, = .72, L/F,= .854, and F/F,,2=LyLy42= 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 expressed
ELLIOTT’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 FI. 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. a8. 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 fociss on Elliott, uses a supe7~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 timefame, conform to the type of patterns you are seeking. This is also true with Elliott, which,requires that prices advance in proportion to the Fibonacci ratios. In the DJIA supercycle,shown in Figure 14-12, -
2 Robert R. Prechter, Jr., “Major sea change IJ,” Futures (March 1996). 
 
358 BEHAVIORAL TECHNIQUES
 
 
FIGURE 14-12 Price relationships in supercycle (¥).
 
5000
4000
     
1.618
At 5444,V=.618x Ml=1.618xI
II 8292 In terms of % gain
$+} 4+ 419321942, 19521962. « 1972 1982 1992This chart includes the 1982 "orthodox" end-of-pattern low.
ys
Source: Robert Prechter,,mission of Futures.
 
-, Futures (March 1996). Copyrighted 1996 by Robert Prechter, Jr. Reprinted with per-
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 IAvave 5 = wave S/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-Elliowt’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. Ruggicro, 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 El/iott 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 and,a 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. A new upward trend begins when the EWO makes a new high for a period, 7, de-termined by the user. This allows, for example, wave 3 to be identified when it goesabove the high of wave 1.
3. A new 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 (@1 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 Elliott, 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. oe
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. a
If the trend turns from up to down in wave 5, then this is a wave 3 down. Resetall values and look for a new wave 3 up when step a is satisfied.
mn 
 
 
 
 
 
 
360 BEHAVIORAL TECHNIQUES
‘CONSTRUCTIONS USING THE FIBONACCI RATIO 361
 
5. The trading rules needed are based on the values of , the number of periods, andthe trigger (the percentage retracement).
a. Buy on open when wave 3 is first identified, whether on a new n-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 falls 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 periods nfrom 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 + low) / 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(0), 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 = -if @lowestiosc,pericd) < 0 and trend ~ -1 and
osc > -I*trigger*@lowest(osc,period) then trend = 1;if @highest(osc,periad) > 0 and trend = 1 and
osc < -L*trigger*@highest(osc,period) then trend = -1;EWTREND = trend;
(FUNCTION ELLIOTTWAVE}{Find the current wave using EWTRENO and EMO}inputs: period(numeric), trigger(numeric)vars: ET(0), mean(O), osc(O), wave(O), hiosc(-999), hiosc2(-999) ,hiprice(-999)hiprice2(-999); . XNosc = EHO;mean = (high + 1ow)/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] = -1 and osc > 0 then beginhiosc = osc; ~hiprice = mean;
 
wave = 3;
end; - ~(If wave 3 and the oscilleter make new highs then save those values)if wave = 3 then begin oo
if mean > hiprice then hipriceif osc > hiosc then hiosc = osc;
(Test for the beginning of wave 4)if osc <= 0 and ET ~ 1 then wave =end;
(Test for the beginning of wave 5}
if wave = 4 and mean = @highest(mean,5)-and osc >= 0 then beginwave =hiosc2 = osc;
mean;
 
 
 
hiprice2 = mean;end;if wave = § then beginif osc > hiosc2 then hiosc2 = osc;if mean > hiprice2 then hiprice2 = mean;end;(Test for wave 5 becoming wave 31if wave = 5 and hiosc2 > hiosc 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 beginwave =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 of a 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 Theory is highly regarded, although it is‘an 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 find
  
 
eeFIGURE 14-13 (a) Pentagon constructed from one diagonal. (b) Pentagon constructed
from one side. -
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
SILVER aw err ower woe ww gn wa a ore7T| Smapeueeet. |L__ cena ear aTae ISTARTING DIAGONALEQUALS 100% 50% CIRCLE.bo “559L : 004as 38%|= 5 fa (62% -—\ ae i = = 0~ 100
 
 
 
(a)
 
 
 
 
 
 
 
 
362
 
 
FISCHER'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 Gould, both ofwhom concentrated on mathematical approaches to charting.
Alternate Arc Measurement
In Chapter 12 (“Chartirig Systems”), it was noted that, for the purposes of finding retrace-ment levels, Tom DeMark?"i 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 éycles 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 Qohn Wiley & Sons, 1994).
% Robert Fischer, The Golden Section Compass Seminar (Fibonacci Trading, Ltd., Hamilton 5, Bermuda, 1984).Also see Robert Fischer, Fibonacci Applications and Strategies for Traders (John Wiley & Sons, 1993).
°8 Robert Fischer, The Golden Section Compass Seminar (Fibonacci Trading, 1984). 
 
