Trend Following Algorithmic Trading with a Reduced Universe of Cryptocurrencies: Using unsupervised learning for universe reduction and trend following strategies to generate profits

MDSAA Mas e ’s Deg ee P og am in Da a Science and Ad anced Analy ics TREND FOLLOWING ALGORITHMIC TRADING WITH A REDUCED UNIVERSE OF CRYPTOCURRENCIES Using unsupe ised lea ning o uni e se educ ion and end ollowing s a egies o gene a e p o i s And é O ão Pe ei a Disse a ion p esen ed as pa ial equi emen o ob aining he Mas e Deg ee P og am in Da a Science and Ad anced Analy ics NOVA In o ma ion Managemen School Ins i u o Supe io de Es a ís ica e Ges ão de In o mação Uni e sidade No a de Lisboa NOVA In o ma ion Managemen School Ins i u o Supe io de Es a ís ica e Ges ão de In o mação Uni e sidade No a de Lisboa T end ollowing algo i hmic ading wi h a educed uni e se o c yp ocu encies Using unsupe ised lea ning o uni e se educ ion and end ollowing s a egies o gene a e p o i s by And é O ão Pe ei a Disse a ion p esen ed as pa ial equi emen o ob aining he Mas e ’s Deg ee in Da a Science and Ad anced Analy ics, wi h a Specializa ion in Da a Science Supe iso : Mau o Cas elli May 2024 ii STATEMENT OF INTEGRITY I he eby decla e ha ing conduc ed his academic wo k wi h in eg i y. I con i m ha I ha e no used plagia ism o any o m o undue use o in o ma ion o alsi ica ion o esul s along he p ocess leading o i s elabo a ion. I u he decla e ha I ha e ully acknowledge he Rules o Conduc and Code o Hono om he NOVA In o ma ion Managemen School. And é O ão Pe ei a Lisboa, May 2024 iii DEDICATION I wan o exp ess my g a i ude o my pa en s o always belie ing in me and encou aging me o aim highe han e e I hough possible. To my b o he s, I wan o exp ess my hea el g a i ude o he pa hs you' e chosen, which ha e se ed as a cons an sou ce o inspi a ion and guidance o me. I wan o ex end my since e hanks o Ahmed Assad and Tomás Juhos o hei inc edible pa ience and willingness o help me h ough he ups and downs o p o essional li e. Lucas Ca alho and Dua e Caldas, you insigh ul alks on inance ha e been inc edibly in luen ial in shaping he di ec ion o his p ojec . To all my iends, hank you o you unwa e ing suppo and iendship h oughou his jou ney. You kindness and ha d wo k inspi e me. He e's o many mo e ad en u es oge he . i ABSTRACT C yp ocu encies ha e e olu ionized ading wi h hei decen alized and ola ile na u e, p esen ing unique oppo uni ies o end- ollowing s a egies. This s udy in es iga es he enhancemen o such s a egies by implemen ing a educ ion in he uni e se o c yp ocu encies based on hei simila i ies, aiming o imp o e ading pe o mance. Addi ionally, a ma ke momen um classi ica ion will be cons uc ed o analyze and compa e pe o mance ac oss di e en ma ke momen um en i onmen s. By u ilizing Suppo Vec o Machines (SVM) and P incipal Componen Analysis (PCA), he o e all uni e se o c yp ocu encies is educed o he mos simila c yp ocu encies based on me ics o momen um, g ow h, and echnical analysis. This app oach aims o add ess ma ke o e load caused by he conside able numbe o a ailable c yp ocu encies, emo ing he mos e a ic c yp ocu encies. To assess he e icacy o wo end- ollowing ading s a egies—an equally weigh ed po olio app oach and a ime-weigh ed po olio app oach—we will u ilize a momen um-based ading s a egy se ing as ou benchma k. All s a egies will be used wi h he educed uni e ses p oduced by ou me hod. Addi ionally, a ma ke momen um classi ica ion will be cons uc ed using ma ke capi aliza ion da a o he c yp o ma ke , wi h he goal o gaining ele an insigh s in o he e ec s o he o e all ma ke momen um en i onmen on he pe o mance o he algo i hmic ading s a egies and educed uni e se combina ions. The inno a ion lies in he me hod o educing he c yp ocu ency uni e se by iden i ying he mos simila okens du ing he same pe iod while asse ing he alue o unsupe ised lea ning models like SVM and PCA in enhancing end- ollowing ading s a egies by educing complexi y. In summa y, his esea ch unde sco es he c i ical di e ences in sho and long end o ma ion pe iods, he e ec i eness o end- ollowing app oaches, and he supe io pe o mance o ime-weigh ed po olios, demons a ing how SVM and PCA can enhance algo i hmic ading s a egies by educing complexi y and op imizing p o i abili y in he dynamic c yp ocu ency ma ke . KEYWORDS C yp o Cu encies; Machine Lea ning; Unsupe ised Lea ning; Algo i hmic T ading; T end Following Sus ainable De elopmen Goals (SGD): Con en 1. In oduc ion ...................................................................................................... 10 1.1 Mo i a ion ................................................................................................ 10 1.2 Aim and Objec i es ................................................................................... 11 1.3 Resea ch Ques ions ................................................................................... 11 1.4 Ou line o he Resea ch ............................................................................. 12 2. Li e a u e Re iew .............................................................................................. 13 2.1. C yp o ....................................................................................................... 13 2.1.1. C yp o Cu encies .............................................................................. 13 2.1.2. C yp o Ma ke ................................................................................... 13 2.2. Algo i hmic T ading ................................................................................... 14 2.2.1. Time Se ies ........................................................................................ 