in a mania frenzy. The NASDAQ carved a massive parabola! Gold
left a similar parabolic slipstream in its own wake during its
gargantuan 1970s
bull.
These parabolas are so fascinating
because they are always unsustainable in financial markets.
A price can rise gradually in the early years of a major move
for quite a long time, but when the really big moves erupt in
the final mania years the parabola has already sown the seeds
for its own destruction. Once a parabola goes vertical it becomes
a kind of mathematical black hole, its own weight guaranteed
to implode it back in on itself.
If you imagine a decade-long
financial parabolic pattern, the final year may have a 50%+ gain.
Well, if you extrapolate this vertical rise out, the resulting
numbers are just plain silly. After 5 more years, this market
would be 7.6 times higher. After 10 more years at +50%
per year, the market would be 57.7 times higher! Obviously this
is just absurd because far before these numbers are reached all
the capital on earth would have been exhausted.
Thus parabolas, when they hit
their final vertical zone, are absolutely guaranteed to fail
in the near future. Any other outcome is mathematically impossible.
As investors and speculators we have to remain aware of this
macro view on parabolas. If we have a decade-long chart that
is accelerating vertically with huge annual gains, then we are
witnessing a mania and need to sell before the inevitable reckoning,
usually a crash, arrives.
Parabolas are certainly not
limited to strategic charts though. Like the markets themselves,
parabolas are totally fractal in nature. A fractal is an identical
shape or pattern that appears at all different scales. The whole
art of technical analysis relies on this fractal nature of price
charts. Just as you can draw support and resistance lines on
any scale of chart from a few hours to a few decades, parabolas
too can be big or small but certainly present at any scale.
I have been pondering parabolas
and fractals of late as I analyze price charts. I have been wondering
if parabolic shapes offer important trading clues of when a market
has become overbought or oversold in an intermediate timeframe.
When a parabolic formation, either bullish or bearish, goes vertical,
do the probabilities swing in our favor for making trades in
the opposite direction?
In order to analyze this thesis,
we are going to take a look at parabolas in the HUI this week.
The HUI is the premier unhedged gold-and-silver stock index,
and probably the best performing sector on the planet over the
last several years. The HUI is up a massive 614% bull to date
from its November 2000 lows to its latest interim top in December
2003. Our subscribers, my partners, and I have been blessed with
enormous realized profits trading this largely overlooked bull
market.
Our first graph outlines the
HUI's bull market to date and reveals large parabolas, both bullish
and bearish, jumping out all over the place in the raw HUI price
data.
Before we delve into the HUI
parabolas, please check out the reference parabola in the lower
right corner of this chart. The dotted red line, of course, is
the parabola, with its constantly accelerating upslope. But the
black lines that frame it are revealing. While they look like
a curve, they are actually six perfectly straight black
lines drawn at sequentially increasing slopes.
Thus one price, increasing
its slope a half-dozen times or so over a major upleg or downleg,
will create a nice approximation of a true curved parabola. This
illustration is important because it helps show that a very parabolic
shape can form in a price chart with only a relatively few changes
in slope over the life of an intermediate trend. I call this
approximation a linear parabola and recently used it in analyzing
a vicious silver
correction earlier this year.
The HUI's bull market to date
has formed at least six major parabolas, all labeled above. We
rendered two identical sets of parabolas in this chart,
one directly superimposed on the blue HUI price data with a second
matching copy pasted in a little higher. While these two sets
of parabolas are the same, it is useful to view them both superimposed
over the HUI to see how well it conforms to them as well as independently
from the HUI so we can get a better sense of the index's true
underlying parabolic nature.
Parabolas are multiplying like
rabbits in this chart, but what is the whole point of this exercise?
I suspect that if we can recognize the terminal vertical stage
of each intermediate-term parabola in time, it can help us determine
when the HUI has a high probability of rising or falling. We
can then buy or sell accordingly based on whether a bullish or
bearish parabola is reaching its unsustainable vertical stage
and therefore hinting that an intermediate trend change is imminent.
A bullish parabola is one that
is carved in a rising market, a HUI upleg. Parabolas 1, 2, 4,
and 5 above are all of the bullish variety. Now if you look carefully
at the lower set of parabolas actually superimposed directly
on top of the HUI, an interesting phenomenon jumps out as these
bullish parabolas go vertical. In all four bull-to-date examples,
the HUI entered a correction without fail soon after the time
the bullish parabolas shot vertical and hence became mathematically
unsustainable.
It is interesting that this
observation has a fractal bent too. Whether a bullish parabola
lasted a long time like last year's massive number 5 or a short
time like the number 1 that kicked off this bull market, once
the HUI started shooting vertical a normal healthy pullback loomed.
