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Harmonic Trading
What is Harmonic Trading?
 Harmonic Trading is a methodology that utilizes the recognition of specific
price structures that possess distinct and consecutive Fibonacci-derived
ratio alignments to quantify and validate harmonic patterns.
 These patterns calculate the ratio aspects of each price structure to
identify the natural reaction / reversal points in the financial markets.
 Harmonic Trading respects the natural phenomenon of cyclical
movements of growth and decline within the markets.
Order within the Chaos of Life (&The Markets):
Many have argued that the financial markets are a random entity.
According to the Random Walk Theory, popularized in the book, The Random
Character of Stock Market Prices, by Paul H. Cootner (ed.), (MIT press, 1964),
price action is "serially independent," claiming that price history is not a reliable
indicator nor of predictive value of future action.
Principle of Harmonicity
Despite the randomness of the markets, J.M. Hurst argued in favor of the
relative importance of price history in his Principle of Harmonicity, which states:
“The periods of neighboring waves in price action
tend to be related by a small whole number.”
(Hurst, J.M., J.M. Hurst Cycles Course, Greenville,
S.C.: Traders Press, 1973.)
Harmonic Trading adapts this Principle to measure “neighboring waves”
through the use of Fibonacci-derived ratios instead of a “small whole number.”
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Fibonacci Foundation - Origin of the Fibonacci Sequence
Fibonacci numbers are based upon the Fibonacci sequence discovered by
Italian mathematician Leonardo de Fibonacci de Pisa (b.1170-d.1240). The
series was devised as the solution regarding rabbits reproductive capabilities.
The Mathematical Problem:
If a newborn pair of rabbits requires one month to mature and
reproduce at the end of the second month and every month thereafter,
how many pairs will one have at the end of “n” months?
The answer is: un
This answer is based upon the following equation:
un +1 = un + un -1.
The sequence of the Fibonacci numbers is as follows:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,144, 233, 377……
(infinity)
Beginning with zero and adding one is the first calculation in the numeric
series. The calculation takes the sum of the two numbers and adds it to the
second number in the addition. The sequence requires a minimum of eight
calculations.
(0+1=1)...(1+1=2)...(1+2=3)...(2+3=5)...(3+5=8)...
(5+8=13)…(8+13=21)…(13+21=34)…(21+34=55)…(34+55=89)
After the eighth sequence of calculations, starting with the sum of the
eighth calculation (34) as the numerator and using the sum of the ninth equation
(55) as the denominator, the result yields 0.618.
34/55 = 0.618181 ~ 0.618
Repeating the process, the next division of the ninth calculation
(21+34=55) and the tenth calculation (34+55=89) equals 0.617978 or 0.618.
55/89 = 0.617978 ~ 0.618
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In the inverse calculation of these numbers, the same rules apply
55/34 = 1.676471 ~ 1.618
Repeating the process, the next division of the tenth calculation
(34+55=89) over the ninth calculation (21+34=55) equals 1.618182 or 1.618.
89/55 = 1.618182 ~ 1.618
Fibonacci Phenomenon - This methodology assumes that harmonic patterns or
cycles, like many patterns and cycles in life, continually repeat.
 Plants - Fibonacci Phyllotaxis is the discipline of studying and classifying
the number of visible spirals, called parastichies, of flowers and seed
growth patterns within plants. Most commonly, various plants grow seeds
or leaves in patterns of successive elements exactly related to the
Fibonacci sequence. A survey of plants of 650 species and 12,500
specimens displaying spiral or multiple phyllotaxis estimated that about
92% of them have Fibonacci phyllotaxis.
(R. V. Jean 1994. Phyllotaxis: A Systemic Study in Plant
Morphogenesis. Cambridge University Press: Cambridge, 1994).
 Human Body – The human body demonstrates many of the same
Golden Proportion relationships, as well. Each tooth is related to each