14 2.2.2. T end Following ................................................................................. 14 2.3. Machine Lea ning Me hods ....................................................................... 14 2.3.1. Suppo ec o machine ..................................................................... 15 2.3.2. P incipal componen analysis ............................................................. 15 2.3.3. Anomalies and ou lie s ...................................................................... 15 2.3.4. Anomaly De ec ion ............................................................................ 16 2.4. Me ics Rele ance ..................................................................................... 17 2.4.1. Momen um ....................................................................................... 17 2.4.2. Technical Indica o s ........................................................................... 17 3. Da a .................................................................................................................. 18 3.1. Da a Sou ce............................................................................................... 18 3.2. Da a Inges ion ........................................................................................... 18 3.2.1. Raw Field Desc ip ions ....................................................................... 18 3.3. Da a P epa a ion ....................................................................................... 19 3.3.1. Fea u e Enginee ing ........................................................................... 19 3.4. Da a No maliza ion ................................................................................... 22 4. Me hodology .................................................................................................... 24 4.1. A chi ec u e .............................................................................................. 24 4.2. Pa ame e ized Uni e se Fo ma ion ............................................................ 25 4.2.1. Me ics G oups .................................................................................. 26 i 4.2.2. Lookback Pe iod ................................................................................ 27 4.2.3. Selec ion Me hod .............................................................................. 27 4.2.4. Uni e se Size ..................................................................................... 28 4.3. Algo i hmic T ading S a egies Back Tes ing ................................................ 29 4.3.1. S a egy Type ..................................................................................... 29 4.3.2. Po olio Weigh ................................................................................ 31 4.4. Ma ke Momen um Signal ......................................................................... 31 4.5. E alua ion Me ics ..................................................................................... 32 5. Resul s and Analysis .......................................................................................... 35 5.1. Resul s ...................................................................................................... 35 5.1.1. Bes o e all alue pe pa ame e ........................................................ 35 5.1.2. Pa ame e Combina ion Analysis ........................................................ 37 5.1.3. Top Ranked Combina ions Analysis ..................................................... 40 5.2. Discussion ................................................................................................. 41 5.3. Limi a ions ................................................................................................ 42 6. Conclusions ....................................................................................................... 44 6.1. Academic Con ibu ion .............................................................................. 44 6.2. Fu u e Wo k .............................................................................................. 44 Bibliog aphical Re e ences ........................................................................................ 46 Appendix A ........................................................................................................... 51 Appendix B ........................................................................................................... 51 Appendix C ........................................................................................................... 51 Appendix D ........................................................................................................... 51 Appendix E ........................................................................................................... 52 ii LIST OF FIGURES Figu e 3.1: Candles ick cha wi h hou ly candles o he pai Bi coin / USD Te he . ..... 18 Figu e 3.2: Simple Pe cen age Change Equa ion ........................................................ 20 Figu e 3.3: Simple Mo ing A e age Equa ion ............................................................. 20 Figu e 3.4: Exponen ial Mo ing A e age Equa ion ..................................................... 20 Figu e 3.5: Bollinge Band Equa ions ......................................................................... 21 Figu e 3.6: Rela i e S eng h Index Equa ion ............................................................. 22 Figu e 3.7: Coe icien o Va iance Equa ion .............................................................. 