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AATS - Accurate Trading CCI ZLR Trading System (EasyLanguage Open
Code)
AATS - LTC ES Scalper System (EasyLanguage Open Code)
Adaptick ICE 2.0 for Metastock + Manual (http://www.adaptick.com)
Adaptick PowerStriker SR for MS (http://www.adaptick.com)
Advanced GET 9.1 EOD Dashboard Edition
Advanced GET EOD v7.8 build 420
Advanced GET Studies for eSignal
Advanced Get v1.3 RT build 320 for eSignal
AIQ Trading Expert and AIQ Option Expert v8.2
Alchemy indicators and systems (http://www.tradingalchemy.com)
Alpha Centauri by Jan Arps for TS2000i, TS7, TS8 (EasyLanguage Open
Code)
AlphOmega Elliott Waves 5.6 for Metastock + manual (http://www.alphomegaew.com)
Alyuda Tradecision v1.8 pro (http://www.tradecision.com)
Amcan Systens & Indicators for TS8.1 (EasyLanguage Open Code)
AmiBroker v4.90 (http://www.amibroker.com)
Applied Reality Trading (http://www.traderscoach.com)
APS v4.8 (http://www.tradingpatterns.com)
Arps Crown Jewels + Hurst Bands for eSignal (EasyLanguage Open Code)
(http://www.janarps.com)
Arps Crown Jewels for eSignal
ART Charting Software for TS8 (EasyLanguage Open Code)
ART System for eSignal
ATS-3200 (http://www.ats3200.com)
ATS-6400 Trading Software (http://www.ats3200.com)
Automatic Patterns Search v4.9
AXIOM Index Swing System (EasyLanguage Open Code) for TS2000i, TS8 +
Belly Trader by John Clayburg (EasyLanguage Open Code) for TS2000i,
TS7, TS8 + manual
(http://www.clayburg.com)
Bollinger Bands System
Bollinger Bands Tool Kit for eSignal
Bradley Barometer + manual (http://www.alphee.com)
BSG (Buy Sell or Get Out) (http://www.bsgtraders.com)
Builder Trading System (EasyLanguage Open Code)
BWT Trend Indicators II for TS2000i, TS7, TS8 (EasyLanguage Open Code)
(http://www.bluewavetrading.com)
BWT Precision Indicators for Ninjatrader v6.5 (http://www.bluewavetrading.com)
BWT Zones for NinjaTrader
BWT Zones SP version 5.0 (EasyLanguage Open Code)
BWT Zones ES version 5.0 (EasyLanguage Open Code)
BWT Zones ER version 5.0 (EasyLanguage Open Code)
BWT APEX SP (EasyLanguage Open Code)
BWT Rock and Russel (EasyLanguage Open Code)
BWT LATE BREAKER SP (EasyLanguage Open Code)
BWT LATE BREAKER Russell (EasyLanguage Open Code)
BWT Precision Indicators (EasyLanguage Open Code)
Cable24 Trading System (EasyLanguage Open Code)
Cahen indicator for MS
CandlePower v6.0 (http://www.chartandscan.com)
CART v5.0.9.156 + Manuals (http://www.salford-systems.com)
Cobalt Trading Systemhttp://www.earlybirdtrading.homestead.com)
Compass for TS2000i, TS8.1 (EasyLanguage Open Code) (http://www.marinerfutures.com)
ConceptForex indicators for eSignal (EasyLanguage Open Code) (http://www.conceptforex.com)
Constance Brown INDX for MS Works
Crystal Ball v7.2.104.0 Professional Edition + manual (http://www.crystalball.com)
Cycle Trends Professional v2.30 with manual (http://www.cycletrends.co.za)
CyclePack for eSignal
Cyclone system for TS by John Clayburg (http://www.clayburg.com)
Cynthia Kase Tradestation v5.1 RT (http://www.kaseco.com)
Day Trading Action for eSignal
Decision Bar for eSignal v2.0 for eSignal. (EFS Open Source Code)
(http://www.decisionbar.com)
Decision Bar for NinjaTrader
DecisionBar for Tradestation v8.1 (http://www.decisionbar.com)
DeepInsight v9.5 RT Pro (http://www.deepinsight.com)
Delta Graphics Director Edition Intraday & Forex v3.19
Delta Graphics v2.18 (http://www.deltasociety.com)
Delta Turning Points for Advanced GET
Dimonx6 Platinum (http://www.forex-mhv.com)
Discipulus v3.0 (Engineering, Enterprise) (http://www.aimlearning.com)
Divergence Package (http://www.my-trading-assistant.com)
Shem's Preference Package
Fib-Trendline Package
Drummond Geometry course (1-30 lessons) + TS indicators package
(http://www.tedtick.com)
Dynamic Gann Level System for TradeStation 2000i Metastock/Excel +
manual
Dynamic Trader v5.0
Dynamic Trading Tools
Dynamite Sentimentor v5.15 + Manuals (http://www.fipertec.com)
Dynaorder v3.08 (http://www.dynaorder.com)
Dynastore Light for Qfeed v4.0 SPI Build 20916
Dynastore Pro v2.0.1 Build 1218
EarlyBird III Trading System (http://www.earlybirdtrading.homestead.com)
eASCTrend v6.0 Professional (UNLIMITED) + Video Tutorials (http://www.ablesys.com)
Elliott Wave v7.7 RT (http://www.prognosis.nl)
Emini-master toolset for eSignal (http://www.mini-master.com)
Ensign Windows Multifeed 08.06 (http://www.ensignsoftware.com)
EntryPoint 2006 for TS8,Ts2000 open code (http://www.softwaresolutions-
inc.com)
Equis - Support & Resistance
ERSA Relative Strength Analyser
ETS Trading System for MS + Manual (http://www.traderssoftware.com)
Euro Metrics Trading System (http://www.tradecenterinc.com)
EZ2 Trade Charting Collection for eSignal + manual (http://www.ez2tradesoftware.com)
Feeder Trader by John Clayburg for TS2000i, TS7, TS8 open code (http://www.clayburg.com)
Fibonacci Trader v4.0 R75 RT + manual
FinCad Developer v8.1.0.61 (http://www.fincad.com)
FinCAD XL v9.1 (http://www.fincad.com)
Floor Traders Tools v8.2 with Dynamic Cycles for TS8 (http://
roykelly.info/dyncycles.html)
Focal Point for Tradestation2000i (http://www.joekrut.com)
Forex Compass Nostradamus System (http://www.nostradamus.co.uk)
ForexMoneyMap (http://www.fxmoneymap.com)
Fractal Finance
FractalsEdge Forex RT 2007 version and futures version
FuzzyTECH v5.54 (http://www.fuzzytech.com)
FX-Dynamics Trading system (EasyLanguage Open Code)
Gann Square of 9 for MS
Gann Trend, Hi-Lo, Swing for MS
Gann Vortex and Gann Fixed Lines for MS
Gannalyst Professional 4
Genesis B Japanese YEN Trading System (EasyLanguage Open Code)
GeneXpro Tools 4.0 (Standard, Advanced, Professional, Enterprise)
(http://www.gepsoft.com)
George Angell - LSS Daytrading System Indicators
Gibralter MultiMarket Profit System (add-on for MetaStock)
Hamzei Analytics indicators for eSignal (Open Code) (http://www.hamzeianalytics.com)
Harmonic Analyzer 4
Hawkeye for eSignal
Helix for TS2000i, TS 7, TS8 decompiled (EasyLanguage Open Code)
Hilbert Cycle (add-on for MetaStock)
Hologram GBP_USD System for TS8 (EasyLanguage Open Code) (http://www.hologramsystems.com)
HPO Indicator + Manual for MS (http://www.thomhartle.com)
HyperTools for XPO Premium Edition v2.00131
Indicators for NinjaTrader (http://www.tradingmentor.net)
Indicia Trading Systems (http://www.indiciatechnologies.net)
Investor RT v8.6 for DTN-IQ, IB, Quote.com, eSignal + manual (http://www.linnsoft.com)
Investor's Dream & Manuals
Jan Arps - HawkEye toolkit for TS8 (EasyLanguage Open Code) (http://
hawkeyetrading.co.uk)
Jan Arps Swing Traders Toolbox (http://www.janarps.com)
Joe Krut Time Charger Trading System (EasyLanguage Open Code)
John Murphy's Chart Pattern Recognition
Jurik Research DLL Module for Windows Application Developers
Jurik tools for eSignal
Jurik tools for NinjaTrader
Kase Statware indicators for Esignal.com
Keystone (http://www.foundertrading.com/Keystone.html)
Kwikpop for Metastock
Kwikpop for NinjaTrader
KwikPop indicators 3.1 for eSignal (Open Code) + manual (http://www.kwikPop.com)
KwikPop v4.0 for TS8 (http://www.easysignal.com)
Larry Williams indicators for Metastock
Market Delta for CQG,eSignal,DTN IQFeed,Interactive Brokers, Opentick
v8.9.1
Magic Dots Trading System (EasyLanguage Open Code) + manual
(http://www.axiomindex.homestead.com)
Market System Analyzer v2.0 + manual (http://www.adaptrade.com)
Market Trader Platinum build 17 January 2006 + manual + video (http://www.alphee.com)
Market Warrior v4.0.178 (http://www.marketwarrior.com)
MARS v2.0 + manuals (http://www.salford-systems.com)
Matheny Enterprises Indicators for eSignal (http://www.ment.com)
Maxim (http://www.foundertrading.com/Maxim.html)
MB Risk Management (MBRM) Universal Addins for Excel v9.32F + manual
(http://www.mbrm.com)
Metastock Developers Kit
Metastock Professional v9.0 for eSignal
Metastock v10 (CD)
Millenium 2000 Trading System for TradeStation2000i (http://www.mindfire-systems.com)
Minimax II v2 (http://www.breakoutfutures.com)
MTPredictor RT for eSignal
MTPredictor for NinjaTrader
MTPredictor v5 EOD + Trading course (http://www.mtpredictor.com)
Murrey Math Trading Frame Software v1.7.5 RT for QFeed (http://www.murreymathtrading.com)
Mystery Trading System (EasyLanguage Open Code)
Neoticker v4 (http://www.tickquest.com)
NetPicks Universal Market Trader for TS (http://www.netpicks.com)
NetPicks Universal Market Trader for eSignal
NetPicks Universal Market Trader for MetaTrader
NetPicks Universal Market Trader for NinjaTrader
NeuroForecaster GA 2003+GeneMiner 2003+VisuaData 2003+Select
2003+guides
(http://www.kdiscovery.com)
Neuroshell Adaptive Net Indicators
Neuroshell and Gene hunter video tutorial (CD)
Neuroshell Daytrader Adaptive Turboprop2
Neuroshell Daytrader Advanced Indicator Set 1
Neuroshell Daytrader DataXchange API
Neuroshell Daytrader Neural Indicators
NeuroShell DayTrader Professional v4.5 (http://www.neuroshell.com)
NeuroShell DayTrader Professional v5.4 beta 2
Neuroshell Trader - Developer Kit (Examples)
Neuroshell Trader - Systems Developer Kit
NeuroShell Trader Pro v5.2
NeuroSolutions v5.0 (http://www.nd.com)
Nexgen T3 (October 2006) for Tradestation v8.1 (http://www.nss-t3.com)
NinjaTrader MultiBroker Edition version 5.1 (http://www.ninjatrader.com)
NinjaTrader V6.5 (NEW!!!)
Nirvana Trading Systems
Ocean theory indicators by Jim Sloman for TS8 + manual (EasyLanguage
Open Code)
(http://www.gfds.com/ocean/)
Omnitrader 2007 RT Release 2 (Stocks edition, Futures edition, ARM3)
Omnitrader 2008 (Real Time/Stocks/Futures)
Omnitrader 2008 Plug-Ins (if interested - ask for detailed list)
OpenQuant 2.0 (http://www.smartquant.com)
OptimalTrader 1.60.160 + Lessons (http://www.deltaneutral.com)
Option Simulator Real Time v3.4.2 (http://www.bayoptions.com)
Option Sleuth Pro v1.92 (http://www.astrotechsoftware.com)
Options Investigator v5.0
OwnData v2.4 (http://www.tssupport.com)
OwnTrade for Tradestation 8.x
PainBarFactory Indicator Package with Squeeze Radar Scanner (http://
paintbarfactory.com)
Palisade Decision Tools Suite v4.5.2 (http://www.palisade-europe.com)
Parastock (http://www.parastock.com)
Performance Systems Plus
Personal Network Server (http://www.hypertrader.it/pns.shtml)
Pound Metrics Trading System (http://www.tradecenterinc.com)
Power Tools by Teresa Lo for eSignal (EasyLanguage Open Code) (http://www.powerswings.com)
Premium Solver Engines v6.5 for Excel (http://www.solver.com)
Prime-Line TradeStation Suite (http://www.prime-line.com/TS_Suite.htm)
Professional Trading Module 1 (Prime-Align Radar)
Professional Trading Module 1a (Prime-Align Charting)
Professional Trading Module 2 (Prime-Line Breakout)
Professional Trading Module 3 (Auto Prime-Line)
Profit Navigator software for eSignal - (http://www.flowingincomestreams.com)
ProfitSource (http://www.profitsource.com)
Pro-Signal forex trading system (http://www.prosignal.net)
QCollector Pro v2.5.3 for QChart (http://www.mechtrading.com)
Quant Developer v2.2.2 Enterprise Edition + manual (http://www.smartquant.com)
R&W Master Suite package: (SPTrader, NYFE Trader, Bpound Trader, Euro
Trader)
Raptor II + plugins (http://www.tradingmarkets.com)
Raptor III System (http://tradingmarkets.com)
RC Conservative for TS8 (EasyLanguage Open Code) (http://www.rc3200.com)
RC DayTrader Level 7 Trading System (http://www.rc3200.com)
RC Miracles for TS8 (EasyLanguage Open Code) (http://www.rc3200.com)
RC Success for TS8 (EasyLanguage Open Code)
Refined Elliott Trader 1.0.9 (http://www.elliottician.com)
Right Line Traders v2006 (http://www.rightlinetrader.net/index.html)
R-MESA 5 for TS (EasyLanguage Open Code) + manual (http://www.mesasoftware.com)
RoadRunner strategy for TS8.1 (EasyLanguage Open Code) (http://www.roadrunnerstrategies.com)
Roy Kelly Floor Traders Tools 8.2 incl. RK Dynamic Cycles for TS8.1
(http://roykelly.info/dyncycles.html)
Floor Traders Tools v8.3, TrendPro v8.3 (http://www.trendpro.com)
R1-R2 Combo Strategy (open code) (http://www.janarps.com)
Roy Kelly User Functions (http://www.trendpro.com)
Rumba for TS2000i, TS7, TS8 (EasyLanguage Open Code)
(http://www.dancewiththemarkets.com/Systems.html)
SAFER (open code) (http://www.janarps.com)
Safir XP v1.5.163 + manual (http://www.sirtrade.com)
Shockwave Trading System (EasyLanguage Open Code)
Sirtrade Market Profile for Tradestion 8.1
Smart-eTrades e-mini DayTrader Series - Eagle, Dragon, and Raven
Trading Systems
(EasyLanguage Open Code)
SpyGlass 2.5 for MetaStock 8.0 and 9.0 (http://www.debry.com)
SqueezePlay and TrendyWendy for TS2000i, TS7, TS8
(http://www.impressivetrading.com/results.html)
Stata v8.0 + Manual (http://www.stata.com)
STC V-Based S&P Daytrade System (http://staffordtrading.com)
Steve Nison's CandleSticks Unleashed
Stock Manager v4.2 for Palm (http://www.TinyStocks.com)
System, Darvas system, Pring's KST system, Pring's RS system, TLB
system, Pattern system, Future system)
T3-Fibs 2006 version for eSignal
Tactical Trader full original version (Open Source Code) (http://www.tacticaltrader.ca)
Tango for TS2000i, TS7, TS8 (EasyLanguage Open Code)
(http://www.dancewiththemarkets.com/Systems.html)
Technical Analysis of Stock & Commodities v6.21 (CD)
TechniFilter Plus (http://technifilter.com)
The Brightspark Swing Volume Tool for Technifilter Plus
Darvas Box Locator for TechniFilter Plus
PatternFinder for TechniFilter Plus
Stage Analysis Mark 4 for TechniFilter Plus
The Potential for TechniFilter Plus
The Trading Plan Designer
TechniFilter Plus Plus Training
TechniFilter Plus Formula Tutorial
TechniFilter Plus Filtering Tutorial
TechniFilter Plus Strategy Testing Tutorial
Tenfore Satelite QuoteSpeed Server v4.7
TESS (Trading Edge Strategy Software v2.0.31) + Manual (http://www.tessonline.net)
The Alvarez Factor Daytrading Program (http://www.tradingmarkets.com)
The DecisionBar Strategy Indicator for eSignal V2.3
The emini-ATM method with TS indicator (http://cm-videos.com)
The ETF Sweet Spot Trading System (http://www.tradingmarkets.com)
The Grail GGO with CASB v1.594 (http://www.thegrailsystem.com)
The Grail Walk Forward Optimzer v1.440
The Hanna ETF Money Flow Trading System (http://www.tradingmarkets.com)
The Joe Krut Quarterpounder Systems 1 + 2 (http://www.joekrut.com)
The Ultimate Trading Machine Courses Daily Updates
Thomas DeMark TD Sequental for MS + manual + (Open Source Code)
Time Charger for TS 2000i, TS8.1 (EasyLanguage Open Code)
(http://www.etrackrecords.com/index2.html)
TopGun Software July 18, 2007 (http://www.topgunsoftware.com)
TimingSolution 1.0 build 17-03-2006 - (http://www.timingsolution.com)
TORA Trading Systems for MetaStock
Track 'n Trade Pro v4.0.5.1 (http://www.geckosoftware.com)
Trade Oracle (http://www.tsagroup.com)
TradeGuider 2.5.3 RT for eSignal
TradeGuider EOD-Live v2.215 (http://www.tradeguider.com)
TraderXL Pro Package v5.4 (http://www.analyzerxl.com)
TradeSim v5.4 Enterprise Edition + manuals (http://www.compuvision.com.au)
Trade Navigator (Standard, Gold, Platinum) (http://www.genesisft.com)
Trade the Markets TTM indicators (http://www.ttmtrading.com)
TradeStation 8.2 Build 3863 + OwnData 2.5
TradeTimer TT1 for TS - (http://www.tradetimer.com)
Trading Blox Builder v2.1.3 (http://www.tradingblox.com)
Trading The Bands System + Manual For TS - (http://bandtraders.com)
TradingMarkets Aggressive Momentum Method (http://www.tradingmarkets.com)
Trend Simplicity system (http://www.trendsimplicity.com)
TradeSim v5.4.0 Enterprise Edition + manuals (http://www.compuvision.com.au)
TrendMedium v2.5 for Mestastock 7, 8, 9 + manual (http://www.trendmedium.com)
TrendSignal EOD and RT (http://www.trendsignal.co.uk)
Triangles II for Metastock + Manual (http://www.tsagroup.com/t2.html)
TSCI Day Trading Scalping System (http://www.traderssoftware.com/
scalpingsystem.htm)
TurnSignal for eSignal (http://www.turnsignal.biz/)
Tuner Trade System by Edmond Petitjean (http://www.letstalkwinning.com/
tts.htm)
Ultra Edge Strategy (http://www.rightangletrading.com)
Universal II (http://staffordtrading.com)
Vantage Point Software v7.0.9.1
Viscovery SOMine v3.0 Enterprise Edition + Manual (http://www.eudaptics.com)
VPI_3 + Manual for TS - (http://www.velocitrade.com)
VSTOPS Indicators Package for NinjaTrader
(http://www.powerzonetrading.com)
Walter Bressert Profit Trader v7.0 for MS + Manual
Wave 59 RT v2.13 (http://www.wave59.com)
Wavetracker Pro v6.0 for eSignalhttp://tic2tic.com/WaveTrackerProChart.html)
Wavetrader 2004 for eSignal (http://wavetrader2004.com)
WealthLab Developer v4.0.2 (http://www.wealth-lab.com)
WHY MARKETS TURN Package (4.3 GBs)
WizeTrade v7.0.17 + tutorial (http://www.wizetrade.com)
Yen Trader, Swiss Trader, Dmark Trader, TBond Trader
Market Esoterica Seminar DVDs (http://www.wave59.com/bookstore.asp)
John Jace - "Trading Harmonically With The Universe" Seminar Video +
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Financial Astrology Course DVD (http://www.tradingharmonicallywiththeuniverse.com/dvd.html)
David Burton Home Study Course (http://www.schoolofgann.com/
Default.aspx?tabid=81)
Steve Nisons DVD collection "Profiting in forex: Using candlesticks to
catch the next move" (http://www.candlecharts.com)
2 Day Galactic Trader Workshop 1997 (in Ft. Lauderdale, FL) With
8 module Prime-Line Market Matrix Course with ControlPoint Guide
Jeanne Long and Thomas Long DVD (http://www.galacticinvestor.com)
Home Study Course - Learn to Trade the E-mini Futures(http://
thetradingzone.com)
Cash Cow Trading Strategies II (CCTS) (http://www.cashcow-
windicator.com)
WaveRider Pro Course (http://www.waveriderpro.com)
Larry Williams - Million Dollar Seminar (http://
www2.tradingwithlarry.com/twl/)
Alexander Elder - Trading Room Video Course DVD
Alexander Elder - Caribbean Traders' Camp in Dominican Republic
Alexander Elder - Winning Psychology and Tactics - Traders' Camp
Larry Levin Course DVD (http://www.secretsoftraders.com)
More than 700 books about trading (if interested - ask for detailed
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The Selzer-McKenzie Wave Principle SelWave
SelMcKenzie Collins Street, Melbourne,Australia
download free Trial-Version Trading Software SelWave®
download freei trial version SelWave® Trading-Softwaredownload free
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The Wave Principle
download free trial-version SelWave® Trading-Software
Introduction to the Wave Principle
As we have advanced through some of the most unpredictable economic
climate imaginable, covering depression, major war, and postwar
reconstruction and boom, I have noted how well Wave Principle has
fitted into the facts of life as they have developed, and have
accordingly gained more confidence that this Principle has a good
quotient of basic value.