Vertical price movements, even over the intermediate term, just
cannot be sustained. When an intermediate bullish parabola is
shooting vertical, it is probably prudent for us speculators
to sell HUI longs, throw short, buy puts, or at the very least
ratchet up our trailing stops.
During corrections following
these vertical-stage bullish parabolas, inverted bearish
parabolas form. Parabolas 3 and 6 above are perfect examples.
In both cases the HUI reached a new bull-to-date interim high
before correcting. These corrections, however, tend to start
out slowly. Once a new high has been reached people are very
hesitant to be anything but euphoric so early-stage corrections
often witness relatively modest declines.
As the correction picks up
steam though, its downslope accelerates. As the latest interim
highs fade in the distance and folks grow more nervous, selling
intensifies considerably. The price decay curve tends to ride
an inverted parabola, falling with a constantly accelerating
downslope. Eventually people get downright scared and the price
drops vertically, the final stage of a bearish parabola. But
just as normal parabolas are not sustainable once they shoot
vertical, neither are inverted ones.
When these bearish parabolas
fall vertical, odds are the correction just witnessed is pretty
much over. When investors and speculators recognize these inverted
parabolas reaching their vertical maturity stage, they can add
new long PM stock positions, close out any shorts, or buy call
options. Probabilities definitely favor the HUI launching a new
bullish upleg once an inverted bearish parabola shoots vertical
in a correction, and the sharp decline this past April is a perfect
example.
Since the markets are ultimately
just a study in probabilities anyway, it makes sense to watch
for these intermediate-term parabolas. They are not precise trading
signals by any means, but they seem to do a fairly good job in
signaling the general season, whether a major upleg or downleg
is getting long in the tooth and hence bets in the opposite direction
may be profitable in the months ahead.
The HUI parabolas help us understand
when the probabilities for a major intermediate trend change
are ballooning, all because parabolic ascents and descents become
inherently unstable and unsustainable in their terminal vertical
stages.
This idea is pretty simple,
but I have been struggling with how to measure it. As
an active speculator, I want to trade on hard empirical data
that I can quantify and compare, not just the subjective ìI
have a feeling this is getting too vertical hereî. I suspect
the HUI parabolas would become the most useful, not to mention
the most emotionally neutral, if there was some way to precisely
measure them.
After weeks of thinking about
this problem, I am disappointed to admit that I haven't found
an elegant solution. One of the reasons I am writing this essay
is to solicit feedback for superior ideas to measure these unfolding
parabolas. So if you have a better idea than this admittedly
sorely lacking one I am going to present, please drop me an e-mail.
If you solve this parabola measurement puzzle I would be honored
to discuss the solution in a future essay, thanking you by name
and granting you all the glory.
Parabolas are constantly accelerating
slopes, and a slope is a rise over run. While not satisfied with
this interim idea, the best I have been able to muster is measuring
HUI parabolic slopes as percentage gains over time. Unlike
building a roof where both the rise and run are in feet, in charts
the rise is in price and the run is over time. Time and price
are not synonymous so this isn't really a pure slope comparison.
After playing with all kinds
of different timing mechanisms to measure the X-axis of time,
the one that struck me as the most interesting was a 15-trading-day
percentage change in the HUI close as an approximation of slope.
15 days is three trading weeks, which seems to feel about right
given how long interim topping and bottoming processes at the
apexes of parabolas typically take to unfold. If a parabola can
shoot vertical to a big gain or loss over three trading weeks,
then perhaps it is vertical enough to anticipate a trend change.
Our final graph attempts to
quantify this initial attempt to measure parabolic slopes. The
HUI slides over to the right axis, and the 15-day percentage
change in the HUI is graphed on the left axis in red. While the
raw red squiggly line looks like the electrocardiogram of Alan
Greenspan the day gold crosses $1000, it actually hides some
provocative data. While this can't be the ideal slope measurement,
it still illustrates the general validity of this parabola trading
principle.
Since this graph is busy even
by my loose standards of busy-ness, we didn't draw in the parabolas
again. But once you see them as we did in the first graph, it
is really hard to miss them. Kind of like those computer-generated
pictures hidden in white and black dots that look like random
visual noise at first, once you finally see the image hidden
within the first time you can't help but focus on it instantly
when you look again.
The key to understanding this
chart is the blue HUI line. We took the greatest trading opportunities
in this entire HUI bull market to date, including all the interim
highs and lows signaled by the parabolas above, and we drew vertical
blue lines through them. In hindsight these were the best moments
to trade, both long and short, to maximize profits during the
HUI's bull market.
Each vertical blue line marking
great moments of opportunity for HUI trades intersects the violent
red 15d percentage change line. These intercepts reveal where
this 15d approximation of the HUI's slope was meandering at each
opportune moment to trade the index.