22 Figu e 3.8: Min-max Fo mula .................................................................................... 23 Figu e 4.1: Hie a chical Flow o In o ma ion in he P oposed Solu ion........................ 24 Figu e 4.2: Pa ame e iza ion Explo a ion o Uni e se Fo ma ion ............................... 26 Figu e 4.3: SVM selec ion me hod example. .............................................................. 28 Figu e 4.4: PCA selec ion me hod example. ............................................................... 28 Figu e 4.5: Algo i hmic T ading S a egy wo k low. .................................................... 29 Figu e 4.6: A e age P o i & Loss Equa ion ................................................................ 32 Figu e 4.7: Sha pe Ra io Equa ion ............................................................................. 32 Figu e 4.8: So ino Ra io Equa ion ............................................................................. 33 Figu e 4.9: Max D aw Down Equa ion ....................................................................... 33 Figu e 4.10: Ku osis Equa ion .................................................................................. 34 Figu e 4.11: Skewness Equa ion ................................................................................ 34 Figu e 5.1: Ne and G oss Re u ns o Bes Long po olio. .......................................... 38 Figu e 5.2: Ne and G oss Re u ns o Bes Sho po olio. ......................................... 39 Figu e 5.3: Bea Ma ke Op imal Combina ion Flow .................................................. 40 iii LIST OF TABLES Table 3.1: Desc ip ion and Type o Da a o All Fields Inges ed Each Hou .................. 19 Table 4.1: Me ics G oups o Uni e se Fo ma ion ..................................................... 27 Table 5.1: Pa ame e O e iew ................................................................................. 35 Table 5.2: Selec ion Me hod Analysis. ....................................................................... 36 Table 5.3: Po olio Ac ion analysis. ........................................................................... 36 Table 5.4: Ma ke Class Con idence Le el Analysis ..................................................... 37 15 pa e ns by u ilizing s a is ical models and algo i hms. The e a e main ca ego ies o machine lea ning algo i hms, each wi h i s unique way o analyzing da a. Supe ised lea ning algo i hms a e augh using labeled da a, in which each aining ins ance is linked o a speci ic goal o esul . The objec i e is o he algo i hm o be able o an icipa e ou comes based on p e iously unseen da a by lea ning a mapping unc ion ha connec s inpu a iables o ou pu a iables. Supe ised lea ning is commonly employed in asks such as diagnosing medical condi ions based on pa ien da a and o ecas ing s ock p ices using his o ical and inancial indica o s. (Ko sian is, 2007) Unsupe ised lea ning is he aining o an algo i hm o iden i y pa e ns o s uc u es in da a wi hou he use o labels o any human in e ac ion. The algo i hm au onomously disco e s no el insigh s and connec ions wi hin he da ase , wi hou equi ing any human inpu o p ede ined a ge a iables. Unsupe ised lea ning o en encompasses asks such as g ouping and dimensionali y educ ion. Dimensionali y educ ion echniques, such as p incipal componen analysis (PCA), unco e la en pa e ns in da a wi h a la ge numbe o dimensions (Gen leman & Ca ey, 2008). Semi-supe ised lea ning algo i hms aim o op imize he pe o mance o supe ised lea ning models by le e aging he addi ional in o ma ion p o ided by unlabeled da a. This app oach excels in scena ios when he e is a sca ci y o labeled da a and a su plus o unlabeled da a, a ci cums ance ha is equen ly seen in eal-wo ld con ex s ( an Engelen & Hoos, 2020). 2.3.1. Suppo ec o machine Suppo Vec o Machine (SVM) is a supe ised lea ning model adep a handling da a classi ica ion and eg ession asks. Ope a ing e ec i ely in high-dimensional spaces, SVM iden i ies he op imal hype plane o maximize he ma gin be ween di e en classes o da a poin s, exhibi ing capabili ies in bo h linea and nonlinea classi ica ion (Pisne & Schnye , 2020). Howe e , SVM's pe o mance may su e wi h la ge da ase s o in he p esence o noise. One-Class SVM, a speci ic case o he suppo ec o machine, exempli ies unsupe ised machine lea ning. I can ain wi h unlabeled da a, dis inguishing be ween inlie s and ou lie s. One-Class SVM achie es his by sepa a ing all da a poin s om he o igin and maximizing he dis ance om his hype plane o he o igin (Schölkop , Williamson, Smola, John , & Pla , 1999). 2.3.2. P incipal componen analysis P incipal Componen Analysis (PCA) is a widely used echnique o dimensionali y educ ion, enhancing in e p e abili y by ex ac ing signi ican ea u es om high- dimensional da ase s. By p ojec ing da a on o a lowe -dimensional subspace, PCA imp o es compu a ional e iciency and minimizes in o ma ion loss. This me hod is in aluable o explo a o y da a analysis, ea u e ex ac ion, and isualiza ion asks ac oss di e se domains (Song, Guo, & Mei, 2010). 