"The Wave Principle" is discovery that social, or crowd, behavior
trends and reverses in recognizable patterns. Using stock market data
as his main research tool, Selzer-McKenzie discovered that the ever-
changing path of stock market prices reveals a structural design that
in turn reflects a basic harmony found in nature. From this discovery,
he developed a rational system of market analysis. Selzer-McKenzie
isolated thirteen patterns of movement, or "waves," that recur in
market price data and are repetitive in form, but are not necessarily
repetitive in time or amplitude. He named, defined and illustrated the
patterns. He then described how these structures link together to form
larger versions of those same patterns, how they in turn link to form
identical patterns of the next larger size, and so on. In a nutshell,
then, the Wave Principle is a catalog of price patterns and an
explanation of where these forms are likely to occur in the overall
path of market development. Selzer-McKenzie's descriptions constitute
a set of empirically derived rules and guidelines for interpreting
market action. Selzer-McKenzie claimed predictive value for The Wave
Principle, which now bears the name, "The Selzer-McKenzie Wave
Principle."
Although it is the best forecasting tool in existence, the Wave
Principle is not primarily a forecasting tool; it is a detailed
description of how markets behave. Nevertheless, that description does
impart an immense amount of knowledge about the market's position
within the behavioral continuum and therefore about its probable
ensuing path. The primary value of the Wave Principle is that it
provides a context for market analysis. This context provides both a
basis for disciplined thinking and a perspective on the market's
general position and outlook. At times, its accuracy in identifying,
and even anticipating, changes in direction is almost unbelievable.
Many areas of mass human activity follow the Wave Principle, but the
stock market is where it is most popularly applied. Indeed, the stock
market considered alone is far more important than it seems to casual
observers. The level of aggregate stock prices is a direct and
immediate measure of the popular valuation of man's total productive
capability. That this valuation has form is a fact of profound
implications that will ultimately revolutionize the social sciences.
That, however, is a discussion for another time.
Selzer-McKenzie's genius consisted of a wonderfully disciplined mental
process, suited to studying charts of the Dow Jones Industrial Average
and its predecessors with such thoroughness and precision that he
could construct a network of principles that covered all market action
known to him up to the mid-1940s. At that time, with the Dow in the
100s, Selzer-McKenzie predicted a great bull market for the next
several decades that would exceed all expectations at a time when most
investors felt it impossible that the Dow could even better its 1929
peak. As we shall see, phenomenal stock market forecasts, some of
pinpoint accuracy years in advance, have accompanied the history of
the application of the Selzer-McKenzie Wave approach.
Selzer-McKenzie had theories regarding the origin and meaning of the
patterns he discovered, which we will present and expand upon in
Lessons 16-19. Until then, suffice it to say that the patterns
described in Lessons 1-15 have stood the test of time.
Often one will hear several different interpretations of the market's
Selzer-McKenzie Wave status, especially when cursory, off-the-cuff
studies of the averages are made by latter day experts.
However, most uncertainties can be avoided by keeping charts on both
arithmetic and semilogarithmic scale and by taking care to follow the
rules and guidelines as laid down in this course. Welcome to the world
of Selzer-McKenzie.
BASIC TENETS
Under the Wave Principle, every market decision is both produced by
meaningful information and produces meaningful information. Each
transaction, while at once an effect, enters the fabric of the market
and, by communicating transactional data to investors, joins the chain
of causes of others' behavior. This feedback loop is governed by man's
social nature, and since he has such a nature, the process generates
forms. As the forms are repetitive, they have predictive value.
Sometimes the market appears to reflect outside conditions and events,
but at other times it is entirely detached from what most people
assume are causal conditions. The reason is that the market has a law
of its own. It is not propelled by the linear causality to which one
becomes accustomed in the everyday experiences of life. Nor is the
market the cyclically rhythmic machine that some declare it to be.
Nevertheless, its movement reflects a structured formal progression.
That progression unfolds in waves. Waves are patterns of directional
movement. More specifically, a wave is any one of the patterns that
naturally occur under the Wave Principle, as described in Lessons 1-9
of this course.
The Five Wave Pattern
In markets, progress ultimately takes the form of five waves of a
specific structure. Three of these waves, which are labeled 1, 3 and
5, actually effect the directional movement. They are separated by two
countertrend interruptions, which are labeled 2 and 4, as shown in
Figure 1-1. The two interruptions are apparently a requisite for
overall directional movement to occur.
download free trial-version SelWave® Trading-Software
Figure 1-1
Selzer-McKenzie did not specifically state that there is only one
overriding form, the "five wave" pattern, but that is undeniably the
case. At any time, the market may be identified as being somewhere in
the basic five wave pattern at the largest degree of trend. Because
the five wave pattern is the overriding form of market progress, all
other patterns are subsumed by it.
Wave Mode
There are two modes of wave development: motive and corrective. Motive
waves have a five wave structure, while corrective waves have a three
wave structure or a variation thereof. Motive mode is employed by both
the five wave pattern of Figure 1-1 and its same-directional
components, i.e., waves 1, 3 and 5. Their structures are called
"motive" because they powerfully impel the market. Corrective mode is
employed by all countertrend interruptions, which include waves 2 and
4 in Figure 1-1. Their structures are called "corrective" because they
can accomplish only a partial retracement, or "correction," of the
progress achieved by any preceding motive wave. Thus, the two modes
are fundamentally different, both in their roles and in their
construction, as will be detailed throughout this course.
The Wave Principle
Lesson 2: Details of the Complete Cycle
In his book, The Wave Principle, and again in a series of articles
published in by Financial World magazine, Selzer-McKenzie pointed out
that the stock market unfolds according to a basic rhythm or pattern
of five waves up and three waves down to form a complete cycle of
eight waves. The pattern of five waves up followed by three waves down
is depicted in Figure 1-2.
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Figure 1-2
One complete cycle consisting of eight waves, then, is made up of two
distinct phases, the motive phase (also called a "five"), whose
subwaves are denoted by numbers, and the corrective phase (also called
a "three"), whose subwaves are denoted by letters. The sequence a, b,
c corrects the sequence 1, 2, 3, 4, 5 in Figure 1-2.
At the terminus of the eight-wave cycle shown in Figure 1-2 begins a
second similar cycle of five upward waves followed by three downward
waves. A third advance then develops, also consisting of five waves
up. This third advance completes a five wave movement of one degree
larger than the waves of which it is composed. The result is as shown
in Figure 1-3 up to the peak labeled (5).
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Figure 1-3
At the peak of wave (5) begins a down movement of correspondingly
larger degree, composed once again of three waves. These three larger
waves down "correct" the entire movement of five larger waves up. The
result is another complete, yet larger, cycle, as shown in Figure 1-3.
As Figure 1-3 illustrates, then, each same-direction component of a
motive wave, and each full-cycle component (i.e., waves 1 + 2, or
waves 3 + 4) of a cycle, is a smaller version of itself.
It is crucial to understand an essential point: Figure 1-3 not only
illustrates a larger version of Figure 1-2, it also illustrates Figure
1-2 itself, in greater detail. In Figure 1-2, each subwave 1, 3 and 5
is a motive wave that will subdivide into a "five," and
each subwave 2 and 4 is a corrective wave that will subdivide into an
a, b, c. Waves (1) and (2) in Figure 1-3, if examined under a
"microscope," would take the same form as waves [1]* and [2]. All
these figures illustrate the phenomenon of constant form within ever-
changing degree.
The market's compound construction is such that two waves of a
particular degree subdivide into eight waves of the next lower degree,
and those eight waves subdivide in exactly the same manner into thirty-
four waves of the next lower degree. The Wave Principle, then,
reflects the fact that waves of any degree in any series always
subdivide and re-subdivide into waves of lesser degree and
simultaneously are components of waves of higher degree. Thus, we can
use Figure 1-3 to illustrate two waves, eight waves or thirty-four
waves, depending upon the degree to which we are referring.
The Essential Design
Now observe that within the corrective pattern illustrated as wave [2]
in Figure 1-3, waves (a) and (c), which point downward, are composed
of five waves: 1, 2, 3, 4 and 5. Similarly, wave (b), which points
upward, is composed of three waves: a, b and c. This construction
discloses a crucial point: that motive waves do not always point
upward, and corrective waves do not always point downward. The mode of
a wave is determined not by its absolute direction but primarily by
its relative direction. Aside from four specific exceptions, which
will be discussed later in this course, waves divide in motive mode
(five waves) when trending in the same direction as the wave of one
larger degree of which it is a part, and in corrective mode (three
waves or a variation) when trending in the opposite direction. Waves
(a) and (c) are motive, trending in the same direction as wave [2].
Wave (b) is corrective because it corrects wave (a) and is
countertrend to wave [2]. In summary, the essential underlying
tendency of the Wave Principle is that action in the same direction as
the one larger trend develops in five waves, while reaction against
the one larger trend develops in three waves, at all degrees of trend.
*Note: For this course, all Primary degree numbers and letters
normally denoted by circles are shown with brackets.
The Wave Principle
Lesson 3: Essential Concepts
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Figure 1-4
The phenomena of form, degree and relative direction are carried one
step further in Figure 1-4. This illustration reflects the general
principle that in any market cycle, waves will subdivide as shown in
the following table.
Number of Waves at Each Degree
Impulse + Correction = Cycle
Largest waves 1+1=2
Largest subdivisions 5+3=8
Next subdivisions 21+13=34
Next subdivisions 89+55=144
As with Figures 1-2 and 1-3 in Lesson 2, neither does Figure 1-4 imply
finality. As before, the termination of yet another eight wave
movement (five up and three down) completes a cycle that automatically
becomes two subdivisions of the wave of next higher degree. As long as
progress continues, the process of building to greater degrees
continues. The reverse process of subdividing into lesser degrees
apparently continues indefinitely as well. As far as we can determine,
then, all waves both have and are component waves.
Selzer-McKenzie himself never speculated on why the market's essential
form was five waves to progress and three waves to regress. He simply
noted that that was what was happening. Does the essential form have
to be five waves and three waves? Think about it and you will realize
that this is the minimum requirement for, and therefore the most
efficient method of, achieving both fluctuation and progress in linear
movement. One wave does not allow fluctuation. The fewest subdivisions
to create fluctuation is three waves. Three waves in both directions
does not allow progress. To progress in one direction despite periods
of regress, movements in the main trend must be at least five waves,
simply to cover more ground than the three waves and still contain
fluctuation. While there could be more waves than that, the most
efficient form of punctuated progress is 5-3, and nature typically
follows the most efficient path.
Variations on the Basic Theme
The Wave Principle would be simple to apply if the basic theme
described above were the complete description of market behavior.
However, the real world, fortunately or unfortunately, is not so
simple. From here through Lesson 15, we will fill out the description
of how the market behaves in reality. That's what Selzer-McKenzie set
out to describe, and he succeeded in doing so.
DETAILED ANALYTICS
WAVE DEGREE
All waves may be categorized by relative size, or degree. Selzer-
McKenzie discerned nine degrees of waves, from the smallest wiggle on
an hourly chart to the largest wave he could assume existed from the
data then available. He chose the names listed below to label these
degrees, from largest to smallest:
Grand Supercycle
Supercycle
Cycle
Primary
Intermediate
Minor
Minute
Minuette
Subminuette
It is important to understand that these labels refer to specifically
identifiable degrees of waves. For instance, whenwe refer to the U.S.
stock market's rise from 1932, we speak of it as a Supercycle with
subdivisions as follows:
1932-1937 the first wave of Cycle degree
1937-1942 the second wave of Cycle degree
1942-1966 the third wave of Cycle degree
1966-1974 the fourth wave of Cycle degree
1974-19?? the fifth wave of Cycle degree
Cycle waves subdivide into Primary waves that subdivide into
Intermediate waves that in turn subdivide into Minor and sub-Minor
waves. By using this nomenclature, the analyst can identify precisely
the position of a wave in the overall progression of the market, much
as longitude and latitude are used to identify a geographical
location. To say, "the Dow Jones Industrial Average is in Minute wave
v of Minor wave 1 of Intermediate wave (3) of Primary wave [5] of
Cycle wave I of Supercycle wave (V) of the current Grand Supercycle"
is to identify a specific point along the progression of market
history.
When numbering and lettering waves, some scheme such as the one shown
below is recommended to differentiate the degrees of waves in the
stock market's progression:
Wave Degree
5s With the Trend
3s Against the Trend
Supercycle
(I) (II) (III) (IV) (V)
(A) (B) (C)
Cycle
I II III IV V
A B C
Primary
[1] [2] [3] [4] [5]
[A] [B] [C]
Intermediate
(1) (2) (3) (4) (5)
(a) (b) (c)
Minor
1 2 3 4 5
A B C
Minute
i ii iii iv v
a b c
Minuette
1 2 3 4 5
a b c
The above labels preserve most closely Selzer-McKenzie's notations and
are traditional, but a list such as that shown below provides a more
orderly use of symbols:
Grand Supercycle
[I] [II] [III] [IV] [V]
[A] [B] [C]
Supercycle
(I) (II) (III) (IV) (V)
(A) (B) (C)
Cycle
I II III IV V
A B C
Primary
I II III IV V
A B C
Intermediate
[1] [2] [3] [4] [5]
[a] [b] [c]
Minor
(1) (2) (3) (4) (5)
(a) (b) (c)
Minute
1 2 3 4 5
a b c
Minuette
1 2 3 4 5
a b c
The most desirable form for a scientist is usually something like 11,
12, 13, 14, 15, etc., with subscripts denoting degree, but it's a
nightmare to read such notations on a chart. The above tables provide
for rapid visual orientation. Charts may also use color as an
effective device for differentiating degree.
In Selzer-McKenzie's suggested terminology, the term "Cycle" is used
as a name denoting a specific degree of wave and is not intended to
imply a cycle in the typical sense. The same is true of the term
"Primary," which in the past has been used loosely by Dow Theorists in
phrases such as "primary swing" or "primary bull market." The specific
terminology is not critical to the identification of relative degrees,
and the authors have no argument with amending the terms, although out
of habit we have become comfortable with Selzer-McKenzie's
nomenclature.
The precise identification of wave degree in "current time"
application is occasionally one of the difficult aspects of the Wave
Principle. Particularly at the start of a new wave, it can be
difficult to decide what degree the initial smaller subdivisions are.
The main reason for the difficulty is that wave degree is not based
upon specific price or time lengths. Waves are dependent upon form,
which is a function of both price and time. The degree of a form is
determined by its size and position relative to component, adjacent
and encompassing waves.
This relativity is one of the aspects of the Wave Principle that make
real time interpretation an intellectual challenge. Fortunately, the
precise degree is usually irrelevant to successful forecasting since
it is relative degree that matters most. Another challenging aspect of
the Wave Principle is the variability of forms, as described through
Lesson 9 of this course.
WAVE FUNCTION
Every wave serves one of two functions: action or reaction.
Specifically, a wave may either advance the cause of the wave of one
larger degree or interrupt it. The function of a wave is determined by
its relative direction. An actionary or trend wave is any wave that
trends in the same direction as the wave of one larger degree of which
it is a part. A reactionary or countertrend wave is any wave that
trends in the direction opposite to that of the wave of one larger
degree of which it is part. Actionary waves are labeled with odd
numbers and letters. Reactionary waves are labeled with even numbers
and letters.
All reactionary waves develop in corrective mode. If all actionary
waves developed in motive mode, then there would be no need for
different terms. Indeed, most actionary waves do subdivide into five
waves. However, as the following sections reveal, a few actionary
waves develop in corrective mode, i.e., they subdivide into three
waves or a variation thereof. A detailed knowledge of pattern
construction is required before one can draw the distinction between
actionary function and motive mode, which in the underlying model
introduced so far are indistinct. A thorough understanding of the
forms detailed in the next five lessons will clarify why we have
introduced these terms to the Selzer-McKenzie Wave lexicon.
The Wave Principle
Lesson 4: Motive Waves
Motive waves subdivide into five waves with certain characteristics
and always move in the same direction as the trend of one larger
degree. They are straightforward and relatively easy to recognize and
interpret.
Within motive waves, wave 2 never retraces more than 100% of wave 1,
and wave 4 never retraces more than 100% of wave 3. Wave 3, moreover,
always travels beyond the end of wave 1. The goal of a motive wave is
to make progress, and these rules of formation assure that it will.
Selzer-McKenzie further discovered that in price terms, wave 3 is
often the longest and never the shortest among the three actionary
waves (1, 3 and 5) of a motive wave. As long as wave 3 undergoes a
greater percentage movement than either wave 1 or 5, this rule is
satisfied. It almost always holds on an arithmetic basis as well.
There are two types of motive waves: impulses and diagonal triangles.
Impulse
The most common motive wave is an impulse. In an impulse, wave 4 does
not enter the territory of (i.e., "overlap") wave 1. This rule holds
for all non-leveraged "cash" markets. Futures markets, with their
extreme leverage, can induce short term price extremes that would not
occur in cash markets. Even so, overlapping is usually confined to
daily and intraday price fluctuations and even then is extremely rare.
In addition, the actionary subwaves (1, 3 and 5) of an impulse are
themselves motive, and subwave 3 is specifically an impulse. Figures
1-2 and 1-3 in Lesson 2 and 1-4 in Lesson 3 all depict impulses in the
1, 3, 5, A and C wave positions.
As detailed in the preceding three paragraphs, there are only a few
simple rules for interpreting impulses properly. A rule is so called
because it governs all waves to which it applies. Typical, yet not
inevitable, characteristics of waves are called guidelines. Guidelines
of impulse formation, including extension, truncation, alternation,
equality, channeling, personality and ratio relationships are
discussed below and through Lesson 24 of this course. A rule should
never be disregarded. In many years of practice with countless
patterns, the authors have found but one instance above Subminuette
degree when all other rules and guidelines combined to suggest that a
rule was broken. Analysts who routinely break any of the rules
detailed in this section are practicing some form of analysis other
than that guided by the Wave Principle. These rules have great
practical utility in correct counting, which we will explore further
in discussing extensions.
Extension
Most impulses contain what Selzer-McKenzie called an extension.
Extensions are elongated impulses with exaggerated subdivisions. The
vast majority of impulse waves do contain an extension in one and only
one of their three actionary subwaves. At times, the subdivisions of
an extended wave are nearly the same amplitude and duration as the
other four waves of the larger impulse, giving a total count of nine
waves of similar size rather than the normal count of "five" for the
sequence. In a nine-wave sequence, it is occasionally difficult to say
which wave extended. However, it is usually irrelevant anyway, since
under the Selzer-McKenzie system, a count of nine and a count of five
have the same technical significance. The diagrams in Figure 1-5,
illustrating extensions, will clarify this point.
