, box size and reversal amount.
BOX SIZETraditionally, the minimum price unit is the smallest fractionalprice increment that a quote currency (or underlying security) canchange. In the currency markets, this increment is a single pip. Forexample, if the EURUSD currency pair is currently trading at1.2451, a single pip is 0.0001 USD.There are three cases where a box size greater than 1 pip mightbe used. One such case is when the parity rate between two currencies is very wide and causes a very large bid/ask spread. Forexample, if the bid/ask spread (transaction cost) for the EURCZKcurrency pair is 350 koruny, then a 1-pip box size will have verynegligible filtering power.A second reason for using a box size greater than 1 pip occurswhen performing historical analysis and a longer time frame is being
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analyzed. In this case, the analyst probably will be scrutinizing majorreversals and may have little interest in minor reversals. This pertainsmore to position traders than to session or day traders.
REVERSAL AMOUNTThe reversal amount is the number of boxes necessary to plot areversal in price direction. For instance, if the current trend isupward and the reversal amount is set at three boxes, then adecline of three box units must be reached before the downwardmovement is plotted. If, instead, a new price continues in the samedirection as the existing trend, then single boxes are added automatically to the last extreme (either a peak or a valley).It is the interaction between the box size and the reversalamount that triggers the reversal mechanism in the reversal algorithm necessary to plot new columns of X’s and O’s while ignoring lateral price movements.There is one final case for increasing box size. If an analyst, forwhatever reasons, has become very partial to one specific reversalamount, it is possible to increase the box size instead of the reversal amount when market conditions change.For example, a three-box reversal amount is favored by manytraders. If traders wish to filter out some of the minor reversals,they can increase either the reversal amount or the box size.However, keep in mind that although an algorithm with a 2-pipbox size and a three-box reversal amount will generate results verysimilar to those of an algorithm with a 1-pip box size and a six-boxreversal amount, they will not be identical. This requires somereflection. The reason is that when you plot a continuation of anexisting trend, smaller distances can be plotted when a smaller boxsize is used.A detailed study of point and figure charts can be found in ForexChartist’s Companion, by Archer and Bickford (Wiley, 2007).
Chapter
8
Renko ChartsOVERVIEWThe renko charting method is thought to have acquired its namefrom renga, which is the Japanese word for “bricks.” Renko chartsare similar to three-line-break charts except that in a renko chart,a line (or brick, as they are called) is drawn in the direction ofthe prior move only if prices move by a minimum amount (i.e., thebox size). The bricks are always equal in size. For example, in a fiveunit renko chart, a 20-point rally is displayed as four five-unit-tallrenko bricks.
ANATOMYBasic trend reversals are signaled with the emergence of a new whiteor black brick. A new white brick indicates the beginning of a newuptrend. A new black brick indicates the beginning of a new downtrend (Figure 8-1).Since the renko chart is a trend-following technique, there aretimes when renko charts produce whipsaws, giving signals near theend of short-lived trends. However, the expectation with a trendfollowing technique is that it allows the trader to ride the majorportion of significant trends. Since a renko chart isolates theunderlying price trend by filtering out the minor price changes,renko charts also can be very helpful when determining supportand resistance levels (Figure 8-2).
45Copyright © 2007 by The McGraw-Hill Companies. Click here for terms of use.
46
Figure 8-1 Renko Peak and Valley Chart.
Figure 8-2 OHLC With Three-Brick Renko Chart.
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BRICK SIZEBrick size is analogous to box size in a point and figure chart anddetermines the minimum price change to display. Renko charts donot have an equivalent to point and figure reversal amountbecause the default is always one brick. To filter out white noise,simply increase the brick size.
ALGORITHMTo draw renko bricks, today’s close is compared with the high andlow of the previous brick (white or black):●
●
●
If the closing price rises above the top of the previous brick byat least the box size, one or more white bricks are drawn in newcolumns. The height of the bricks is always equal to the box size.If the closing price falls below the bottom of the previous brickby at least the box size, one or more black bricks are drawn innew columns. Again, the height of the bricks is always equal tothe box size.If prices move more than the box size but not enough to createtwo bricks, only one brick is drawn. For example, in a two-unitrenko chart, if the prices move from 100 to 103, only one whitebrick is drawn from 100 to 102. The rest of the move, from 102to 103, is not shown on the chart.
Note that the x axis does not represent time in a perfectly linearfashion because there is always one x-axis unit per brick. If the background grid is set at 1  1, then vertices also will be at right angles.
