a pure sci-ence and probes of this sort may lead the way to further understanding. The following sec-tions deal with ideas such as these—-sometimes reasonable and other times seeming tostretch the imagination.
ELLIOTT’S WAVE PRINCIPLE
RN. Elliott was responsible for one of the more highly regarded and complex forms ofmarket technical analysis. The Elliott Wave Theory is a sophisticated method of pricemotion analysis and has received careful study by A.H. Bolton (1960), and later by CharlesCollins. His works are fully covered in two more recent publications by Robert Prechter;brief summaries of the analysis appear in some of the comprehensive books on marketanalysis.” This presentation of Elliott's technique will include both the original principlesand extensions with examples.
The Wave Theory is an analysis of behavioral patterns based on mathematics andimplemented using price charts; its original application was stocks and it is credited withpredictive ability with respect to the Dow Jones Industrial Averages, which is second onlyto the occurrence of Haley's comet. It is understood that Elliott never intended to applyhis principle to individual stocks, perhaps because the relatively low activity might dis-tort those patterns that would have appeared as the result of mass behavior. If so, cau-tion must be exercised when applying this method to individual stocks and futuresmarkets, :
The successes of the Elliott Wave Theory are fascinating and serve to reinforce the useof the technique; most summaries of Elliott’s work recount them and the reader is encour-aged to read these. The waves referred to in the theory are price peaks and valleys, not theformal oscillations of sound waves or harmonics described in the science of physics. Thewaves of price motion are overreactions to both supply and demand factors within majorbull moves developed in five waves and corrected in three. His broad concept was relatedto tidal wave bull markets that have such large upward thrusts that each wave could bedivided into five subwaves satisfying the same principle. After each primary wave of themajor bull trend there was a major corrective move of three waves, which could be furtherdivided into subwaves of three (see Figure 14-8).
The types of waves could be classified into the broad categories of triangles and ABCs,representing a main trend and a correction, respectively. The term triangle was taken fromthe consolidating or broadening shape that the waves form within trendlines, although inlater works Elliott eliminated the expanding form of the triangle (see Figure 14-9).
An interesting aspect of the theory is its compound-complex nature, by which eachsequence of triangles can occur in subwaves within waves (Figure 14-10). More recent worksuggests that in futures markets, a three-wave development is more common than fivewaves. Prechter, a well-known interpreter of Elliott's principles, has shown many majorstock index moves that conform tothe ratio of 1.618. The stock index, which has great par-ticipation, is most likely to represent the generalized patterns of human behavior.”
75 Robert R. Prechter, Jr., The Major Works of R.N. Elliott (New Classics Library, Chappaqua, NY (circa. 1980); andAJ. Frost and Robert R. Prechter, Jr., Elliott Wave Principle (New Classics Library, Chappaqua, NY, 1978); Merrill(1960) Appendices 5 and 6 contain one of the more thorough summaries and analyses of the basic Wave Theory,including performance. ~
26 Robert R, Prechter, Jr., David Weiss, and David Allman, “Forecasting Prices with the Elliott Wave Principle,” inTrading Tactics: A Livestock Futures Anthology, Todd Lofton (ed.) (Chicago Mercantile Exchange, 1986).354 BEHAVIORAL TECHNIQUES
 
 
FIGURE 14-8 Basic Elliott wave.
    
    
7 CayTHE BULL MOVE Bs THE CORRECTION"
 
 
©2 Bz C3
Subwaves show 5 waves in the main move and 3 wave correction.
 
Elliott’s Sideways Markets ‘ -Occasionally, the market pauses during a major move, or it may move sideways in a volatilepattern after completing the fifth leg of a wave. This has been described as “stock pricesseen to be waiting for economic fundamentals to catch up with the market expectations.”?”These periods can be represented by a single three, a simple zigzag or flat formation, or bythe more extended double or triple three (Figure 14-11). .
A small variation of the single three has been noted to occur following the third wave,when the zigzag forms a minor swing reversal with b lower than its preceding top, and clower than a. Elliott has also recognized this asa descending zigzag in an upward trend.”
Fitting the Market to the Patterns oe
One point to remember when applying an intricate set of rules is that an exact fit will notoccur often. The best trading opportunities that will arise will be for those price patternsthat fit best as the move is progressing; each successful step will serve as positive rein-
7 See Robert R. Prechter, Forecasting Prices (1986). -
* Robert R. Prechter, Jr., “Computerizing Elliou,” Technical Analysis of Stocks & Commodities Quly 1983), givessome general observations on how he would go about adapting Elliott’s interpretations to a computer program.ELLIOTT’S WAVE PRINCIPLE 355
 
 
FIGURE 14-9 Triangles and ABCs.
 