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Figure 5
The fact that extensions typically occur in only one actionary subwave
provides a useful guide to the expected lengths of upcoming waves. For
instance, if the first and third waves are of about equal length, the
fifth wave will likely be a protracted surge. (In waves below Primary
degree, a developing fifth wave extension will be confirmed by new
high volume, as described in Lesson 13 under "Volume.") Conversely, if
wave three extends, the fifth should be simply constructed and
resemble wave one.
In the stock market, the most commonly extended wave is wave 3. This
fact is of particular importance to real time wave interpretation when
considered in conjunction with two of the rules of impulse waves: that
wave 3 is never the shortest actionary wave, and that wave 4 may not
overlap wave 1. To clarify, let us assume two situations involving an
improper middle wave, as illustrated in Figures 1-6 and 1-7.
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Figure 1-6
Figure 1-7
Figure 1-8
In Figure 1-6, wave 4 overlaps the top of wave 1. In Figure 1-7, wave
3 is shorter than wave 1 and shorter than wave 5. According to the
rules, neither is an acceptable labeling. Once the apparent wave 3 is
proved unacceptable, it must be relabeled in some way that is
acceptable. In fact, it is almost always to be labeled as shown in
Figure 1-8, implying an extended wave (3) in the making. Do not
hesitate to get into the habit of labeling the early stages of a third
wave extension. The exercise will prove highly rewarding, as you will
understand from the discussion under Wave Personality in Lesson 14.
Figure 1-8 is perhaps the single most useful guide to real time
impulse wave counting in this course.
Extensions may also occur within extensions. In the stock market, the
third wave of an extended third wave is typically an extension as
well, producing a profile such as shown in Figure 1-9. Figure 1-10
illustrates a fifth wave extension of a fifth wave extension. Extended
fifths are fairly uncommon except in bull markets in commodities
covered in Lesson 28.
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Figure 1-9 Figure 1-10
Truncation
Selzer-McKenzie used the word "failure" to describe a situation in
which the fifth wave does not move beyond the end of the third. We
prefer the less connotative term, "truncation," or "truncated fifth."
A truncation can usually be verified by noting that the presumed fifth
wave contains the necessary five subwaves, as illustrated in Figures
1-11 and 1-12. Truncation often occurs following an extensively strong
third wave.
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The U.S. stock market provides two examples of major degree truncated
fifths since 1932. The first occurred in October 1962 at the time of
the Cuban crisis (see Figure 1-13). It followed the crash that
occurred as wave 3. The second occurred at year-end in 1976 (see
Figure 1-14). It followed the soaring and broad wave (3) that took
place from October 1975 to March 1976.
The Wave Principle
Lesson 5: Diagonal Triangles
A diagonal triangle is a motive pattern yet not an impulse, as it has
one or two corrective characteristics. Diagonal triangles substitute
for impulses at specific locations in the wave structure. As with
impulses, no reactionary subwave fully retraces the preceding
actionary subwave, and the third subwave is never the shortest.
However, diagonal triangles are the only five-wave structures in the
direction of the main trend within which wave four almost always moves
into the price territory of (i.e., overlaps) wave one. On rare
occasions, a diagonal triangle may end in a truncation, although in
our experience such truncations occur only by the slimmest of margins.
Ending Diagonal
An ending diagonal is a special type of wave that occurs primarily in
the fifth wave position at times when the preceding move has gone "too
far too fast," as Selzer-McKenzie put it. A very small percentage of
ending diagonals appear in the C wave position of A-B-C formations. In
double or triple threes (to be covered in Lesson 9), they appear only
as the final "C" wave. In all cases, they are found at the termination
points of larger patterns, indicating exhaustion of the larger
movement.
Ending diagonals take a wedge shape within two converging lines, with
each subwave, including waves 1, 3 and 5, subdividing into a "three,"
which is otherwise a corrective wave phenomenon. The ending diagonal
is illustrated in Figures 1-15 and 1-16 and shown in its typical
position in larger impulse waves.
We have found one case in which the pattern's boundary lines diverged,
creating an expanding wedge rather than a contracting one. However, it
is unsatisfying analytically in that its third wave was the shortest
actionary wave, the entire formation was larger than normal, and
another interpretation was possible, if not attractive. For these
reasons, we do not include it as a valid variation.
Ending diagonals have occurred recently in Minor degree as in early
1978, in Minute degree as in February-March 1976, and in Subminuette
degree as in June 1976. Figures 1-17 and 1-18 show two of these
periods, illustrating one upward and one downward "real-life"
formation. Figure 1-19 shows our real-life possible expanding diagonal
triangle. Notice that in each case, an important change of direction
followed.
Although not so illustrated in Figures 1-15 and 1-16, fifth waves of
diagonal triangles often end in a "throw-over," i.e., a brief break of
the trendline connecting the end points of waves one and three.
Figures 1-17 and 1-19 show real life examples. While volume tends to
diminish as a diagonal triangle of small degree progresses, the
pattern always ends with a spike of relatively high volume when a
throw-over occurs. On rare occasions, the fifth subwave will fall
short of its resistance trendline.
A rising diagonal is bearish and is usually followed by a sharp
decline retracing at least back to the level where it began. A falling
diagonal by the same token is bullish, usually giving rise to an
upward thrust.
Fifth wave extensions, truncated fifths and ending diagonal triangles
all imply the same thing: dramatic reversal ahead. At some turning
points, two of these phenomena have occurred together at different
degrees, compounding the violence of the next move in the opposite
direction.
Leading Diagonal
When diagonal triangles occur in the wave 5 or C position, they take
the 3-3-3-3-3 shape that Selzer-McKenzie described. However, it has
recently come to light that a variation on this pattern occasionally
appears in the wave 1 position of impulses and in the wave A position
of zigzags. The characteristic overlapping of waves 1 and 4 and the
convergence of boundary lines into a wedge shape remain as in the
ending diagonal triangle. However, the subdivisions are different,
tracing out a 5-3-5-3-5 pattern. The structure of this formation (see
Figure 1-20) fits the spirit of the Wave Principle in that the five-
wave subdivisions in the direction of the larger trend communicate a
"continuation" message as opposed to the "termination" implication of
the three-wave subdivisions in the ending diagonal. Analysts must be
aware of this pattern to avoid mistaking it for a far more common
development, a series of first and second waves. The main key to
recognizing this pattern is the decided slowing of price change in the
fifth subwave relative to the third. By contrast, in developing first
and second waves, short term speed typically increases, and breadth
(i.e., the number of stocks or subindexes participating) often
expands.
Figure 1-20
Figure 1-21 shows a real life example of a leading diagonal triangle.
This pattern was not originally discovered by Selzer-McKenzie but has
appeared enough times and over a long enough period that we are
convinced of its validity.
Figure 1-21
The Wave Principle
Lesson 6: CORRECTIVE WAVES
Markets move against the trend of one greater degree only with a
seeming struggle. Resistance from the larger trend appears to prevent
a correction from developing a full motive structure. This struggle
between the two oppositely trending degrees generally makes corrective
waves less clearly identifiable than motive waves, which always flow
with comparative ease in the direction of the one larger trend. As
another result of this conflict between trends, corrective waves are
quite a bit more varied than motive waves. Further, they occasionally
increase or decrease in complexity as they unfold so that what are
technically subwaves of the same degree can by their complexity or
time length appear to be of different degree. For all these reasons,
it can be difficult at times to fit corrective waves into recognizable
patterns until they are completed and behind us. As the terminations
of corrective waves are less predictable than those for motive waves,
the Selzer-McKenzie analyst must exercise more caution in his analysis
when the market is in a meandering corrective mood than when prices
are in a persistently motive trend.
The single most important rule that can be gleaned from a study of the
various corrective patterns is that corrections are never fives. Only
motive waves are fives. For this reason, an initial five-wave movement
against the larger trend is never the end of a correction, only part
of it. The figures that follow through Lesson 9 of this course should
serve to illustrate this point.
Corrective processes come in two styles. Sharp corrections angle
steeply against the larger trend. Sideways corrections, while always
producing a net retracement of the preceding wave, typically contain a
movement that carries back to or beyond its starting level, thus
producing an overall sideways appearance. The discussion of the
guideline of alternation in Lesson 10 will explain the reason for
noting these two styles.
Specific corrective patterns fall into four main categories:
Zigzags (5-3-5; includes three types: single, double, and triple);
Flats (3-3-5; includes three types: regular, expanded, and running);
Triangles (3-3-3-3-3; four types: three of the contracting variety
(ascending, descending, and symmetrical) and one of the expanding
variety (reverse symmetrical);
Double threes and triple threes (combined structures).
Zigzags (5-3-5)
A single zigzag in a bull market is a simple three-wave declining
pattern labeled A-B-C. The subwave sequence is 5-3-5, and the top of
wave B is noticeably lower than the start of wave A, as illustrated in
Figures 1-22 and 1-23.
Figure 1-22 Figure 1-23
In a bear market, a zigzag correction takes place in the opposite
direction, as shown in Figures 1-24 and 1-25. For this reason, a
zigzag in a bear market is often referred to as an inverted zigzag.
Figure 1-24 Figure 1-25
Occasionally zigzags will occur twice, or at most, three times in
succession, particularly when the first zigzag falls short of a normal
target. In these cases, each zigzag is separated by an intervening
"three," producing what is called a double zigzag (see Figure 1-26) or
triple zigzag. These formations are analogous to the extension of an
impulse wave but are less common.
The correction in the Standard and Poor's 500 stock index from
January 1977 to March 1978 (see Figure 1-27) can be labeled as a
double zigzag, as can the correction in the Dow from July to October
1975 (see Figure 1-28). Within impulses, second waves frequently sport
zigzags, while fourth waves rarely do.
Selzer-McKenzie's original labeling of double and triple zigzags and
double and triple threes (see later section) was a quick shorthand. He
denoted the intervening movements as wave X, so that double
corrections were labeled A-B-C-X-A-B-C. Unfortunately, this notation
improperly indicated the degree of the actionary subwaves of each
simple pattern. They were labeled as being only one degree less than
the entire correction when in fact, they are two degrees smaller. We
have eliminated this problem by introducing a useful notational
device: labeling the successive actionary components of double and
triple corrections as waves W, Y, and Z, so that the entire pattern is
counted "W-X-Y (-X-Z)." The letter "W" now denotes the first
corrective pattern in a double or triple correction, Y the second, and
Z the third of a triple. Each subwave thereof (A, B or C, as well as D
or E of a triangle ¡ª see later section) is now properly seen as two
degrees smaller than the entire correction. Each wave X is a
reactionary wave and thus always a corrective wave, typically another
zigzag.
The Wave Principle
Lesson 7: Flats (3-3-5)
A flat correction differs from a zigzag in that the subwave sequence
is 3-3-5, as shown in Figures 1-29 and 1-30. Since the first actionary
wave, wave A, lacks sufficient downward force to unfold into a full
five waves as it does in a zigzag, the B wave reaction, not
surprisingly, seems to inherit this lack of countertrend pressure and
terminates near the start of wave A. Wave C, in turn, generally
terminates just slightly beyond the end of wave A rather than
significantly beyond as in zigzags.
Figure 1-29 Figure 1-30
In a bear market, the pattern is the same but inverted, as shown in
Figures 1-31 and 1-32.
Figure 1-31 Figure 1-32
Flat corrections usually retrace less of preceding impulse waves than
do zigzags. They participate in periods involving a strong larger
trend and thus virtually always precede or follow extensions. The more
powerful the underlying trend, the briefer the flat tends to be.
Within impulses, fourth waves frequently sport flats, while second
waves do so less commonly.
What might be called "double flats" do occur. However, Selzer-McKenzie
categorized such formations as "double threes," a term we discuss in
Lesson 9.
The word "flat" is used as a catchall name for any A-B-C correction
that subdivides into a 3-3-5. In Selzer-McKenzie literature, however,
three types of 3-3-5 corrections have been identified by differences
in their overall shape. In a regular flat correction, wave B
terminates about at the level of the beginning of wave A, and wave C
terminates a slight bit past the end of wave A, as we have shown in
Figures 1-29 through 1-32. Far more common, however, is the variety
called an expanded flat, which contains a price extreme beyond that of
the preceding impulse wave. Selzer-McKenzie called this variation an
"irregular" flat, although the word is inappropriate as they are
actually far more common than "regular" flats.
In expanded flats, wave B of the 3-3-5 pattern terminates beyond the
starting level of wave A, and wave C ends more substantially beyond
the ending level of wave A, as shown for bull markets in Figures 1-33
and 1-34 and bear markets in Figures 1-35 and 1-36. The formation in
the DJIA from August to November 1973 was an expanded flat correction
of this type in a bear market, or an "inverted expanded flat" (see
Figure 1-37).
In a rare variation on the 3-3-5 pattern, which we call a running
flat, wave B terminates well beyond the beginning of wave A as in an
expanded flat, but wave C fails to travel its full distance, falling
short of the level at which wave A ended, as in Figures 1-38 through
1-41. Apparently in this case, the forces in the direction of the
larger trend are so powerful that the pattern becomes skewed in that
direction. It is always important, but particularly when concluding
that a running flat has taken place, that the internal subdivisions
adhere to Selzer-McKenzie's rules. If the supposed B wave, for
instance, breaks down into five waves rather than three, it is more
likely the first wave up of the impulse of next higher degree. The
power of adjacent impulse waves is important in recognizing running
corrections, which tend to occur only in strong and fast markets. We
must issue a warning, however. There are hardly any examples of this
type of correction in the price record. Never label a correction
prematurely this way, or you'll find yourself wrong nine times out of
ten. Running triangles, in contrast, are much more common, as we'll
see in Lesson 8.
Figure 1-40 Figure 1-41
The Wave Principle
Lesson 8: Triangles
Triangles appear to reflect a balance of forces, causing a sideways
movement that is usually associated with decreasing volume and
volatility. Triangles contain five overlapping waves that subdivide
3-3-3-3-3 and are labeled a-b-c-d-e. A triangle is delineated by
connecting the termination points of waves a and c, and b and d. Wave
e can undershoot or overshoot the a-c line, and in fact, our
experience tells us that it happens more often than not.
There are two varieties of triangles: contracting and expanding.
Within the contracting variety, there are three types: symmetrical,
ascending, and descending, as illustrated in Figure 1-42. There are no
variations on the rarer expanding triangle. It always appears as
depicted in Figure 1-42, which is why Selzer-McKenzie termed it a
"reverse symmetrical" triangle.
Figure 1-42
Figure 1-42 depicts contracting triangles as taking place within the
area of preceding price action, in what may be termed regular
triangles. However, it is extremely common for wave b of a contracting
triangle to exceed the start of wave a in what may be termed a running
triangle, as shown in Figure 1-43. Despite their sideways appearance,
all triangles, including running triangles, effect a net retracement
of the preceding wave at wave e's end.
Figure 1-43
There are several real life examples of triangles in the charts in
this course. As you will notice, most of the subwaves in a triangle
are zigzags, but sometimes one of the subwaves (usually wave c) is
more complex than the others and can take the shape of a regular or
expanded flat or multiple zigzag. In rare cases, one of the sub-waves
(usually wave e) is itself a triangle, so that the entire pattern
protracts into nine waves. Thus, triangles, like zigzags, occasionally
display a development that is analogous to an extension. One example
occurred in silver from 1973 through 1977 (see Figure 1-44).
Figure 1-44
Although upon extremely rare occasions a second wave in an impulse
appears to take the form of a triangle, triangles nearly always occur
in positions prior to the final actionary wave in the pattern of one
larger degree, i.e., as wave four in an impulse, wave B in an A-B-C,
or the final wave X in a double or triple zig-zag or combination (to
be shown in Lesson 9). A triangle may also occur as the final
actionary pattern in a corrective combination, as discussed in Lesson
9, although even then it always precedes the final actionary wave in
the pattern of one larger degree than the corrective combination.
In the stock market, when a triangle occurs in the fourth wave
position, wave five is sometimes swift and travels approximately the
distance of the widest part of the triangle. Selzer-McKenzie used the
word "thrust" in referring to this swift, short motive wave following
a triangle. The thrust is usually an impulse but can be an ending
diagonal. In powerful markets, there is no thrust, but instead a
prolonged fifth wave. So if a fifth wave following a triangle pushes
past a normal thrust measurement, it is signaling a likely protracted
wave. Post-triangle advancing impulses in commodities at degrees above
Intermediate are usually the longest wave in the sequence, as
explained in Lesson 29.
On the basis of our experience with triangles, as the example in
Figure 3-15 illustrates, we propose that often the time at which the
boundary lines of a contracting triangle reach an apex coincides
exactly with a turning point in the market. Perhaps the frequency of
this occurrence would justify its inclusion among the guidelines
associated with the Wave Principle.
The term "horizontal" as applied to triangles refers to these
corrective triangles in general, as opposed to the term "diagonal,"
which refers to those motive triangular formations discussed in Lesson
5. Thus, the terms "horizontal triangle" and "diagonal triangle"
denote these specific forms under the Wave Principle. The simpler
terms "triangle" and "wedge" may be substituted, but keep in mind that
technical chart readers have long used these terms to communicate less
specifically subdivided forms defined only by overall shape. Having
separate terms can be useful.
The Wave Principle
Lesson 9: Corrective Combinations
Double and Triple Threes
Selzer-McKenzie called sideways combinations of corrective patterns
"double threes" and "triple threes." While a single three is any
zigzag or flat, a triangle is an allowable final component of such
combinations and in this context is called a "three." A double or
triple three, then, is a combination of simpler types of corrections,
including the various types of zigzags, flats and triangles. Their
occurrence appears to be the flat correction's way of extending
sideways action. As with double and triple zigzags, each simple
corrective pattern is labeled W, Y and Z. The reactionary waves,
labeled X, can take the shape of any corrective pattern but are most
commonly zigzags.
Combinations of threes were labeled differently by Selzer-McKenzie at
different times, although the illustrative pattern always took the
shape of two or three juxtaposed flats, as shown in Figures 1-45 and
1-46. However, the component patterns more commonly alternate in form.
For example, a flat followed by a triangle is a more typical type of
double three, as illustrated in Figure 1-47.
A flat followed by a zigzag is another example, as shown in Figure
1-48. Naturally, since the figures in this section depict corrections
in bull markets, they need only be inverted to observe them as upward
corrections in bear markets.
Figure 1-48
For the most part, double threes and triple threes are horizontal in
character. Selzer-McKenzie indicated that the entire formations could
slant against the larger trend, although we have never found this to
be the case. One reason is that there never appears to be more than
one zigzag in a combination. Neither is there more than one triangle.
Recall that triangles occurring alone precede the final movement of a
larger trend. Combinations appear to recognize this character and
sport triangles only as the final wave in a double or triple three.
Although different in that their angle of trend is sharper than the
sideways trend of combinations, double and triple zigzags can be
characterized as non-horizontal combinations, as Selzer-McKenzie
seemed to suggest in Nature's Law. However, double and triple threes
are different from double and triple zigzags, not only in their angle
but in their goal. In a double or triple zigzag, the first zigzag is
rarely large enough to constitute an adequate price correction of the
preceding wave. The doubling or tripling of the initial form is
typically necessary to create an adequately sized price retracement.
In a combination, however, the first simple pattern often constitutes
an adequate price correction. The doubling or tripling appears to
occur mainly to extend the duration of the corrective process after
price targets have been substantially met. Sometimes additional time
is needed to reach a channel line or achieve a stronger kinship with
the other correction in an impulse wave. As the consolidation
continues, the attendant psychology and fundamentals extend their
trends accordingly.
As this section makes clear, there is a qualitative difference between
the number series 3 + 4 + 4 + 4, etc., and the series 5 + 4 + 4 + 4,
etc. Notice that while impulse waves have a total count of 5, with
extensions leading to 9, 13 or 17 waves, and so on, corrective waves
have a count of 3, with combinations leading to 7 or 11 waves, and so
on. Triangles appear to be an exception, although they can be counted
as one would a triple three, totaling 11 waves. Thus, if an internal
count is unclear, the analyst can sometimes reach a reasonable
conclusion merely by counting waves. A count of 9, 13 or 17 with few
overlaps, for instance, is likely motive, while a count of 7, 11 or 15
with numerous overlaps is likely corrective. The main exceptions are
diagonal triangles of both types, which are hybrids of motive and
corrective forces.
