process before actually filtering out fluctuations of a specifiedmagnitude (i.e., lack of magnitude).This process “unravels” the four OHLC quotes into four consecutive “closes” as it were, thus creating a stream of univariate dataideal for the swing reversal algorithm (also four times the size ofthe input data). Obviously, the opening and closing quotes pose
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no problem with regard to temporal order. The following rulesdetermine which extreme occurred first:Case 1: The open is closer to the high than the close (Figure 27-1).Case 2: The open is closer to the low than the close (Figure 27-2).Case 3: The open equals the close, and the open is closer to thehigh than the low (Figure 27-3).Case 4: The open equals the close, and the open is closer to thelow than the high (Figure 27-4).Case 5: This is the unusually rare instance where the open equalsthe close, and both are equidistant from the extremes(Figure 27-5).Rather than opt for a random determination of the high-loworder, we decided to check the previous bar for any pertinent information and found two solutions (Figure 27-6).
Figure 27-1 Order  O → H → L → C.
Data Operations
Figure 27-2 Order  O → L → H → C.
Figure 27-3 Order  O → H → L → C.
169
170
Figure 27-4 Order  O → L → H → C.
Figure 27-5 Open  Close.
Part 10: Advanced Topics
171
Data Operations
Figure 27-6 Two Cases.
The two new rules for these conditions areCase 5A: If the previous close is less than the current open (theleft diagram), then the direction is upward. Therefore,Order = O → H → L → CCase 5B: If the previous close is greater than the current open(the right diagram), then the direction is downward.Therefore,Order = O → L → H → CUnfortunately, there remains one final case:Case 5C: If the previous close equals the current open, then itis time to generate an equal-distribution random number (Figure 27-7).We searched our 7 million  EURUSD 2005 database and foundseveral instances of this condition. Fortunately, in every case thehigh equaled the low. Thus this occurs during periods of low activity and lateral congestion. We therefore feel justified in our verylimited use of random numbers in a science where deterministicnumbers are treasured.As a matter of curiosity, currency traders may be interestedto know just how many ticks can occur within a single minute
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Figure 27-7 Order  O → ? → ? → C.
because this quantity less four quotes is being discarded by the“intervalizing” process. We searched our historical and morerecent files and isolated the following:Date:Time:Open:High:Low:Close:Upticks:Downticks:
Wednesday, August 4, 20048:07 a.m. ET1.20041.20061.19701.1975142157
This amounts to 299 ticks in 1 minute with a range of 36 pips.Currency trading continues to grow at a phenomenal rate, so weexpect this “record” to be broken in the very near future, quite possibly in one of the other major USD pairs or even a cross rate.
Chapter
28
Swing OperationsFRACTAL LEVELSIn earlier chapters we mentioned using swing analysis at differentfractal levels to determine the possible strength of a subsequentwave and its component waves. One method to perform thisoperation is to calculate swing data using two different minimumreversal amounts, say, a 5-pip reversal amount for the “child” fractaldata and a 10-pip reversal amount for the “parent” swing data.To perform this operation successfully, both sets of swing datamust end on the same point, preferably the last known price in theraw data. Then, by using height-ratio wave comparisons at two levels, the trader can determine if the predicted waves will extend inthe same price direction.The disadvantage to this method is that prolonged experimentation may be required to discover a “perfect” child–parent fractal relationship. As markets become more volatile, higher reversalamounts may be required to filter out undesired white noise. Asmarkets lose volatility, lower reversal amounts may be preferable.Also, there is the possibility that the difference in the two reversalamounts may be set too high. This will cause the fractal relationship to jump from a child–parent relationship to a child–grandparent relationship. An alternative method that progressesthrough each fractal level one at a time is given below.