2.3.3. Anomalies and ou lie s While he e ms "ou lie s" and "anomalies" a e o en used in e changeably, hei dis inc ion is nuanced ye c ucial in da a analysis, as hey ep esen dis inc concep s 16 wi h sub le di e ences in meaning and in e p e a ion. Ou lie s, as de ined by G ubbs (1969), a e da a poin s ha signi ican ly de ia e om he majo i y o da a poin s in a da ase . These de ia ions a e ypically cha ac e ized by excep ional alues o placemen s ela i e o he dis ibu ion o he da a. Ou lie s may a ise due o measu emen inaccu acies, inhe en a iabili y, o in equen occu ences wi hin he da a. They a e o en iden i ied using s a is ical me ics such as s anda d de ia ion, z-sco es, o in e qua ile ange, wi h a ocus on he dis ibu ional p ope ies o he da a. Impo an ly, ou lie s do no necessa ily imply de ian beha io o pose signi ican h ea s o he unde lying sys em o p ocess. As such, hey may be ea ed as benign da a poin s ha can be sa ely igno ed o emo ed om he da ase wi hou signi ican consequences. On he o he hand, anomalies encompass a b oade ange o a ypical o un o eseen obse a ions wi hin a da ase . While ou lie s ep esen a subse o anomalies, anomalies can include a ious ypes o i egula i ies, pa e ns, o beha io s ha de ia e om expec ed no ms o dis ibu ions (Chandola, Bane jee, & Kuma , 2009). Anomalies may a ise om sys emic ailu es, audulen ac i i ies, unexpec ed e en s, o eme ging ends ha a e no adequa ely cap u ed by he exis ing da a model. Consequen ly, mo e sophis ica ed algo i hms may be equi ed o iden i y anomalies ha a e no eadily appa en h ough simple s a is ical analyses. The dis inc ion be ween ou lie s and anomalies unde sco es he impo ance o conside ing he b oade con ex , domain knowledge, and speci ic objec i es when analyzing da a and iden i ying i egula i ies. By unde s anding hese dis inc ions, da a analys s and decision-make s can e ec i ely in e p e he esul s o anomaly de ec ion me hods and make in o med decisions o add ess po en ial isks o oppo uni ies wi hin hei da ase s. 2.3.4. Anomaly De ec ion Anomaly de ec ion, also known as ou lie de ec ion, is a c i ical ask in a ious ields, including cybe secu i y, inance, heal hca e, and indus ial moni o ing (Singh & Upadhyaya, 2012). Anomaly de ec ion echniques le e age a ious me hods, including s a is ical analysis, machine lea ning algo i hms, and domain-speci ic knowledge. One common app oach is o use machine lea ning algo i hms o au oma ically lea n pa e ns om da a and de ec anomalies based on de ia ions om hose pa e ns. Supe ised anomaly de ec ion in ol es aining a model on labeled da a, whe e anomalies a e explici ly ma ked. The model lea ns o dis inguish be ween no mal and anomalous ins ances based on he p o ided labels. This app oach is e ec i e when labeled da a is eadily a ailable and when anomalies a e well-de ined. Howe e , i may no pe o m well in cases whe e labeled da a is sca ce o when anomalies a e no clea ly de ined. Unsupe ised anomaly de ec ion, on he o he hand, does no equi e labeled da a. Ins ead, i elies on iden i ying ins ances ha a e signi ican ly di e en om mos o he da a. Clus e ing algo i hms, densi y es ima ion echniques, and dis ance-based me hods a e commonly used in unsupe ised anomaly de ec ion. While unsupe ised me hods a e mo e e sa ile and applicable o a wide ange o scena ios, hey may s uggle o accu a ely de ec anomalies in complex da ase s wi h high-dimensional ea u es (Gu h ie, Gu h ie, Allison, & Wilks, 2007). 17 Anomaly de ec ion me hods mus be ca e ully selec ed based on he cha ac e is ics o he da a and he speci ic equi emen s o he applica ion. Fac o s such as he ype o anomalies p esen , he a ailabili y o labeled da a, and he compu a ional esou ces equi ed o aining and in e ence play c ucial oles in de e mining he mos sui able app oach. 2.4. Me ics Rele ance 2.4.1. Momen um Time-se ies momen um, a s a egy ocusing on an asse 's absolu e pe o mance o e a his o ical pe iod, has ga ne ed a en ion in inancial esea ch. Moskowi z e al. (2012) ound compelling e idence suppo ing his s a egy ac oss a ious secu i ies, sugges ing ha pas e u ns posi i ely p edic u u e e u ns. This phenomenon, known as he ime- se ies momen um e ec , is a ibu ed o signi ican au oco a iance in e u ns, pa icula ly du ing pe iods o ma ke ola ili y. Howe e , skep icism exis s ega ding he obus ness o hese indings, wi h some esea che s a ibu ing he obse ed e u ns o ola ili y scaling a he han ue p edic i e powe (Kim, Tse , & Wald, 2016). Despi e i s popula i y, ime-se ies momen um ules o en unde pe o m mo ing a e age ules, indica ing he complexi ies o implemen ing his s a egy e ec i ely. 2.4.2. Technical Indica o s Technical analysis is a me hodology ha use his o ical ma ke da a o o ecas u u e p ice changes. The idea behind i s ope a ion is ha ma ke ac i i y encompasses all accessible in o ma ion and ha p e ious p icing pa e ns end o ecu . Analys s employ a ange o echniques and indica o s, including mo ing a e ages and cha pa e ns, o disce n ends and p o ide ade ecommenda ions. While echnical analysis o e s a sys ema ic app oach o ma ke analysis, i s e ec i eness emains un egula o e ime (Zakamulin, 2014). Some s udies sugges ha ma ke iming wi h mo ing a e ages can ou pe o m passi e s a egies, highligh ing he po en ial alue o echnical analysis in in es men decision-making (Kilgallen, 2012). 18 3. Da a 3.1. Da a Sou ce The ounda ion o he p oposed sys em elies on a cu a ed collec ion o ime se ies da a, which is undamen al o ex ac ing meaning ul ea u es. This s udy u ilizes c yp ocu ency ime se ies da a sou ced om Binance's API, a leading da a p o ide enowned o i s ex ensi e co e age o c yp ocu encies. Each ime se ies co esponds o a c yp ocu ency exchange pai , consis ing o a base cu ency and a quo e cu ency, and is acqui ed o a p ede ined ime ame and equency. The s udy ocuses exclusi ely on c yp ocu ency pai s wi h he quo e cu ency USDT (Te he ) o ensu e ha all da a poin s a e s anda dized. While Binance o e s a ange o ime esolu ions om one minu e o one mon h, his hesis ocuses exclusi ely on hou ly in e als. This s a egic decision s ikes a balance be ween g anula i y and space e iciency, aligning wi h he objec i es o his hesis. This wo k acks a o al o 457 symbols du ing he analysis pe iod aiming o achie e a comp ehensi e ye manageable explo a ion o c yp ocu ency ma ke dynamics. 