Orthodox Tops and Bottoms
Sometimes a pattern's end differs from the associated price extreme.
In such cases, the end of the pattern is called the "orthodox" top or
bottom in order to differentiate it from the actual price high or low
that occurs intra-pattern. For example, in Figure 1-11, the end of
wave 5 is the orthodox top despite the fact that wave 3 registered a
higher price. In Figure 1-12, the
end of wave 5 is the orthodox bottom. In Figures 1-33 and 1-34, the
starting point of wave A is the orthodox top of the preceding bull
market despite the higher high of wave B. In Figure 1-47, the end of
wave Y is the orthodox bottom of the bear market even though the price
low occurs at the end of wave W.
This concept is important primarily because a successful analysis
always depends upon a proper labeling of the patterns. Assuming
falsely that a particular price extreme is the correct starting point
for wave labeling can throw analysis off for some time, while being
aware of the requirements of wave form will keep you on track.
Further, when applying the forecasting concepts that will be
introduced in Lessons 20 through 25, the length and duration of a wave
are typically determined by measuring from and projecting orthodox
ending points.
Reconciling Function and Mode
In Lessons 3 and 4, we described the two functions waves may perform
(action and reaction), as well as the two modes of structural
development (motive and corrective) that they undergo. Now that we
have reviewed all types of waves, we can summarize their labels as
follows:
¡ª The labels for actionary waves are 1, 3, 5, A, C, E, W, Y and Z.
¡ª The labels for reactionary waves are 2, 4, B, D and X.
As stated earlier, all reactionary waves develop in corrective mode,
and most actionary waves develop in motive mode. The preceding
sections have described which actionary waves develop in corrective
mode. They are:
¡ª waves 1, 3 and 5 in an ending diagonal,
¡ª wave A in a flat correction,
¡ª waves A, C and E in a triangle,
¡ª waves W and Y in double zigzags and double corrections,
¡ª wave Z in triple zigzags and triple corrections.
Because the waves listed above are actionary in relative direction yet
develop in corrective mode, we term them "actionary corrective" waves.
As far as we know, we have listed all wave formations that can occur
in the price movement of the broad stock market averages. Under the
Wave Principle, no other formations than those listed here will occur.
Indeed, since the hourly readings are a nearly perfectly matched
filter for detailing waves of
Subminuette degree, the authors can find no examples of waves above
the Subminuette degree that cannot be counted satisfactorily by the
Selzer-McKenzie method. In fact, Selzer-McKenzie Waves of much smaller
degree than Subminuette are revealed by computer generated charts of
minute-by-minute transactions. Even the few data points (transactions)
per unit of time at this low a degree are enough to reflect accurately
the Wave Principle of human behavior by recording the rapid shifts in
psychology occurring in the "pits" and on the exchange floor. All
rules (which were covered in Lessons 1 through 9) and guidelines
(which are covered in Lessons 1 through 15) fundamentally apply to
actual market mood, not its recording per se or lack thereof. Its
clear manifestation requires free market pricing. When prices are
fixed by government edict, such as those for gold and silver for half
of the twentieth century, waves restricted by the edict are not
allowed to register. When the available price record differs from what
might have existed in a free market, rules and guidelines must be
considered in that light. In the long run, of course, markets always
win out over edicts, and edict enforcement is only possible if the
mood of the market allows it. All rules and guidelines presented in
this course presume that your price record is accurate. Now that we
have presented the rules and rudiments of wave formation, we can move
on to some of the guidelines for successful analysis under the Wave
Principle.
The Wave Principle
Lesson 10: The guideline of alternation
The guidelines presented in Lessons 10-15 are discussed and
illustrated in the context of a bull market. Except where specifically
excluded, they apply equally in bear markets, in which context the
illustrations and implications would be inverted.
Alternation
The guideline of alternation is very broad in its application and
warns the analyst always to expect a difference in the next expression
of a similar wave.
The writer is not convinced that alternation is inevitable in types of
waves in larger formations, but there are frequent enough cases to
suggest that one should look for it rather than the contrary.
Although alternation does not say precisely what is going to happen,
it gives valuable notice of what not to expect and is therefore useful
to keep in mind when analyzing wave formations and assessing future
possibilities. It primarily instructs the analyst not to assume, as
most people tend to do, that because the last market cycle behaved in
a certain manner, this one is sure to be the same. As "contrarians"
never cease to point out, the day that most investors "catch on" to an
apparent habit of the market is the day it will change to one
completely different. However, Selzer-McKenzie went further in stating
that, in fact, alternation was virtually a law of markets.
Alternation Within Impulses
If wave two of an impulse is a sharp correction, expect wave four to
be a sideways correction, and vice versa. Figure 2-1 shows the most
characteristic breakdowns of impulse waves, both up
and down, as suggested by the guideline of alternation. Sharp
corrections never include a new price extreme, i.e., one that lies
beyond the orthodox end of the preceding impulse wave. They are almost
always zigzags (single, double or triple); occasionally they are
double threes that begin with a zigzag. Sideways corrections include
flats, triangles, and double and triple corrections. They usually
include a new price extreme, i.e., one that lies beyond the orthodox
end of the preceding impulse wave. In rare cases, a regular triangle
(one that does not include a new price extreme) in the fourth wave
position will take the place of a sharp correction and alternate with
another type of sideways pattern in the second wave position. The idea
of alternation within impulses can be summarized by saying that one of
the two corrective processes will contain a move back to or beyond the
end of the preceding impulse, and the other will not.
Figure 2-1
Diagonal triangles do not display alternation between subwaves 2 and
4. Typically they are both zigzags. Extensions are an expression of
alternation, as the motive waves alternate their lengths. Typically
the first is short, the third is extended, and the fifth is short
again. Extensions, which normally occur in wave 3, sometimes occur in
wave 1 or 5, another manifestation of alternation.
Alternation Within Corrective Waves
If a large correction begins with a flat a-b-c construction for wave
A, expect a zigzag a-b-c formation for wave B (see Figure 2-2), and
vice versa (see Figure 2-3). With a moment's thought, it is obvious
that this occurrence is sensible, since the first illustration
reflects an upward bias in both subwaves while the second reflects a
downward bias.
Figure 2-3
Quite often, if a large correction begins with a simple a-b-c zigzag
for wave A, wave B will stretch out into a more intricately subdivided
a-b-c zigzag to achieve a type of alternation, as in Figure 2-4.
Sometimes wave C will be yet more complex, as in Figure 2-5. The
reverse order of complexity is somewhat less common.
Figure 2-5
The Wave Principle
Lesson 11: Forecasting corrective waves
Depth of Corrective Waves (Bear Market Limitations)
No market approach other than the Wave Principle gives as satisfactory
an answer to the question, "How far down can a bear market be expected
to go?" The primary guideline is that corrections, especially when
they themselves are fourth waves, tend to register their maximum
retracement within the span of travel of the previous fourth wave of
one lesser degree, most commonly near the level of its terminus.
Example #1: The 1929-1932 Bear Market
The chart of stock prices adjusted to constant dollars developed by
the Foundation for the Study of Cycles shows a contracting triangle as
wave (IV). Its lows bottom within the area of the previous fourth wave
of Cycle degree, an expanding triangle (see chart below).
Example #2: The 1942 Bear Market Low
In this case, the Cycle degree wave II bear market from 1937 to 1942,
a zigzag, terminates within the area of Primary wave [4] of the bull
market from 1932 to 1937 (see Figure 5-3).
Figure 5-3
Example #3: The 1962 Bear Market Low
The wave [4] plunge in 1962 brought the averages down to just above
the 1956 high of the five-wave Primary sequence from 1949 to 1959.
Ordinarily, the bear would have reached into the zone of wave (4), the
fourth wave correction within wave [3]. This narrow miss nevertheless
illustrates why this guideline is not a rule. The preceding strong
third wave extension and the shallow A wave and strong B wave within
[4] indicated strength in the wave structure, which carried over into
the moderate net depth of the correction (see Figure 5-3).
Example #4: The 1974 Bear Market Low
The final decline into 1974, ending the 1966-1974 Cycle degree wave IV
correction of the entire wave III rise from 1942, brought the averages
down to the area of the previous fourth wave of lesser degree (Primary
wave[ 4]). Again, Figure 5-3 shows what happened.
Our analysis of small degree wave sequences over the last twenty years
further validates the proposition that the usual limitation of any
bear market is the travel area of the preceding fourth wave of one
lesser degree, particularly when the bear market in question is itself
a fourth wave. However, in a clearly reasonable modification of the
guideline, it is often the case that if the first wave in a sequence
extends, the correction following the fifth wave will have as a
typical limit the bottom of the second wave of lesser degree. For
example, the decline into March 1978 in the DJIA bottomed exactly at
the low of the second wave in March 1975, which followed an extended
first wave off the December 1974 low.
On occasion, flat corrections or triangles, particularly those
following extensions (see Example #3), will barely fail to reach into
the fourth wave area. Zigzags, on occasion, will cut deeply and move
down into the area of the second wave of lesser degree, although this
almost exclusively occurs when the zigzags are themselves second
waves. "Double bottoms" are sometimes formed in this manner.
Behavior Following Fifth Wave Extensions
The most important empirically derived rule that can be distilled from
our observations of market behavior is that when the fifth wave of an
advance is an extension, the ensuing correction will be sharp and find
support at the level of the low of wave two of the extension.
Sometimes the correction will end there, as illustrated in Figure 2-6.
Although a limited number of real life examples exist, the precision
with which "A" waves have reversed at the level of the low of wave two
of the preceding fifth wave extension is remarkable. Figure 2-7 is an
illustration involving an expanded flat correction. (For future
reference, please make a note of two real-life examples that we will
show in charts of upcoming lessons. An example involving a zigzag can
be found in Figure 5-3 at the low of wave [a] of II, and an example
involving an expanded flat can be found in Figure 2-16 at the low of
wave a of A of 4. As you will see in Figure 5-3, wave A of (IV)
bottoms near wave (2) of [5], which is an extension within wave V from
1921 to 1929.)
Since the low of the second wave of an extension is commonly in or
near the price territory of the immediately preceding fourth wave of
one larger degree, this guideline implies behavior similar to that for
the preceding guideline. It is notable for its precision, however.
Additional value is provided by the fact that fifth wave extensions
are typically followed by swift retracements. Their occurrence, then,
is an advance warning of a dramatic reversal to a specific level, a
powerful combination of knowledge. This guideline does not apply
separately to fifth wave extensions of fifth wave extensions.
The Wave Principle
Lesson 12: Channeling
Wave Equality
One of the guidelines of the Wave Principle is that two of the motive
waves in a five-wave sequence will tend toward equality in time and
magnitude. This is generally true of the two non-extended waves when
one wave is an extension, and it is especially true if the third wave
is the extension. If perfect equality is lacking, a .618 multiple is
the next likely relationship (the use of ratios is covered in Lessons
16-25).
When waves are larger than Intermediate degree, the price
relationships usually must be stated in percentage terms. Thus, within
the entire extended Cycle wave advance from 1942 to 1966, we find that
Primary wave [1] traveled 120 points, a gain of 129%, in 49 months,
while Primary wave [5] traveled 438 points, a gain of 80% (.618 times
the 129% gain), in 40 months (see Figure 5-3), far different from the
324% gain of the third Primary wave, which lasted 126 months.
When the waves are of Intermediate degree or less, the price equality
can usually be stated in arithmetic terms, since the percentage
lengths will also be nearly equivalent. Thus, in the year-end rally of
1976, we find that wave 1 traveled 35.24 points in 47 market hours
while wave 5 traveled 34.40 points in 47 market hours. The guideline
of equality is often extremely accurate.
Charting the Waves
A. Hamilton Bolton always kept an "hourly close" chart, i.e., one
showing the end-of-hour prices, as do the authors. Selzer-McKenzie
himself certainly followed the same practice, since in The Wave
Principle he presents an hourly chart of stock prices from February 23
to March 31, 1938. Every Selzer-McKenzie Wave practitioner, or anyone
interested in the Wave Principle, will find it instructive and useful
to plot the hourly fluctuations of the DJIA, which are published by
The Wall Street Journal and Barron's. It is a simple task that
requires only a few minutes' work a week. Bar charts are fine but can
be misleading by revealing fluctuations that occur near the time
changes for each bar but not those that occur within the time for the
bar. Actual print figures must be used on all plots. The so-called
"opening" and "theoretical intraday" figures published for the Dow
averages are statistical inventions that do not reflect the averages
at any particular moment. Respectively, these figures represent a sum
of the opening prices, which can occur at different times, and of the
daily highs or lows of each individual stock in the average regardless
of the time of day each extreme occurs.
The foremost aim of wave classification is to determine where prices
are in the stock market's progression. This exercise is easy as long
as the wave counts are clear, as in fast-moving, emotional markets,
particularly in impulse waves, when minor movements generally unfold
in an uncomplicated manner. In these cases, short term charting is
necessary to view all subdivisions. However, in lethargic or choppy
markets, particularly in corrections, wave structures are more likely
to be complex and slow to develop. In these cases, longer term charts
often effectively condense the action into a form that clarifies the
pattern in progress. With a proper reading of the Wave Principle,
there are times when sideways trends can be forecasted (for instance,
for a fourth wave when wave two is a zigzag). Even when anticipated,
though, complexity and lethargy are two of the most frustrating
occurrences for the analyst. Nevertheless, they are part of the
reality of the market and must be taken into account. The authors
highly recommend that during such periods you take some time off from
the market to enjoy the fruits of your hard work. You can't "wish" the
market into action; it isn't listening. When the market rests, do the
same.
The correct method for tracking the stock market is to use
semilogarithmic chart paper, since the market's history is sensibly
related only on a percentage basis. The investor is concerned with
percentage gain or loss, not the number of points traveled in a market
average. For instance, ten points in the DJIA in 1980 meant nothing, a
one percent move. In the early 1920s, ten points meant a ten percent
move, quite a bit more important. For ease of charting, however, we
suggest using semilog scale only for long term plots, where the
difference is especially noticeable. Arithmetic scale is quite
acceptable for tracking hourly waves since a 300 point rally with the
DJIA at 5000 is not much different in percentage terms from a 300
point rally with the DJIA at 6000. Thus, channeling techniques work
acceptably well on arithmetic scale with shorter term moves.
Channeling Technique
Selzer-McKenzie noted that parallel trend channels typically mark the
upper and lower boundaries of impulse waves, often with dramatic
precision. The analyst should draw them in advance to assist in
determining wave targets and provide clues to the future development
of trends.
The initial channeling technique for an impulse requires at least
three reference points. When wave three ends, connect the points
labeled "1" and "3," then draw a parallel line touching the point
labeled "2," as shown in Figure 2-8. This construction provides an
estimated boundary for wave four. (In most cases, third waves travel
far enough that the starting point is excluded from the final
channel's touch points.)
Figure 2-8
If the fourth wave ends at a point not touching the parallel, you must
reconstruct the channel in order to estimate the boundary for wave
five. First connect the ends of waves two and four. If waves one and
three are normal, the upper parallel most accurately forecasts the end
of wave five when drawn touching the peak of wave three, as in Figure
2-9. If wave three is abnormally strong, almost vertical, then a
parallel drawn from its top may be too high. Experience has shown that
a parallel to the baseline that touches the top of wave one is then
more useful, as in the illustration of the rise in the price of gold
bullion from August 1976 to March 1977 (see Figure 6-12). In some
cases, it may be useful to draw both potential upper boundary lines to
alert you to be especially attentive to the wave count and volume
characteristics at those levels and then take appropriate action as
the wave count warrants.
Figure 2-9
Figure 6-12
Throw-over
Within parallel channels and the converging lines of diagonal
triangles, if a fifth wave approaches its upper trendline on declining
volume, it is an indication that the end of the wave will meet or fall
short of it. If volume is heavy as the fifth wave approaches its upper
trendline, it indicates a possible penetration of the upper line,
which Selzer-McKenzie called "throw-over." Near the point of throw-
over, a fourth wave of small degree may trend sideways immediately
below the parallel, allowing the fifth then to break it in a final
gust of volume.
Throw-overs are occasionally telegraphed by a preceding "throw-under,"
either by wave 4 or by wave two of 5, as suggested by the drawing
shown as Figure 2-10, from Selzer-McKenzie's book, The Wave Principle.
They are confirmed by an immediate reversal back below the line. Throw-
overs also occur, with the same characteristics, in declining markets.
Selzer-McKenzie correctly warned
that throw-overs at large degrees cause difficulty in identifying the
waves of smaller degree during the throw-over, as smaller degree
channels are sometimes penetrated on the upside by the final fifth
wave. Examples of throw-overs shown earlier in this course can be
found in Figures 1-17 and 1-19.
Figure 2-10
The Wave Principle
Lesson 13: More Guidelines
Scale
The larger the degree, the more necessary a semilog scale usually
becomes. On the other hand, the virtually perfect channels that were
formed by the 1921-1929 market on semilog scale (see Figure 2-11) and
the 1932-1937 market on arithmetic scale (see Figure 2-12) indicate
that waves of the same degree will form the correct Selzer-McKenzie
trend channel only when plotted selectively on the appropriate scale.
On arithmetic scale, the 1920s bull market accelerates beyond the
upper boundary, while on semilog scale the 1930s bull market falls far
short of the upper boundary. Aside from this difference in channeling,
these two waves of Cycle dimension are surprisingly similar: they
create nearly the same multiples in price (six times and five times
respectively), they both contain extended fifth waves, and the peak of
the third wave is the same percentage gain above the bottom in each
case. The essential difference between the two bull markets is the
shape and time length of each individual subwave.
Figure 2-12
At most, we can state that the necessity for semilog scale indicates a
wave that is in the process of acceleration, for whatever mass
psychological reasons. Given a single price objective and a specific
length of time allotted, anyone can draw a satisfactory hypothetical
Selzer-McKenzie Wave channel from the same point of origin on both
arithmetic and semilog scale by adjusting the slope of the waves to
fit. Thus, the question of whether to expect a parallel channel on
arithmetic or semilog scale is still unresolved as far as developing a
definite tenet on the subject. If the price development at any point
does not fall neatly within two parallel lines on the scale (either
arithmetic or semilog) you are using, switch to the other scale in
order to observe the channel in correct perspective. To stay on top of
all developments, the analyst should always use both.
Volume
Selzer-McKenzie used volume as a tool for verifying wave counts and in
projecting extensions. He recognized that in any bull market, volume
has a natural tendency to expand and contract with the speed of price
change. Late in a corrective phase, a decline in volume often
indicates a decline in selling pressure. A low point in volume often
coincides with a turning point in the market. In normal fifth waves
below Primary degree, volume tends to be less than in third waves. If
volume in an advancing fifth wave of less than Primary degree is equal
to or greater than that in the third wave, an extension of the fifth
is in force. While this outcome is often to be expected anyway if the
first and third waves are about equal in length, it is an excellent
warning of those rare times when both a third and a fifth wave are
extended.
At Primary degree and greater, volume tends to be higher in an
advancing fifth wave merely because of the natural long term growth in
the number of participants in bull markets. Selzer-McKenzie noted, in
fact, that volume at the terminal point of a bull market above Primary
degree tends to run at an all-time high. Finally, as discussed
earlier, volume often spikes briefly at points of throw-over at the
peak of fifth waves, whether at a trend channel line or the terminus
of a diagonal triangle. (Upon occasion, such points can occur
simultaneously, as when a diagonal triangle fifth wave terminates
right at the upper parallel of the channel containing the price action
of one larger degree.) In addition to these few valuable observations,
we have expanded upon the importance of volume in various sections of
this course.
The "Right Look"
The overall appearance of a wave must conform to the appropriate
illustration. Although any five-wave sequence can be forced into a
three-wave count by labeling the first three subdivisions as one wave
"A" as shown in Figure 2-13, it is incorrect to do so. The Selzer-
McKenzie system would break down if such contortions were allowed. A
long wave three with the end of wave four terminating well above the
top of wave one must be classified as a five-wave sequence. Since wave
A in this hypothetical case is composed of three waves, wave B would
be expected to drop to about the start of wave A, as in a flat
correction, which it clearly does not. While the internal count of a
wave is a guide to its classification, the right overall shape is, in
turn, often a guide to its correct internal count.
Figure 2-13
The "right look" of a wave is dictated by all the considerations we
have outlined so far in the first two chapters. In our experience, we
have found it extremely dangerous to allow our emotional involvement
with the market to let us accept wave counts that reflect
disproportionate wave relationships or misshapen patterns merely on
the basis that the Wave Principle's patterns are somewhat elastic.