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Part 10: Advanced Topics
PIVOT CHARTSThe pivot chart is a subset of the swing reversal chart that uses thebare minimum criteria as the parameters of the reversal algorithm.That is, the reversal increment is set to the minimum legal pricefluctuation in the time series, and the number of reversal units isset to one. Paradoxically, this chart does not filter any reversals inprice. The reason for this will become apparent shortly.The pivot chart does, however, have the advantage of merginga multipoint trend into a single diagonal line. It also filters out horizontal price movements. Another advantage is that a pivot can beconstructed easily by hand without the use of a software utility. Allcontinuous upward movements resolve to the diagonal line, as doall continuous downward movements. There is no need to calculate a minimum reversal amount with each new price. The pivotchart is the only swing chart that can never have a child fractalchart. In other words, it is the lowest common denominator of allswing charts (Figure 28-1).
Figure 28-1 Pivot Chart.
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Swing Operations
We note in Figure 28-1 that no reversal is filtered out. A standardswing reversal chart of the same raw data (the solid curve) usinga 15-pip reversal amount would generate only two diagonals, onebull wave followed by one bear wave.
CHANNEL LINESThe classification of the basic three-wave cycles discussed earlierwill employ a rigid methodology that prevents any ambiguity:channeling. This is a purely mathematical process and has nothingto do with excursions into the supernatural.All three-wave cycles always can be inscribed inside a channelquadrangle or triangle using the coordinate system shown inTable 28-1 (see Figure 28-2).The upper boundary of the channel polygon (either a triangleor a parallelogram) passes through the two points x2, y2 andx4, y4, whereas the lower boundary of the channel shapepasses through the two points x1, y1 and x3, y3, as depicted inFigure 28-3.The criteria for classifying any three-wave cycle are derived fromthe slopes of its two identifying channel lines. In Figure 28-2, bothslopes are positive, or travel from the lower left to the upper rightof the diagram (the standard bull impulse cycle described earlier).The slope property of either channel line may have one of threemathematical attributes: positive, negative, or zero. These equate toupward, downward, and horizontal price movements.The nine basic bull cycles with channel lines are shown inFigure 28-4.Concerning the naming convention for triangles, the modifiercontracting signifies that the channel lines converge on the right
Table 28-1 Cycle Coordinate SystemWave No.123
Starting Point
Ending Point
x1, y1x2, y2x3, y3
x2, y2x3, y3x4, y4
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Figure 28-2 Impulse Cycle with Coordinates.
side of the cycle. Conversely, expanding indicates that the channellines converge on the left of the cycle.
COLLAPSING CYCLESThe pivot chart in Figure 28-1 facilitates a very simple and directapproach to determining the parent fractal level of any swingdata, which we refer to as cycle collapsing. To collapse any of the
Figure 28-3 Three-Wave Impulse Cycle with Channel Lines.
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177
Figure 28-4 The Nine Basic Bull Cycles with Channel Lines.
three-wave bull cycles shown in Figure 28-4 into a single wave, thefollowing two rules must be observed:1. Using the coordinate system in Table 28-1, the starting point y1must be lower than or equal to y3.2. The ending point y4 must be greater than or equal to point y2.If both conditions are satisfied, then the collapsing method ispurely mechanical: Extend a straight line from the cycle startingcoordinates x1, y1 to the cycle end point x4, y4. Examples areshown in Figure 28-5.The four examples in this figure are, in fact, the only bull cyclesthat can be collapsed into a single wave in one operation. The
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Figure 28-5 Collapsing Bull Cycles.
remaining five bull cycles (contracting descending triangle,contracting symmetrical triangle, expanding descending triangle,expanding symmetrical triangle, and the connector cycle) allviolate one of the preceding rules (the bull connector cycle violatesboth rules).Surprisingly, though, a second pass through the collapsed datawill again collapse several three-wave cycles into a single wave. No
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179
more than two passes through the data are required to convert aset of swing data to its parent fractal data.