364 BEHAVIORAL TECHNIQUES
 
FIGURE 14-15 Elliott'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 Moe - BB 34 complete cyclesMinor waves 89 55 144 complete 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 Ly Lys) + Ly
 
or =
Ty.) = 1.618 x (H,-H,_-) + i
where L, and H, are the days on which lows and highs occurred, and Z, occurred before 1.
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 7,was calculated from lows L, and L, before-time-goal day T; 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 likelihood of a major reversal increases.
 
 
FISCHER'S GOLDEN ~cCTION COMPASS SYSTEM 365
 
eee
FIGURE 14-16 Calculation of time-goal days.
 
1618x(Hy-HD
1.618 X (H3~ H)
1.618 x (Hp - Hy)
Ts, 1.618 x (Hs — Ha)
T,
     
T618 X (La ~ Ly) La 4g 1.618 X (Ls — La)1.618 X (L3 — Lp) Ts
cee
1.618 x (Lg —L3)
 
Specific entry signals occur on a 5-day price reversal. A long signal is given following atime-goal day when the closing price is higher than the high of the past 5 days. This is suf-ficient to identify a trend change and allows the stop-loss to be the recent low or a fixedpoint below the entry point.
“Price Goals -
Price objectives are determined using the same highs and lows. Elliott's wave theory isrefined by Fischer, as shown in Figure 14-17. Once the low has been found, followed bywave 1, the price objectives for waves 3 and 5 can be calculated as a function of wave 1:
‘Wave 3 objective = .618 x (wave 1 — low) + lowWave 5 objective = 1.618 x (wave 1 - low) + low
‘The pullbacks to points 2 and 4 are not determined in this calculation, and the proba-bility of the five-wave formation occurring is not confirmed unless the wave 3 objective issatisfied. Price goals are used for profit-taking rather than new entry points. The GSC Sys-tem, however, does not require that markets move in five-wave patterns. Price objectivescan be calculated from long-term lows as 1.618 x initial move up. When price and timegoals occur at the same point, there is greater reliance on the signal.*4
In general, retracements from sustained moves can be expected to approximate orexceed 38.2% (1 — .618) of the initial move. Once a high-level objective has been reachedand a reversal occurs, consistent profits may be taken using this goal. If prices fail to make
» Examples of time and price objectives can be found in Tucker J. Emmett, “Fibonacci Cycles,” Technical Analy-sis of Stocks & Commodities (May 1983 and March/April 1984). 
 
 
 
 
 
366 BEHAVIORAL TECHNIQUES
 
SSSFIGURE 14-17 Price goals for standard five-wave moves.
 
 
new highs following the first retracement, objectives for the next lower levels down can beset according to the inverted Elliott wave patterns, or 1.618 x initial downward move.
Filtering Highs and Lows
The GSC System can be made to identify with more significant highs and lows by increas-ing the selection filter. For example, a sensitive system would select highs and lows in goldthat are separated by a minimum swing of $10 per ounce. More significant points may beidentified by swings of $20 per ounce. It can be demonstrated that a small filter will gen-erate highs and lows that are produced by noise rather than significant behavioral actions.‘The system cannot be forced to produce more signals than the natural patterns allow.
The selection filter should be adjusted for market volatility. At higher price levels thenoise also inéreases and will obscure the more important high and low points. AlthoughFischer only briefly touches on this, traders who. apply this method should be prepared toadjust the selection filter from time to time, .
W.D. GANN—TIME AND SPACE
‘The works of WD. Gann cannot be explained with any thoroughness in a few words, butsome of his main ideas have been selected and presented in this section. Gann was a puretechnician using charts for all his analyses. His methods varied substantially from conven-tional charting techniques, but his philosophy was one of a professional trader: Conserveyour capital and wait for the right time. Gann traded primarily grains for many years, andin his writings he attempted to summarize his most important observations; some of themare reminiscent of other well-known market lore. :_ Price moves are fever exact. Gann was a believer in support and resistance lines, but‘expected some violation of the objectives because of lost motion, his way of accounting for
-the momentum that carries prices higher or lower than their likely goals. Nearly a cross _
between Elliott's waves and Angas's cycles, Gann classifies bull and bear moves into fourstages, each one compared with a trending move and a subsequent reversal culminating ina major top or bottom. He observed that bull markets last longer than bear markets. Heconcluded that reversal patterns must reduce in magnitude as the move develops and per-sists. A similar argument is expressed in the theory of contrary thinking. Much of Gann’swork is related in 1940 cents and requires an economic inflator close at hand to adjustprices to today’s levels.
 