   
INVERTED TRIANGLE
 
 
FIGURE 14-10 Compound correction waves. ~
 
2 Correction B correction
 
 
FIGURE 14-11 Elfiott’s threes.b
I 6 of 6 6 eo |i / j /| i / i / / { i ii\i\y } ! J | | { 1i i Ii acace™ / @e¢ ae a@,e .
aoc ISingle Double Triple356 BEHAVIORAL TECHNIQUES
 
forcement for continuing. The critical period in the identification process is the fifth wave.The failure of the fifth wave to form indicates that the last correction of three waves will beretraced. In a bull market, an extension of the fifth wave is often followed by a correctivethree-wave function. In addition, the recognition of a five-wave sequence should be fol-lowed by further analysis to determine whether that cycle was part of a more complexseries. One of the difficulties in the method is the orientation of the current position to thewave formation; the multitude of primary and secondary waves makes some of the situa-tions subjective until further developments clarify the position. Anyone interested in thefurther complexities of wave formation should refer directly to Bolton’s work.
Elliott’s Use of the Fibonacci Series
The application of the Elliott Wave Theory was unique in its use of the Fibonacci series.Besides the natural phenomena mentioned earlier, the summation series has the mathe-matical properties that
The ratio of any number to its successor (E/F;,1) approaches .618.
The ratio of any number to its previous element (F,,/F,) approaches 1.618.The ratio of F,.2/F, is 2.618.
The two ratios (F/Fi+1) X Fis /F)) = .618 x 1.618 =1
Elliott was also able to link certain measurements of the Great Pyramid to theFibonacci series and connect the number of days in the year as well as the geometric figureof a circle to his theory. Both time and the circle will play a role in Elliott wave analysis.
While Elliott used the lower end of the Fibonacci series to describe the patterns in thestock market, it should be noted that there are increasingly larger gaps between successiveentries as the series increases. To be consistent with the original principle, each gap couldbe subdivided into another Fibonacci series in the same manner that the waves take onacomplex formation. Harahus offers an alternate approach to filling these spaces by use ofLucas numbers, formed in the same way as the Fibonacci summation beginning with (1, 3)and resulting in (1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, .. .). The two sets are combined,eliminating common numbers, to form (1, 2, 3, 4, 5, 7, 8 13, 18, 21, 29, 34, 47, 55, 76, 89,123, 144, 199, 233, .. .). The Fibonacci numbers have been italicized since they will receivethe most emphasis, whereas the Lucas numbers will serve as intermediate levels of less sig-nificance. The numbers themselves are applied to predict the length in days of a pricemove. A bull move that lasts for more than 34 days should meet major resistance or reverseon the 55th day or on the 89th day (considering Fibonacci numbers only). It is suggestedthat a penetration of the 89th day should permit the series to start again with the beginningof the series added to 89 (e.g.,..- , 94, 96, 97, 102, 107, 110, 118, 123, 136, ...), includ-ing the more important Lucas and Fibonacci numbers from the original series. This effectis similar to the complex wave-within-a-wave motion,
The same numbers are used to express key levels in a trend reversal. For example, abull move that carries prices up for about 47 days before a reversal should meet resistanceat the price level on the 34th day. If that price does not s! stop the reversal, either the behav-ioral implications of the number 'series do not hold for this situation or prices are in a dif-ferent part of the cycle. -
With the introduction of Lucas numbers (Z), there are some additional key ratios. In thecombined Fibonacci-Lucas series (FL), denote an element with / if it is the first element ofthe other series following entry i; L, is the first Lucas number entry following F; that is aFibonacci number. This results in the ratios F/L, = .72, L/F, = 854, and F/F,,2=L/L;.2= 382.
The important ratio of a Fibonacci number to its following entry can be represented bythe ratio of successive numbers (1/2, 2/3, 3/5, 5/8, 8/13, 13/21, 21/144, . . .). When expressedELLIOTT’S WAVE PRINCIPLE 357
 
