Trading Tactics in the Financial Market: Mathematical Methods to Improve Performance

270 Pages·2021·12.894 MB·English

by  Don K. Mak

Management for Professionals
Don K. Mak
Trading Tactics
in the Financial
Market
Mathematical Methods to
Improve Performance
Management for Professionals
Moreinformationaboutthisseriesathttp://www.springer.com/series/10101
Don K. Mak
Trading Tactics in
the Financial Market
Mathematical Methods to Improve
Performance
DonK.Mak
Ottawa,ON,Canada
ISSN2192-8096 ISSN2192-810X (electronic)
ManagementforProfessionals
ISBN978-3-030-70621-0 ISBN978-3-030-70622-7 (eBook)
https://doi.org/10.1007/978-3-030-70622-7
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Preface
I published the book Science of Financial Market Trading in 2003. The idea is to
introduce concepts in Physics and techniques in Mathematics to financial market
trading,especiallyinthearenaoftechnicalanalysis.Thebookwasquicklyadopted
asatextbookforagraduatecourseinmathematicalfinancebyauniversityinUSA,
and continually used as a reference in various disciplines in institutes and
universities worldwide. Thus, we think that we have forged the right approach—
thatsomepeoplewouldliketoseetradingconceptstobeputonasolidscientificand
mathematicalground.
Nevertheless, other than occasional mentions of some of the ideas presented in
the book in trading forums, the concepts were basically ignored in the trading
community.Tradingguruscontinuetoadvocatetheirtradingtactics,andhowthey
wouldmakeprofits.Traderswouldcontinuetobelievethem,withoutaskingwhythe
tacticswouldwork,i.e.,iftheyworkatall.
In this book, we expand some of the earlier ideas, and apply them to analyze
trading tactics, which we believe are more relevant to the trading community. We
would try to explain, by using Fourier Analysis, why some of the indicators and
trading tactics would work better than others and why some indicators and trading
tactics would perform poorly and should be steered away from. We will start off
applying the trading tactics on some dummy artificial data, and then eventually on
realmarketdata.
Chapter1isanintroductiontoTradingTacticsasrelatedtoTechnicalAnalysis.
Chapter2,theMarketTurningPoints,containsthekeyideasinthebook.Itexplains
why and when a trading tactic is profitable, and how money can be lost. Fourier
Analysis would be employed to divide the frequency spectrum of a technical
indicatorintoProfitZoneandLossZone.Datasamplingalsohasasubstantialeffect
on profitability, proffering the Profit Zone to be divided into Sure Profit Zone and
Unsure ProfitZone.As thetiming ofdata sampling canbe critical, anew concept,
calledskippedconvolution,isintroducedtobettertimethemarketturns.Chapter3,
Simple Moving Average, discusses how market price data can be smoothed to
eliminate the high frequency noise using Simple Moving Average (SMA). The
populartradingtactic,thecrossoverofPricewithitsSMA,isanalyzedwithFourier
Analysis.TheproblemofthistacticisthatSMAsuffersfromthedisappearanceof
some signals at certain frequencies. In Chapter 4, Exponential Moving Average
(EMA),anothersmoothingtechnique,isdescribed.Thetradingtactic,thecrossover
v
vi Preface
ofPricewithitsEMA,isanalyzedwithFourierAnalysis.InChapter5,twopopular
trading tactics, Awesome Oscillator and Accelerator Oscillator, are examined and
theircharacteristicsdetailed.Theproblemwiththesetacticsisthatwrappedphases
areusedbytraders, while unwrapped phases shouldhavebeenused.InChapter 6,
Moving Average Convergence-Divergence (MACD), a popular tool of the trader,
togetherwitharelatedandalsopopularindicator,theMACDHistogram(MACDH),
aremathematicallycharacterized.InChapter7,varioustradingtactics,somepopular
andsomenotsopopulartotraders,areappliedtorealmarketdata,likeS&P500,the
Hang Seng Index, the FTSE100, and the CAC40. Performance of different tactics
arecompared.TheresultssomewhatconfirmtheoutcomeoftheFourierAnalysis-
why some trading tactics have a higher probability of profitability. Chapter 8,
Analysis of the Trading Tactics, discusses the tactics that would be recommended,
andthosethatshouldbeavoided.Chapter9istheSummary.