 
W.D. GANN—TIME 4D SPACE 367
 
Gann’s techniques combine mathematics and geometry with time and space; he findsduration as important as the size of the price change. One of his principles reflects the ideaof a longer consolidation period resulting in a longer price move after a breakout. Onepopular approach to price objectives in bar charting is exactly this idea.
Time and Price
Gann proposed certain natural divisions for price swings expressed as percents. Zero and100% are the most important of these. Based on behavioral awareness, he considered apotential resistance level at 100% of the original point of the move or 100% of the highestor lowest (the best guide) price of that market. In a reversal, 100% was a full retracementof the original move. The rationale for this theory is behavioral, as is his conclusion thatmost traders like even numbers; for this reason orders in grains are most often placed at 5and 10¢ levels. Even now, traders will find more activity as prices attempt to cross wholenumber barriers, such as each 100 for the S&P or each 1,000 for the DOW.
After the 100% level, decreased importance goes to increments of 50%, 25%, 12%%,and so on. For a grain, this would mean that major resistance could be expected at theeven dollar levels with the next resistance at 50¢ intervals, then every 25¢, and so on; aftera bull move of $1, the major support would be $1 lower, then 50¢, 25¢ and 75¢, and so on.The use of successive halving of intervals was also extended to time. A year is a full cycle of360°, which makes one-half of a year equal to 26 weeks, one-quarter of a year 13 weeks,one-eighth of a year 45 days, and one-sixteenth of a year 22% days. In cases of conflict, timealways took precedence over price. The combination of a key price level (percentagemove) occurring at a periodic time interval is the basis for much of Gann's work.
Geometric Angles
‘The most popular of Gann’s methods is his use of geometric angles for relating price andtime. By using square graph paper, it was not necessary to know the exact angle becausethe construction was based on the number of boxes up versus the number of boxes to theright. A 1x 1 angle (45°) was drawn diagonally from the bottom of the lowest point of aprice move through the intersection 1 box up and 1 box to the right. This is the primarybullish support line. A bearish resistance line is drawn down from left to right from thehighest price using the 1 x 1 angle. The next most important angles in order of significanceare 2x 1, 4x 1, and 8 x 1; for lower support areas there is also 1x 2, 1x 4, and 18. Placeswhere the support and resistance lines cross are of special significance, indicating a majorcongestion area.
Figure 14-18 is taken from Gann’s private papers and shows the use of geometricangles in an actual trading situation. Lines were first drawn where Gann expected a bot-tom, then redrawn.The initial upward move followed the primary 45° line; the secondimportant support line, 1 x 2, met the primary downward line at the point of wide con-gestion at the center of the chart. The highest point on this congestion phase became thé _pivot point for the next 45° downward angle defining the next breakout. Traders havefound the primary 1 x 1, or 45° line, an important tool for staying with the major trend. Itis used to filter out small reversals in both standard charting techniques and point-and-figure.
Gann combined this method with a more remarkable technique, the squaring of priceand time. \t was fortunate to find a chart that complemented Figure 14-18, based on thelowest recorded cash price of soybeans, 44¢ per bushel. Figure 14-19 shows how Gannconstructed this square, beginning with the lowest price at the center and moving onesquare to the right, circling counterclockwise and continuing the process. The basic geo-metric lines (horizontal, vertical, and diagonal) indicate the major support and resistanceprice levels; the most important one being 44, the junction of all lines. 
 
 
 
 
 
FIGURE 14-18 Gann’s soybean worksheet.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
W.D. GANN—-TIME AND SPACE 369
 
FIGURE 14-19 May soybean square.-. i ! L :
? | MAY Soy BEAN ” t
PREGAME Aye 7b |Ue p22 eat 440439 49eldp7 aaelaas glass 4343)
169 367' 306 365'364 $63;3%2 36/' 1358. 355)
1299 298'297/29629% 294,293|29p| 291 290,289 269
|370}30r [