REFERENCESNison, Steven, Beyond Candlesticks: More Japanese Charting TechniquesRevealed (New York: Wiley, 1994).Nison, Steven, Japanese Candlestick Charting Techniques (New York: Hall,1991).www. linnsoft.com/welcome/charts.htm.
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Chapter
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Swing ChartsOVERVIEWA swing chart is another member of a genre of charts referred toas reversal charts. As stated in Chapter 7, a reversal chart is any chartthat filters raw data in order to accentuate significant points ofinterest while ignoring points of less interest. All technical analystsfind peaks and valleys of great interest, whereas they find areas oflateral price movements less interesting. Peaks and valleys are thosepoints of inflection where price directions reverse and the slopeof an existing trend changes its arithmetic sign (minus to plus andplus to minus) (Figure 9-1).
DEFINITIONSIn this book, we prefer to use the original terms of trader/theoretician R. N. Elliott to avoid any unnecessary confusion withterms used by other swing analysts.• A wave is a single straight line in a swing chart. Waves are always
diagonal lines with positive or negative slope, never perfectlyhorizontal or vertical.• A peak is the point of intersection between an upward wave on
the left and a downward wave on the right. This represents alocal maximum in the raw data.
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Peaks
Peaks
Valleys
Figure 9-1 Peaks and Valleys.
• A valley (or trough) is the point of intersection between a down-
ward wave on the left and an upward wave on the right. Thisrepresents a local minimum in the raw data.• A cycle is a series of adjacent interconnected waves depicting
specific price formations.To convert a sequence of raw tick data or OHLC interval datato swing data, a swing-reversal algorithm is employed in which twouser-supplied variables must be initialized, the minimum fluctuationunit and the minimum reversal amount.
MINIMUM FLUCTUATION UNITTraditionally, the minimum price unit is the smallest fractional priceincrement that a quote currency (or underlying security) canchange. This is very similar to box size in point and figure charting. In the currency markets, this increment is a single pip. Forexample, if the EURUSD currency pair is currently trading at1.2451, a single pip is 0.0001 USD.There are three cases where a minimum fluctuation unit greaterthan 1 pip might be used. One such case is when the parity rate
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between two currencies is very wide and causes a very large bid/askspread. For example, if the bid/ask spread (transaction cost) forthe EURCZK currency pair is 350 koruny, then a 1-pip box size willhave very negligible filtering power.A second reason for using a box size greater than 1 pip occurswhen performing historical analysis and a longer time frame isbeing analyzed. In this case, the analyst probably will be scrutinizing major reversals and may have little interest in minor reversals.This pertains more to long-term position traders rather than tosession or day traders.Lastly, a larger box size may be used to align peaks and valleyswith the grid lines of the chart. This is purely a display preference,though.
MINIMUM REVERSAL AMOUNTThe reversal amount is the number of minimum fluctuation unitsnecessary to plot a reversal in price direction. For instance, if thecurrent trend is upward, and the reversal amount is set at threeunits, then a decline of three fluctuation units must be reachedbefore the downward movement is plotted. If, instead, a new pricecontinues in the same direction as the existing trend, then singleboxes are added automatically to the last extreme (either a peakor a valley).It is the interaction between the minimum fluctuation unit andthe reversal amount that triggers the reversal mechanism in theswing algorithm necessary to plot peaks and valleys while ignoringlateral price movements.There is one final case for increasing the minimum fluctuationunit. If an analyst, for whatever reasons, has become very partialto one specific reversal amount, it is possible to increase the minimum fluctuation unit instead of the reversal amount when market conditions change.For example, a three-unit reversal amount is favored by manytraders. If traders wish to filter out some of the minor swings, theycan increase either the reversal amount or the minimum fluctuation unit. However, keep in mind that although an algorithm with
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a 2-pip unit size and a three-unit reversal amount will generateresults very similar to an algorithm with a 1-pip unit size and asix-unit reversal amount, they will not be identical. This requiressome reflection. The reason is that when you plot a continuationof an existing trend, smaller distances can be plotted.