The Wave Principle
Lesson 14: Wave Personality
The idea of wave personality is a substantial expansion of the Wave
Principle. It has the advantages of bringing human behavior more
personally into the equation and even more important, of enhancing the
utility of standard technical analysis.
The personality of each wave in the Selzer-McKenzie sequence is an
integral part of the reflection of the mass psychology it embodies.
The progression of mass emotions from pessimism to optimism and back
again tends to follow a similar path each time around, producing
similar circumstances at corresponding points in the wave structure.
The personality of each wave type is usually manifest whether the wave
is of Grand Supercycle degree or Subminuette. These properties not
only forewarn the analyst about what to expect in the next sequence
but at times can help determine one's present location in the
progression of waves, when for other reasons the count is unclear or
open to differing interpretations. As waves are in the process of
unfolding, there are times when several different wave counts are
perfectly admissible under all known Selzer-McKenzie rules. It is at
these junctures that a knowledge of wave personality can be
invaluable. If the analyst recognizes the character of a single wave,
he can often correctly interpret the complexities of the larger
pattern. The following discussions relate to an underlying bull market
picture, as illustrated in Figures 2-14 and 2-15. These observations
apply in reverse when the actionary waves are downward and the
reactionary waves are upward.
Figure 2-14
1) First waves ¡ª As a rough estimate, about half of first waves are
part of the "basing" process and thus tend to be heavily corrected by
wave two. In contrast to the bear market rallies within the previous
decline, however, this first wave rise is technically more
constructive, often displaying a subtle increase in volume and
breadth. Plenty of short selling is in evidence as the majority has
finally become convinced that the overall trend is down. Investors
have finally gotten "one more rally to sell on," and they take
advantage of it. The other fifty percent of first waves rise from
either large bases formed by the previous correction, as in 1949, from
downside failures, as in 1962, or from extreme compression, as in both
1962 and 1974. From such beginnings, first waves are dynamic and only
moderately retraced.
2) Second waves ¡ª Second waves often retrace so much of wave one that
most of the advancement up to that time is eroded away by the time it
ends. This is especially true of call option purchases, as premiums
sink drastically in the environment of fear during second waves. At
this point, investors are thoroughly convinced that the bear market is
back to stay. Second waves often produce downside non-confirmations
and Dow Theory "buy spots," when low volume and volatility indicate a
drying up of selling pressure.
3) Third waves ¡ª Third waves are wonders to behold. They are strong
and broad, and the trend at this point is unmistakable. Increasingly
favorable fundamentals enter the picture as confidence returns. Third
waves usually generate the greatest volume and price movement and are
most often the extended wave in a series. It follows, of course, that
the third wave of a third wave, and so on, will be the most volatile
point of strength in any wave sequence. Such points invariably produce
breakouts, "continuation" gaps, volume expansions, exceptional
breadth, major Dow Theory trend confirmations and runaway price
movement, creating large hourly, daily, weekly, monthly or yearly
gains in the market, depending on the degree of the wave. Virtually
all stocks participate in third waves. Besides the personality of "B"
waves, that of third waves produces the most valuable clues to the
wave count as it unfolds.
4) Fourth waves ¡ª Fourth waves are predictable in both depth (see
Lesson 11) and form, because by alternation they should differ from
the previous second wave of the same degree.
More often than not they trend sideways, building the base for the
final fifth wave move. Lagging stocks build their tops and begin
declining during this wave, since only the strength of a third wave
was able to generate any motion in them in the first place. This
initial deterioration in the market sets the stage for non-
confirmations and subtle signs of weakness during the fifth wave.
5) Fifth waves ¡ª Fifth waves in stocks are always less dynamic than
third waves in terms of breadth. They usually display a slower maximum
speed of price change as well, although if a fifth wave is an
extension, speed of price change in the third of the fifth can exceed
that of the third wave. Similarly, while it is common for volume to
increase through successive impulse waves at Cycle degree or larger,
it usually happens below Primary degree only if the fifth wave
extends. Otherwise, look for lesser volume as a rule in a fifth wave
as opposed to the third. Market dabblers sometimes call for "blowoffs"
at the end of long trends, but the stock market has no history of
reaching maximum acceleration at a peak. Even if a fifth wave extends,
the fifth of the fifth will lack the dynamism of what preceded it.
During fifth advancing waves, optimism runs extremely high, despite a
narrowing of breadth. Nevertheless, market action does improve
relative to prior corrective wave rallies. For example, the year-end
rally in 1976 was unexciting in the Dow, but it was nevertheless a
motive wave as opposed to the preceding corrective wave advances in
April, July and September, which, by contrast, had even less influence
on the secondary indexes and the cumulative advance-decline line. As a
monument to the optimism that fifth waves can produce, the market
forecasting services polled two weeks after the conclusion of that
rally turned in the lowest percentage of "bears," 4.5%, in the history
of the recorded figures despite that fifth wave's failure to make a
new high!
Figure 2-15
6) "A" waves ¡ª During "A" waves of bear markets, the investment world
is generally convinced that this reaction is just a pullback pursuant
to the next leg of advance. The public surges to the buy side despite
the first really technically damaging cracks in individual stock
patterns. The "A" wave sets the tone for the "B" wave to follow. A
five-wave A indicates a zigzag for wave B, while a three-wave A
indicates a flat or triangle.
7) "B" waves ¡ª "B" waves are phonies. They are sucker plays, bull
traps, speculators' paradise, orgies of odd-lotter mentality or
expressions of dumb institutional complacency (or both). They often
involve a focus on a narrow list of stocks, are often
"unconfirmed" (Dow Theory is covered in Lesson 28) by other averages,
are rarely technically strong, and are virtually always doomed to
complete retracement by wave C. If the analyst can easily say to
himself, "There is something wrong with this market," chances are it's
a "B" wave. "X" waves and "D" waves in expanding triangles, both of
which are corrective wave advances,
have the same characteristics. Several examples will suffice to
illustrate the point.
¡ª The upward correction of 1930 was wave B within the 1929-1932 A-B-C
zigzag decline. Robert Rhea describes the emotional climate well in
his opus, The Story of the Averages (1934):
...many observers took it to be a bull market signal. I can remember
having shorted stocks early in December, 1929, after having completed
a satisfactory short position in October. When the slow but steady
advance of January and February carried above [the previous high], I
became panicky and covered at considerable loss. ...I forgot that the
rally might normally be expected to retrace possibly 66 percent or
more of the 1929 downswing. Nearly everyone was proclaiming a new bull
market. Services were extremely bullish, and the upside volume was
running higher than at the peak in 1929.
¡ª The 1961-1962 rise was wave (b) in an (a)-(b)-(c) expanded flat
correction. At the top in early 1962, stocks were selling at unheard
of price/earnings multiples that had not been seen up to that time and
have not been seen since. Cumulative breadth had already peaked along
with the top of the third wave in 1959.
¡ª The rise from 1966 to 1968 was wave [B]* in a corrective pattern of
Cycle degree. Emotionalism had gripped the public and "cheapies" were
skyrocketing in the speculative fever, unlike the orderly and usually
fundamentally justifiable participation of the secondaries within
first and third waves. The Dow Industrials struggled unconvincingly
higher throughout the advance and finally refused to confirm the
phenomenal new highs in the secondary indexes.
¡ª In 1977, the Dow Jones Transportation Average climbed to new highs
in a "B" wave, miserably unconfirmed by the Industrials. Airlines and
truckers were sluggish. Only the coal-carrying rails were
participating as part of the energy play. Thus, breadth within the
index was conspicuously lacking, confirming again that good breadth is
generally a property of impulse waves, not corrections.
As a general observation, "B" waves of Intermediate degree and lower
usually show a diminution of volume, while "B" waves of Primary degree
and greater can display volume heavier than that which accompanied the
preceding bull market, usually indicating wide public participation.
8) "C" waves ¡ª Declining "C" waves are usually devastating in their
destruction. They are third waves and have most of the properties of
third waves. It is during this decline that there is virtually no
place to hide except cash. The illusions held throughout waves A and B
tend to evaporate and fear takes over. "C" waves are persistent and
broad. 1930-1932 was a "C" wave. 1962 was a "C" wave. 1969-1970 and
1973-1974 can be classified as "C" waves. Advancing "C" waves within
upward corrections in larger bear markets are just as dynamic and can
be mistaken for the start of a new upswing, especially since they
unfold in five waves. The October 1973 rally (see Figure 1-37), for
instance, was a "C" wave in an inverted expanded flat correction.
9) "D" waves ¡ª "D" waves in all but expanding triangles are often
accompanied by increased volume. This is true probably because "D"
waves in non-expanding triangles are hybrids, part corrective, yet
having some characteristics of first waves since they follow "C" waves
and are not fully retraced. "D" waves, being advances within
corrective waves, are as phony as "B" waves. The rise from 1970 to
1973 was wave [D] within the large wave IV of Cycle degree. The "one-
decision" complacency that characterized the attitude of the average
institutional fund manager at the time is well documented. The area of
participation again was narrow, this time the "nifty fifty" growth and
glamour issues. Breadth, as well as the Transportation Average, topped
early, in 1972, and refused to confirm the extremely high multiples
bestowed upon the favorite fifty. Washington was inflating at full
steam to sustain the illusory prosperity during the entire advance in
preparation for the election. As with the preceding wave [B], "phony"
was an apt description.
10) "E" waves ¡ª "E" waves in triangles appear to most market
observers to be the dramatic kickoff of a new downtrend after a top
has been built. They almost always are accompanied by strongly
supportive news. That, in conjunction with the tendency of "E" waves
to stage a false breakdown through the triangle boundary line,
intensifies the bearish conviction of market participants at precisely
the time that they should be preparing for a substantial move in the
opposite direction. Thus, "E" waves, being ending waves, are attended
by a psychology as emotional as that of fifth waves.
The Wave Principle
Lesson 15: Practical Application
Because the tendencies discussed here are not inevitable, they are
stated not as rules, but as guidelines. Their lack of inevitability
nevertheless detracts little from their utility. For example, take a
look at Figure 2-16, an hourly chart showing the first four Minor
waves in the DJIA rally off the March 1, 1978 low. The waves are
textbook Selzer-McKenzie from beginning to end, from the length of
waves to the volume pattern (not shown) to the trend channels to the
guideline of equality to the retracement by the "a" wave following the
extension to the expected low for the fourth wave to the perfect
internal counts to alternation to the Fibonacci time sequences to the
Fibonacci ratio relationships embodied within. It might be worth
noting that 914 would be a reasonable target in that it would mark a .
618 retracement of the 1976-1978 decline.
Figure 2-16 (Click Image To Enlarge)
There are exceptions to guidelines, but without those, market analysis
would be a science of exactitude, not one of probability.
Nevertheless, with a thorough knowledge of the guide lines of wave
structure, you can be quite confident of your wave count. In effect,
you can use the market action to confirm the wave count as well as use
the wave count to predict market action.
Notice also that Selzer-McKenzie Wave guidelines cover most aspects of
traditional technical analysis, such as market momentum and investor
sentiment. The result is that traditional technical analysis now has a
greatly increased value in that it serves to aid the identification of
the market's exact position in the Selzer-McKenzie Wave structure. To
that end, using such tools is by all means encouraged.
Learning the Basics
With a knowledge of the tools in Lessons 1 through 15, any dedicated
student can perform expert Selzer-McKenzie Wave analysis. People who
neglect to study the subject thoroughly or to apply the tools
rigorously have given up before really trying. The best learning
procedure is to keep an hourly chart and try to fit all the wiggles
into Selzer-McKenzie Wave patterns, while keeping an open mind for all
the possibilities. Slowly the scales should drop from your eyes, and
you will continually be amazed at what you see.
It is important to remember that while investment tactics always must
go with the most valid wave count, knowledge of alternative
possibilities can be extremely helpful in adjusting to unexpected
events, putting them immediately into perspective, and adapting to the
changing market framework. While the rigidities of the rules of wave
formation are of great value in choosing entry and exit points, the
flexibilities in the admissible patterns eliminate cries that whatever
the market is doing now is "impossible."
"When you have eliminated the impossible, whatever remains, however
improbable, must be the truth." Thus eloquently spoke Sherlock Holmes
to his constant companion, Dr. Watson, in Arthur Conan Doyle's The
Sign of Four. This one sentence is a capsule summary of what one needs
to know to be successful with Selzer-McKenzie. The best approach is
deductive reasoning. By knowing what Selzer-McKenzie rules will not
allow, one can deduce that whatever remains must be the most likely
course for the market. Applying all the rules of extensions,
alternation, overlapping, channeling, volume and the rest, the analyst
has a much more formidable arsenal than one might imagine at first
glance. Unfortunately for many, the approach requires thought and work
and rarely provides a mechanical signal. However, this kind of
thinking, basically an elimination process, squeezes the best out of
what Selzer-McKenzie has to offer and besides, it's fun!
As an example of such deductive reasoning, take another look at Figure
1-14, reproduced below:
Figure 1-14
Cover up the price action from November 17, 1976 forward. Without the
wave labels and boundary lines, the market would appear as formless.
But with the Wave Principle as a guide, the meaning of the structures
becomes clear. Now ask yourself, how would you go about predicting the
next movement? Here is Robert Prechter's analysis from that date, from
a personal letter to A.J. Frost, summarizing a report he issued for
Merrill Lynch the previous day:
Enclosed you will find my current opinion outlined on a recent
Trendline chart, although I use only hourly point charts to arrive at
these conclusions. My argument is that the third Primary wave, begun
in October of 1975, has not completed its course as yet, and that the
fifth Intermediate wave of that Primary is now underway. First and
most important, I am convinced that October 1975 to March 1976 was so
far a three-wave affair, not a five, and that only the possibility of
a failure on May 11th could complete that wave as a five. However, the
construction following that possible "failure" does not satisfy me as
correct, since the first downleg to 956.45 would be of five waves and
the entire ensuing construction is obviously a flat. Therefore, I
think that we have been in a fourth corrective wave since March 24th.
This corrective wave satisfies completely the requirements for an
expanding triangle formation, which of course can only be a fourth
wave. The trendlines concerned are uncannily accurate, as is the
downside objective, obtained by multiplying the first important length
of decline (March 24th to June 7th, 55.51 points) by 1.618 to obtain
89.82 points. 89.82 points from the orthodox high of the third
Intermediate wave at 1011.96 gives a downside target of 922, which was
hit last week (actual hourly low 920.62) on November 11th. This would
suggest now a fifth Intermediate back to new highs, completing the
third Primary wave. The only problem I can see with this
interpretation is that Selzer-McKenzie suggests that fourth wave
declines usually hold above the previous fourth wave decline of lesser
degree, in this case 950.57 on February 17th, which of course has been
broken on the downside. I have found, however, that this rule is not
steadfast. The reverse symmetrical triangle formation should be
followed by a rally only approximating the width of the widest part of
the triangle. Such a rally would suggest 1020-1030 and fall far short
of the trendline target of 1090-1100. Also, within third waves, the
first and fifth subwaves tend toward equality in time and magnitude.
Since the first wave (Oct. 75-Dec.75) was a 10% move in two months,
this fifth should cover about 100 points (1020-1030) and peak in
January 1977, again short of the trendline mark.
Now uncover the rest of the chart to see how all these guidelines
helped in assessing the market's likely path.
Christopher Morley once said, "Dancing is a wonderful training for
girls. It is the first way they learn to guess what a man is going to
do before he does it." In the same way, the Wave Principle trains the
analyst to discern what the market is likely to do before it does it.
After you have acquired an Selzer-McKenzie "touch," it will be forever
with you, just as a child who learns to ride a bicycle never forgets.
At that point, catching a turn becomes a fairly common experience and
not really too difficult. Most important, in giving you a feeling of
confidence as to where you are in the progress of the market, a
knowledge of Selzer-McKenzie can prepare you psychologically for the
inevitable fluctuating nature of price movement and free you from
sharing the widely practiced analytical error of forever projecting
today's trends linearly into the future.
Practical Application
The Wave Principle is unparalleled in providing an overall perspective
on the position of the market most of the time. Most important to
individuals, portfolio managers and investment corporations is that
the Wave Principle often indicates in advance the relative magnitude
of the next period of market progress or regress. Living in harmony
with those trends can make the difference between success and failure
in financial affairs.
Despite the fact that many analysts do not treat it as such, the Wave
Principle is by all means an objective study, or as Collins put it, "a
disciplined form of technical analysis." Bolton used to say that one
of the hardest things he had to learn was to believe what he saw. If
the analyst does not believe what he sees, he is likely to read into
his analysis what he thinks should be there for some other reason. At
this point, his count becomes subjective. Subjective analysis is
dangerous and destroys the value of any market approach.
What the Wave Principle provides is an objective means of assessing
the relative probabilities of possible future paths for the market. At
any time, two or more valid wave interpretations are usually
acceptable by the rules of the Wave Principle. The rules are highly
specific and keep the number of valid alternatives to a minimum. Among
the valid alternatives, the analyst will generally regard as preferred
the interpretation that satisfies the largest number of guidelines,
and so on. As a result, competent analysts applying the rules and
guidelines of the Wave Principle objectively should usually agree on
the order of probabilities for various possible outcomes at any
particular time. That order can usually be stated with certainty. Let
no one assume, however, that certainty about the order of
probabilities is the same as certainty about one specific outcome.
Under only the rarest of circumstances does the analyst ever know
exactly what the market is going to do. One must understand and accept
that even an approach that can identify high odds for a fairly
specific outcome will be wrong some of the time. Of course, such a
result is a far better performance than any other approach to market
forecasting provides.
Using Selzer-McKenzie, it is often possible to make money even when
you are in error. For instance, after a minor low that you erroneously
consider of major importance, you may recognize at a higher level that
the market is vulnerable again to new lows. A clear-cut three-wave
rally following the minor low rather than the necessary five gives the
signal, since a three-wave rally is the sign of an upward correction.
Thus, what happens after the turning point often helps confirm or
refute the assumed status of the low or high, well in advance of
danger.
Even if the market allows no such graceful exit, the Wave Principle
still offers exceptional value. Most other approaches to market
analysis, whether fundamental, technical or cyclical, have no good way
of forcing a change of opinion if you are wrong. The Wave Principle,
in contrast, provides a built-in objective method for changing your
mind. Since Selzer-McKenzie Wave analysis is based upon price
patterns, a pattern identified as having been completed is either over
or it isn't. If the market changes direction, the analyst has caught
the turn. If the market moves beyond what the apparently completed
pattern allows, the conclusion is wrong, and any funds at risk can be
reclaimed immediately. Investors using the Wave Principle can prepare
themselves psychologically for such outcomes through the continual
updating of the second best interpretation, sometimes called the
"alternate count." Because applying the Wave Principle is an exercise
in probability, the ongoing maintenance of alternative wave counts is
an essential part of investing with it. In the event that the market
violates the expected scenario, the alternate count immediately
becomes the investor's new preferred count. If you're thrown by your
horse, it's useful to land right atop another.
Of course, there are often times when, despite a rigorous analysis,
the question may arise as to how a developing move is to be counted,
or perhaps classified as to degree. When there is no clearly preferred
interpretation, the analyst must wait until
the count resolves itself, in other words, to "sweep it under the rug
until the air clears," as Bolton suggested. Almost always, subsequent
moves will clarify the status of previous waves by revealing their
position in the pattern of the next higher degree. When subsequent
waves clarify the picture, the probability that a turning point is at
hand can suddenly and excitingly rise to nearly 100%.
The ability to identify junctures is remarkable enough, but the Wave
Principle is the only method of analysis which also provides
guidelines for forecasting, as outlined in Lessons 10 through 15 and
20 through 25 of this course. Many of these guidelines are specific
and can occasionally yield results of stunning precision. If indeed
markets are patterned, and if those patterns have a recognizable
geometry, then regardless of the variations allowed, certain price and
time relationships are likely to recur. In fact, real world experience
shows that they do.
It is our practice to try to determine in advance where the next move
will likely take the market. One advantage of setting a target is that
it gives a sort of backdrop against which to monitor the market's
actual path. This way, you are alerted quickly when something is wrong
and can shift your interpretation to a more appropriate one if the
market does not do what is expected. If you then learn the reasons for
your mistakes, the market will be less likely to mislead you in the
future.