other based on type. DNA molecules measure 34 angstroms long by 21
angstroms wide for each full cycle of its double helix spiral. The numbers
21 and 34, are the 7th and 8th results of the Fibonacci sequence,
respectively and possess golden proportions.
 Astronomic examples - Venus takes 225 days to complete a revolution
around the sun. As we all know, the Earth requires 365 days to complete
one revolution. If you divide 225 by 365, the result is approximately 0.618
of a year (225/365 = 0.616 ~ 0.618) and the inverse (365/225 = 1.622 ~
1.618) results in 1.618 of a year.
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Related to the Markets: The key is to identify complex cyclical situations with
phi and phi-derived ratios that pinpoint discernable segments of price action.
These levels define the “natural” levels of support and resistance that can be
anticipated. Applied to the markets, these measured segments within the relative
larger cycle define trade opportunities.
 Measured Moves – Each situation is measured to gauge the “readings”
of the situation.
 Structural price measurements are applied the same regardless of
timeframe – intraday vs. daily.
 Harmonic patterns define order within the chaos of the markets but
require specific conditions to be met to generate valid technical
signals.
What Harmonic Trading is Not…There has been a great deal of
misunderstanding regarding Fibonacci ratios and their application to the financial
markets.
 Not Astrology
 Not Voodoo
 Not a secret code
Harmonic Trading employs Fibonacci-derived ratios (aka Harmonic
Ratios) to quantify the natural cycles (price patterns) that are manifested within
the chaos of the markets.
Wave Theory: Harmonic Trading is similar to other Wave Theory approaches in
its examination of the structure of price history on a chart. However, this
approach applies precise ratios derived directly or indirectly from the Fibonacci
sequence. Harmonic Trading focuses on the combination of such ratios to define
patterns as precise structural signals.
Elliott Wave and Harmonic Trading: Harmonic Trading is similar to Elliott
Wave as both focus on the structure of price history segments to quantify
technical signals.
W.D. Gann and Harmonic Trading: Although Gann Theory is more complex,
including the use of his Natural Squares Calculator, both approaches utilize
relative geometric price calculations of cyclical trends in an attempt to define
critical turning points in the markets. The premise of Mr. Gann’s approach
should be considered as one of the primary forerunners to Harmonic Trading with
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one of the earliest references to Harmonic Trading mentioned in his 1927 book,
The Tunnel Thru the Air. Mr. Gann stated:
"But mathematical science, which is the only real science
that the entire civilized world has agreed upon, furnishes
unmistakable proof of history repeating itself and shows that
the cycle theory, or harmonic analysis, is the only thing that we
can rely upon to ascertain the future.”
(The Tunnel Thru the Air; Lambert-Gann Publishing;
Pomeroy Washington; 1927; pg. 77.)
Merrill’s Filtered Waves and Harmonic Trading: Arthur Merrill examined a
variety of price waves – in particular M- and W-type structures - in his 1977 book,
“Filtered Waves, Basic Theory: A Tool for Stock Market Analysis” (Analysis Press
1977). Merrill differentiated a gamut of price structures as unique technical
events. Although many of these structures seemed similar, he argued that they
were unique.
Harmonic Pattern Ratio Alignments
 As Merrill asserted, many price patterns may appear to be similar in
structure but are not and require precise quantification.
 The differentiation of patterns is the underlying basis and primary
effectiveness of Harmonic Trading identification techniques.
 In real trading situations, the specification of similar price structures that
possess different Fibonacci alignments can substantially reduce overall
risk.
 The ability to differentiate price structures is essential for identifying the
best trade opportunities and handling each situation in the most effective
manner.
Harmonic Trading Technical Tools