SWING-REVERSAL ALGORITHMGiven the information and user-supplied variables generated earlier, we will now define the swing-reversal algorithm as follows (thisalgorithm assumes that we are using daily OHLC quotes as theinput data rather than simply the closing prices):Step 1: Initialize BoxSize and ReversalAmountvariables.Step 2: Create a new variable called Direction.Step 3: Create two array variables called Priceand Time to hold the swing data.Step 4: Set Price(1)  Close(1) and Time(1)  1.Step 5: If High(2) – Price(1)  BoxSize *ReversalAmount, thenSet Price(2)  High(2).Set Time(2)  2.Set Direction  UP.ElseIf Price(1) – Low(2)  BoxSize *ReversalAmount, thenSet Price(2)  Low(2).Set Time(2)  2.Set Direction  DOWN.ElseIncrement day number and repeat step 5End IfStep 6: Increment DayNo.If DayNo  Number of OHLC quotes, thenGo to step 9.If Direction  DOWN, thenGo to step 8.End If
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Step 7: If High(DayNo) – Price(Idx)  BoxSize,thenSet Price(Idx)  High(DayNo).Set Time(Idx)  DayNo.ElseIf Price(Idx) – Low(DayNo)  BoxSize *ReversalAmount, thenIncrement Swing Idx.Set Price(Idx)  Low(DayNo).Set Time(Idx)  DayNo.Set Direction  DOWN.End IfGo to step 6.Step 8: If High(DayNo) – Price(Idx)  BoxSize *ReversalAmount, thenIncrement Swing Idx.Set Price(Idx)  High(DayNo).Set Time(Idx)  DayNo.Set Direction  UP.ElseIf Price(Idx) – Low(DayNo)  BoxSize,thenSet Price(Idx)  Low(DayNo).Set Time(Idx)  DayNo.End IfGo to step 6.Step 9: Set Number of Swings  Swing Idx.Exit
At this point, the two swing arrays Price(·) and Time(·) havebeen populated with corresponding pairs of swing data.
TIME ALIGNMENTAdherents of the point and figure charting method believe that thecompression of time along the x axis is an advantage because thetrader can focus solely on price movements. Proponents of swingcharts, on the other hand, are more comfortable viewing the pointsof inflection (peaks and valleys) as they occur in real time. Whena swing chart is displayed directly below an OHLC bar chart,the respective peaks and valleys will align vertically with the
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corresponding bar above. Swing charts also display the velocityof the market; that is, the slope of each wave determines howquickly the market is moving.The point and figure chart versus swing chart debate is, inthe final analysis, a matter of preference. Any swing chart can bereadily “massaged” into a point and figure chart simply by converting the straight lines to columns of X’s and O’s. The converse,however, is not true because point and figure charts normally donot record the day numbers at the reversal vertices. We prefer theswing chart because in later chapters the number of time units ineach wave will be used in numerous mathematical calculations.
PRACTICAL EXAMPLESIn the swing charts in Figures 9-2 through 9-5, the minimumfluctuation unit is set to 1 pip, whereas four different reversalamounts (3, 6, 9, and 12) are employed.
Figure 9-2 Three-box Reversal.
Swing Charts
Figure 9-3 Six-box Reversal.
Figure 9-4 Nine-box Reversal.
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Figure 9-5 Twelve-box Reversal.
Figure 9-6 Composite Swing Chart.
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Swing Charts
As stated earlier, the number of waves generated by the swingalgorithm has an inverse relationship with the reversal amount,i.e., as the reversal amount increases, the number of wavesdecreases, and vice versa (Table 9-1). Using the EURUSD currencypair for the time frame specified earlier, this equates to
Table 9-1 Inverse RelationshipReversal amount3456789101112131415
Swings656565615949372319151197
COMPOSITE SWING CHARTSFigure 9-6, an aggregate of the preceding four swing charts, isincluded here so that traders can conceptually scrutinize the effectof different reversal amounts when using the same OHLC data.
USAGEThe advantages of comparing identical raw data time frames usingdifferent reversal amounts are twofold. First, any time traders viewa single data set from different perspectives, there is a greater likelihood of discovering one particular nuance in one of the chartsthat may not be readily apparent in the sibling charts (more isbetter). Additionally, several trading systems are based on specificswing patterns, such as Elliott cycles and other patterns discussed
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later in this book. Some of these systems generate a discrete priceestimate or at least predict price direction. Systematically varyingthe reversal amount allows traders to compare and log the forecasts at different levels, which adds an additional tier of reliabilityin the signal confirmation mechanism.
4
PARTBrief Historyof WaveTheory
Copyright © 2007 by The McGraw-Hill Companies. Click here for terms of use.