in decimal, these ratios approach the number .618 in a convergent oscillating series (1.000,.500, .667, .625, .615, .619, . . .). These ratios, the key Fibonacci-Lucas ratios, and the alter-nate entry ratios, represent the potential resistance levels (in terms of percentage) for priceadjustments within a well-defined move. For example, a price advance of $1.00 in silver to$5.00 might correct 100%, 50%, or 62%, to $4.00, $4.50, or $4.38, respectively, according tothe most important ratios.
Trading Elliott
Elliott also knew that there was great variability in this adherence to waves and ratios. Theappearance of the waves is not regular in either length or duration and should not beexpected to continually increase as they develop, although the fifth wave is generally thelongest. The waves must be identified by peaks only. Elliott introduced a channel into histheory to determine the direction of the wave being analyzed as well as to establish inter-mediate price objectives. Looking back at the diagram of the basic wave, note the channeldrawn touching the peaks and bottoms of the bull move. For every two peaks, a channelcan be drawn that will serve as a trendline for price objectives. This same technique is cov-ered in detail in a later section of Chapter 12. A break of the lower trendline in the bullmove will serve to tell when a correction has begun.
The Elliott Wave Theory is very intricate and should not be attempted without carefulstudy of the original material, but some rules are presented here to help understand thenature of the method:
1, Identify a main trend.2. Determine the current status of the main trend by locating the major peaks and bot-toms that will form the five key waves.
3. Look for three wave corrections and five wave subtrends or extensions.
4, Draw trendlines to determine the direction.
5. Measure the length of the waves in days to determine its adherence to the Fi-bonacci-Lucas sequence, measure the size of reactions as compared with FL ratios.
6. Watch for reactions at points predicted by the FL sequence and: corresponding tothe patterns described by the five-wave main trend and three-wave correction.
7. Use the ratios, day counts, and trendlines as predictive devices to select price ob-jectives,
8. Use the trendlines to determine changes of direction.
As can be seen below, much of this systematic identification of waves has been done usinga computer,
The Supercycle
When the short-term patterns fail to fit the rules, the bigger formations are likely to work. Thisapproach applies to all chart analysis, and Elliott’s wave theory is not an exception. Shortertime periods include relatively more noise, which may be difficult to separate from the sig-nificant market movement. Robert Prechter, well known for his focus on Elliott, uses a super-cycle to describe the fifth wave of the prolonged bull move, which is still intact in 1997 (seeFigure 14-12), applying Fibonacci ratios to forecast targets and explain the past moves.”
When using a charting technique, it is best to look for markets that, in some timeframe, conform to the type of patterns you are seeking. This is also true with Elliott, whichrequires that prices advance in proportion to the Fibonacci ratios. In the DJIA supercycle,shown in Figure 14-12, -
?9 Robert R. Prechter, Jr., “Major sea change Il,” Futures (March 1996).358 BEHAVIORAL TECHNIQUES
 
 
FIGURE 14-12 Price relationships in supercycle (V).
5000
1000
       
At 5444,V=.618xII=1.618x!Iin terms of % gain
II 9292
  
1932 1942,s«1952,s«st962—=s=—i‘é972~s—=é<“‘égBA];é1992This chart includes the 1982 “orthodox” end-of-pattern low.
 
Source: Robert Prechter, Jr, Futures (March 1996). Copyrighted 1996 by Robert Prechter, jr. Reprinted with per-mission of Futures,
1. Wave 1 begins at the 1932 low of 41.22, peaking in 1937 at the high of 194.40, a gainof 371.61%.
2. Awave 2 retracement follows,
3, Wave 3 starts in 1942 at the low of 92.29 and ends in 1966 at the high of 995.15, again of 970.975%. Note that when you divide the first gain by the second gain,371.616/970.975, you get the classic Fibonacci ratio .3827. -
4, The fifth wave should then follow the same pattern, and gain 600,692%. This targetis found by solving for the value of wave 5, where
wave I/wave 5 = wave 5/wave 3 = .618
This gain of 600% is based on the low of 776.92, and gives a target price of 5,444.Traders are cautioned that the high volatility and unusual extension of the currentmove is likely to cause very specific targets, such as this, to be violated by as muchas 10%.
Automating Elliott’s Wave Analysis
While analysts believe that there is substantial value in-Ellioit’s method, it has been con-sidered too subjective and cannot be evaluated with the rigorous historic testing that hasbecome popular. Recent years, however, have shown that a talented analyst and muchmore computer power can combine to produce programs that can come close to a trueversion of what was once the exclusive domain of human interpretation. Elliott’s wave the-ory has not been immune to this technology.”
* The content of this section is based on Murray A. Ruggiero, Jr., “Building the wave,” Futures (April 1996). He cred-its Tom Joseph for the development of the computer ‘software, which is the basis for the product, Advanced GET.ELLIOTT’S WAVE PRINCIPLE 359
 
