<s> FOREXWAVE THEORY
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FOREXWAVE THEORYA Technical Analysis for Spotand Futures Currency Traders
JAMES L. BICKFORD
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Copyright © 2007 by The McGraw-Hill Companies. All rights reserved. Manufactured in theUnited States of America. Except as permitted under the United States Copyright Act of 1976, nopart of this publication may be reproduced or distributed in any form or by any means, or storedin a database or retrieval system, without the prior written permission of the publisher.0-07-151046-XThe material in this eBook also appears in the print version of this title: 0-07-149302-6.All trademarks are trademarks of their respective owners. Rather than put a trademark symbolafter every occurrence of a trademarked name, we use names in an editorial fashion only, and tothe benefit of the trademark owner, with no intention of infringement of the trademark. Wheresuch designations appear in this book, they have been printed with initial caps.McGraw-Hill eBooks are available at special quantity discounts to use as premiums and sales promotions, or for use in corporate training programs. For more information, please contact GeorgeHoare, Special Sales, at george_hoare@mcgraw-hill.com or (212) 904-4069.TERMS OF USEThis is a copyrighted work and The McGraw-Hill Companies, Inc. (“McGraw-Hill”) and its licensors reserve all rights in and to the work. Use of this work is subject to these terms. Except as permitted under the Copyright Act of 1976 and the right to store and retrieve one copy of the work,you may not decompile, disassemble, reverse engineer, reproduce, modify, create derivative worksbased upon, transmit, distribute, disseminate, sell, publish or sublicense the work or any part of itwithout McGraw-Hill’s prior consent. You may use the work for your own noncommercial andpersonal use; any other use of the work is strictly prohibited. Your right to use the work may beterminated if you fail to comply with these terms.THE WORK IS PROVIDED “AS IS.” McGRAW-HILL AND ITS LICENSORS MAKE NOGUARANTEES OR WARRANTIES AS TO THE ACCURACY, ADEQUACY OR COMPLETENESS OF OR RESULTS TO BE OBTAINED FROM USING THE WORK, INCLUDING ANYINFORMATION THAT CAN BE ACCESSED THROUGH THE WORK VIA HYPERLINK OROTHERWISE, AND EXPRESSLY DISCLAIM ANY WARRANTY, EXPRESS OR IMPLIED,INCLUDING BUT NOT LIMITED TO IMPLIED WARRANTIES OF MERCHANTABILITYOR FITNESS FOR A PARTICULAR PURPOSE. McGraw-Hill and its licensors do not warrantor guarantee that the functions contained in the work will meet your requirements or that its operation will be uninterrupted or error free. Neither McGraw-Hill nor its licensors shall be liable toyou or anyone else for any inaccuracy, error or omission, regardless of cause, in the work or forany damages resulting therefrom. McGraw-Hill has no responsibility for the content of any information accessed through the work. Under no circumstances shall McGraw-Hill and/or its licensors be liable for any indirect, incidental, special, punitive, consequential or similar damages thatresult from the use of or inability to use the work, even if any of them has been advised of the possibility of such damages. This limitation of liability shall apply to any claim or cause whatsoeverwhether such claim or cause arises in contract, tort or otherwise.DOI: 10.1036/0071493026
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ContentsList of Figures and TablesAcknowledgmentIntroduction
ixxvxvii
Part 1. Currency Markets
1
1. Spot Currencies
3
2. Currency Futures
9
Part 2. Technical Analysis
13
3. Pattern Recognition
15
4. Econometric Models
23
5. Crossover Trading Systems
27
6. Wave Theory
37
Part 3. Reversal Charts
39
7. Point and Figure Charts
41
8. Renko Charts
45
9. Swing Charts
49v
vi
Contents