3.2. Da a Inges ion Candles ick cha s se e as aluable ools o gaining insigh s used in a ious echnical indica o s. They isually depic he ela ionship be ween wo asse s alues o e ime, ypically in ol ing a leas one cu ency. Technical analysis equen ly cen e s on examining hese cha s o disce n pa e ns and ends. The undamen al uni o a candles ick cha is a candle, which ep esen s a consis en ime leng h. Each candle p o ides in o ma ion on he highes , lowes , opening and closing p ices o ha speci ic pe iod. Addi ionally, sepa a e g aphs o en depic he o al asse olume aded and he o al numbe o ades associa ed wi h each pe iod. Figu e 3.1: Candles ick cha wi h hou ly candles o he pai Bi coin / USD Te he . 3.2.1. Raw Field Desc ip ions In he ollowing able, we can obse e he desc ip ion and ype o da a o all ields inges ed each hou . Candle S ick Cha s 19 Table 3.1: Desc ip ion and Type o Da a o All Fields Inges ed Each Hou Field Name Field desc ip ion Da a Type symbol A ading pai composed o a base cu ency and a quo e cu ency Tex Open Time The s a ime o he candles ick Times amp Open P ice The p ice o he asse when he candles ick opened Nume ic (25,10) High P ice The highes p ice o he asse du ing he candles ick's du a ion Nume ic (25,10) Low P ice The lowes p ice o he asse du ing he candles ick's du a ion Nume ic (25,10) Close P ice The p ice o he asse when he candles ick closed Nume ic (25,10) Close Time The closing ime o he candles ick Times amp Quo e Asse Volume The olume o he asse aded in e ms o he quo e asse du ing he candles ick's du a ion Nume ic (25,10) Numbe o T ades The numbe o ades execu ed du ing he candles ick's du a ion In ege Take Buy Base Asse Volume The olume o he asse bough by ake s du ing he candles ick's du a ion Nume ic (25,10) Take Buy Quo e Asse Volume The olume o he quo e asse bough by ake s du ing he candles ick's du a ion Nume ic (25,10) 3.3. Da a P epa a ion A da ase comp ises mul iple obse a ions, e med a sample, cha ac e ized by a se o alues e e ed o as ea u es. Missing da a is a p e alen sou ce o e o s in code, o en igge ing excep ions. A emp ing o emo e missing alues may signi ican ly educe he a ailable da a while dis o ing he u h, a scena io de imen al in machine lea ning. One o he mos amilia challenges encoun e ed in da a cleaning and explo a o y analysis is managing missing alues. To main ain ideli y o Binance's p o ided u h, his hesis op s no o manage any missing alues. Ins ead, missing da a is in e p e ed as indica i e o pe iods o ma ke o c yp ocu ency ading pai inac i i y. The da ase unde goes p ep ocessing and no maliza ion be o e analysis o op imize he da a o said analysis. 3.3.1. Fea u e Enginee ing Fea u e enginee ing (FE) is a machine lea ning echnique aimed a enhancing he e ec i eness o models by ans o ming aw da a in o mo e meaning ul a iables known as ea u es. By ex ac ing domain-speci ic ea u es om he da a, FE no only accele a es he lea ning p ocess bu also ele a es he model's pe o mance, ensu ing a mo e accu a e ep esen a ion o he unde lying p oblem. 20 This wo k adop s a me hodology ha calcula es pe cen age changes in a iables by means o di e en speeds (o lookback pe iods): 𝑅𝑡,𝑡−ℎ 𝑐=𝑃𝑡𝑐 𝑃𝑡−ℎ 𝑐− 1 Figu e 3.2: Simple Pe cen age Change Equa ion • 𝑅𝑡,𝑡−ℎ 𝑐 is he e u n o c yp ocu ency 𝑐 be ween hou 𝑡−ℎ and 𝑡 • 𝑃𝑡−ℎ 𝑐 is he p ice o c yp ocu ency 𝑐 a close o hou 𝑡−ℎ • 𝑃𝑡𝑐 is he p ice o c yp ocu ency 𝑐 a close o hou 𝑡 The mo ing a e age (MA) is a widely employed echnical indica o in inancial analysis (Glend ange & T ei en, 2016). I s p ima y ole is o smoo h ou sho - e m luc ua ions, imp o ing he in e p e a ion o ends h ough a line de i ed om successi e a e ages. As new ading pe iods un old, he mo ing a e age is ecompu ed by in oducing cu en in o ma ion while disca ding he oldes in o ma ion, he eby shi ing he a e age along he ime scale. This indica o is he e o e classi ied as a lagging indica o due o i s eac i e na u e elying solely on pas p ices o con i m ends e en hough i aids in end p edic ion by il e ing ou noise om andom p ice luc ua ions, achie ed h ough a e aging a ixed size o his o ical p ice le els known as he lookback pe iod. In his hesis, wo ypes o MA a e employed: he Simple Mo ing A e age (SMA), which assigns equal weigh s o all ime scales, and he Exponen ial Mo ing A e age (EMA), which uses exponen ial weigh ing wi h a decay ac o 𝜆 as a sensi i i y adjus men o ecen p ices. 𝑆𝑀𝐴𝑡,𝑙=1 𝑙+1 ∑𝑃𝑡−𝑖 𝑐 𝑙 𝑖=0 Figu e 3.3: Simple Mo ing A e age Equa ion 𝐸𝑀𝐴𝑡,𝑙=∑𝜆𝑖𝑃𝑡−𝑖 𝑐𝑙𝑖=0 ∑𝜆𝑖 𝑙𝑖=0 Figu e 3.4: Exponen ial Mo ing A e age Equa ion • 𝑃𝑡−𝑖 𝑐 is he p ice o c yp ocu ency c a close o hou 𝑡−𝑖 • 𝜆 is he decay ac o ,0≺𝜆≼1 • 𝑙 is he lookback pe iod in hou s Bollinge Bands (BB) ocus on ola ili y as a key by using s anda d de ia ion in band calcula ions. The bands a e made by a cen al line using SMA, and uppe and lowe Simple Pe cen age Change Mo ing A e ages Bollinge Bands 21 bands mi o ing his a e age by s anda d de ia ions c ea ing non-symme ic bands unlike mo ing a e age en elopes, which shi bands ela i e o he a e age. Aimed a c ea ing bands sensi i e o ex eme de ia ions wi h quick eac ion o la ge p ice luc ua ions, his app oach sugges s a lookback pe iod o wen y uni s wi h wo s anda d de ia ions (Williams, 2006). Bollinge Bands a e e sa ile, applicable o a ious da a equencies om in aday o mon hly. Ra he han gi ing absolu e buy o sell signals, Bollinge Bands assess whe he p ices a e high o low ela i e o ecen his o y. They o e a amewo k o unde s anding p ice mo emen s in ela ion o indica o s, emphasizing a ela i e pe spec i e. 