Murray Ruggiero has defined the trading opportunities for a basic Elliott wave patternto be:
1, Enter wave 3 in the direction of the trend.
2. Stay out of the market during wave 4 (a retracement).3. Enter wave 5 in the direction of the trend.
4, Take the countertrend trade at the top of wave 5.
When a wave appears in two time frames, such as both daily and weekly charts, the like-lihood of the success of this formation increases. This concept is well accepted through-out technical analysis and can be found in many sections of this book, including Chapter19 (“Multiple Time Frames”). Without confirmation of a pattern or trade, the riskincreases.
The key to automating Elliott’s technique is the creation of the Elliott wave oscillator(EWO), A series of extensions and pullbacks can be found using the EWO, combined witha method of counting waves that locates the current price within the standard Elliott wavepattern. The following steps present the bull move only, although the downside is treatedas just the reverse set of rules.
1. Calculate the Elliott wave oscillator (EWO) as the difference between a 5-period anda 35-period simple moving average, applied to the average of the high and lowprices,mean = (high + low) / 2EWO = @average(mean,5) - @average(mean, 35)
2. Anew upward trend begins when the EWO makes a new high for a period, n, de-termined by the user. This allows, for example, wave 3 to be identified when it goesabove the high of wave 1.
3, Anew upward trend also begins when the current value of EWO is below zero (the5-day average is below the 35-day average), and the trend is down (Step 2), but theEWO has rallied by a percentage (called the trigger) of the lowest oscillator value ofthe past 7 periods (@] owes t (EWO,n)). Then the trend is up if EWO is below zero, theprevious trend value is down, and
EWO > trigger*@lowest(EWO,n)
This rule allows the next wave to be found based on the retracement that comes be-
tween each wave.
4, To relate this to Eliott, we must know where prices are located in the five-wave se-quence. For an uptrend, this is done in the following order:
a, When the trend turns from down to up we assume it is the beginning of wave 3and save the current values of EWO and price.
b. Continue to save the new high EWO value and new high price for wave 3.
c. Wave 4 begins when EWO falls to zero.
d. If wave 4 is currently active and the price is a 5-period high and EWO > 0, thenwave 5 begins. Save the highest EWO value and highest price of wave ’5 wheneverthey occur.
e. If EWO in wave 5 becomes higher than the highest EWO value in wave 3, then weare still in wave 3. Label the current wave 5 values to indicate wave 3, and con-
- tinue as in wave 3 with step b.
f. If the trend turns from up to down in wave 5, then this is a wave 3 down. Resetali values and look for a new wave 3 up when step a is satisfied.360 BEHAVIORAL TECHNIQUES
 