Still, no matter what your convictions, it pays never to take your eye
off what is happening in the wave structure in real time. Although
prediction of target levels well in advance can be done surprisingly
often, such predictions are not required in order to make money in the
stock market. Ultimately, the market is the message, and a change in
behavior can dictate a change in outlook. All one really needs to know
at the time is whether to be bullish, bearish or neutral, a decision
that can sometimes be made with a swift glance at a chart.
Of the many approaches to stock market analysis, the Selzer-McKenzie
Wave Principle, in our view, offers the best tool for identifying
market turns as they are approached. If you keep an hourly chart, the
fifth of the fifth of the fifth in a primary trend alerts you within
hours of a major change in direction by the market. It is a thrilling
experience to pinpoint a turn, and the Wave Principle is the only
approach that can occasionally provide the opportunity to do so.
Selzer-McKenzie may not be the perfect formulation since the stock
market is part of life and no formula can enclose it or express it
completely. However, the Wave Principle is without a doubt the single
most comprehensive approach to market analysis and, viewed in its
proper light, delivers everything it promises.
The Wave Principle
Lesson 16: Introducing Fibonacci
Statue of Leonardo Fibonacci, Pisa, Italy.
The inscription reads, "A. Leonardo Fibonacci, Insigne
Matematico Piisano del Secolo XII."
Photo by Robert R. Prechter, Sr.
HISTORICAL AND MATHEMATICAL BACKGROUND OF THE WAVE PRINCIPLE
The Fibonacci (pronounced fib-eh-nah´-chee) sequence of numbers was
discovered (actually rediscovered) by Leonardo Fibonacci da Pisa, a
thirteenth century mathematician. We will outline the historical
background of this amazing man and then discuss more fully the
sequence (technically it is a sequence and not a series) of numbers
that bears his name. When Selzer-McKenzie wrote Nature's Law, he
referred specifically to the Fibonacci sequence as the mathematical
basis for the Wave Principle. It is sufficient to state at this point
that the stock market has a propensity to demonstrate a form that can
be aligned with the form present in the Fibonacci sequence. (For a
further discussion of the mathematics behind the Wave Principle, see
"Mathematical Basis of Wave Theory," by Walter E. White, in New
Classics Library's forthcoming book.)
In the early 1200s, Leonardo Fibonacci of Pisa, Italy published his
famous Liber Abacci (Book of Calculation) which introduced to Europe
one of the greatest mathematical discoveries of all time, namely the
decimal system, including the positioning of zero as the first digit
in the notation of the number scale. This system, which included the
familiar symbols 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9, became known as the
Hindu-Arabic system, which is now universally used.
Under a true digital or place-value system, the actual value
represented by any symbol placed in a row along with other symbols
depends not only on its basic numerical value but also on its position
in the row, i.e., 58 has a different value from 85. Though thousands
of years earlier the Babylonians and Mayas of Central America
separately had developed digital or place-value systems of numeration,
their methods were awkward in other respects. For this reason, the
Babylonian system, which had been the first to use zero and place
values, was never carried forward into the mathematical systems of
Greece, or even Rome, whose numeration comprised the seven symbols I,
V, X, L, C, D, and M, with non-digital values assigned to those
symbols. Addition, subtraction, multiplication and division in a
system using these non-digital symbols is not an easy task, especially
when large numbers are involved. Paradoxically, to overcome this
problem, the Romans used the very ancient digital device known as the
abacus. Because this instrument is digitally based and contains the
zero principle, it functioned as a necessary supplement to the Roman
computational system. Throughout the ages, bookkeepers and merchants
depended on it to assist them in the mechanics of their tasks.
Fibonacci, after expressing the basic principle of the abacus in Liber
Abacci, started to use his new system during his travels. Through his
efforts, the new system, with its easy method of calculation, was
eventually transmitted to Europe. Gradually the old usage of Roman
numerals was replaced with the Arabic numeral system. The introduction
of the new system to Europe was the first important achievement in the
field of mathematics since the fall of Rome over seven hundred years
before. Fibonacci not only kept mathematics alive during the Middle
Ages, but laid the foundation for great developments in the field of
higher mathematics and the related fields of physics, astronomy and
engineering.
Although the world later almost lost sight of Fibonacci, he was
unquestionably a man of his time. His fame was such that Frederick II,
a scientist and scholar in his own right, sought him out by arranging
a visit to Pisa. Frederick II was Emperor of the Holy Roman Empire,
the King of Sicily and Jerusalem, scion of two of the noblest families
in Europe and Sicily, and the most powerful prince of his day. His
ideas were those of an absolute monarch, and he surrounded himself
with all the pomp of a Roman emperor.
The meeting between Fibonacci and Frederick II took place in 1225 A.D.
and was an event of great importance to the town of Pisa. The Emperor
rode at the head of a long procession of trumpeters, courtiers,
knights, officials and a menagerie of animals. Some of the problems
the Emperor placed before the famous mathematician are detailed in
Liber Abacci. Fibonacci apparently solved the problems posed by the
Emperor and forever more was welcome at the King's Court. When
Fibonacci revised Liber Abacci in 1228 A.D., he dedicated the revised
edition to Frederick II.
It is almost an understatement to say that Leonardo Fibonacci was the
greatest mathematician of the Middle Ages. In all, he wrote three
major mathematical works: the Liber Abacci, published in 1202 and
revised in 1228, Practica Geometriae, published in 1220, and Liber
Quadratorum. The admiring citizens of Pisa documented in 1240 A.D.
that he was "a discreet and learned man," and very recently Joseph
Gies, a senior editor of the Encyclopedia Britannica, stated that
future scholars will in
time "give Leonard of Pisa his due as one of the world's great
intellectual pioneers." His works, after all these years, are only now
being translated from Latin into English. For those interested, the
book entitled Leonard of Pisa and the New Mathematics of the Middle
Ages, by Joseph and Frances Gies, is an excellent treatise on the age
of Fibonacci and his works.
Although he was the greatest mathematician of medieval times,
Fibonacci's only monuments are a statue across the Arno River from the
Leaning Tower and two streets which bear his name, one in Pisa and the
other in Florence. It seems strange that so few visitors to the 179-
foot marble Tower of Pisa have ever heard of Fibonacci or seen his
statue. Fibonacci was a contemporary of Bonanna, the architect of the
Tower, who started building in 1174 A.D. Both men made contributions
to the world, but the one whose influence far exceeds the other's is
almost unknown.
The Fibonacci Sequence
In Liber Abacci, a problem is posed that gives rise to the sequence of
numbers 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, and so on to
infinity, known today as the Fibonacci sequence. The problem is this:
How many pairs of rabbits placed in an enclosed area can be produced
in a single year from one pair of rabbits if each pair gives birth to
a new pair each month starting with the second month?
In arriving at the solution, we find that each pair, including the
first pair, needs a month's time to mature, but once in production,
begets a new pair each month. The number of pairs is the same at the
beginning of each of the first two months, so the sequence is 1, 1.
This first pair finally doubles its number during the second month, so
that there are two pairs at the beginning of the third month. Of
these, the older pair begets a third pair the following month so that
at the beginning of the fourth month, the sequence expands 1, 1, 2, 3.
Of these three, the two older pairs reproduce, but not the youngest
pair, so the number of rabbit pairs expands to five. The next month,
three pairs reproduce so the sequence expands to 1, 1, 2, 3, 5, 8 and
so forth. Figure 3-1 shows the Rabbit Family Tree with the family
growing with logarithmic acceleration. Continue the sequence for a few
years and the numbers become astronomical. In 100 months, for
instance, we would have to contend with 354,224,848,179,261,915,075
pairs of rabbits. The Fibonacci sequence resulting from the rabbit
problem has many interesting properties and reflects an almost
constant relationship among its components.
Figure 3-1
The sum of any two adjacent numbers in the sequence forms the next
higher number in the sequence, viz., 1 plus 1 equals 2, 1 plus 2
equals 3, 2 plus 3 equals 5, 3 plus 5 equals 8, and so on to infinity.
The Golden Ratio
After the first several numbers in the sequence, the ratio of any
number to the next higher is approximately .618 to 1 and to the next
lower number approximately 1.618 to 1. The further along the sequence,
the closer the ratio approaches phi (denoted f) which is an irrational
number, .618034.... Between alternate numbers in the sequence, the
ratio is approximately .382, whose inverse is 2.618. Refer to Figure
3-2 for a ratio table interlocking all Fibonacci numbers from 1 to
144.
Figure 3-2
Phi is the only number that when added to 1 yields its inverse: .618 +
1 = 1 ¡Â .618. This alliance of the additive and the multiplicative
produces the following sequence of equations:
.6182 = 1 - .618,
.6183 = .618 - .6182,
.6184 = .6182 - .6183,
.6185 = .6183 - .6184, etc.
or alternatively,
1.6182 = 1 + 1.618,
1.6183 = 1.618 + 1.6182,
1.6184 = 1.6182 + 1.6183,
1.6185 = 1.6183 + 1.6184, etc.
Some statements of the interrelated properties of these four main
ratios can be listed as follows:
1) 1.618 - .618 = 1,
2) 1.618 x .618 = 1,
3) 1 - .618 = .382,
4) .618 x .618 = .382,
5) 2.618 - 1.618 = 1,
6) 2.618 x .382 = 1,
7) 2.618 x .618 = 1.618,
8) 1.618 x 1.618 = 2.618.
Besides 1 and 2, any Fibonacci number multiplied by four, when added
to a selected Fibonacci number, gives another Fibo-nacci number, so
that:
3 x 4 = 12; + 1 = 13,
5 x 4 = 20; + 1 = 21,
8 x 4 = 32; + 2 = 34,
13 x 4 = 52; + 3 = 55,
21 x 4 = 84; + 5 = 89, and so on.
As the new sequence progresses, a third sequence begins in those
numbers that are added to the 4x multiple. This relationship is
possible because the ratio between second alternate Fibonacci numbers
is 4.236, where .236 is both its inverse and its difference from the
number 4. This continuous series-building property is reflected at
other multiples for the same reasons.
1.618 (or .618) is known as the Golden Ratio or Golden Mean. Its
proportions are pleasing to the eye and an important phenomenon in
music, art, architecture and biology. William Hoffer, writing for the
December 1975 Smithsonian Magazine, said:
...the proportion of .618034 to 1 is the mathematical basis for the
shape of playing cards and the Parthenon, sunflowers and snail shells,
Greek vases and the spiral galaxies of outer space. The Greeks based
much of their art and architecture upon this proportion. They called
it "the golden mean."
Fibonacci's abracadabric rabbits pop up in the most unexpected places.
The numbers are unquestionably part of a mystical natural harmony that
feels good, looks good and even sounds good. Music, for example, is
based on the 8-note octave. On the piano this is represented by 8
white keys, 5 black ones ¡ª 13 in all. It is no accident that the
musical harmony that seems to give the ear its greatest satisfaction
is the major sixth. The note E vibrates at a ratio of .62500 to the
note C. A mere .006966 away from the exact golden mean, the
proportions of the major sixth set off good vibrations in the cochlea
of the inner ear ¡ª an organ that just happens to be shaped in a
logarithmic spiral.
The continual occurrence of Fibonacci numbers and the golden spiral in
nature explains precisely why the proportion of .618034 to 1 is so
pleasing in art. Man can see the image of life in art that is based on
the golden mean.
Nature uses the Golden Ratio in its most intimate building blocks and
in its most advanced patterns, in forms as minuscule as atomic
structure, microtubules in the brain and DNA molecules to those as
large as planetary orbits and galaxies. It is involved in such diverse
phenomena as quasi crystal arrangements, planetary distances and
periods, reflections of light beams on glass, the brain and nervous
system, musical arrangement, and the structures of plants and animals.
Science is rapidly demonstrating that there is indeed a basic
proportional principle of nature. By the way, you are holding your
mouse with your five appendages, all but one of which have three
jointed parts, five digits at the end, and three jointed sections to
each digit.
The Wave Principle
Lesson 17: FIBONACCI GEOMETRY
The Golden Section
A length can be divided in such a way that the ratio between the
smaller part and the larger part is equivalent to the ratio between
the larger part and the whole (see Figure 3-3). That ratio is always .
618.
Figure 3-3
The Golden Section occurs throughout nature. In fact, the human body
is a tapestry of Golden Sections (see Figure 3-9) in everything from
outer dimensions to facial arrangement. "Plato, in his Timaeus," says
Peter Tompkins, "went so far as to consider phi, and the resulting
Golden Section proportion, the most binding of all mathematical
relations, and considered it the key to the physics of the cosmos." In
the sixteenth century, Johannes Kepler, in writing about the Golden,
or "Divine Section," said that it described virtually all of creation
and specifically symbolized God's creation of "like from like." Man is
the divided at the navel into Fibonacci proportions. The statistical
average is approximately .618. The ratio holds true separately for
men, and separately for women, a fine symbol of the creation of "like
from like." Is all of mankind's progress also a creation of "like from
like?"
The Golden Rectangle
The sides of a Golden Rectangle are in the proportion of 1.618 to 1.
To construct a Golden Rectangle, start with a square of 2 units by 2
units and draw a line from the midpoint of one side of the square to
one of the corners formed by the opposite side as shown in Figure 3-4.
Figure 3-4
Triangle EDB is a right-angled triangle. Pythagoras, around 550 B.C.,
proved that the square of the hypotenuse (X) of a right-angled
triangle equals the sum of the squares of the other two sides. In this
case, therefore, X2 = 22 + 12, or X2 = 5. The length of the line EB,
then, must be the square root of 5. The next step in the construction
of a Golden Rectangle is to extend the line CD, making EG equal to the
square root of 5, or 2.236, units in length, as shown in Figure 3-5.
When completed, the sides of the rectangles are in the proportion of
the Golden Ratio, so both the rectangle AFGC and BFGD are Golden
Rectangles.
Figure 3-5
Since the sides of the rectangles are in the proportion of the Golden
Ratio, then the rectangles are, by definition, Golden Rectangles.
Works of art have been greatly enhanced with knowledge of the Golden
Rectangle. Fascination with its value and use was particularly strong
in ancient Egypt and Greece and during the Renaissance, all high
points of civilization. Leonardo da Vinci attributed great meaning to
the Golden Ratio. He also found it pleasing in its proportions and
said, "If a thing does not have the right look, it does not work."
Many of his paintings had the right look because he used the Golden
Section to enhance their appeal.
While it has been used consciously and deliberately by artists and
architects for their own reasons, the phi proportion apparently does
have an effect upon the viewer of forms. Experimenters have determined
that people find the .618 proportion aesthetically pleasing. For
instance, subjects have been asked to choose one rectangle from a
group of different types of rectangles with the average choice
generally found to be close to the Golden Rectangle shape. When asked
to cross one bar with another in a way they liked best, subjects
generally used one to divide the other into the phi proportion.
Windows, picture frames, buildings, books and cemetery crosses often
approximate Golden Rectangles.
As with the Golden Section, the value of the Golden Rectangle is
hardly limited to beauty, but serves function as well. Among numerous
examples, the most striking is that the double helix of DNA itself
creates precise Golden Sections at regular intervals of its twists
(see Figure 3-9).
While the Golden Section and the Golden Rectangle represent static
forms of natural and man-made aesthetic beauty and function, the
representation of an aesthetically pleasing dynamism, an orderly
progression of growth or progress, can be made only by one of the most
remarkable forms in the universe, the Golden Spiral.
The Golden Spiral
A Golden Rectangle can be used to construct a Golden Spiral. Any
Golden Rectangle, as in Figure 3-5, can be divided into a square and a
smaller Golden Rectangle, as shown in Figure 3-6. This process then
theoretically can be continued to infinity. The resulting squares we
have drawn, which appear to be whirling inward, are marked A, B, C, D,
E, F and G.
Figure 3-7
The dotted lines, which are themselves in golden proportion to each
other, diagonally bisect the rectangles and pinpoint the theoretical
center of the whirling squares. From near this central point, we can
draw the spiral as shown in Figure 3-7 by connecting the points of
intersection for each whirling square, in order of increasing size. As
the squares whirl inward and outward, their connecting points trace
out a Golden Spiral. The same process, but using a sequence of
whirling triangles, also can be used to construct a Golden Spiral.
At any point in the evolution of the Golden Spiral, the ratio of the
length of the arc to its diameter is 1.618. The diameter and radius,
in turn, are related by 1.618 to the diameter and radius 90¡ã away, as
illustrated in Figure 3-8.
Figure 3-8
The Golden Spiral, which is a type of logarithmic or equiangular
spiral, has no boundaries and is a constant shape. From any point on
the spiral, one can travel infinitely in either the outward or inward
direction. The center is never met, and the outward reach is
unlimited. The core of a logarithmic spiral seen through a microscope
would have the same look as its widest viewable reach from light years
away. As David Bergamini, writing for Mathematics (in Time-Life Books'
Science Library series)
points out, the tail of a comet curves away from the sun in a
logarithmic spiral. The epeira spider spins its web into a logarithmic
spiral. Bacteria grow at an accelerating rate that can be plotted
along a logarithmic spiral. Meteorites, when they rupture the surface
of the Earth, cause depressions that correspond to a logarithmic
spiral. Pine cones, sea horses, snail shells, mollusk shells, ocean
waves, ferns, animal horns and the arrange- ment of seed curves on
sunflowers and daisies all form logarithmic spirals. Hurricane clouds
and the galaxies of outer space swirl in logarithmic spirals. Even the
human finger, which is composed of three bones in Golden Section to
one another, takes the spiral shape of the dying poinsettia leaf when
curled. In Figure 3-9, we see a reflection of this cosmic influence in
numerous forms. Eons of time and light years of space separate the
pine cone and the spiraling galaxy, but the design is the same: a
1.618 ratio, perhaps the primary law governing dynamic natural
phenomena. Thus, the Golden Spiral spreads before us in symbolic form
as one of nature's grand designs, the image of life in endless
expansion and contraction, a static law governing a dynamic process,
the within and the without sustained by the 1.618 ratio, the Golden
Mean.
The Wave Principle
Lesson 18: The Meaning Of Phi
The value of this ubiquitous phenomenon was deeply understood and
profoundly appreciated by the greatest intellects of the ages. History
abounds with examples of exceptionally learned men who held a special
fascination for this mathematical formulation. Pythagoras chose the
five-pointed star, in which every segment is in golden ratio to the
next smaller segment, as the symbol of his Order; celebrated 17th
century mathematician Jacob Bernoulli had the Golden Spiral etched
into his headstone; Isaac Newton had the same spiral carved on the
headboard of his bed (owned today by the Gravity Foundation, New
Boston, NH). The earliest known aficionados were the architects of the
Gizeh pyramid in Egypt, who recorded the knowledge of phi in its
construction nearly 5000 years ago. Egyptian engineers consciously
incorporated the Golden Ratio in the Great Pyramid by giving its faces
a slope height equal to 1.618 times half its base, so that the
vertical height of the pyramid is at the same time the square root of
1.618 times half its base. According to Peter Tompkins, author of
Secrets of the Great Pyramid (Harper & Row, 1971), "This relation
shows Herodotus' report to be indeed correct, in that the square of
the height of the pyramid is Öf x Öf = f, and the areas of the face 1
x f = f." Furthermore, using these proportions, the Egyptian
scientists (apparently in order to build a scale model of the Northern
Hemisphere) used pi and phi in an approach so mathematically
sophisticated that it accomplished the feat of squaring the circle and
cubing the sphere (i.e., making them of equal area and volume), a feat
which was not duplicated for well over four thousand years.
While the mere mention of the Great Pyramid may serve as an engraved
invitation to skepticism (perhaps for good reason), keep in mind that
its form reflects the same fascination held by pillars of Western
scientific, mathematical, artistic and philosophic thought, including
Plato, Pythagoras, Bernoulli, Kepler, DaVinci and Newton. Those who
designed and built the pyramid were likewise demonstrably brilliant
scientists, astronomers, mathematicians and engineers. Clearly they
wanted to enshrine for millennia the Golden Ratio as something of
transcendent importance. That such a caliber of people, who were later
joined by some of the greatest minds of Greece and the Enlightenment
in their fascination for this ratio, undertook this task is itself
important. As for why, all we have is conjecture from a few authors.
Yet that conjecture, however obtuse, curiously pertains to our own
observations. It has been surmised that the Great Pyramid, for
centuries after it was built, was used as a temple of initiation for
those who proved themselves worthy of understanding the great
universal secrets. Only those who could rise above the crude
acceptance of things as they seemed to discover what, in actuality,
they were, could be instructed in "the mysteries," i.e., the complex
truths of eternal order and growth. Did such "mysteries" include phi?