𝑀𝐵𝑡,ℎ=∑𝑃𝑡−𝑖 𝑐ℎ 𝑖=0ℎ 𝑈𝐵𝑡,ℎ=𝑀𝐵𝑡,ℎ+ 𝐷 √∑(𝑃𝑡−𝑖 𝑐−𝑀𝐵𝑡,ℎ ) ℎ 𝑖=0 ℎ 𝐿𝐵𝑡,ℎ=𝑀𝐵𝑡,ℎ− 𝐷 √∑(𝑃𝑡−𝑖 𝑐−𝑀𝐵𝑡,ℎ ) ℎ 𝑖=0 ℎ 𝐵𝐵𝑃𝑡,ℎ=𝑃𝑡𝑐−𝐿𝐵𝑡,ℎ 𝑈𝐵𝑡,ℎ−𝐿𝐵𝑡,ℎ Figu e 3.5: Bollinge Band Equa ions • 𝑃𝑡−𝑖 𝑐 is he p ice o c yp ocu ency 𝑐 a close o hou 𝑡−𝑖 • ℎ is he numbe o hou s in he lookback pe iod • 𝑡 is he cu en hou • 𝑀𝐵𝑡,ℎ ,𝑈𝐵𝑡,ℎ 𝑎𝑛𝑑 𝐿𝐵𝑡,ℎ a e espec i ely he Middle, Uppe and Lowe Band alues a he close o hou 𝑡 ha ing a lookback pe iod o ℎ hou s • 𝐵𝐵𝑃𝑡,ℎ is he Bollinge Bands Pe cen age (BBP), which is a me ic used o gauge whe e he cu en p ice is ela i e o he Bollinge Bands. The Rela i e S eng h Index (RSI) se es as a momen um oscilla o , e alua ing he speed and size o p ice changes o de e mine i a ma ke is o e bough o o e sold. Typically calcula ed using a lookback pe iod o ou een uni s, he RSI compa es he a e age gain o up pe iods o he a e age loss o down pe iods wi hin his ime ame. I s alues ange om 0 o 100, wi h eadings abo e 70 indica ing o e bough condi ions and hose below 30 sugges ing o e sold condi ions wi h di e gence be ween RSI and p ice o en an icipa ing a po en ial end e e sal (Rani, 2020). 𝑅𝑆ℎ= 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐺𝑎𝑖𝑛ℎ 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐿𝑜𝑠𝑠ℎ Rela i e S eng h Index 22 𝑅𝑆𝐼ℎ=100−( 100 1+𝑅𝑆ℎ) Figu e 3.6: Rela i e S eng h Index Equa ion • ℎ is he numbe o hou s in he lookback pe iod • 𝑡 is he cu en hou • 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐺𝑎𝑖𝑛ℎ= 𝑆𝑢𝑚 𝑜𝑓 𝐺𝑎𝑖𝑛𝑠𝑡 ℎ • 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐿𝑜𝑠𝑠ℎ= 𝑆𝑢𝑚 𝑜𝑓 𝐿𝑜𝑠𝑠𝑒𝑠𝑡 ℎ • 𝐺𝑎𝑖𝑛𝑠𝑡={∆𝑃𝑡𝑐 | 𝑃𝑡𝑐>0} • 𝐿𝑜𝑠𝑠𝑒𝑠𝑡={∆𝑃𝑡𝑐 | 𝑃𝑡𝑐<0} The coe icien o a ia ion (CV) measu es he ela i e a iabili y o a da ase compa ed o i s a e age, i.e. 𝐶𝑉= 𝜎 𝜇 Figu e 3.7: Coe icien o Va iance Equa ion • Whe e 𝜎 is he a e age o he da ase , • And 𝜇 is he measu e o he dispe sion o a iabili y o he da ase . 3.4. Da a No maliza ion Da ase scaling, o no maliza ion, is a c i ical p ep ocessing s ep in machine lea ning pipelines aimed a ha monizing ea u e scales o ensu e uni o mi y. This adjus men is essen ial o enhancing he pe o mance o classi ica ion models. Equalizing he scales o ea u es p e en s a ibu es wi h la ge o wide nume ical anges om domina ing hose wi h na owe o lowe anges. This p e en s biases ha could o he wise a ise, ensu ing ha a ibu es con ibu e p opo ionally o he analysis ega dless o scale. Consequen ly, da ase scaling mi iga es bias and imp o es classi ica ion pe o mance. Resea ch consis en ly suppo s he idea ha scaling da a be o e model aining signi ican ly boos s pe o mance compa ed o using non-scaled da a. Selec ing he mos sui able echnique is a c ucial me hodological decision, as s udies ha e shown ha an inapp op ia e scaling me hod can be mo e de imen al han no scaling he da a a all. Thus, ca e ul conside a ion is necessa y o op imize model pe o mance (Amo im, Ca alcan i, & C uz, 2023). Min-max Scale The Min-max Scale is a echnique used o ans o m ea u e scales, ensu ing ha he ans o med alues all wi hin he in e al [0,1]. In his me hod, he scaling ac o is Coe icien o Va iance 23 de e mined by he a ibu e's ange, while he minimum alue de e mines he ansla ional ec o . As a esul , his echnique gua an ees a new minimum o ze o and a new maximum o one. Howe e , i is impo an o conside ha he Min-max Scale may encoun e di icul ies in equalizing means and a iances o dis ibu ions, pa icula ly when dealing wi h da a con aining ou lie s. This limi a ion should be conside ed when deciding whe he o use his me hod in da a p ep ocessing. 𝑥𝑖′= 𝑥𝑖− 𝑥𝑚𝑖𝑛 𝑥𝑚𝑎𝑥− 𝑥𝑚𝑖𝑛 Figu e 3.8: Min-max Fo mula 24 4. Me hodology The me hodology sec ion o his hesis del es in o he comp ehensi e a chi ec u e o he amewo k employed o he analysis. I begins wi h an o e iew o he o e all design, p o iding insigh in o how he a ious componen s in e ac and unc ion cohesi ely. Following his, each sec ion o he amewo k is examined in de ail, highligh ing he speci ic oles and ope a ions ha con ibu e o he sys em's pe o mance. By sys ema ically b eaking down he a chi ec u e and i s componen s, his sec ion aims o o e a clea and p ecise unde s anding o he me hodology unde pinning he esea ch. 4.1. A chi ec u e The sys em's a chi ec u al amewo k is o ganized in o i e hie a chical laye s, each designed o suppo speci ic s ages o da a p ocessing and analy ical inqui y. Figu e 4.1 p o ides a isual ep esen a ion o he low o in o ma ion wi hin he p oposed solu ion. As depic ed, he ou pu o each laye se es as he inpu o he subsequen laye . Figu e 4.1: Hie a chical Flow o In o ma ion in he P oposed Solu ion. 31 • 𝛼 is he slope o linea eg ession • 𝐴𝑐𝑡𝑖𝑜𝑛𝑐 is he ac ion o c yp ocu ency 𝑐 4.3.2. Po olio Weigh The po olio weigh is esponsible o de e mining he weigh o each c yp ocu ency wi h he same ac ion o buy o sell un il he nex ebalancing pe iod o 4 hou s. In his hesis, wo ypes o decision c i e ia we e implemen ed. Fi s , an equally weigh ed app oach was u ilized, whe e all c yp ocu encies a e gi en he same amoun o ele ance in ou po olio. This me hod is employed in bo h he momen um and end- ollowing ading s a egy app oaches, and he po olio weigh is de ined as: 𝑃𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜𝑊𝑒𝑖𝑔𝑡ℎ𝑐=1 ∑𝑐 • Whe e ∑𝑐 is he summa ion o c yp ocu encies in he po olio. Second, he ime-weigh ed app oach is solely used wi h he end- ollowing s a egy. In his app oach, he weigh o each oken in he po olio is de e mined by he numbe o consecu i e ebalancing pe iods i has emained an inlie , i ’s du a ion. This me hod aims o adjus he po olio dynamically based on bo h he end di ec ion and he oken's s abili y. Addi ionally, a maximum ime limi o i e pe iods is implemen ed o p e en