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Chapter
10
Origins of WaveTheoryOVERVIEWThe study of cycles dates back to ancient Greek, Babylonian, andHindu mathematicians who all contributed to the disciplinethat we now called trigonometry, where the original applicationswere surveying and astronomy. In time, periodic functions, suchas the sine and cosine functions, were developed to explain thenature of cycles.The first major breakthrough in the cyclical study of time seriesoccurred in 1822 when the French mathematician Joseph Fourierpublished his treatise entitled, Analytical Theory of Heat, whichdescribed his discoveries on the sinusoidal diffusion of heattransfer. This has evolved into a forecasting method presentlyreferred to as the discrete Fourier transform. Many contemporarytraders use Fourier analysis regularly as an integral component oftheir trading systems.
CHARLES DOWCharles Henry Dow (1851–1902) was an American journalist whocofounded Dow Jones & Company and the Wall Street Journal, whichbecame the most respected financial publication in the world.61Copyright © 2007 by The McGraw-Hill Companies. Click here for terms of use.
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Dow began his career in journalism at age 21 as a reporter withthe Daily Republican in Springfield, MA. In 1875, he left Springfieldto join the Morning Star and Evening Press in Providence, RI, wherehe met Edward Jones.Dow relocated to New York City in 1879 and later joined theKiernan News Agency, a firm that delivered handwritten news tobanks and brokerage houses. By coincidence, Jones also had leftthe Providence Morning Star for the Kiernan News Agency. InNovember 1882, Dow and Jones formed Dow Jones & Company.Their first office was at 15 Wall Street, adjacent to the stockexchange. The first edition of the Wall Street Journal appearedJuly 8, 1889, with Dow as editor.
DOW JONES INDUSTRIALAVERAGEIn the late nineteenth century, Dow identified financial marketsas bull markets and bear markets, the upper and lower regions ofa business cycle, respectively. Much of Dow’s works focused on theperformance of a single stock or security in relation to compositeindustry indexes, for which Dow is also credited. This performanceindex, now called a stock’s beta, is the security’s slope divided byan aggregate market slope as derived from two ordinary leastsquares (OLS) linear regressions.First published on May 26, 1896, the Dow Jones IndustrialAverage (DJIA) represented the average of 12 stocks from variousimportant American industries. Of those original 12, only GeneralElectric remains part of the average today. The other 11 are listedin Table 10-1.When it was first published, the DJIA stood at 40.94. It was computed as a direct average by first adding up stock prices of its components and then dividing by the number of stocks. In 1916, thenumber of stocks in the DJIA was increased to 20 and in 1928,finally to 30. On November 14, 1972, the average closed above1,000 (1,003.16) for the first time. The DJIA currently consists ofthe 30 companies listed in Table 10-2.The exact weighting coefficients for each stock component arepublished daily by Dow Jones.
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Table 10-1 First Dow Jones Industrial AverageAmerican Cotton Oil Company, a predecessor of Best FoodsAmerican Sugar Company, now Amstar HoldingsAmerican Tobacco Company, broken up in 1911Chicago Gas Company, bought by Peoples Gas Light &Coke Co. in 1897Distilling & Cattle Feeding Company, now MillenniumChemicalsLaclede Gas Light Company, still in operation asThe Laclede GroupNational Lead Company, now NL IndustriesNorth American Company (Edison), electric companybroken up in the 1950sTennessee Coal, Iron and Railroad Company, bought byU.S. Steel in 1907U.S. Leather Company, dissolved in 1952United States Rubber Company, bought by Michelin in 1990
DOW THEORYDow theory is a theory on stock price movements that provides thebasis for technical analysis. The theory was derived from 255 WallStreet Journal editorials written by Dow. Following his death, WilliamP. Hamilton, Charles Rhea, and E. George Schaefer organized andcollectively represented “Dow theory” based on Dow’s editorials.Dow himself never used the term Dow theory, though.The six basic tenets of Dow theory, as summarized by Hamilton,Rhea, and Schaefer, are as follows:1. Markets have three trends. To start with, Dow defined an uptrend(trend 1) as a time when successive rallies in a security price closeat levels higher than those achieved in previous rallies and whenlows occur at levels higher than previous lows. Downtrends(trend 2) occur when markets make lower lows and lower highs.It is this concept of Dow theory that provides the basis of technical analysis definition of a price trend. Dow described what hesaw as a recurring theme in the market: Prices would movesharply in one direction, recede briefly in the opposite direction,and then continue in their original direction (trend 3).2. Trends have three phases. Dow theory asserts that major markettrends are composed of three phases: an accumulation phase,