5. The trading rules needed are based on the values of m, the number of periods, andthe trigger (the percentage retracement).a. Buy on open when wave 3 is first identified, whether on a new m-period high ora retracement of the previous downturn (step a).b. Buy on the open when wave 5 is first identified (step d).c. Buy on the open when wave 5 turns into wave 3 (step e).d. Close out any long position when EWO falis below zero.
With these rules, a long position is taken during the strongest parts of wave 3 and wave5. As a guideline for selecting both the period and the trigger values, a test of theDeutschemark for 20 years from 1976 through 1995 showed robust results for periodsfrom 50 to 140 and for retracement trigger values of .70 or less.
{FUNCTION EWO}
{Find the Elliott Wave Oscillator (EWO)}
vars: mean(0);
mean = (high + Tow) / 2;
EWO = 0; :
if @average(mean,35) <> 0 then EWO = @average(mean,5) - @average(mean, 35);{FUNCTION EWTREND)
{Find the trend using EWO}!
inputs: period(numeric), trigger(numeric);
vars: trend(Q), osc(0);
osc = EWO;if osc = @highest(osc, period) and trend = 0 then trend = 1;if osc = @lowest(osc;- period) and trend = 0 then trend = “1;if @lowest(osc,period) < 0 and trend = -1 andosc > -l*trigger*@lowest(osc,period) then trend = 1if @highest(osc,perfod) > 0 and trend = 1 andosc < -1l¥trigger*@highest(osc,period) then trend = -1;-EWTREND = trend;
{FUNCTION ELLIOTTWAVE}{Find the current wave using EWTREND and EWO}inputs: period(numeric), trigger(numeric)vars; ET(Q), mean(0), osc(0), wave(0), hiosc(-999), hiosc2(-999),hiprice(-999),hiprice2(-999); . \osc = EWO;mean = (high + low)/2;{Is the current wave sequence up or down?}ET = EWTREND( period, trigger); :{When the trend changes from down to up, label it wave 3 and save the current oscand price}if ET = 1 and ET[1] = -2 and osc > 0 then beginhiosc = osc; ~hiprice = mean;
wave = 3;
end; . ~{If wave 3 and the oscillator make new highs then save those values}if wave = 3 then begin oe
if mean > hiprice then hiprice = meanif osc > hiosc then hiosc = osc;(Test for the beginning of wave 4}if osc <= 0 and ET = 1 then wave = 4;end;(Test for the beginning of wave 5}if wave = 4 and mean = @highest(mean,5)-and osc >= 0 then beginwave = 5;hiosc2 = osc:CONSTRUCTIONS USING THE FIBONACCI RATIO 361ee
hiprice2 = mean;end;if wave = 5 then beginif osc > hiose2 then hiosc2 = osc;if mean > hiprice2 then hiprice2 = mean;end;(Test for wave 5 becoming wave 3}if wave = 5 and hiosc2 > hiosce and ET = 1 then beginwave = 3;hiosc = hiosc2;hiprice = hiprice2;
hiosc2 = -999;hiprice2 = -999;end;
{Identify a wave 3 down while in wave 5}if wave = 5 and ET = -1 then begin
wave = 3;hiosc = -999;hiprice = -999;hiosc2 = -999;hiprice2 = -999;end;{Return function value}EWO = wave;
CONSTRUCTIONS USING THE FIBONACCI RATIO
Harahus shows interesting constructions using Fibonacci ratios; these are referred to asthe golden rectangle, golden triangle, and golden spiral. Although there is no doubt oftheir importance, the application to markets can be complicated. As a behavioral model,any technique is subject to gross inaccuracy at times. In using a method as sophisticated asthe Elliott Wave Theory, it is necessary to select situations that are representative examplesof the phenomenon described by the FL sequence. Confirmation of such action can onlybe found by careful monitoring and development of an awareness of the nature of theprice motion important to the system.
Harahus further introduced the regular pentagon as a tool for measuring corrections.This geometric figure has the property that any diagonal is 1.618 times the length ofa side,exactly a Fibonacci ratio.
By constructing a regular pentagon so that the major trend falls along one diagonal (orone side), the other line connecting the corners of the pentagon will serve as support orresistance to price moves. In addition, the circumscribed and inscribed circle will serve asa measurement of support and/or resistance (Figure 14-13).
Harahus further extends the charting techniques of the Elliott Wave Theory using cir-cles and arcs, a technique previously seen in measuring retracements, A circle drawn fromthe top or bottom of a wave, representing the 38%, 50%, or 62% levels serves as a conve-nient measurement of either elapsed time or a price_adjustment, either of which couldoccur within the bounds of the rules. Prices are expected to meet resistance at any attemptto penetrate the key circles formed about either A or B in Figure 14-14.
The Elliott Wave Théory is highly regarded, although it isan odd combination of math-ematics and chart interpretation bordering slightly on the mystic. Because it is primarilybased on chart patterns it has been criticized as being too interpretive. The developmentof the fifth wave receives the most comment-—sometimes it never develops; at other times,it must be extended into another subset of waves. In an analysis by Merrill, it is shown thatthe median stock market bull move has seven legs and the bear move has five legs; this mayaccount for the need for the compound form of the Elliott wave. Those analysts who findFIGURE 14-13 (a) Pentagon constructed from one diagonal. (b) Pentagon constructedfrom one side. .
[SILVER aon nang antigay ——paspene—,——g“FLoi
 