o e ly s able coins om domina ing he po olio dynamics, ensu ing a balanced alloca ion. The po olio weigh is de ined as: 𝑇𝑖𝑚𝑒𝑐= 𝑚𝑖𝑛(𝑁𝑐,5) 𝑃𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜𝑊𝑒𝑖𝑔𝑡ℎ𝑐=𝑇𝑖𝑚𝑒𝑐 ∑𝑇𝑖𝑚𝑒𝑐 • Whe e 𝑁𝑐 is he numbe o consecu i e ebalance pe iods wi h c yp ocu ency 𝑐 conside ed inline • And ∑𝑇𝑖𝑚𝑒𝑐 is he summa ion o all 𝑇𝑖𝑚𝑒𝑐 o all c yp ocu encies in he same ebalance pe iod 4.4. Ma ke Momen um Signal In addi ion o e alua ing a educed uni e se and a ading s a egy componen , we aim o assess he combina ions' pe o mance ac oss empo al spaces de ined as bullish, bea ish, o neu al, ac oss mul iple con idence le els. These con idence le els se e as pa ame e s ha in oduce sensi i i y egula o s o he classi ica ion o ma ke momen um. This assessmen will help us unde s and i he e is ele an in o ma ion o be ob ained om he o e all ma ke momen um ha can signi ican ly impac ou decision o educed uni e se and ading s a egy combina ion, and i so, how impo an i is. The classi ica ion ask begins by compu ing he daily pe cen age change o he ma ke capi aliza ion da a, ollowed by he calcula ion o i s 5-day simple mo ing a e age. 32 Following a sys ema ic app oach, we e alua e i e con idence le els o classi ying daily ma ke momen um. I is impo an o no e ha he classi ica ion p o ided o day 𝑑 a e used on day 𝑑+ 1 o a oid in oducing lookahead bias. The ma ke classi ica ion can be de ined as: 𝑀𝑎𝑟𝑘𝑒𝑡 𝐶𝑙𝑎𝑠𝑠𝑑+1= { 𝐵𝑢𝑙𝑙, 𝑆𝑀𝐴5 𝑑≥ 𝑏𝑝𝑠 𝑁𝑒𝑢𝑡𝑟𝑎𝑙, − 𝑏𝑝𝑠≤𝑆𝑀𝐴5 𝑑≤ 𝑏𝑝𝑠 𝐵𝑒𝑎𝑟, 𝑆𝑀𝐴5 𝑑≤− 𝑏𝑝𝑠 • 𝑀𝑎𝑟𝑘𝑒𝑡 𝐶𝑙𝑎𝑠𝑠𝑑+1 is he ma ke momen um classi ica ion o he day 𝑑 + 1 • 𝑆𝑀𝐴5 𝑑 is he simple mo ing a e age o he pe cen age change o e 5 days on he day 𝑑 • 𝑏𝑝𝑠 is he le el o con idence in he classi ica ion p o ided • 𝑏𝑝𝑠 ∈ {10,20,30,40,50} in basis poin s. 4.5. E alua ion Me ics To gauge he s a egies' e ec i eness, we ha e c a ed a sys ema ic e alua ion me hod. This includes acking key me ics, namely A e age P o i and Loss (APL), Sha pe Ra io, So ino Ra io, Max D aw Down (MDD), Ku osis and Skewness which we desc ibe nex . A e age P o i and Loss (APL) quan i ies he gain o loss om a se ies o ades by a e aging he p o i s and losses o indi idual ebalancing pe iods. A high APL sugges s a p o i able s a egy, while a low APL may indica e a less success ul app oach. 𝐴𝑃𝐿= ∑𝑅𝑖 𝑛 Figu e 4.6: A e age P o i & Loss Equa ion • ∑𝑅𝑖 is he ime se ies con aining e u ns on in es men • n is he numbe o ebalancing pe iods. The Sha pe Ra io is a me ic used o e alua e isk-adjus ed e u ns by compa ing he excess e u n o an in es men o i s isk. While no s a is ically signi ican on i s own, i se es as a aluable ool o compa ing he pe o mance o asse s o po olios. Highe Sha pe a ios indica e be e isk-adjus ed e u ns, which is ypically p e e ed by in es o s (Sha pe, 1998). 𝑆𝑅= 𝑅𝑂𝐼𝑝− 𝑅𝑓 𝜎𝑝 Figu e 4.7: Sha pe Ra io Equa ion A e age P o i and Loss Sha pe Ra io 33 • 𝑅𝑂𝐼𝑝 is he a e age e u n o he asse /po olio • 𝑅𝑓 is he isk- ee a e • 𝜎𝑝 is he s anda d de ia ion o he asse /po olio The So ino a io o e s a nuanced al e na i e o he Sha pe a io. While he Sha pe a io conside s all ola ili y, including posi i e ola ili y, he So ino a io ocuses solely on nega i e ola ili y. This adjus men add esses a limi a ion o he Sha pe a io, whe e posi i e ola ili y can un ai ly penalize he a io. The So ino a io eplaces he s anda d de ia ion wi h he downside de ia ion, which measu es he ola ili y o e u ns below a speci ied minimum accep able e u n (MAR), ypically se o ze o (So ino, 1994). 𝐷𝑜𝑤𝑛𝑠𝑖𝑑𝑒𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛(𝑅𝑥)= √∑(𝑅𝑖−𝑀𝐴𝑅)2 𝑤ℎ𝑒𝑟𝑒 𝑅𝑖≺𝑀𝐴𝑅 𝑛 𝑆𝑜𝑟𝑡𝑖𝑛𝑜𝑅𝑎𝑡𝑖𝑜(𝑥)= 𝑅𝑂𝐼𝑝− 𝑅𝑓 𝐷𝑜𝑤𝑛𝑠𝑖𝑑𝑒𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛(𝑅𝑥) Figu e 4.8: So ino Ra io Equa ion • 𝑅𝑂𝐼𝑝 is he a e age e u n o he asse /po olio • 𝑅𝑓 is he isk- ee a e • 𝑅𝑖 is he ime se ies con aining e u ns on in es men Maximum d awdown is c ucial o assessing downside isk in in es men s o s a egies, ep esen ing he la ges decline in a po olio's alue om peak o ough be o e a new peak is es ablished. I p o ides insigh in o ela i e downside isk and is pa icula ly ele an in ola ile c yp ocu ency ma ke s. Conside ing maximum d awdown alongside ola ili y is essen ial when e alua ing in es men isks. (Magdon-Ismail, 2004) 𝑀𝐷𝐷= 𝑚𝑎𝑥𝑡 ∈ ( 𝑆𝑡𝑎𝑟𝑡𝐷𝑎𝑡𝑒, 𝐸𝑛𝑑𝐷𝑎𝑡𝑒)[𝑚𝑎𝑥𝑡 ∈ ( 𝑆𝑡𝑎𝑟𝑡𝐷𝑎𝑡𝑒, 𝑇)(𝑅𝑂𝐼𝑡)−𝑅𝑂𝐼𝑇] Figu e 4.9: Max D aw Down Equa ion Ku osis desc ibes he ail shape o da a dis ibu ions by compa ing he weigh o he ails o he cen e o he dis ibu ion. I is no a measu e o he peakedness o he dis ibu ion. High ku osis alues indica e ha he ails ex end u he om he cen e , while low ku osis alues indica e sho e ails and a sha pe peak (Chouksey, 2018). 𝐾𝑢𝑟𝑡𝑜𝑠𝑖𝑠 = ∑(𝑌𝑖− 𝑌)4/𝑁 𝑁 𝑖=0 𝑆4 So ino Ra io Max D aw Down Ku osis 34 Figu e 4.10: Ku osis Equa ion • 𝑌 is he mean • 𝑆 is he s anda d de ia ion • 𝑁 is he numbe o da a poin s Skewness desc ibes he symme y o a dis ibu ion. Nega i e alues indica e le skewness, while posi i e alues indica e igh skewness. When skewness is close o ze o, he dis ibu ion app oxima es o symme ic (Chouksey, 2018). 