Thebookiswrittenforbothtradersandacademics.Minimalmathematicsisused
inthemaintext,whichisfilledwithfiguresandtablesforeaseofunderstandingof
the concepts presented. Most of the mathematics is put in the appendices for the
academics who may want to comprehend the basis of the ideas. The last appendix
containsalltheMATLABprogramsusedinthebook.Theprogramswouldbeuseful
forreaderswhowouldliketoseehowthecharacteristicsofthetradingtacticswould
change by altering the parameters of the indicators. Also, programs analyzing real
marketdatawouldallow thedata tobeanalyzedbydifferent trading tactics,aswe
cannot possibly put all the examples in the book. As well, readers can substitute
otherrealmarketdataintheprogramstogaugetheprofitabilityofthevarioustrading
tactics.
The book basically analyzes tactics that have mostly been used by traders, and
havenotanalyzedsomeofthenewonesproposed(e.g.,Mak2006).Thesewouldbe
leftasexercisestothereaders.
Hence, for the academics, there are quite a lot of ideas that can be followed
up. More research would be needed to substantiate and fine-tune some of the
concepts.Andforthetraders,thecurrentideasshouldhelpthemdecidewhattrading
tacticstouse,andhopefullymakemoreprofit.
Ottawa,ON,Canada DonK.Mak
Contents
1 TradingTacticsinTechnicalAnalysis. . . . . . . . . . . . . . . . . . . . . . . 1
1.1 WhyArtificialData?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Evidence-Based. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Science-Based. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Mathematics-Based. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 MarketTurningPoints. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1 PriceData. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Velocity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 VelocityIndicators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3.1 ProfitZoneandLossZone. . . . . . . . . . . . . . . . . . . . . . . 12
2.4 Sampling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.4.1 SamplingCanAffecttheProfitabilityofaTrade. . . . . . . 12
2.4.2 LossintheProfitZone. . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.4.3 SureProfitZoneandUnsureProfitZone. . . . . . . . . . . . . 19
2.4.4 SkippedConvolution. . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4.5 ProfitintheLossZone. . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.4.6 Multiplefrequencies. . .. . . .. . . .. . . .. . . .. . . .. . . .. 23
2.5 Acceleration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.6 AccelerationIndicators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3 SimpleMovingAverage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.1 SimpleMovingAverage(SMA). . . . . . . . . . . . . . . . . . . . . . . . 29
3.1.1 SimpleMovingAverage,N¼10. . . . . . . . . . . . . . . . . . 31
3.1.2 SimpleMovingAverage,N¼20. . . . . . . . . . . . . . . . . . 39
3.1.3 SimpleMovingAverage,N¼100. . . . . . . . . . . . . . . . . 42
3.2 TradingTacticsUsingSimpleMovingAverage. . . . . . . . . . . . . 45
3.2.1 Price(cid:2)SimpleMovingAverageofPrice,N¼10. . . . . . 45
3.2.2 Price(cid:2)SimpleMovingAverageofPrice,N¼20. . . . . . 50
3.2.3 Price(cid:2)SimpleMovingAverageofPrice,N¼100. . . . . 53
3.2.4 ComparisonofPrice(cid:2)SimpleMovingAverage
ofPrice,N¼10,20and100. . . . . . . . . . . . . . . . . . . . . 55
vviiii
viii Contents
4 ExponentialMovingAverage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.1 ExponentialMovingAverage(EMA). . . . . . . . . . . . . . . . . . . . . 57
4.2 TradingTacticsUsingExponentialMovingAverage. . . . . . . . . . 61
4.2.1 Price(cid:2)ExponentialMovingAverageofPrice,M¼3. . . 61
4.2.2 Price(cid:2)ExponentialMovingAverageofPrice,M¼6. . . 64
4.2.3 EMAofPrice,M¼3(cid:2)EMAofPrice,M¼6. . . . . . . . 67
4.2.4 EMAACCEL.. . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. 69
5 AwesomeOscillatorandAcceleratorOscillator. . . . . . . . . . . . . . . . 73
5.1 AwesomeOscillator(AO). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.2 AcceleratorOscillator(AC). . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
6 MovingAverageConvergence-DivergenceandIts
Histogram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
6.1 MovingAverageConvergence-Divergence(MACD). . . . . . . . . . 85
6.2 MovingAverageConvergence-DivergenceHistogram
(MACDH). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
6.3 MACDH1,MACDHwithPriceReplacingtheFastEMA. . . . . . 92
7 TradingTacticsintheRealMarket. . . . . . . . . . . . . . . . . . . . . . . . 97
7.1 S&P500Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