Part 4. Brief History of Wave Theory
59
10. Origins of Wave Theory
61
11. Gann Angles
69
12. Kondratiev Wave
75
13. Elliott Wave Theory
79
14. Gartley Patterns
89
15. Goodman Swing Count System
95
Part 5. Two-Wave Cycles
103
16. Properties of Two-Wave Cycles
105
17. Enhancing the Forecast
109
Part 6. Three-Wave Cycles
113
18. Basic Types of Three-Wave Cycles
115
19. Forecasting the Third Wave
123
Part 7. Four-Wave Cycles
127
20. Names of Multiwave Cycles
129
21. Properties of Four-Wave Cycles
133
Part 8. Five-Wave Cycles
137
22. Properties of Five-Wave Cycles
139
23. Forecasting the Fifth Wave
143
Contents
vii
Part 9. Six-Wave Cycles
149
24. Properties of Six-Wave Cycles
151
25. Forecasting the Sixth Wave
153
26. Double-Wave Forecasting
159
Part 10. Advanced Topics
163
27. Data Operations
165
28. Swing Operations
173
29. Practical Studies
181
Appendices
189
A. ISO Currencies Pairs
191
B. Exchange Rates
197
C. Global Banking Hours
201
D. Basic Three-Wave Cycles
203
E. Resources
205
Index
213
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List of Figuresand TablesPart 1. Currency MarketsChapter 1 Spot CurrenciesFigure 1-1Figure 1-2
Pips versus Ticks RelationshipCalculating Transaction Costs
Chapter 2 Currency FuturesTable 2-1Table 2-2Table 2-3
Currency Contract SpecificationsFutures Volume and Open InterestUS Dollar Index Weights
Part 2. Technical AnalysisChapter 3 Pattern RecognitionFigure 3-1 Double TopFigure 3-2 Double BottomFigure 3-3 Head and Shoulders TopFigure 3-4 Head and Shoulders BottomFigure 3-5 Flag or PennantFigure 3-6 Symmetrical TriangleFigure 3-7 Ascending TriangleFigure 3-8 Descending TriangleFigure 3-9 Rectangle
ixCopyright © 2007 by The McGraw-Hill Companies. Click here for terms of use.
x
List of Figures and Tables
Chapter 4 Econometric ModelsNo Graphics
Chapter 5 Crossover Trading SystemsFigure 5-1 Daily Close with 5-Day Moving AverageFigure 5-2 Residual DifferenceFigure 5-3 Relative-strength IndexFigure 5-4 Stochastic OscillatorsFigure 5-5 Bollinger Bands
Chapter 6 Wave TheoryFigure 6-1
Simple Wave Chart
Part 3. Reversal ChartsChapter 7 Point and Figure ChartsFigure 7-1Figure 7-2
Point and Figure ChartPoint and Figure Chart Anatomy
Chapter 8 Renko ChartsFigure 8-1Figure 8-2
Renko Peak and Valley ChartOHLC with Three-Brick Renko Chart
Chapter 9 Swing ChartsFigure 9-1Figure 9-2Figure 9-3Figure 9-4Figure 9-5Figure 9-6Table 9-1
Peaks and ValleysThree-box ReversalSix-box ReversalNine-box ReversalTwelve-box ReversalComposite Swing ChartInverse Relationship
Part 4. Brief History of Wave TheoryChapter 10 Origins of Wave TheoryTable 10-1Table 10-2
Chapter 11Table 11-1Figure 11-1Figure 11-2
First Dow Jones Industrial AverageMost Recent Dow Jones Industrial Average
Gann AnglesSignificant Gann AnglesS&P 500 with Gann AnglesS&P 500 with Gann Grid
List of Figures and Tables
Chapter 12 Kondratiev WaveNo graphics
Chapter 13 Elliott Wave TheoryFigure 13-1Figure 13-2Figure 13-3Figure 13-4Figure 13-5Figure 13-6Figure 13-7Figure 13-8Table 13-1
Impulse PatternCorrective PatternSecond-Wave RetracementThird-Wave RallyThird-Wave Shorts Stopped OutThird-Wave AcceleratesCompleted Impulse CycleWaves within WavesCycle Names
Chapter 14 Gartley PatternsFigure 14-1Figure 14-2Figure 14-3Figure 14-4
Gartley PatternButterfly PatternBat PatternCrab Pattern
Chapter 15 Goodman Swing Count SystemFigure 15-1Figure 15-2Figure 15-3Figure 15-4Figure 15-5
Fifty Percent Retracement and Measured MoveCongestion PhaseMarket Tug of WarThe Measured Move and UnwindingThe Markets Are Recursive
Part 5. Two-Wave CyclesChapter 16 Properties of Two-Wave CyclesFigure 16-1Figure 16-2Figure 16-3Table 16-1Table 16-2
Wave 1 > Wave 2Wave 1 = Wave 2Wave 1< Wave 2Two-Wave Relationship FrequenciesAutoregressive Partial Coefficients