COLLAPSING MODESThere are two “modes” by which cycles may be collapsed: (1) singlethree-wave cycle collapsing and (2) continuous multiwave cyclecollapsing.Only one cycle at a time is converted when using the single threewave cycle collapsing mode. On the other hand, the multiwavecycle collapsing mode will collapse any number of cycles until anoncollapsible cycle is encountered (Figure 28-6).The leftmost cycle in this figure is a seven-wave bull impulse cyclewithout any collapsing. The center cycle is the result of singlethree-wave cycle collapsing. Note that the original cycle, designated“AiAiA,” has been reduced to an “Ai” cycle.We see that the rightmost “AiAiA” cycle has been converted toa single bull wave using continuous multiwave cycle collapsing.Extended impulse cycles always will reduce to a single diagonalregardless of the number of waves in the cycle.Figures 28-7 and 28-8 present real-world examples of the different collapsing modes for the same data.Single three-wave cycle collapsing produced a total of 39 waves,whereas continuous multiwave cycle collapsing reduced thisamount to 13 diagonals.
Figure 28-6 Collapsing Modes.
Figure 28-7 Single Three-Wave Cycle Collapsing.
Figure 28-8 Continuous Multiwave Cycle Collapsing.
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29
Practical StudiesOVERVIEWBelow are examples of how different minimum reversal amountsemphasize peaks and valleys under various market environments.Three dates were selected (01/06/2006, 02/03/2006, and03/16/2006) on the basis of the sharp price spikes caused by newsannouncements from a variety of regulatory agencies. In all cases,price surges over 25 pips occurred in a single minute.Each study has four 1-minute open, high, low, close (OHLC)charts overlaid with a swing reversal chart. Reversal amounts are5, 10, 15, and 20 pips.
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STUDY NO. 1—JANUARY 6, 2006(Figures 29-1 through 29-4)
Figure 29-1 EURUSD 01/06/2006 5-Pip Reversal Amount.
Figure 29-2 EURUSD 01/06/2006 10-Pip Reversal Amount.
182
Figure 29-3 EURUSD 01/06/2006 15-Pip Reversal Amount.
Figure 29-4 EURUSD 01/06/2006 20-Pip Reversal Amount.
183
STUDY NO. 2—FEBRUARY 3, 2006(Figures 29-5 through 29-8)
Figure 29-5 EURUSD 02/03/2006 5-Pip Reversal Amount.
Figure 29-6 EURUSD 02/03/2006 10-Pip Reversal Amount.
184
Figure 29-7 EURUSD 02/03/2006 15-Pip Reversal Amount.
Figure 29-8 EURUSD 02/03/2006 20-Pip Reversal Amount.
185
STUDY NO. 3—MARCH 16, 2006(Figures 29-9 through 29-12)
Figure 29-9 EURUSD 02/16/2006 5-Pip Reversal Amount.
Figure 29-10 EURUSD 03/16/2006 10-Pip Reversal Amount.
186
Figure 29-11 EURUSD 03/16/2006 15-Pip Reversal Amount.
Figure 29-12 EURUSD 03/16/2006 20-Pip Reversal Amount.
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SUMMARYCalculating the number of swings that each reversal amountgenerates can be very useful when trying to determine the reversal amount for the next higher fractal level (Table 29-1). Flip booksof fractal levels might be handy is this case.Again, we will mention that swing data are bivariate in nature,that is, one price and one corresponding time index. In the chartsshown in this chapter we see numerous instances where the slopesof the diagonal waves vary radically from just over a 0-degreehorizontal line to an almost 90-degree incline. Generally speaking,the greater the absolute magnitude of the slope, the greater is thevolume of trading.If the cycle collapsing method were used to locate the nexthigher fractal level, the number of swings would be reduced byapproximately three.At this point, traders should have plenty of ammunition for applying wave theory to daily currency analysis. Granted, the majority ofthe tables in this book refer to the EURUSD currency pair, but withonly minor modifications, they can be applied to the other majorcurrency pairs as well.
Table 29-1 Reversal Amounts versus Number of SwingsRev Amt
1/6/2006
2/3/2006
3/16/2006
5 Pips10 Pips15 Pips20 Pips
57 Swings32 Swings11 Swings7 Swings
59 Swings35 Swings22 Swings11 Swings
58 Swings26 Swings8 Swings3 Swings
Appendices
Copyright © 2007 by The McGraw-Hill Companies. Click here for terms of use.