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Table 10-2 Most Recent Dow Jones Industrial Average3M Co. (conglomerates, manufacturing)ALCOA, Inc. (aluminum)Altria Group, Inc. (tobacco, foods)American International Group, Inc. (property and casualty insurance)American Express Co. (credit services)AT&T, Inc. (telecoms)Boeing Co. (aerospace/defense)Caterpillar, Inc. (farm and construction equipment)Citigroup, Inc. (money-center banks)Coca-Cola Co. (beverages)E. I. du Pont de Nemours & Co. (chemicals)Exxon Mobil Corp. (major integrated oil and gas)General Electric Co. (conglomerates, media)General Motors Corporation (automobile manufacturer)Hewlett-Packard Co. (diversified computer systems)Home Depot, Inc. (home-improvement stores)Honeywell International, Inc. (conglomerates)Intel Corp. (semiconductors)International Business Machines Corp. (diversified computer systems)JPMorgan Chase and Co. (money-center banks)Johnson & Johnson, Inc. (consumer and health care products)McDonald’s Corp. (restaurant franchises)Merck & Co., Inc. (drug manufacturers)Microsoft Corp. (software)Pfizer, Inc. (drug manufacturers)Procter & Gamble Co. (consumer goods)United Technologies Corp. (conglomerates)Verizon Communications (telecoms)Wal-Mart Stores, Inc. (discount, variety stores)Walt Disney Co. (entertainment)
a public participation phase, and a distribution phase. Theaccumulation phase (phase 1) occurs when investors “in theknow” are actively buying (selling) stock against the generalopinion of the market. During this phase, the stock price doesnot change much because these investors are in the minority,absorbing (releasing) stock that the market at large is supplying (demanding). Eventually, the market catches on to theseastute investors, and a rapid price change occurs (phase 2). Thisis when trend followers and other technically oriented investorsparticipate. This phase continues until rampant speculationoccurs. At this point, the astute investors begin to distributetheir holdings to the market (phase 3).
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3. The stock market discounts all news. Stock prices quickly incorporate new information as soon as it becomes available. Once newsis released, stock prices will change to reflect this new information. On this point Dow theory agrees with one of thepremises of the efficient-market hypothesis.4. Stock market averages must confirm each other. In Dow’s time, theUnited States was a growing industrial power. The United Stateshad population centers, but factories were scattered throughout the country. Factories had to ship their goods to market,usually by rail. Dow’s first stock averages were an index ofindustrial (manufacturing) companies and rail companies.To Dow, a bull market in industrials could not occur unless therailway average rallied as well, usually first. The logic is simpleto follow: If manufacturers’ profits are rising, it follows that theyare producing more. If they produce more, then they have toship more goods to consumers. Hence, if an investor is lookingfor signs of health in manufacturers, he or she should look atthe performance of the companies that ship manufacturers’output to market, the railroads. The two averages should bemoving in the same direction. When the performance of theaverages diverges, it is a warning that change is in the air.5. Trends are confirmed by volume. Dow believed that volume confirmed price trends. When prices move on low volume, therecould be many different explanations why. An overly aggressiveseller could be present, for example. However, when pricemovements are accompanied by high volume, Dow believedthat this represented the true market view. If many participantsare active in a particular security, and the price moves significantly in one direction, Dow maintained that this was the direction in which the market anticipated continued movement. Tohim, it was a signal that a trend is developing.6. Trends exist until definitive signals prove that they have ended. Dowalso believed that trends existed despite market noise. Marketsmight move in the direction opposite the trend temporarily, butthey soon will resume the prior move. The trend should begiven the benefit of the doubt during these reversals.Determining whether a reversal is the start of a new trend ora temporary movement in the current trend is not easy. Dow
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theorists often disagree in this determination. Technical analysis tools attempt to clarify this, but they can be interpreteddifferently by different investors.