 
  
[CHART REPRINTED FROM.Commodity Chant Service
"a weesly Poteowat0oUTY RESEARCH BUREAU, INC,
“Tey PIMee, Haw Yorn M.¥. 10008"
     
 
 
    
 
  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
- TSTARTING DIAGONALEQUALS 100% 50% CIRCLE._ 1 el| ?{ 500]4a 38%~- 50%,7 62% ——am = ~~ 50): | 4 : .
 
 
 
 
(CHART REPRINTED FROM:Commodity, chart Service
CcomMoDiTY RESEARCH BUREAU, ne,1 Lipari Pla, Maw York, W.¥. 10506
 
 
61.8% CIRCLE
 
 
(b)
 
362FISCHER’S GOLDEN SECTION COMPASS SYSTEM 363
 
 
FIGURE 14-14 Using circles to find support and resistance.
 
 
this study of interest should also read the works of WD. Gann and Edson Gouid, both ofwhom concentrated on mathematical approaches to charting.
Alternate Arc Measurement
In Chapter 12 (“Charting Systems”), it was noted that, for the purposes of finding retrace-ment levels, Tom DeMark* identified the extent of a price move differently. In hisapproach, if the market is currently at a low, rather than judging the distance of this dropfrom the most recent swing high, he chooses to look for the highest point that hasoccurred since the last time the market traded at this low level. He then applies his choiceof ratios to isolate key retracement levels. DeMark also uses this measurement from highto low to draw arcs identical to those shown in Figure 14-8 but limited to the Fibonacciratio .618 and its complement .382.
FISCHER’S GOLDEN SECTION COMPASS SYSTEM
Although there are many systems that use the Fibonacci ratios, Fischer’s Golden SectionCompass (GSC) System is the only one based primarily on that concept.** The system isfounded on the premise that human behavior reflects the Fibonacci ratios; the humandecision-making process unconsciously selects points to act that appear to be the righttime or the right price level. The behavior-based rules are combined with practical entryand stop-loss rules to eliminate those situations that do not properly develop.
__ Fischer is not alone in his observation of these patterns. Elliott, discussed in the previ-ous sections, defined market Cycles in five wave patterns with three wave corrections (Fig-ure 14-15). In Nature’s Law, Elliott shows the complete market cycle™ as:
>) Tom DeMark, “Retracing your steps,” Futures (November 1995). Also see Chapter 2 of DeMark, The New Scienceof Technical Analysis John Wiley & Sons, 1994).
» Robert Fischer, The Golden Section Compass Seminar (Fibonacci ‘Trading, Ltd., Harfiilton 5, Bermuda, 1984).Also see Robert Fischer, Fibonacci Applications and Strategies for Traders john Wiley & Sons, 1993).
* Robert Fischer, The Golden Section Compass Seminar (Fibonacci Trading, 1984).364 BEHAVIORAL TECHNIQUES
 
 
FIGURE 14-15 Elfiott’s complete wave cycle.
 
 
 
 
 
 
Source: Fischer, Golden Section Compass Seminar (1984, p. 28).
 
 
Number of Bull Market Bear Market Total
Major waves 5 3 8 complete cyclesIntermediate waves alos - 13 34 complete cyclesMinor waves 89 55 144 compiete cycles
 
Time-Goal Days
The GSC System states that a new price direction will begin on, or shortly after, the day cal-culated as:
Ty =1.618 X (Lj ~ Lj-1) + Ly
or >’
Tyo = 1.618 x (HH, — Ay) + Hi .
where Z, and H, are the days on which lows and highs occurred, and L, occurred before 4.
For simplicity, an extreme may be used only twice—once as the first point and once asthe second. Figure 14-16 shows the order in which the calculations occur. Time-goal day 75was calculated from lows Z; and ZL, before-time-goal day 7; occurred. When more than onetime-goal day occurs at the same point, or when the highs or lows that formed the time-goal days are more significant, the