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Appendix A: ISOCurrencies PairsThis is a list of global currencies and the three-character currencycodes that we generally are used to represent them. Often, but notalways, this code is the same as the ISO 4217 Standard. [TheInternational Organization for Standardization (ISO) is a worldwide federation of national standards.]In most cases, the currency code is composed of the country’stwo-character Internet country code plus an extra character todenote the currency unit. For example, the code for Canadian dollars is simply Canada’s two-character Internet country code (CA)plus a one-character currency designator (D).We have endeavored to list the codes that, in our experience,are actually in general industry use to represent the currencies.Currency names are given in the plural form. This list does notcontain obsolete Euro-zone currencies.
191Copyright © 2007 by The McGraw-Hill Companies. Click here for terms of use.
192
Appendices
Table A-1 World CurrenciesSymbol
Region
Currency name
AEDAFAALLAMDANGAOAARSAUDAWGAZMBAMBBDBDTBGNBHDBIFBMDBNDBOBBRLBSDBTNBWPBYRBZDCADCDFCHFCLPCNYCOPCRCCUPCVECYPCZKDJFDKKDOPDZDEEKEGPERNETBEUR
United Arab EmiratesAfghanistanAlbaniaArmeniaNetherlands AntillesAngolaArgentinaAustraliaArubaAzerbaijanBosnia, HerzegovinaBarbadosBangladeshBulgariaBahrainBurundiBermudaBrunei DarussalamBoliviaBrazilBahamasBhutanBotswanaBelarusBelizeCanadaCongo/KinshasaSwitzerlandChileChinaColombiaCosta RicaCubaCape VerdeCyprusCzech RepublicDjiboutiDenmarkDominican RepublicAlgeriaEstoniaEgyptEritreaEthiopiaEuro member countries
DirhamsAfghanisLekeDramsGuildersKwanzaPesosDollarsGuildersManatsConvertible markaDollarsTakaLevaDinarsFrancsDollarsDollarsBolivianosBrazil realDollarsNgultrumPulasRublesDollarsDollarsCongolese francsFrancsPesosRenminbiPesosColonesPesosEscudosPoundsKorunyFrancsKronerPesosAlgeria dinarsKrooniPoundsNakfaBirrEuro(Continued )
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Appendix A: ISO Currencies Pairs
Table A-1 (Continued)Symbol
Region
Currency name
FJDFKPGBPGELGGPGHCGIPGMDGNFGTQGYDHKDHNLHRKHTGHUFIDRILSIMPINRIQDIRRISKJEPJMDJODJPYKESKGSKHRKMFKPWKRWKWDKYDKZTLAKLBPLKRLRDLSLLTLLVLLYDMAD
FijiFalkland IslandsUnited KingdomGeorgiaGuernseyGhanaGibraltarGambiaGuineaGuatemalaGuyanaHong KongHondurasCroatiaHaitiHungaryIndonesiaIsraelIsle of ManIndiaIraqIranIcelandJerseyJamaicaJordanJapanKenyaKyrgyzstanCambodiaComorosKorea (North)Korea (South)KuwaitCayman IslandsKazakstanLaosLebanonSri LankaLiberiaLesothoLithuaniaLatviaLibyaMorocco