CONTROVERSYAs with many investment theories, there is conflicting evidence insupport of and opposition to Dow theory. Alfred Cowles, in a studyin Econometrica in 1934, showed that trading based on Dow’s editorial advice would have earned less than a buy-and-hold strategyusing a well-diversified portfolio. Cowles concluded that a buy-andhold strategy produced 15.5 percent annualized returns from1902 to 1929, whereas the Dow strategy produced annualizedreturns of 12 percent. After numerous studies supported Cowlesover the following years, many academics stopped studying Dowtheory, believing that Cowles’ results were conclusive.In recent years, however, some in the academic communityhave revisited Dow theory and question Cowles’ conclusions.William Goetzmann, Stephen Brown, and Alok Kumar believe thatCowles’ study was incomplete and that Dow theory producesexcess risk-adjusted returns. Specifically, the absolute return ofa buy-and-hold strategy was higher than that of a Dow theory portfolio by 2 percent, but the risk and volatility of the Dow theoryportfolio were so much lower that the Dow theory portfolioproduced higher risk-adjusted returns, according to their study.The Chicago Board of Trade also notes that there is growing interest in market-timing strategies such as Dow theory. Today, there isa plethora of investment strategies that claim to outperform abuy-and-hold strategy.One key problem with any analysis of Dow theory is that the editorials of Charles Dow did not contain explicitly defined investingrules, so some assumptions and interpretations are necessary.Moreover, as with many academic studies of investing strategies,practitioners often disagree with academics.Many technical analysts consider Dow theory’s definition of atrend and its insistence on studying price action as the mainpremises of modern technical analysis. See www.en/wikipedia.orgfor further details on Dow theory.
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DOW’S CONCEPT OF WAVESDow was one of the first market analysts to ascertain that marketsfluctuate in more than one time frame at the same time:Nothing is more certain than that the market has three welldefined movements which fit into each other according to Dow.
The first fluctuation is the daily variation owing to local causesand the balance of buying and selling at that particular time(a ripple). The second movement covers a period ranging fromdays to weeks, averaging probably between six to eight weeks (awave). The third move is the great swing covering anything frommonths to years, averaging between 6 to 48 months (a tide).Nowadays, this multiple-cycle property is referred to as fractality,signifying that each individual wave in a cycle is composed of a setof smaller waves. Conversely, each wave is a component in a set ofwaves that compose an even larger wave. The concept of fractalitywill be examined in detail later in this book.
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Chapter
11
Gann AnglesW. D. GANNWilliam Delbert Gann (1878–1955) was one of the most successfulstock and commodity traders in history. He has become a legendamong open-minded traders the world over. He was famous not onlyfor his legendary trading abilities but also for his financial marketforecasts, which achieved a spectacular track record of accuracy.Gann started trading in stocks and commodities in 1902, and in1908, he moved to New York City, where he opened his own brokerage firm. His early trading career was far from successful, and hewent bust more than once. This impelled him to look deeper intothe markets. A unique analyst, his investigations led him to reachsome startling conclusions, although controversy surrounds theclaims of his trading successes and whether he did indeed reveal hisreal methods or took his secrets to the grave.Gann reputedly made over $50 million in profits from his market forecasting and trading. In the early twentieth century, the U.S.dollar was worth far more than in the new millennium, so in current money this would be roughly $500 million. After five decadesof success with his forecasting and trading, Gann moved to Florida,where he continued writing, publishing, teaching, and studyingthe markets until his death in June 1955.Gann also was a prolific writer whose books include the following:• Tunnel Through the Air• Truth of the Stock Tape69Copyright © 2007 by The McGraw-Hill Companies. Click here for terms of use.
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• Wall Street Stock Selector• How to Make Profits Trading in Commodities• 45 Years in Wall Street• Magic Word• How to Make Profits Trading in Puts and Calls (an early text on trading options)• Face Facts America
BASIC ASSUMPTIONSGann based his predictions of price movements on three premises:1. Price, time, and range are the only three factors to consider.2. The markets are cyclical in nature.3. The markets are geometric in their design and function.By studying the past, we can predict the future. Gann believedthat human nature was constant, and this showed up in repetitiveprice patterns that are identifiable and that therefore can beacted on to increase profit potential.
GEOMETRIC ANGLESGann designed several unique techniques for studying pricecharts. Central to his techniques was the concept of geometricangles in conjunction with time and price. Gann believed that specific geometric patterns and angles had unique characteristics thatcould be used to predict price action.All Gann’s techniques require that equal time and price intervalsbe used on the charts so that a rise/run of 11 will always equal a45-degree angle.
INTERPRETATIONGann believed that the ideal balance between time and price existswhen prices rise or fall at a 45-degree angle relative to the time axis.
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Gann Angles
Table 11-1 Significant Gann Angles18141