Chapter 17 Enhancing the ForecastTable 17-1 First-Tercile Regression CoefficientsTable 17-2 Second-Tercile Regression CoefficientsTable 17-3 Third-Tercile Regression CoefficientsFigure 17-1 Third-Wave Forecast
xi
xii
List of Figures and Tables
Part 6. Three-Wave CyclesChapter 18 Basic Types of Three-Wave CyclesFigure 18-1Figure 18-2Figure 18-3Figure 18-4Figure 18-5Figure 18-6Figure 18-7Figure 18-8Figure 18-9Table 18-1Table 18-2
Impulse CycleRectangleContracting Descending TriangleContracting Ascending TriangleContracting Symmetrical TriangleExpanding Ascending TriangleExpanding Descending TriangleExpanding Symmetrical TriangleConnectorBear-Cycle ConversionsThree-Wave-Cycle Frequencies
Chapter 19 Forecasting the Third WaveFigure 19-1Figure 19-2Table 19-1Table 19-2
Two-wave Pattern (Wave 1 > Wave 2)Possible Third-Wave ContinuationsRaw PercentagesAdjusted Percentages
Part 7. Four-Wave CyclesChapter 20 Names of Multiwave CyclesFigure 20-1Figure 20-2Figure 20-3Table 20-1Figure 20-4
Basic Four-Wave CycleComponents of a Four-wave CycleSix-Wave CycleComponent WavesFour-Wave Bear Cycle
Chapter 21 Properties of Four-Wave CyclesTable 21-1Table 21-2Figure 21-1Figure 21-2Table 21-3
Four-Wave Cycles Sorted By 25-Pip ReversalFour-Wave Cycle Percentages Sorted by Cycle IDThree-Wave Bull Connector CyclePossible Fourth-Wave ContinuationsConnector Cycle Percentages
Part 8. Five-Wave CyclesChapter 22 Properties of Five-Wave CyclesTable 22-1 Secondary Cycle TypesTable 22-2 Primary Cycle TypesTable 22-3 Five-wave Cycles Sorted By 25-Pip ReversalAmount
List of Figures and Tables
xiii
Chapter 23 Forecasting the Fifth WaveTable 23-1Figure 23-1Figure 23-2Figure 23-3Figure 23-4
Five-Wave Cycle Frequencies Sorted by Cycle IDPotential Five-Wave Elliott Impulse CycleHead and Shoulders with Descending NecklineExtended Contracting Symmetrical TriangleExtended Expanding Symmetrical Triangle
Part 9. Six-Wave CyclesChapter 24 Properties of Six-Wave CyclesTable 24-1
Six-Wave Cycles Sorted by 25-PipReversal Amount
Chapter 25 Forecasting the Sixth WaveTable 25-1Figure 25-1Figure 25-2Figure 25-3
Six-Wave Cycles Sorted By Cycle IDExtended Impulse CycleHead and Shoulders ForecastChimera Cycle Forecast
Chapter 26 Double-Wave ForecastingFigure 26-1 Double-Wave ExtrapolationFigure 26-2 Four-Wave “Ah” CycleTable 26-1Raw Frequencies for “Ah” CycleFigure 26-3 Double-Wave Forecast for “Ah” CycleTable 26-2 Double-Wave Forecast Percentages
Part 10. Advanced TopicsChapter 27 Data OperationsTable 27-1Table 27-2Figure 27-1Figure 27-2Figure 27-3Figure 27-4Figure 27-5Figure 27-6Figure 27-7
Chapter 28Figure 28-1Table 28-1
EURUSD Streaming Tick DataEURUSD 1-Minute Interval DataOrder = O → H → L → COrder = O → L → H → COrder = O → H → L → COrder = O → L → H → COpen = CloseTwo CasesOrder = O → ? → ? → C
Swing OperationsPivot ChartCycle Coordinate System
xiv
List of Figures and Tables
Figure 28-2Figure 28-3Figure 28-4Figure 28-5Figure 28-6Figure 28-7Figure 28-8
Chapter 29
Impulse Cycle with CoordinatesThree-Wave Impulse Cycle with Channel LinesThe Nine Basic Bull Cycles with Channel LinesCollapsing Bull CyclesCollapsing ModesSingle Three-Wave Cycle CollapsingContinuous Multi-wave Cycle Collapsing
Practical Studies
Figure 29-1Figure 29-2Figure 29-3Figure 29-4Figure 29-5Figure 29-6Figure 29-7Figure 29-8Figure 29-9Figure 29-10Figure 29-11Figure 29-12Table 29-1
EURUSD 01/6/2006 5-Pip Reversal AmountEURUSD 01/6/2006 10-Pip Reversal AmountEURUSD 01/6/2006 15-Pip Reversal AmountEURUSD 01/6/2006 20-Pip Reversal AmountEURUSD 02/3/2006 5-Pip Reversal AmountEURUSD 02/3/2006 10-Pip Reversal AmountEURUSD 02/3/2006 15-Pip Reversal AmountEURUSD 02/3/2006 20-Pip Reversal AmountEURUSD 02/16/2006 5-Pip Reversal AmountEURUSD 03/16/2006 10-Pip Reversal AmountEURUSD 03/16/2006 15-Pip Reversal AmountEURUSD 03/16/2006 20-Pip Reversal AmountReversal Amounts versus Number of Swings