Fibonacci / Harmonic Ratios
Price Patterns
Trend Channel Analysis
Price Bar (Candlestick) Analysis
 Relative Strength Index (RSI)
 Other Considerations: Volume, Volatility Bands, Time and Sales
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Harmonic Trading Ratios
Primary Ratios:
(Directly derived from the Fibonacci Number Sequence)
 0.618 = Primary Ratio
 1.618 = Primary Projection
Primary Derived Ratios:

____
0.786 = Square root of the 0.618 (0.618)

0.886 = Fourth root of 0.618 or
____
Square root of the 0.786 (0.786)

1.13 = Fourth root of 1.618 or ___
Square root of the 1.27 (1.27)
____
1.27 = Square root of the 1.618 (1.618)

Complimentary Derived Ratios:









0.382 = (1-0.618) or 0.6182
0.50 = 0.7072
0.707 = Square root of 0.50_ (0.50)
1.41 = Square root of 2.0 (2 )
2.0 = (1+1)
__
2.24 = Square root of 5 (5 )
2.618 = 1.6182
3.14 = Pi (See page 34)
3.618 = (1+2.618)
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Harmonic Patterns – The Importance of Differentiation
 Pattern analysis often too vague.
 Similar structures must be differentiated to define the most relevant
structural signals.
 Harmonic Trading employs the Fibonacci-derived ratios to measure price
segments as the primary means of classifying distinct structures and
quantifying zones of support and resistance.
Potential Reversal Zone (PRZ)
Although a variety of technical approaches have measured zones of
support and resistance based upon structural analysis, the concept of a
convergence of ratios to define these areas – termed first Potential Reversal
Zone (P.R.Z.) - was originally outlined in “The Harmonic Trader.”
“History has proven that a convergence of Fibonacci numbers
and price patterns provides a highly probable area for a
reversal…This area of convergence is called the potential reversal
zone. When three, four or even five numbers come together within
a specific area, you must respect the high probability for some type
of reversal.”
(The Harmonic Trader, pg. 11. Nevada: HarmonicTrader.com, L.L.C. 1999.)
The effectiveness of these structural considerations is dependent upon the
application of the correct ratio alignments to quantify the most ideal formations.
(Harmonic) Head and Shoulders




One of the first price patterns identified
“Technical Analysis of Stock Trends” 1966 Edwards and Magee
Oversimplified = Least Measured, Most Cited
The general characteristics of the Edwards & Magee definition requires
symmetry. Harmonic Trading ratios applied to the pattern can refine the
most symmetrical situations and define the most precise structural points,
resulting in a measured Head and Shoulders.
 Such a refined structure pinpoints the price level for the pattern completion
and offers a distinct price level for trade execution.
 Look for pattern that completes at the reciprocal ratio (1/x) of the prior
shoulder.
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Inverted Harmonic Head and Shoulders
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Japanese Yen (JPY_A0-FX): Daily
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Harmonic Head and Shoulders
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Xinhua China 25 Index ETF (FXI): Weekly
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M&W-Type Pattern Differentiation
Arthur Merrill differentiated a variety of M&W type price formations but did
not apply relative ratios to the structure. Although others have applied ratios to
such price structures, Harmonic Trading has refined these much further to
include specific measurements for each point in the pattern. The prescribed
Harmonic Trading rules are designed to filter potentially flawed structural
formations and develop pattern-specific trading strategies for each situation.
The Bat vs. Gartley Pattern
The Bat Pattern
The Bat pattern is a precise harmonic pattern that I released in 2001.
Bullish
Bearish
 B point at a less than a 0.618 retracement of XA, preferably
a distinct 50% or 38.2% retracement.
 BC projection must be at least 1.618.
 AB=CD pattern is usually extended.
 0.886 XA retracement.
 C point with range between 0.382 and 0.886.
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Intel
(INTC): 60-Minute
This following intra-day example of the Intel shows a perfect Bullish Bat
pattern with a precise Potential Reversal Zone (PRZ). The ratio alignment was
quite precise, especially the 50% B point and extended BC projection. The three
numbers of the PRZ defined a tight zone in the 15.80 area to get long.
Specifically, the set-up possessed a 1.27 AB=CD pattern at 15.75, with the 2.0
BC projection and the 0.886 retracement competing at 15.80.
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NASDAQ 100 Tracking Stock
(QQQQ): 5-Minute
The Bearish Bat in this example possesses a perfect structure with a precise
alignment of the required Fibonacci ratios to validate the pattern. Starting with a
perfect 50% B point retracement, the price action formed an Alternate 1.27
AB=CD pattern that completed in the same exact area as the 2.0 BC projection.
In combination with the 0.886 XA retracement, the Potential Reversal Zone
(PRZ) possessed three numbers in a 5-cent range that defined resistance just
above $30 a share.
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The Gartley Pattern
These rules for the ideal Gartley pattern was released in “The Harmonic
Trader” (1999) and it has become the standard in the technical community.