DollarsPoundsPoundsLariPoundsCedisPoundsDalasiFrancsQuetzalesDollarsDollarsLempirasKunaGourdesForintRupiahsNew shekelsPoundsRupeesDinarsRialsKronurPoundsDollarsDinarsYenShillingsSomsRielsFrancsWonWonDinarsDollarsTengeKipsPoundsRupeesDollarsMalotiLitaiLatiDinarsDirhams(Continued)
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Appendices
Table A-1 (Continued)Symbol
Region
Currency name
MDLMGAMKDMMKMNTMOPMROMTLMURMVRMWKMXNMYRMZMNADNGNNIONOKNPRNZDOMRPABPENPGKPHPPKRPLNPYGQARROLRURRWFSARSBDSCRSDDSEKSGDSHPSITSKKSLLSOSSPLSRG
MoldovaMadagascarMacedoniaMyanmar (Burma)MongoliaMacauMauritaniaMaltaMauritiusMaldivesMalawiMexicoMalaysiaMozambiqueNamibiaNigeriaNicaraguaNorwayNepalNew ZealandOmanPanamaPeruPapua New GuineaPhilippinesPakistanPolandParaguayQatarRomaniaRussiaRwandaSaudi ArabiaSolomon IslandsSeychellesSudanSwedenSingaporeSaint HelenaSloveniaSlovakiaSierra LeoneSomaliaSeborgaSuriname
LeiAriaryDenarsKyatsTugriksPatacasOuguiyasLiriRupeesRufiyaaKwachasPesosRinggitsMeticaisDollarsNairasGold cordobasKroneNepal rupeesDollarsRialsBalboaNuevos solesKinaPesosRupeesZlotychGuaraniRialsLeiRublesRwanda francsRiyalsDollarsRupeesDinarsKronorDollarsPoundsTolarsKorunyLeonesShillingsLuiginiGuilders(Continued)
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Appendix A: ISO Currencies Pairs
Table A-1 (Continued)Symbol
Region
Currency name
STDSVCSYPSZLTHBTJSTMMTNDTOPTRLTTDTVDTWDTZSUAHUGXUSDUYUUZSVEBVNDVUVWSTXAF
São Tome, PrincipeEl SalvadorSyriaSwazilandThailandTajikistanTurkmenistanTunisiaTongaTurkeyTrinidad, TobagoTuvaluTaiwanTanzaniaUkraineUgandaUnited States of AmericaUruguayUzbekistanVenezuelaViet NamVanuatuSamoaCommunautéFinancière AfricaineSilverGoldEast CaribbeanInternationalMonetary FundCommunautéFinancière AfricainePalladiumComptoirs Françaisdu PacifiquePlatinumYemenYugoslaviaSouth AfricaZambiaZimbabwe
DobrasColonesPoundsEmalangeniBahtSomoniManatsDinarsPa’angaLirasDollarsTuvalu dollarsNew dollarsShillingsHryvniaShillingsDollarsPesosSumsBolivaresDongVatuTalaFrancs
XAGXAUXCDXDRXOFXPDXPFXPTYERYUMZARZMKZWD
OuncesOuncesDollarsSpecial drawingrightsFrancsOuncesFrancsOuncesRialsNew dinarsRandKwachaZimbabwe dollars
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Appendix B:Exchange Rates
Table B-1 shows the international foreign exchange rates on04/21/2006 compared with the USD.