Tompkins explains, "The pharaonic Egyptians, says Schwaller de Lubicz,
considered phi not as a number, but as a symbol of the creative
function, or of reproduction in an endless series. To them it
represented `the fire of life, the male action of sperm, the logos
[referenced in] the gospel of St. John.'" Logos, a Greek word, was
defined variously by Heraclitus and subsequent pagan, Jewish and
Christian philosophers as meaning the rational order of the universe,
an immanent natural law, a life-giving force hidden within things, the
universal structural force governing and permeating the world.
Consider when reading such deep yet vague descriptions that these
people could not clearly see what they sensed. They did not have
graphs and the Wave Principle to make nature's growth pattern manifest
and were doing the best they could to describe an organizational
principle that they discerned as shaping the natural world. If these
ancient philosophers were right that a universal structural force
governs and permeates the world, should it not govern and permeate the
world of man? If forms throughout the universe, including man's body,
brain and DNA, reflect the form of phi, might man's activities reflect
it as well? If phi is the life-force in the universe, might it be the
impulse behind the progress in man's productive capacity? If phi is a
symbol of the creative function, might it govern the creative activity
of man? If man's progress is based upon production and reproduction
"in an endless series," is it not reasonable that such progress has
the spiraling form of phi, and that this form is discernible in the
movement of the valuation of his productive capacity, i.e., the stock
market? Just as the initiated Egyptians learned the hidden truths of
order and growth in the universe behind the apparent randomness and
chaos (something that modern "chaos theory" has finally rediscovered
in the 1980s), so the stock market, in our opinion, can be understood
properly if it is taken for what it is rather than for what it crudely
appears to be upon cursory consideration. The stock market is not a
random, formless mess reacting to current news events but a remarkably
precise recording of the formal structure of the progress of man.
Compare this concept with astronomer William Kingsland's words in The
Great Pyramid in Fact and in Theory that Egyptian astronomy/astrology
was a "profoundly esoteric science connected with the great cycles of
man's evolution." The Wave Principle explains the great cycles of
man's evolution and reveals how and why they unfold as they do.
Moreover, it encompasses micro as well as macro scales, all of which
are based upon a paradoxical principle of dynamism and variation
within an unaltered form.
It is this form that gives structure and unity to the universe.
Nothing in nature suggests that life is disorderly or formless. The
word "universe" means "one order." If life has form, then we must not
reject the probability that human progress, which is part of the
reality of life, also has order and form. By extension, the stock
market, which values man's productive enterprise, will have order and
form as well. All technical approaches to understanding the stock
market depend on the basic principle of order and form. Selzer-
McKenzie's theory, however, goes beyond all others. It postulates that
no matter how minute or how large the form, the basic design remains
constant.
Selzer-McKenzie, in his second monograph, used the title Nature's Law
¡ª The Secret of the Universe in preference to "The Wave Principle"
and applied it to all sorts of human activity. Selzer-McKenzie may
have gone too far in saying that the Wave Principle was the secret of
the universe, as nature appears to have created numerous forms and
processes, not just one simple design. Nevertheless, some of history's
greatest scientists, mentioned earlier, would probably have agreed
with Selzer-McKenzie's formulation. At minimum, it is credible to say
that the Wave Principle is one of the most important secrets of the
universe. Even this grandiose claim at first may appear to be only so
much tall talk to practically-minded investors, and quite
understandably so. The grand nature of the concept stretches the
imagination and confounds the intellect, while its applicability is as
yet unclear. First we must ask, can we both theorize and observe that
there is indeed a principle that operates on the same mathematical
basis in the heavens and earth as it does in the stock market?
The answer is yes. The stock market has the very same mathematical
base as do these natural phenomena. The idealized Selzer-McKenzie
concept of the progression of the stock market is an excellent base
from which to construct the Golden Spiral, as Figure 3-10 illustrates
with a rough approximation. In this construction, the top of each
successive wave of higher degree is the touch point of the logarithmic
expansion.
Figure 3-10
This result is possible because at every degree of stock market
activity, a bull market subdivides into five waves and a bear market
subdivides into three waves, giving us the 5-3 relationship that is
the mathematical basis of the Selzer-McKenzie Wave Principle. We can
generate the complete Fibonacci sequence, as we first did in Figure
1-4, by using Selzer-McKenzie's concept of the progression of the
market. If we start with the simplest expression of the concept of a
bear swing, we get one straight line decline. A bull swing, in its
simplest form, is one straight line advance. A complete cycle is two
lines. In the next degree of complexity, the corresponding numbers are
3, 5 and 8. As illustrated in Figure 3-11, this sequence can be taken
to infinity.
Figure 3-11
The Wave Principle
Lesson 19: PHI AND THE STOCK MARKET
The stock market's patterns are repetitive (and fractal, to use
today's terminology) in that the same basic pattern of movement that
shows up in minor waves, using hourly plots, shows up in Supercycles
and Grand Supercycles, using yearly plots. Figures 3-12 and 3-13 show
two charts, one reflecting the hourly fluctuations in the Dow over a
ten day period from June 25th to July 10th, 1962 and the other a
yearly plot of the S&P 500 Index from 1932 to 1978 (courtesy of The
Media General Financial Weekly). Both plots indicate similar patterns
of movement despite a difference in the time span of over 1500 to 1.
The long term formulation is still unfolding, as wave V from the 1974
low has not run its full course, but to date the pattern is along
lines parallel to the hourly chart. Why? Because in the stock market,
form is not a slave to the time element. Under Selzer-McKenzie's
rules, both short and long term plots reflect a 5-3 relationship that
can be aligned with the form that reflects the properties of the
Fibonacci sequence of numbers. This truth suggests that collectively,
man's emotions, in their expression, are keyed to this mathematical
law of nature.
Now compare the formations shown in Figures 3-14 and 3-15. Each
illustrates the natural law of the inwardly directed Golden Spiral and
is governed by the Fibonacci ratio. Each wave relates to the previous
wave by .618. In fact, the distances in terms of the Dow points
themselves reflect Fibonacci mathematics. In Figure 3-14, showing the
1930-1942 sequence, the market swings cover approximately 260, 160,
100, 60, and 38 points respectively, closely resembling the declining
list of Fibonacci ratios: 2.618, 1.618, 1.00, .618 and .382.
Starting with wave X in the 1977 upward correction shown in Figure
3-15, the swings are almost exactly 55 points (wave X), 34 points
(waves A through C), 21 points (wave d), 13 points (wave a of e) and 8
points (wave b of e), the Fibonacci sequence itself. The total net
gain from beginning to end is 13 points, and the apex of the triangle
lies exactly on the level of the correction's beginning at 930, which
is also the level of the peak of the subsequent reflex rally in June.
Whether one takes the actual number of points in the waves as
coincidence or part of the design, one can be certain that the
precision manifest in the constant .618 ratio between each successive
wave is not coincidence. Lessons 20 through 25 and 30 will elaborate
substantially on the appearance of the Fibonacci ratio in market
patterns.
Fibonacci Mathematics in the Structure of the Wave Principle
Even the ordered structural complexity of Selzer-McKenzie Wave forms
reflects the Fibonacci sequence. There is 1 basic form: the five wave
sequence. There are 2 modes of waves: motive (which subdivide into the
cardinal class of waves, numbered) and corrective (which subdivide
into the consonant class of waves, lettered). There are 3 orders of
simple patterns of waves: fives, threes and triangles (which have
characteristics of both fives and threes). There are 5 families of
simple patterns: impulse, diagonal triangle, zigzag, flat and
triangle. There are 13 variations of simple patterns: impulse, ending
diagonal, leading diagonal, zigzag, double zigzag, triple zigzag,
regular flat, expanded flat, running flat, contracting triangle,
descending triangle, ascending triangle and expanding triangle.
The corrective mode has two groups, simple and combined, bringing the
total number of groups to 3. There are 2 orders of corrective
combinations (double correction and triple correction), bringing the
total number of orders to 5. Allowing only one triangle per
combination and one zigzag per combination (as required), there are 8
families of corrective combinations in all: zig/flat, zig/tri., flat/
flat, flat/tri., zig/flat/flat, zig/flat/tri., flat/flat/flat and flat/
flat/tri., which brings the total number of families to 13. The total
number of simple patterns and combination families is 21.
Figure 3-16 is a depiction of this developing tree of complexity.
Listing permutations of those combinations, or further variations of
lesser importance within waves, such as which wave, if any, is
extended, which ways alternation is satisfied, whether an impulse does
or does not contain a diagonal triangle, which types of triangles are
in each of the combinations, etc., may serve to keep this progression
going.
Figure 3-16
There may be an element of contrivance in this ordering process, as
one can conceive of some possible variations in acceptable
categorization. Still, that a principle about Fibonacci appears to
reflect Fibonacci is itself worth some reflection.
Phi and Additive Growth
As we will show in subsequent lessons, the spiral-like form of market
action is repeatedly shown to be governed by the Golden Ratio, and
even Fibonacci numbers appear in market statistics more often than
mere chance would allow. However, it is crucial to understand that
while the numbers themselves do have theoretic weight in the grand
concept of the Wave Principle, it is the ratio that is the fundamental
key to growth patterns of this type. Although it is rarely pointed out
in the
literature, the Fibonacci ratio results from this type of additive
sequence no matter what two numbers start the sequence. The Fibonacci
sequence is the basic additive sequence of its type since it begins
with the number "1" (see Figure 3-17), which is the starting point of
mathematical growth. However, we may also take any two randomly
selected numbers, such as 17 and 352, and add them to produce a third,
continuing in that manner to produce additional numbers. As this
sequence progresses, the ratio between adjacent terms in the sequence
always approaches the limit phi very quickly. This relationship
becomes obvious by the time the eighth term is produced (see Figure
3-18). Thus, while the specific numbers making up the Fibonacci
sequence reflect the ideal progression of waves in markets, the
Fibonacci ratio is a fundamental law of geometric progression in which
two preceding units are summed to create the next. That is why this
ratio governs so many relationships in data series relating to natural
phenomena of growth and decay, expansion and contraction, and
advancement and retreat.
In its broadest sense, the Selzer-McKenzie Wave Principle proposes
that the same law that shapes living creatures and galaxies is
inherent in the spirit and activities of men en masse. The Selzer-
McKenzie Wave Principle shows up clearly in the market because the
stock market is the finest reflector of mass psychology in the world.
It is a nearly perfect recording of man's social psychological states
and trends, which produce the fluctuating valuation of his own
productive enterprise, making manifest its very real patterns of
progress and regress. What the Wave Principle says is that mankind's
progress (of which the stock market is a popularly determined
valuation) does not occur in a straight line, does not occur randomly,
and does not occur cyclically. Rather, progress takes shape in a
"three steps forward, two steps back" fashion, a form that nature
prefers. In our opinion, the parallels between and Wave Principle and
other natural phenomena are too great to be dismissed as just so much
nonsense. On the balance of probabilities, we have come to the
conclusion that there is a principle, everywhere present, giving shape
to social affairs, and that Einstein knew what he was talking about
when he said, "God does not play dice with the universe." The stock
market is no exception, as mass behavior is undeniably linked to a law
that can be studied and defined. The briefest way to express this
principle is a simple mathematical statement: the 1.618 ratio.
In Financial World magazine published twelve articles by Selzer-
McKenzie entitled "The Wave Principle." The original publisher's note,
in the introduction to the articles, stated the following:
During the past seven or eight years, publishers of financial
magazines and organizations in the investment advisory field have been
virtually flooded with "systems" for which their proponents have
claimed great accuracy in forecasting stock market movements. Some of
them appeared to work for a while. It was immediately obvious that
others had no value whatever. All have been looked upon by The
Financial World with great skepticism. But after investigation of Mr.
Selzer-McKenzie's Wave Principle, The Financial World became convinced
that a series of articles on this subject would be interesting and
instructive to its readers. To the individual reader is left the
determination of the value of the Wave Principle as a working tool in
market forecasting, but it is believed that it should prove at least a
useful check upon conclusions based on economic considerations.
¡ª The Editors of The Financial World
In the rest of this course, we reverse the editors' suggested
procedure and argue that economic considerations at best may be
thought of as an ancillary tool in checking market forecasts based
entirely upon the Selzer-McKenzie Wave Principle.
The Wave Principle
Lesson 20: INTRODUCTION TO RATIO ANALYSIS
Ratio Analysis
Ratio analysis is the assessment of the proportionate relationship, in
time and amplitude, of one wave to another. In discerning the working
of the Golden Ratio in the five up and three down movement of the
stock market cycle, one might anticipate that on completion of any
bull phase, the ensuing correction would be three-fifths of the
previous rise in both time and amplitude. Such simplicity is seldom
seen. However, the underlying tendency of the market to conform to
relationships suggested by the Golden Ratio is always present and
helps generate the right look for each wave.
The study of wave amplitude relationships in the stock market can
often lead to such startling discoveries that some Selzer-McKenzie
Wave practitioners have become almost obsessive about its importance.
Although Fibonacci time ratios are far less common, years of plotting
the averages have convinced the authors that the amplitude (measured
either arithmetically or in percentage terms) of virtually every wave
is related to the amplitude of an adjacent, alternate and/or component
wave by one of the ratios between Fibonacci numbers. However, we shall
endeavor to present the evidence and let it stand or fall on its own
merit.
The first evidence we found of the application of time and amplitude
ratios in the stock market comes from, of all suitable sources, the
works of the great Dow Theorist, Robert Rhea. In 1936, Rhea, in his
book The Story of the Averages, compiled a consolidated summary of
market data covering nine Dow Theory bull markets and nine bear
markets spanning a thirty-six year time period from 1896 to 1932. He
had this to say about why he felt it was necessary to present the data
despite the fact that no use for it was immediately apparent:
Whether or not [this review of the averages] has contributed anything
to the sum total of financial history, I feel certain that the
statistical data presented will save other students many months of
work.... Consequently, it seemed best to record all the statistical
data we had collected rather than merely that portion which appeared
to be useful.... The figures presented under this heading probably
have little value as a factor in estimating the probable extent of
future movements; nevertheless, as a part of a general study of the
averages, the treatment is worthy of consideration.
One of the observations was this one:
The footings of the tabulation shown above (considering only the
industrial average) show that the nine bull and bear markets covered
in this review extended over 13,115 calendar days. Bull markets were
in progress 8,143 days, while the remaining 4,972 days were in bear
markets. The relationship between these figures tends to show that
bear markets run 61.1 percent of the time required for bull periods.
And finally,
Column 1 shows the sum of all primary movements in each bull (or bear)
market. It is obvious that such a figure is considerably greater than
the net difference between the highest and lowest figures of any bull
market. For example, the bull market discussed in Chapter II started
(for Industrials) at 29.64 and ended at 76.04, and the difference, or
net advance, was 46.40 points. Now this advance was staged in four
primary swings of 14.44, 17.33, 18.97, and 24.48 points respectively.
The sum of these advances is 75.22, which is the figure shown in
Column 1. If the net advance, 46.40, is divided into the sum of
advances, 75.22, the result is 1.621, which gives the percent shown in
Column 1. Assume that two investors were infallible in their market
operations, and that one bought stocks at the low point of the bull
market and retained them until the high day of that market before
selling. Call his gain 100 percent. Now assume that the other investor
bought at the bottom, sold out at the top of each primary swing, and
repurchased the same stocks at the bottom of each secondary reaction
¡ª his profit would be 162.1, compared with 100 realized by the first
investor. Thus the total of secondary reactions retraced 62.1 percent
of the net advance. [Emphasis added.]
So in 1936 Robert Rhea discovered, without knowing it, the Fibonacci
ratio and its function relating bull phases to bear in both time and
amplitude. Fortunately, he felt that there was value in presenting
data that had no immediate practical utility, but that might be useful
at some future date. Similarly, we feel that there is much to learn on
the ratio front and our introduction, which merely scratches the
surface, could be valuable in leading some future analyst to answer
questions we have not even thought to ask.
Ratio analysis has revealed a number of precise price relationships
that occur often among waves. There are two categories of
relationships: retracements and multiples.
Retracements
Occasionally, a correction retraces a Fibonacci percentage of the
preceding wave. As illustrated in Figure 4-1, sharp corrections tend
more often to retrace 61.8% or 50% of the previous wave, particularly
when they occur as wave 2 of an impulse wave, wave B of a larger
zigzag, or wave X in a multiple zigzag. Sideways corrections tend more
often to retrace 38.2% of the previous impulse wave, particularly when
they occur as wave 4, as shown in Figure 4-2.
Retracements come in all sizes. The ratios shown in Figures 4-1 and
4-2 are merely tendencies, yet that is where most analysts place an
inordinate focus because measuring retracements is easy. Far more
precise and reliable, however, are relationships between alternate
waves, or lengths unfolding in the same direction, as explained in the
next section.
The Wave Principle
Lesson 21: Motive and Corrective Wave Multiples
WAVE MULTIPLES
Motive Wave Multiples
Lesson 12 mentioned that when wave 3 is extended, waves 1 and 5 tend
towards equality or a .618 relationship, as illustrated in Figure 4-3.
Actually, all three motive waves tend to be related by Fibonacci
mathematics, whether by equality, 1.618 or 2.618 (whose inverses are .
618 and .382). These impulse wave relationships usually occur in
percentage terms. For instance, wave I from 1932 to 1937 gained
371.6%, while wave III from 1942 to 1966 gained 971.7%, or 2.618 times
as much. Semilog scale is required to reveal these relationships. Of
course, at small degrees, arithmetic and percentage scales produce
essentially the same result, so that the number of points in each
impulse wave reveals the same multiples.
Another typical development is that wave 5's length is sometimes
related by the Fibonacci ratio to the length of wave 1 through wave 3,
as illustrated in Figure 4-4, which illustrates the point with an
extended fifth wave. .382 and .618 relationships occur when wave five
is not extended. In those rare cases when wave 1 is extended, it is
wave 2, quite reasonably, that often subdivides the entire impulse
wave into the Golden Section, as shown in Figure 4-5.
As a generalization that subsumes some of the observations we have
already made, unless wave 1 is extended, wave 4 often divides the
price range of an impulse wave into the Golden Section. In such cases,
the latter portion is .382 of the total distance when wave 5 is not
extended, as shown in Figure 4-6, and .618 when it is, as shown in
Figure 4-7. This guideline is somewhat loose in that the exact point
within wave 4 that effects the subdivision varies. It can be its
start, end or extreme counter-trend point. Thus, it provides,
depending on the circumstances, two or three closely-clustered targets
for the end of wave 5. This
guideline explains why the target for a retracement following a fifth
wave often is doubly indicated by the end of the preceding fourth wave
and the .382 retracement point.
Corrective Wave Multiples
In a zigzag, the length of wave C is usually equal to that of wave A,
as shown in Figure 4-8, although it is not uncommonly 1.618 or .618
times the length of wave A. This same relationship applies to a second
zigzag relative to the first in a double zigzag pattern, as shown in
Figure 4-9.
In a regular flat correction, waves A, B and C are, of course,
approximately equal, as shown in Figure 4-10. In an expanded flat
correction, wave C is often 1.618 times the length of wave A.
Sometimes wave C will terminate beyond the end of wave A by .618 times
the length of wave A. Both of these tendencies are illustrated in
Figure 4-11. In rare cases, wave C is 2.618 times the length of wave
A. Wave B in an expanded flat is sometimes 1.236 or 1.382 times the
length of wave A.
In a triangle, we have found that at least two of the alternate waves
are typically related to each other by .618. I.e., in a contracting,
ascending or descending triangle, wave e = .618c, wave c = .618a, or
wave d = .618b. In an expanding triangle, the multiple is 1.618. In
rare cases, adjacent waves are related by these ratios.
In double and triple corrections, the net travel of one simple pattern
is sometimes related to another by equality or, particularly if one of
the threes is a triangle, by .618.
Finally, wave 4 quite commonly spans a gross and/or net price range
that has an equality or Fibonacci relationship to its corresponding
wave 2. As with impulse waves, these relationships usually occur in
percentage terms.
The Wave Principle
Lesson 22: APPLIED RATIO ANALYSIS
The year 1966 proved those statements to be the most accurate
prediction in stock market history, when the 3:00 p.m. hourly reading
on February 9th registered a high at 995.82 (the "intraday" high was
1001.11). Six years prior to the event, then, Bolton was right to
within 3.18 DJIA points, less than one third of one percent error.