Precise 61.8% B point retracement of XA leg.
BC projection must not exceed 1.618.
Equivalent AB=CD pattern is most common.
0.786 XA retracement.
C point within range of 0.382-0.886 retracement.
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Dow Jones Industrial Average Tracking Stock
(DIA): Daily
The Dow Diamonds formed this Bullish Gartley on the following daily chart
with three numbers in a tight range between 118-120. The pattern possessed a
distinct structure with a perfect 0.618 B point retracement.
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Swiss Franc
(CHF_A0-FX): 60-Minute
The next example of a Bearish Gartley in the Swiss Franc shows another
excellent harmonic pattern in the currency markets. The 60-minute chart
possessed a distinct pattern, clearly defining the critical harmonic resistance.
The pattern formed the required Fibonacci alignment to validate the structure,
especially the precise 0.618 B point. The price action stabilized nicely after
testing the entire PRZ and the pattern represented an excellent intra-day selling
opportunity.
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Other Harmonic Patterns: In addition to the (Harmonic) Head and Shoulders,
Bat and Gartley patterns, the other structures within the Harmonic Trading
arsenal include:







AB=CD
Alternate AB=CD
Alternate Bat
5-0
Butterfly
Crab
Three Drives
For more information, go to www.HarmonicTrader.com
Case Study: S&P500 Double Dip Scenario
The current situation in the S&P 500 underscores the effectiveness of
Harmonic Trading strategies to define current state of the predominant trend.
There has been much discussion lately regarding a “dounle-dip” scenario for the
equity markets. Despite the recent pessimism, I believe it is important to review
the long-term significance of the action in the Standard and Poor’s 500 index
since last year’s low to define what this truly means.
From a broader view, the index rallied in March to take out the weekly Bearish
50% retracement @ 1120. The weekly price action has formed a distinct Bearish
5-0 pattern at this retracement. In fact, this structure has developed in each of
the last four bear markets that declined more than 30% - going back to1974.
This is significant for two reasons:
1 The breakout of a 5-0 pattern typically results in an accelerated move to
the 88.6% retracement of the measured leg, regardless of the time frame.
In this case, the weekly chart points to the 88.6% retracement level at
1475.
2 This historic precedent defines price limits for the current market, as the
S&P 500 pullback in each of the prior cases did not retrace any more than
50%. Currently, this would establish the 940 area as a make-or-break
support point.
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Standard and Poor’s 500 (^GSPC): Weekly
Bearish 5-0 Violation
 Historically, the S&P 500 has experienced accelerated price action after
testing the 50% retracement area of a prior multi-year bear market. The
index has consolidated at this critical 50% level for the past 6 months.
 I have analyzed prior bear markets of the past 40 years in the S&P 500
index. There have been four major market declines that have exceeded
30% and formed a Bearish 5-0 pattern structure following the completion
of their respective ultimate low.
 In each case, the price action rallied to the 50% area and reacted
nominally on the first test of the pattern's completion. However, this
structure served only as temporary resistance. In each case, the eventual
breakout resulted in a decisive rally to the corresponding 88.6%
retracement. The following charts outline each case.
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Standard and Poor’s 500 (^GSPC): Weekly
Bearish 5-0 Violation 2004
In 2004, the S&P 500 formed a distinct structure on the weekly chart. After
losing nearly 50 percent of its value, the S&P 500 rallied sharply from the 2002
low. The price action tested the 50 percent retracement at 1160 and reversed
approximately 10 percent over the course of a few months before resuming the
multiyear up trend.
The index was able to rally to the weekly 88.6% retracement. Despite an
eventual collapse that resulted in an entire retracement of this rally, the breakout
in 2004 accurately defined the predominant trend for the next three years. In the