AppendicesTable A-1World CurrenciesTable B-1Exchange RatesFigure C-1 Global Banking HoursFigure D-1 Basic Three-Wave Cycles
AcknowledgmentI wish to thank Paul J. Szeligowski, friend and economic analyst, for hiseditorial assistance in the preparation of this book. His insightful recommendations and novel ideas proved invaluable in researching thenature and occasionally cryptic relationships that arise when scrutinizingfinancial wave theories.
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IntroductionTrading in the foreign exchange currency markets recently has exceeded$2 trillion a day, and this figure is expected to double within the next fiveyears. The reason for this astonishing surge in trading popularity is quitesimple: no commissions, low transaction costs, easy access to onlinecurrency markets, no middlemen, no fixed-lot order sizes, high liquidity,low margin with high leverage, and limited regulations. These factorsalready have attracted the attention of both neophyte traders and veteranspeculators in other financial markets. Traders who have not yet passed thecurrency rites of initiation are encouraged to read Getting Started in CurrencyTrading, by Michael Archer and James Bickford (Wiley, 2005).
ABOUT THIS BOOKThe purpose of this book is to provide spot and futures currency traderswith an innovative approach to the technical analysis of price fluctuationsin the foreign exchange markets. Financial markets move in waves.These waves, in turn, form business cycles that are components of evenlarger cycles. Knowledge of why this phenomenon occurs is not critical(although very absorbing) to technical analysts. This aspect of trading isleft to fundamental analysts. Instead, it is the where and the when questions that are critical to all technical analysts. Determining the directionof subsequent cycles (and component waves) is the paramount goal.
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xviii
Introduction
HOW THIS BOOK IS ORGANIZEDThere are ten major divisions within this book.Part 1:
Currency Markets
Much of the material in this section is a quick overview of both spotcurrency markets and currency futures. This includes definitions for thetechnical jargon used throughout the remainder of this book.Part 2:
Technical Analysis
The four most significant categories within technical analysis (i.e., patternrecognition, econometric models, crossover trading systems, and wavetheory) are reviewed in the section.Part 3:
Reversal Charts
The essential reversal charts used by wave theoreticians are explainedin detail, with the advantages and disadvantages of each method beinghighlighted. This section lays down the foundation for the remainder ofthe book.Part 4:
Brief History of Wave Theory
Wave theory has a long and intriguing history. All the major systems arescrutinized with close attention to the Elliott wave principle.Parts 5–9:
Cycles
Different length cycles (two through six waves) are analyzed in detail, withspecial emphasis on their predictive reliability. Ratio analysis and cyclefrequencies play an important role in determining the level of confidencefor each forecast.Part 10:
Advanced Topics
The salient cycle property called fractality is examined in detail. This isthe characteristic where a single wave may be composed of even smallerwaves. In this fashion, forecasts may be calculated at two different fractallevels, thus providing a higher degree of confidence prior to entering themarket.
Introduction
xix
DISCLAIMERWe wish to emphasize that spot and futures currency trading may not besuited to everyone’s disposition. All investors must be keenly aware of therisks involved and of the consequences of poor trading habits and/ormismanaged resources. Neither the publisher nor the author is liable forany losses incurred by readers while trading currencies.