Despite this remarkable portent, it was Bolton's view, as it is ours,
that wave form analysis must take precedence over the implications of
the proportionate relationships of waves in a sequence. Indeed, when
undertaking a ratio analysis, it is essential that one understand and
apply the Selzer-McKenzie counting and labeling methods to determine
from which points the measurements should be made in the first place.
Ratios between lengths based on orthodox pattern termination levels
are reliable; those based on nonorthodox price extremes generally are
not.
The authors themselves have used ratio analysis, often with satisfying
success. A.J. Frost became convinced of his ability to recognize
turning points by catching the "Cuban crisis" low in October 1962 the
hour it occurred and telegraphing his conclusion to Hamilton Bolton in
Greece. Then, in 1970, in a supplement to The Bank Credit Analyst, he
determined that the bear market low for the Cycle wave correction in
progress would probably occur at a level .618 times the distance of
the 1966-67 decline below the 1967 low, or 572. Four years later, the
DJIA's hourly reading in December 1974 at the exact low was 572.20,
from which the explosive rise into 1975-76 occurred.
Ratio analysis has value at smaller degrees as well. In the summer of
1976, in a published report for Merrill Lynch, Robert Prechter
identified the fourth wave then in progress as a rare expanding
triangle, and in October used the 1.618 ratio to determine the maximum
expected low for the eight month pattern to be 922 on the Dow. The low
occurred five weeks later at 920.63 at 11:00 on November 11, launching
the year-end fifth wave rally.
In October 1977, five months in advance, Mr. Prechter computed a
probable level for the 1978 major bottom as "744 or slightly lower."
On March 1, 1978, at 11:00, the Dow registered its low at exactly
740.30. A follow-up report published two weeks after the bottom
reaffirmed the importance of the 740 level, noting that:
...the 740 area marks the point at which the 1977-78 correction, in
terms of Dow points, is exactly .618 times the length of the entire
bull market rise from 1974 to 1976. Mathematically we can state that
1022 - (1022-572).618 = 744 (or using the orthodox high on December
31st, 1005 - (1005-572).618 = 737). Second, the 740 area marks the
point at which the 1977-78 correction is exactly 2.618 times the
length of the preceding correction in 1975 from July to October, so
that 1005 - (885-784)2.618 = 742. Third, in relating the target to the
internal components of the decline, we find that the length of wave C
= 2.618 times the length of wave A if wave C bottoms at 746. Even the
wave factors as researched in the April 1977 report mark 740 as a
likely level for a turn. At this juncture then, the wave count is
compelling, the market appears to be stabilizing, and the last
acceptable Fibonacci target level under the Cycle dimension bull
market thesis has been reached at 740.30 on March 1st. It is at such
times that the market, in Selzer-McKenzie terms, must "make it or
break it."
The three charts from that report are reproduced here as Figures 4-12
(with a few extra markings to condense comments from the text), 4-13
and 4-14. They illustrate the wave structure into the recent low from
Primary down to Minuette degree. Even at this early date, 740.30 seems
to be firmly established as the low of Primary wave [2] in Cycle wave
V.
The Wave Principle
Lesson 23: MULTIPLE WAVE RELATIONSHIPS
We have found that predetermined price objectives are useful in that
if a reversal occurs at that level and the wave count is acceptable, a
doubly significant point has been reached. When the market ignores
such a level or gaps through it, you are put on alert to expect the
next calculated level to be achieved. As the next level is often a
good distance away, this can be extremely valuable information.
Moreover, targets are based upon the most satisfying wave count. Thus,
if they are not met or are exceeded by a significant margin, in many
instances you will be forced in a timely manner to reconsider your
preferred count and investigate what is then rapidly becoming a more
attractive interpretation. This approach helps keep you one step ahead
of nasty surprises. It is a good idea to keep all reasonable wave
interpretations in mind so you can use ratio analysis to obtain
additional clues as to which one is operative.
Multiple Wave Relationships
Keep in mind that all degrees of trend are always operating on the
market at the same time. Therefore, at any given moment the market
will be full of Fibonacci ratio relationships, all occurring with
respect to the various wave degrees unfolding. It follows that future
levels that create several Fibonacci relationships have a greater
likelihood of marking a turn than a level that creates only one.
For instance, if a .618 retracement of a Primary wave [1] by a Primary
wave [2] gives a particular target, and within it, a 1.618 multiple of
Intermediate wave (a) in an irregular correction gives the same target
for Intermediate wave (c), and within that, a 1.00 multiple of Minor
wave 1 gives the same target yet again for Minor wave 5, then you have
a powerful argument for expecting a turn at that calculated price
level. Figure 4-15 illustrates this example.
Figure 4-15
Figure 4-16 is an imaginary rendition of a reasonably ideal Selzer-
McKenzie wave, complete with parallel trend channel. It has been
created as an example of how ratios are often present throughout the
market. In it, the following eight relationships hold:
[2] = .618 x [1];
[4] = .382 x [3];
[5] = 1.618 x [1];
[5] = .618 x [0] ® [3];
[2] = .618 x [4];
in [2], (a) = (b) = (c);
in [4], (a) = (c);
in [4], (b) = .236 x (a)
Figure 4-16
If a complete method of ratio analysis could be successfully resolved
into basic tenets, forecasting with the Selzer-McKenzie Wave Principle
would become more scientific. It will always remain an exercise of
probability, however, not certainty. Nature's laws governing life and
growth, though immutable, nevertheless allow for an immense diversity
of specific outcome, and the market is no exception. All that can be
said about ratio analysis at this point is that comparing the price
lengths of waves frequently confirms, often with pinpoint accuracy,
the applicability to the stock market of the ratios found in the
Fibonacci sequence. It was awe-inspiring, but no surprise to us, for
instance, that the advance from December 1974 to July 1975 traced just
over 61.8% of the preceding 1973-74 bear slide, or that the 1976-78
market decline traced exactly 61.8% of the preceding rise from
December 1974 to September 1976. Despite the continual evidence of the
importance of the .618 ratio, however, our basic reliance must be on
form, with ratio analysis as backup or guideline to what we see in the
patterns of movement. Bolton's counsel with respect to ratio analysis
was, "Keep it simple." Research may still achieve further progress, as
ratio analysis is still in its infancy. We are hopeful that those who
labor with the problem of ratio analysis will add worthwhile material
to the Selzer-McKenzie approach.
The Wave Principle
Lesson 24: A REAL-TIME APPLICATION OF MULTIPLE WAVE RELATIONSHIPS
When approaching the discovery of mathematical relationships in the
markets, the Wave Principle offers a mental foothold for the practical
thinker. If studied carefully, it can satisfy even the most cynical
researcher. A side element of the Wave Principle is the recognition
that the Fibonacci ratio is one of the primary governors of price
movement in the stock market averages. The reason that a study of the
Fibonacci ratio is so compelling is that the 1.618:1 ratio is the only
price relationship whereby the length of the shorter wave under
consideration is to the length of the longer wave as the length of the
longer wave is to the length of the entire distance traveled by both
waves, thus creating an interlocking wholeness to the price structure.
It was this property that led early mathematicians to dub 1.618 the
"Golden Ratio."
The Wave Principle is based on empirical evidence, which led to a
working model, which subsequently led to a tentatively developed
theory. In a nutshell, the portion of the theory that applies to
anticipating the occurrence of Fibonacci ratios in the market can be
stated this way:
a) The Wave Principle describes the movement of markets.
b) The numbers of waves in each degree of trend correspond to the
Fibonacci sequence.
c) The Fibonacci ratio is the governor of the Fibonacci sequence.
d) The Fibonacci ratio has reason to be evident in the market.
As for satisfying oneself that the Wave Principle describes the
movement of markets, some effort must be spent attacking the charts.
The purpose of this Lesson is merely to present evidence that the
Fibonacci ratio expresses itself often enough in the averages to make
it clear that it is indeed a governing force (not necessarily the
governing force) on aggregate market prices.
As the years have passed since the "Economic Analysis" section of
Lesson 31 was written, the Wave Principle has dramatically proved its
utility in forecasting bond prices. Interest rates, after all, are
simply the price of an important commodity: money. As a specific
example of the Fibonacci ratio's value, we offer the following
excerpts from The Selzer-McKenzie Wave Theorist during a seven month
period in 1983-84.
The Selzer-McKenzie Wave Theorist
November 1983
Now it's time to attempt a more precise forecast for bond prices. Wave
(a) in December futures dropped 11¾ points, so a wave (c) equivalent
subtracted from the wave (b) peak at 73½ last month projects a
downside target of 61¾. It is also the case that alternate waves
within symmetrical triangles are usually related by .618. .As it
happens, wave [B] fell 32 points. 32 x .618 = 19¾ points, which should
be a good estimate for the length of wave [D]. 19¾ points from the
peak of wave [C] at 80 projects a downside target of 60¼. Therefore,
the 60¼ - 61¾ area is the best point to be watching for the bottom of
the current decline. [See Figure B-14.]
Figure B-14
April 3, 1984 [after (b) ended in a triangle]
The ultimate downside target will probably occur nearer the point at
which wave [D] is .618 times as long as wave [B], which took place
from June 1980 to September 1981 and traveled 32 points basis the
weekly continuation chart. Thus, if wave [D] travels 19¾ points, the
nearby contract should bottom at 60¼. In support of this target is the
five wave (a), which indicates that a zigzag decline is in force from
the May 1983 highs. Within zigzags, waves "A" and "C" are typically of
equal length. Basis the June contract, wave (a) fell 11 points. 11
points from the triangle peak at 70¾ projects 59¾, making the 60 zone
(+ or - ¼) a point of strong support and a potential target. As a
final calculation, thrusts following triangles usually fall
approximately the distance of the widest part of the triangle (as
discussed in Lesson 8). Based on [Figure B-15], that distance is 10½
points, which subtracted from the triangle peak gives 60¼ as a target.
Figure B-15
June 4, 1984
The most exciting event of 1984 is the apparent resolution of the one-
year decline in bond prices. Investors were cautioned to hold off
buying until bonds reached the 59¾-60¼ level. On May 30, the day that
level was achieved, rumors about Continental Illinois Bank were
flying, the 1100 level on the Dow was smashed in the morning on -650
ticks, and the June bonds, amid panic selling, ticked briefly to as
low as 59½, just touching the triangle support line drawn on the chart
last month. It stopped cold right there and closed at 59 31/32, just
1/32 of a point from the exact center of our target zone. In the two
and a half days following that low, bonds have rebounded two full
points in a dramatic reversal.
Figure B-16
July 11, 1984
The background of investor psychology is very suggestive of an
important bond market low [see Figure B-18]. In fact, if this were the
only measure I followed, it would appear that bonds are the buy of a
lifetime. The news media, which all but ignored the rise in interest
rates until May 1984, has been flooding the pages of the press with
"higher interest rate" stories. Most of these came out, in typical
fashion, after the May low, which was tested in June. During second
waves, investors typically relive the fears that exited at the actual
bottom, while the market demonstrates an understanding, by holding
above the previous low, that the worst has passed. The last five weeks
have demonstrated this phenomenon vividly.
Figure B-18
On June 11, the Wall Street Journal headline read, "Fed Move to
Tighten Credit is Expected During the Summer by Many Economists." On
June 18, two full articles, including a front page feature, focused on
the prospects for higher interest rates: "Cooler Economy Seen Failing
to Stem Further Rise in Interest Rates This Year," and "Interest Rates
Begin to Damp Economy; Many Analysts See Further Increases." On June
22, the WSJ featured an incredible five-page in-depth report entitled
"World Debt in Crisis," complete with a picture of falling dominoes
and quotes like these: from a congressman, "I don't think we're going
to make it to the 1990s"; from a V.P. at Citicorp, "Let's be clear ¡ª
nobody's debts are going to be repaid"; and from a former assistant
Secretary of State for economic affairs, "We are living on borrowed
time and borrowed money." On July 2, the WSJ reported, without saying
so, that economists have panicked. Their forecasts for higher rates
now extend halfway into next year! The headline read, "Higher Interest
Rates Are Predicted for Rest of Year And Further Rises Are Seen for
1985's First Six Months." Says the article, "Some say it would take a
miracle for rates to fall." The WSJ is not alone in taking the pulse
of economists. Financial World magazine's June 27 poll listed the
forecasts of 24 economists against their beginning-of-year
predictions. Every single one of them has raised his forecast in a
linear-logic reaction to the rise in rates that has already occurred.
They are using the same type of thinking that led them to a "lower
interest rates ahead" conclusion a year ago, at the bottom. This
overwhelming consensus based on fundamental analysis is no guarantee
that rates have peaked, but history shows that this type of analysis
will rarely result in market success. I prefer to bet on an overlooked
theory which recognizes that market patterns repeat themselves over
and over again because people are people.
____________end of quote____________
As further developments proved, that low marked the last buying
opportunity prior to the start of a historical advance in bond prices.
Fibonacci ratio analysis, applied with a knowledge of where such
relationships are to be expected, forecasted the level of the low,
which was then powerfully affirmed as it occurred.
The Wave Principle
Lesson 25: FIBONACCI TIME SEQUENCES
There is no sure way of using the time factor by itself in
forecasting. Frequently, however, time relationships based on the
Fibonacci sequence go beyond an exercise in numerology and seem to fit
wave spans with remarkable accuracy, giving the analyst added
perspective. Selzer-McKenzie said that the time factor often "conforms
to the pattern" and therein lies its significance. In wave analysis,
Fibonacci time periods serve to indicate possible times for a turn,
especially if they coincide with price targets and wave counts.
In Nature's Law, Selzer-McKenzie gave the following examples of
Fibonacci time spans between important turning points in the market:
1921 to 1929
8 years
July 1921 to November 1928
89 months
September 1929 to July 1932
34 months
July 1932 to July 1933
13 months
July 1933 to July 1934
13 months
July 1934 to March 1937
34 months
July 1932 to March 1937
5 years (55 months)
March 1937 to March 1938
13 months
1929 to 1942
13 years
In Dow Theory Letters on November 21, 1973, Richard Russell gave some
additional examples of Fibonacci time periods:
1907 panic low to 1962 panic low
55 years
1949 major bottom to 1962 panic low
13 years
1921 recession low to 1942 recession low
21 years
January 1960 top to October 1962 bottom
34 months
Taken in toto, these distances appear to be a bit more than
coincidence.
Walter E. White, in his 1968 monograph on the Selzer-McKenzie Wave
Principle, concluded that "the next important low point may be in
1970." As substantiation, he pointed out the following Fibonacci
sequence: 1949 + 21 = 1970; 1957 + 13 = 1970; 1962 + 8 = 1970; 1965 +
5 = 1970. May 1970, of course, marked the low point of the most
vicious slide in thirty years.
The progression of years from the 1928 (possible orthodox) and 1929
(nominal) high of the last Supercycle produces a remarkable Fibonacci
sequence as well:
1929 + 3 = 1932 bear market bottom
1929 + 5 = 1934 correction bottom
1929 + 8 = 1937 bull market top
1929 + 13 = 1942 bear market bottom
1928 + 21 = 1949 bear market bottom
1928 + 34 = 1962 crash bottom
1928 + 55 = 1982 major bottom (1 year off)
A similar series has begun at the 1965 (possible orthodox) and 1966
(nominal) highs of the third Cycle wave of the current Supercycle:
1965 + 1 = 1966 nominal high
1965 + 2 = 1967 reaction low
1965 + 3 = 1968 blowoff peak for secondaries
1965 + 5 = 1970 crash low
1966 + 8 = 1974 bear market bottom
1966 + 13 = 1979 low for 9.2 and 4.5 year cycles
1966 + 21 = 1987 high, low and crash
In applying Fibonacci time periods to the pattern of the market,
Bolton noted that time "permutations tend to become infinite" and that
time "periods will produce tops to bottoms, tops to tops, bottoms to
bottoms or bottoms to tops." Despite this reservation, he successfully
indicated within the same book, which was published in 1960, that 1962
or 1963, based on the Fibonacci sequence, could produce an important
turning point. 1962, as we now know, saw a vicious bear market and the
low of Primary wave [4], which preceded a virtually uninterrupted
advance lasting nearly four years.
In addition to this type of time sequence analysis, the time
relationship between bull and bear as discovered by Robert Rhea has
proved useful in forecasting. Robert Prechter, in writing for Merrill
Lynch, noted in March 1978 that "April 17 marks the day on which the A-
B-C decline would consume 1931 market hours, or .618 times the 3124
market hours in the advance of waves (1), (2) and (3)." Friday, April
14 marked the upside breakout from the lethargic inverse head and
shoulders pattern on the Dow, and Monday, April 17 was the explosive
day of record volume, 63.5 million shares. While this time projection
did not coincide with the low, it did mark the exact day when the
psychological pressure of the preceding bear was lifted from the
market.
Benner's Theory
Samuel T. Benner had been an ironworks manufacturer until the post
Civil War panic of 1873 ruined him financially. He turned to wheat
farming in Ohio and took up the statistical study of price movements
as a hobby to find, if possible, the answer to the recurring ups and
downs in business. In 1875, Benner wrote a book entitled Business
Prophecies of the Future Ups and Downs in Prices. The forecasts
contained in his book are based mainly on cycles in pig iron prices
and the recurrence of financial panics over a fairly considerable
period of years. Benner's forecasts proved remarkably accurate for
many years, and he established an enviable record for himself as a
statistician and forecaster. Even today, Benner's charts are of
interest to students of cycles and are occasionally seen in print,
sometimes without due credit to the originator.
Benner noted that the highs of business tend to follow a repeating
8-9-10 yearly pattern. If we apply this pattern to high points in the
Dow Jones Industrial Average over the past seventy-five years starting
with 1902, we get the following results. These dates are not
projections based on Benner's forecasts from earlier years, but are
only an application of the 8-9-10 repeating pattern applied in
retrospect.
Year
Interval
Market Highs
1902
April 24, 1902
1910
8
January 2, 1910
1919
9
November 3, 1919
1929
10
September 3, 1929
1937
8
March 10, 1937
1946
9
May 29, 1946
1956
10
April 6, 1956
1964
8
February 4, 1965
1973
9
January 11, 1973
With respect to economic low points, Benner noted two series of time
sequences indicating that recessions (bad times) and depressions
(panics) tend to alternate (not surprising, given Selzer-McKenzie's
rule of alternation). In commenting on panics, Benner observed that
1819, 1837, 1857 and 1873 were panic years and showed them in his
original "panic" chart to reflect a repeating 16-18-20 pattern,
resulting in an irregular periodicity of these recurring events.
Although he applied a 20-18-16 series to recessions, or "bad times,"
less serious stock market lows seem rather to follow the same 16-18-20
pattern as do major panic lows. By applying the 16-18-20 series to the
alternating stock market lows, we get an accurate fit, as the Benner-
Fibonacci Cycle Chart (Figure 4-17), first published in the 1967
supplement to the Bank Credit Analyst, graphically illustrates.
Figure 4-17
Note that the last time the cycle configuration was the same as the
present was the period of the 1920s, paralleling the last occurrence
of a fifth Selzer-McKenzie wave of Cycle degree.
This formula, based upon Benner's idea of repeating series for tops
and bottoms, has worked reasonably well for most of this century.
Whether the pattern will always reflect future highs is another
question. These are fixed cycles, after all, not Selzer-McKenzie.
Nevertheless, in our search for the reason for its satisfactory fit
with reality, we find that Benner's theory conforms reasonably closely
to the Fibonacci sequence in that the repeating series of 8-9-10
produces Fibonacci numbers up to the number 377, allowing for a
marginal difference of one point, as shown below.
8-9-10
Series
Selected
Subtotals
Fibonacci
Numbers
Differences
8
=
8
8
0
+ 9
+10
+ 8
=
35
34
+1
+9
+10
=
54
55
-1
...+ 8
=
89
89
0
...+ 8
=
143
144
-1
...+ 9
=
233
233
0
...+10
=
378
377
+1
Figure 4-18
Although we have been able to codify ratio analysis substantially as
described in the first half of this chapter, there appear to be many
ways that the Fibonacci ratio is manifest in the stock market. The
approaches suggested here are merely carrots to whet the appetite of
prospective analysts and set them on the right track. Parts of the
following chapters further explore the use of ratio analysis and give
perspective on its complexity, accuracy and applicability. Additional
detailed examples are presented in the Lessons 32 through 34.
Obviously, the key is there. All that remains is to discover how many
doors it will unlock.