same manner, the current situation in the S&P 500 is clearly pointing to further
upside with an eventual test of its relative 88.6% retracement.
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Standard and Poor’s 500 (^GSPC): Weekly
Bearish 5-0 Violation 1988
The price action following the crash of 1987 possessed the same structure
as in the 2004 example. The market tested the Potential Reversal Zone (PRZ) of
the pattern, reacted nominally after the completion and rallied decisively after the
initial reaction. The interesting aspect of this situation is the accelerated breakout
that occurred following the violation of the pattern.
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Standard and Poor’s 500 (^GSPC): Weekly
Bearish 5-0 Violation 1976
In 1974, the market was cut in half from its peak. Following the
devastating decline of the 1973-1974 bear market, the index formed a 5-0 pattern
structure on the weekly chart. The price action reversed briefly at the initial
completion of the pattern. The index rallied above this reaction peak and
eventually tested the 88.6% retracement within a few years after the initial
breakout.
The index did pullback nearly 50% for most of 1977 before reaching for
the upside objective. It is common for the retest of a prior Potential Reversal
Zone (PRZ) to occur after being violated. The 1977 situation defines the pull back
limit within this historic precedent.
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What This Means from an HT Perspective
This simple ratio analysis establishes a historic technical precedent that is
relative to the current state of the index. The “Double-Dip” scenario will only be
triggered below the previous limit – the 1976 general limit or the price action will
violate the long-term upside bias segment.
Recent Developments:
Standard & Poor's 500 Index (^$SPX)
Bullish 38.2% Retracement
Last month, the index reversed exactly at an important harmonic ratio - a
38.2% weekly bullish retracement. This is extremely significant, as it exemplifies
the degree of Harmonicity that the price action is exhibiting.
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Standard & Poor's 500 Index (^$SPX)
Bullish 5-0
One other consideration from an HT perspective is a Bullish 5-0 pattern
that completes slightly lower. The exact 50% retracement pattern completes
943.
The Double Dip scenario must be assessed from a pure price perspective.
Although the recent rally from the 38.2% retracement has stabilized this year’s
correction, these larger pattern and historic retracement considerations are
undeniable technical evidence that the market must hold this support or truly face
a double dip – more like, a double dump!
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Harmonic Trading Conclusion
My goal in this presentation was to offer a general overview of Fibonacciderived ratios combined with prescribed price patterns. Harmonic Trading
possesses many unprecedented technical strategies that can define the state of
price action within trends in a unique fashion. Each pattern possesses
statistically validated strategies to optimize trading decisions. The finer points
and research can be found at www.HarmonicTrader.com. In conclusion, it is
important to be mindful of a few of the following concepts:
 If there is anything that I have learned in 20 years of following the
markets, it is the importance of respecting the clear structural
signals that price action provides.
 The current situation in the S&P500 clearly demonstrates the
importance in understanding simple ratio analysis and defined
pattern considerations.
 There is a great deal of technical information that can be garnered
from such analysis.
 Harmonic Trading seeks to refine general structural signals to offer
precise levels of support/resistance based upon prescribed pattern
specification.
 The inherent value of Fibonacci-derived ratios is effective when
related to the markets. Although these situations are not found in
every market at all times, the key is to wait for those conditions to
develop and employ HT strategies to capitalize on such order within
the chaos of the financial markets.
 It is important to remember that pattern and ratio analysis are a
starting point but offer effectively reliable technical tools unlike any
other approach.
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