Per the parabola theory, the
15d slopes of the HUI should be extremely high near major interim
tops and extremely low near major interim bottoms, marking the
final vertical stage of major parabolas. This indeed proved to
be the case as the graph above reveals. This HUI slope chart
is easiest to interpret if we start our analysis at major interim
highs in the HUI.
The five red percentage numbers
on top of this chart show where the HUI 15d percentage change
slope approximation happened to be at or near major interim highs
in the HUI. The blue numbers underneath these percentage changes
show the offset, in days, between the 15d HUI slope top and the
actual interim top in the HUI itself. A -1d number indicates
that the 15d HUI slope topped one day before the HUI itself,
while a +1d indicates the slope topped one day after the
HUI.
It is interesting that every
major HUI interim top happened when the 15d slope of the HUI
was extremely high, running from a 23% gain over the past 15
trading days alone on the low side to a massive 35% on the high
side. Can you imagine the HUI blasting up 35% higher in only
15 trading days? Wow! The average 15d HUI slope at these major
tops was 28%, very high. Thus if we see a situation in the future
where the HUI has advanced by 25%ish or more in only three weeks,
odds are its current parabola is shooting vertical and is hence
unsustainable so a healthy correction is due.
The offsets between 15d HUI
slope tops and the actual HUI tops are revealing as well. First,
note that the three biggest HUI uplegs to date, parabolas 1,
2, and 5 from the first graph, all ended with fresh new bull-to-date
highs, slopes nearing vertical, and trivial offsets of only plus
or minus a single trading day. So it looks like the maximum 15d
HUI slopes do indeed occur very close to major new bull-to-date
highs signaling the end of each major upleg.
But if we get stuck in a largely
sideways trading range where the uplegs and corrections are fairly
minor, like in late 2002 and early 2003, then the offsets balloon
quite a bit. Thus the parabolas, or at least this imperfect 15d
approximation of the HUI's slope, are not as useful in a sideways
grinding market between major uplegs and downlegs.
Shifting our attention to the
major interim lows in the HUI, the 15d HUI slope numbers and
offsets are still useful but less precise. Of the five greatest
buying opportunities in the HUI since its bull launched, the
average 15d HUI slope during these times weighs in at -19%, but
the range is pretty broad running from -12% to -25%. In light
of this data, if the HUI is correcting and an inverted bearish
parabola is forming, once the HUI trades down 15%+ in only three
weeks odds are that a major new upleg is imminent.
The offsets are all over the
map at these major interim lows in the HUI, with its 15d slope
tending to bottom anywhere from six weeks to one week before
the HUI itself. On the bright side, I looked through all of these
offsets individually, both on the high and low side, and found
that generally even buying or selling as appropriate at the 15d
HUI slope high or low would have been very profitable. Usually
the difference between the HUI on the 15d slope extreme day and
the actual interim extreme day in the index itself was trivial,
within a few percent or so.
While this particular approximation
of the HUI parabolas is certainly not precise enough to define
a hard and fast trading tool, it does still seem useful for helping
us understand when probabilities swing in our favor for major
uplegs or corrections.
If the HUI is in an upleg shaped
like a parabola, that is accelerating higher, and the index has
rocketed up 25% or more in only three trading weeks, then odds
are that particular upleg is waxing too euphoric and a correction
is imminent. In these situations, if other trading indicators
concur, speculators can liquidate HUI longs, throw short, buy
HUI puts,
or at the very least ratchet up their trailing stops in anticipation
of weakness.
Conversely if the HUI is languishing
in a correction shaped like an inverted parabola, that is accelerating
lower, and the index has plummeted by 15% or more in only 15
trading days, then odds are that particular correction is growing
too fear-laden and an upleg is imminent. During these
exciting times like this past May, if other trading indicators
concur, investors can buy PM stocks while speculators can buy
stocks, close shorts, or buy HUI
calls.
If you are interested in trading
these major uplegs and corrections in the HUI, which have been
very profitable bull to date, please consider subscribing
to our acclaimed monthly Zeal
Intelligence newsletter. We have been painstakingly analyzing
and actively trading this entire 614% HUI bull to date and have
been blessed with some awesome realized gains in past uplegs
and unrealized gains in this current upleg. We will continue
to refine our analysis and tools and alert you to potentially
stellar HUI-related trading opportunities going forward.
The bottom line is intermediate
parabolas formed on price charts have great potential for helping
speculators define probabilities weighing whether an intermediate
trend change is imminent. When you see any multi-month trend
accelerating vertically to the upside or downside, chances
are this move is unsustainable and the inevitable reversal is
looming.
While I don't particularly
like this clumsy 15d HUI slope approximation described here,
I am confident that there is some elegant way to measure these
parabolas empirically and perhaps even distill these measurements
into a promising trading tool. Please let me know if you figure
it out!
October 15, 2004
Adam Hamilton, CPA
email:
zelotes@zealllc.com
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