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1
PARTCurrencyMarkets
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Chapter
1
Spot CurrenciesOVERVIEWForeign exchange is the simultaneous buying of one currency and selling of another. Currencies are traded through a broker or dealer andare executed in pairs, for example, the Euro and the U.S. dollar(EUR/USD) or the British pound and the Japanese yen (GBP/JPY).The foreign exchange market (Forex) is the largest financial market in the world, with a volume of over $2 trillion daily. This is morethan three times the total amount of the stocks, options, andfutures markets combined.Unlike other financial markets, the Forex spot market has nophysical location, nor a central exchange. It operates through anelectronic network of banks, corporations, and individuals tradingone currency for another. The lack of a physical exchange enablesthe Forex to operate on a 24-hour basis, spanning from onetime zone to another across the major financial centers. This facthas a number of ramifications that we will discuss throughoutthis book.A spot market is any market that deals in the current price of afinancial instrument. Futures markets, such as the Chicago Boardof Trade (CBOT), offer commodity contracts whose delivery datemay span several months into the future. Settlement of Forex spottransactions usually occurs within two business days.
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Part 1: Currency Markets
CURRENCY PAIRSEvery Forex trade involves the simultaneous buying of one currency and the selling of another currency. These two currenciesare always referred to as the currency pair in a trade.
BASE CURRENCYThe base currency is the first currency in any currency pair. It showshow much the base currency is worth, as measured against thesecond currency. For example, if the USD/CHF rate is 1.6215, thenone U.S. dollar is worth 1.6215 Swiss francs. In the Forex markets,the U.S. dollar normally is considered the base currency for quotes,meaning that quotes are expressed as a unit of US$1 per the othercurrency quoted in the pair. The primary exceptions to this rule arethe British pound, the Euro, and the Australian dollar.
QUOTE CURRENCYThe quote currency is the second currency in any currency pair. Thisis frequently called the pip currency, and any unrealized profit orloss is expressed in this currency.
PIPS AND TICKSA pip is the smallest unit of price for any foreign currency. Nearlyall currency pairs consist of five significant digits, and most pairshave the decimal point immediately after the first digit; that is,EUR/USD equals 1.2812. In this instance, a single pip equals thesmallest change in the fourth decimal place, that is, 0.0001.Therefore, if the quote currency in any pair is USD, then one pipalways equals 1/100 of a cent.One notable exception is the USD/JPY pair, where a pip equalsUS$0.01 (one U.S. dollar equals approximately 107.19 Japaneseyen). Pips sometimes are called points.Just as a pip is the smallest price movement (the y axis), a tick isthe smallest interval of time along the x axis that occurs between
5
Spot Currencies
Pips
TicksFigure 1-1 Pips versus Ticks Relationship.
two trades. (Occasionally, the term tick is also used as a synonymfor pip.) When trading the most active currency pairs (such asEUR/USD and USD/JPY) during peak trading periods, multipleticks may (and will) occur within the span of one second. Whentrading a low-activity minor cross-pair (such as the Mexican pesoand the Singapore dollar), a tick may occur only once every twoor three hours (Figure 1-1).Ticks, therefore, do not occur at uniform intervals of time.Fortunately, most historical data vendors will group sequences ofstreaming data and calculate the open, high, low, and close over regular time intervals (1, 5, and 30 minutes, 1 hour, daily, and so forth).
BID PRICEThe bid is the price at which the market is prepared to buy a specific currency pair in the Forex market. At this price, the tradercan sell the base currency. The bid price is shown on the left sideof the quotation. For example, in the quote USD/CHF 1.4527/32,the bid price is 1.4527, meaning that you can sell one U.S. dollarfor 1.4527 Swiss francs.
6
Part 1: Currency Markets
ASK PRICEThis ask is the price at which the market is prepared to sell aspecific currency pair in the Forex market. At this price, the tradercan buy the base currency. The ask price is shown on the rightside of the quotation. For example, in the quote USD/CHF1.4527/32, the ask price is 1.4532, meaning that you can buy oneU.S. dollar for 1.4532 Swiss francs. The ask price is also called theoffer price.