Table B-1 Exchange RatesCurrency
Units/USD
USD/Units
Algerian dinarArgentine pesoAustralian dollarBaharaini dinarBolivian bolivianoBrazilian realBritish poundBotswana pulaCanadian dollarChilean pesoChinese yuanColumbian pesoCypriot poundCzech korunaDanish kroneEcuador sucreEuroGhanaian cedi
0.013790.327010.744202.652660.125080.472791.782800.187140.878270.001930.124770.000432.147770.043590.165470.000041.234500.00011
72.525003.058001.343730.376987.995002.115100.560925.343601.13860517.549998.014502,337.000040.4656022.942006.0435025,000.000630.810059,106.99988(Continued)
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Appendices
Table B-1 (Continued)Currency
Units/USD
USD/Units
Guatemalan quetzalHong Kong dollarHungarian forintIsraeli shekelIndian rupeeIndonesian rupiahJapanese yenJordanian dinarKenyan shillingKuwaiti dinarMalaysian ringgitMexican pesoMoroccan dirhamNamibian dollarNew Zealand dollarNorwegian kroneOmani rialPakistan rupeePeruvian nuevo solQatari rialRussian rubleSaudi riyalSingapore dollarSouth African randSouth Korean wonSwedish kronaSwiss francTaiwan dollarTanzanian shillingThai bahtTunisian dinarTurkish liraUAR Emirati dirhamU.S. dollarVenezualan bolivarVietnamese dongZimbabwe dollar
0.132010.128970.004670.220150.022160.000110.008551.411430.014043.424070.273190.090160.111910.165870.633300.157482.597740.016680.302330.274670.036390.266630.626610.167070.001060.132480.784750.030980.000830.026450.747380.756830.272281.000000.000470.000060.00001
7.575007.75400213.960014.5423045.135008,882.99974116.930010.7085071.220000.292053.6605011.091208.935506.029001.579036.350000.3849559.970003.307703.6407027.480003.750501.595905.98550948.000057.548601.2743032.275001,211.9999637.810001.338001.321303.672701.000002,144.0000515,924.9991699,202.00100
Appendix B: Exchange Rates
199
It is interesting to note that as of the date above, only six worldcurrencies have a parity rate with the USD greater than 1.0000:Kuwaiti dinar (3.42407), Baharaini dinar (2.65266), Omani rial(2.59774), Cypriot pound (2.14777), British pound (1.78280),and the Euro (1.23450). Coincidentally, at the bottom of the list,both alphabetically and parity-wise, is the Zimbabwe dollar, whichrequires over 99,000 to equal 1 USD.Additional information on current exchange rates can be foundat http://moneycentral.msn.com/investor/market/rates.asp.
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Appendix C:Global BankingHours
Price fluctuations in the spot currency markets are essentiallynews-driven. Or more accurately, it is the human reaction to newsdriven events that makes trading possible and profitable. Howtraders interpret these news events determines which direction themarket will travel. As in all financial markets, the Forex market alsohas its share of contrarians who keep runaway breakouts in checkwhile supplying additional volatility to the overall situation.Despite all the fundamental and technical influences on theForex, one major constant in determining periods of high volatility is the hours of operation for the central banks of each majorcurrency country.The following table emphasizes the importance of the effect oftime of day on Forex market activity and volatility based on hoursof operation around the globe. Because banking hours vary fromcountry to country, we have arbitrarily set hours of operation from9:00 a.m. to 5:00 p.m. for consistency. The top row is expressed asCentral European Time (Greenwich Mean Time ⫹ 1 hour), whichaligns with the Central Bank of Europe in Frankfurt, the most prestigious central bank in the European Monetary Union.
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202
Appendices
GLOBAL BANKING HOURSBased on Central European Time (GMT+1)1EUR
Euro Currency
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
Frankfurt
CHF
Swiss Franc
Zurich
CBP
British Pound
London
BRL
Brazilian Real
Rio de Janeiro
USD
United Sataes Dollar
New York
CAD
Canadian Dollar
Montreal
NZD
New Zealand Dollar
Wellington
AUD
Australian Dollar
Sydney
JPY
Japanese Yen
Tokyo
HKD
Hong Kong Dollar
Hong Kong
SGD
Singapore Dollar
Singapore
THB
Thai Baht
Banghok
RUR
Russian Ruble
Moscow
ZAR
South African Rand
Johannesburg
Figure C-1 Global Banking Hours.
This table allows traders to view overlapping time periods whencentral banks for different currencies are operating and thus guarantees a certain degree of mutual activity.For example, when banks open in New York City at 9:00 a.m.EST, the Frankfurt bank already has been operating for six hours.Thus there is a two-hour overlap of trading in the EURUSD currency pair on both sides of the Atlantic Ocean (9:00 to 11:00 a.m.EST). This can be readily recognized in the time-of-day activitychart for the EURUSD pair.If we are interested in initiating a trade in the EURHKD crossrate pair, we note that there is a one-hour overlap in banking operations between central Europe and Hong Kong that occursbetween 9:00 and 10:00 a.m. in Frankfurt (or 3:00 to 4:00 a.m. inNew York).Dedicated currency