7.1.1 MACDH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
7.1.2 MACD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
7.1.3 Price(cid:2)EMA3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
7.1.4 FastFourierTransformandInverseFastFourier
TransformofS&P500Index. . . . . . . . . . . . . . . . . . . . . . 103
7.2 HangSengIndex. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
7.2.1 Price(cid:2)SMA10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
7.2.2 AwesomeOscillator. . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
7.2.3 AcceleratorOscillator. . . . .. . . . . . . . . . . . . . . . . . .. . . 107
7.2.4 FastFourierTransformoftheHangSengindex. . . . . . . . 108
7.3 FTSE100Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
7.3.1 Price(cid:2)EMA6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
7.3.2 MACDH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
7.3.3 FastFourierTransformoftheFTSE100index. . . . . . . . 112
7.4 CAC40Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
7.4.1 MACDH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
7.4.2 MACDH1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
7.4.3 FastFourierTransformofCAC40index. . .. . . . .. . . .. 114
7.5 ComparisonofDifferentTradingTactics. . . . . . . . . . . . . . . . . . 115
8 AnalysisoftheTradingTactics. . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
8.1 ProfitZoneandLossZone. . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
8.2 Price(cid:2)EMAofPriceComparedtoPrice(cid:2)SMAofPrice. . . . . 119
8.3 AwesomeOscillator(AO)andMovingAverage
ConvergenceDivergence(MACD). . . . . . . . . . . . . . . . . . . . . . 122
Contents ix
8.4 AcceleratorOscillator(AC). . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
8.5 MACDH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
8.6 Recommendations. . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. 123
9 Epilogue. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
AppendixA:SureandUnsureProfitandLossZones. . . . . . . . . . . . . . . 127
AppendixB:SimpleMovingAverage. . . . . . . . . . . . . . . . . . . . . . . . . . . 137
AppendixC:ExponentialMovingAverage,MovingAverage
Convergence-Divergence. . . . . . . . . . . . . . . . . . . . . . . . . . 141
AppendixD:MATLABPrograms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Bibliography. . . . . . .. . . . . . .. . . . . . . .. . . . . . .. . . . . . . .. . . . . . .. . 263
Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
1
Trading Tactics in Technical Analysis
In financial market trading, technical analysis plays a significant role. Technical
analysis bases the buy and sell decisions on market behavior such as price and
volume, with price being more important (Mak 2003). The data are quite often
plotted in charts. Past financial data would be employed to forecast future market
movement.
Indicators have been created to operate on series of past financial data. Quite a
numberofindicatorshavebeendeveloped,allaimingatillustratingwhatthemarket
situationis,andattemptingtoforecastwhatitwillbe.Theyareactuallyequivalentto
filters in electrical engineering, or operators in mathematics (Mak 2003). The
operator will convolute with the past financial time series to produce another
functionindicativeofthestateofthemarketcondition.
The terms velocity indicator andaccelerationindicator wereintroduced in2003
(Mak2003),andfurtherexplainedin2006(Mak2006).Thesetermsareborrowed
fromthetermsvelocityandaccelerationinPhysics.Theideaistoapplytheconcepts
and mathematical techniques in Physics to technical analysis in financial market
trading, so as to simplify and clarify the terminology and the trading tactics then
used. The terms never caught on (googling the terms did not show these items
displayed)untilabout2017.Evenafterthen,whilethetermsusedbysometradersdo
conformtothemeaningsinPhysics,therearecaseswheretheymeansomethingelse.
Even worse, sometimes the terms used are totally misleading. In one YouTube
video,accelerationisusedwhilevelocityshouldhavebeenemployed.
In Physics, velocity measures the rate of change of distance over time, and
acceleration measures the rate of change of velocity (these definitions have been
simplified, as velocity and acceleration in Physics are vector quantities that have
directions).Intrading,distanceisreplacedbyprice.
Whenpriceisplottedagainsttime,thedatatracesacurve.Therateofchangeof
price on the curve can be called the slope of the curve. We will call the slope the
velocity,and theslope ofthe slope theacceleration.Whenthe velocity ispositive,
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