BID/ASK SPREADThe difference between the bid price and ask price is called thespread. The big-figure quote is a dealer expression referring to the firstfew digits of an exchange rate. These digits often are omitted indealer quotes. For example, a USD/JPY rate might be 117.30/117.35but would be quoted verbally without the first three digits as 30/35.The critical characteristic of the bid/ask spread is that it is alsothe transaction cost for a round-turn trade. Round turn means botha buy (or sell) trade and an offsetting sell (or buy) trade of thesame size in the same currency pair. In the case of the EUR/USDrate above, the transaction cost is 3 pips (Figure 1-2).
FORWARDS AND SWAPSOutright forwards are structurally similar to spot transactions inthat once the exchange rate for a forward deal has been agreed,the confirmation and settlement procedures are the same as in thecash market. Forwards are spot transactions that have been heldover 48 hours but less than 180 days when they mature and areliquidated at the prevailing spot price.
Transaction Cost = Ask Price – Bid Price
Figure 1.2 Calculating Transaction Costs.
Spot Currencies
7
Forex swaps are transactions involving the exchange of two currency amounts on a specific date and a reverse exchange of thesame amounts at a later date. Their purpose is to manage liquidity and currency risk by executing foreign exchange transactionsat the most appropriate moment. Effectively, the underlyingamount is borrowed and lent simultaneously in two currencies, forexample, by selling U.S. dollars for the Euro for spot value andagreeing to reverse the deal at a later date.Since currency risk is replaced by credit risk, such transactionsare different conceptually from Forex spot transactions. They are,however, closely linked because Forex swaps often are initiated tomove the delivery date of a foreign currency originating from spotor outright forward transactions to a more optimal moment intime. By keeping maturities to less than a week and renewing swapscontinuously, market participants maximize their flexibility inreacting to market events. For this reason, swaps tend to haveshorter maturities than outright forwards. Swaps with maturitiesof up to one week account for 71 percent of deals, compared with53 percent for outright forwards. For additional information, seewww.aforextrust.com/spot-forex-forex-forwards-forex-swaps.htm.
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Chapter
2
Currency FuturesFUTURES CONTRACTSA futures contract is an agreement between two parties: a shortposition, the party who agrees to deliver a commodity, and a longposition, the party who agrees to receive a commodity. For example, a grain farmer would be the holder of the short position(agreeing to sell the grain), whereas the bakery would be theholder of the long position (agreeing to buy the grain).In every futures contract, everything is specified precisely: thequantity and quality of the underlying commodity, the specificprice per unit, and the date and method of delivery. The price ofa futures contract is represented by the agreed-on price of theunderlying commodity or financial instrument that will be delivered in the future. For example, in the preceding scenario, theprice of the contract is 5,000 bushels of grain at a price of $4 perbushel, and the delivery date may be the third Wednesday inSeptember of the current year.The Forex market is essentially a cash or spot market in whichover 90 percent of the trades are liquidated within 48 hours.Currency trades held longer than this normally are routed throughan authorized commodity futures exchange such as theInternational Monetary Market (IMM). IMM was founded in 1972and is a division of the Chicago Mercantile Exchange (CME) that
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10
Part 1: Currency Markets
specializes in currency futures, interest-rate futures, and stockindex futures, as well as options on futures. Clearinghouses (thefutures exchange) and introducing brokers are subject tomore stringent regulations from the Securities and ExchangeCommission (SEC), Commodity Futures Trading Commission(CFTC), and National Futures Association (NFA) than the Forexspot market (see www.cme.com for more details).It also should be noted that Forex traders are charged only asingle transaction cost per trade, which is simply the differencebetween the current bid and ask prices. Currency futures tradersare charged a round-turn commission that varies from brokeragehouse to brokerage house. In addition, margin requirements forfutures contracts usually are slightly higher than the requirementsfor the Forex spot market.
CONTRACT SPECIFICATIONSTable 2-1 presents a list of currencies traded through the IMM atthe CME and their contract specifications.
CURRENCY TRADING VOLUMETable 2-2 summarizes the trading activity of selected futurescontracts in currencies, precious metals, and some financial instruments. The volume and open interest (OI) readings are not trading signals. They are intended only to provide a brief synopsis ofeach market’s liquidity and volatility based on the average of 30trading days.
U.S. DOLLAR INDEXThe U.S. Dollar Index (ticker symbol DX) is an openly tradedfutures contract offered by the New York Board of Trade(NYBOT). It is computed using a trade-weighted geometric average of the six currencies listed in Table 2