𝑆𝑘𝑒𝑤𝑛𝑒𝑠𝑠 = ∑(𝑌𝑖− 𝑌)3/𝑁 𝑁 𝑖=0 𝑆3 Figu e 4.11: Skewness Equa ion • 𝑌 is he mean • 𝑆 is he s anda d de ia ion • 𝑁 is he numbe o da a poin s Skewness 35 5. Resul s and Analysis 5.1. Resul s Fo he discussion o esul s, we will ha e access o a o al o 16,200 eco ds. The a ionale behind his numbe o eco ds can be ound in he able below, which desc ibes each pa ame e used du ing he s udy, i s ela ion o a p ocess and he numbe o di e en alues used. Table 5.1: Pa ame e O e iew Pa ame e s Combina ions Uni e se Fo ma ion 90 Lookback Pe iod 3 Me ics G oup 3 Selec ion Me hod 2 Uni e se Size 5 S a egy De ini ion 12 Ac ion 2 S a egy 3 T ansac ion Cos s 2 Ma ke Momen um Signal 15 Con idence Le el 5 Ma ke Class 3 To al Resul s 16200 The sys ema ic app oach o in oducing pa ame e s o es se e al alues a each decision-making s ep o he algo i hm has le us wi h a high dimensionali y p oblem ha can be assessed in a la ge a ie y o ways. This p ojec adop s h ee di e en pe spec i es deemed ele an o he esea ch ques ions p oposed. Fi s ly, he examina ion o he a e age pe o mance me ics o each pa ame e ’s alues, emaining agnos ic o all o he pa ame e s in he s udy. This in ol es analyzing how each pa ame e independen ly in luences he ou come, p o iding a clea unde s anding o hei isola ed e ec s. Secondly, an analysis o he low o he op imal se o pa ame e alues ac oss a ious o ganiza ional s uc u es. This analysis includes a comp ehensi e examina ion o bo h he ne and g oss e u ns o he po olios, ac o ing in ansac ion cos s. Finally, he hi d iewpoin ocuses on he op 20 pe cen o eco ds anked by A e age P o i and Loss (APL). This high-pe o ming subse is sc u inized o iden i y common cha ac e is ics ha lead o supe io pe o mance, p o iding insigh s in o he mos e ec i e pa ame e con igu a ions. 5.1.1. Bes o e all alue pe pa ame e In his sec ion, 16,200 combina ions gene a ed h oughou his p ojec a e g ouped solely on indi idual pa ame e s. 36 PCA consis en ly ou pe o ms SVM ac oss a ious e u n me ics as well as ola ili y and isk me ics, lea ing no oom o doub abou i s o e all supe io i y. Momen um me ics eme ge as he op pe o me s, while g ow h-o ien ed me ics exhibi he leas skewness. A clea posi i e co ela ion is obse ed be ween uni e se size and pe o mance, e ealing low signi icance o he uni e se educ ion e o . A mid- e m lookback pe iod o 12 hou s p o es o be he mos eliable, o e ing balanced e u ns and isk managemen (see Appendix A). Table 5.2: Selec ion Me hod Analysis. Bo h equally weigh ed and ime-weigh ed end- ollowing ading s a egies su pass he benchma k momen um s a egy, exhibi ing simila isk le els. No ably, he weigh ed op ion s ands ou wi h supe io e u n me ics and a highe Sha pe a io (see Appendix B). A subs an ial pe o mance di e en ial is obse ed wi hin he po olio ac ion decision, sho po olios ou pe o m long po olios, despi e sligh ly highe ku osis. Table 5.3: Po olio Ac ion analysis. Ac ion T ades Sha pe So ino MDD APL Ku osis Skewed Coun Buy 2329 -2.4704 -0.0681 -0.9314 -0.001184 17.2754 -0.2824 8100 Sell 2329 -0.1269 -0.0018 -0.6959 0.000001 23.4231 -0.0371 8100 The neu al ma ke class demons a es he mos p omising alues in e ms o e u ns and isk me ics. Howe e , i is impo an o no e ha he sample size o he neu al ma ke is signi ican ly smalle compa ed o he bull and bea ma ke s, which educes ou con idence in hese esul s. The bull ma ke , wi h a sample size wice as la ge, anks second, sligh ly ou pe o ming he bea ma ke in APL (see Appendix C). The analysis o ma ke classi ica ion con idence le els indica es a nega i e co ela ion wi h pe o mance me ics. In o he wo ds, as ma ke con idence le els ise, pe o mance ends o dec ease. Uni e se Fo ma ion Pa ame e s Me hod T ades Sha pe So ino MDD APL Ku osis Skewed Coun PCA 2328 -1.1234 -0.0304 -0.7944 -0.0005 13.8905 -0.0411 8100 SVM 2328 -1.4739 -0.0395 -0.8329 -0.0007 26.8080 -0.2784 8100 S a egy De ini ion Pa ame e s Ma ke Momen um Signal Pa ame e s 37 Table 5.4: Ma ke Class Con idence Le el Analysis Con . Le el T ades Sha pe So ino MDD APL Ku osis Skewed Coun 10 2329 -1.2214 -0.0322 -0.7712 -0.0005 19.9119 -0.1135 3240 20 2329 -1.2912 -0.0350 -0.8033 -0.0006 20.4440 -0.1574 3240 30 2329 -1.3094 -0.0352 -0.8197 -0.0006 21.0207 -0.1912 3240 40 2329 -1.3290 -0.0359 -0.8323 -0.0006 20.3526 -0.1737 3240 50 2329 -1.3423 -0.0364 -0.8416 -0.0006 20.0170 -0.1630 3240 In summa y, PCA, end- ollowing s a egies wi h weigh ed po olios, and lowe con idence le el ma ke classi ica ions eme ge as he op pe o me s in hei espec i e ca ego ies. 5.1.2. Pa ame e Combina ion Analysis In his sec ion, he app oach g adually educes he combina ions in he subg oups deemed mos wo hy o u he analysis, p oceeding in he o de o ma ke momen um signal pa ame e s o s a egy de ini ion pa ame e s o uni e se o ma ion pa ame e s. In his sec ion, 8100 combina ions o long po olios a e analyzed o de e mine he op imal pa ame e con igu a ion o buying s a egies. The esul s indica e ha he bull ma ke class should be used o u he analysis. While he neu al ma ke class exhibi s be e isk ac o s, i s smalle sample size and lowe e u ns make i less sui able as he bes app oach. Wi hin he bull ma ke , he highes con idence le el consis en ly ou pe o ms ac oss all me ics, excep o skewness, which shows an in e es ing nega i e co ela ion by imp o ing wi h lowe con idence le els. Fo he s a egy componen , he ime-weigh ed end- ollowing ading s a egy eme ges as he bes choice. The s a egy is selec ed due o i s high e u ns’ po en ial and balanced isk ac o s, clea ly ou pe o ming o he s a egies in e ms o bo h e u n me ics and isk managemen . Bo h he me ics g oup and selec ion me hod show no ambigui y, wi h he g ow h me ics g oup and PCA selec ion me hod pe o ming he bes among hei pee s. Al hough hese combina ions indica e a mo e isk-p one app oach, hey o e highe ewa ds. When i comes o he uni e se size pa ame e , educing he uni e se does no seem e ec i e o long po olios. Pe o mance shows a clea end o imp o emen as he size o he uni e se inc eases. This sugges s ha a la ge uni e se p o ides be e di e si ica ion and oppo uni ies o highe e u ns. The lookback pe iod, whe he mid- e m o sho - e m, pe o ms simila ly, allowing o some lexibili y in his pa ame e ’s choice. Amongs he long po olios, his app oach anks 35 h in e ms o APL and 355 h a e accoun ing o ansac ion cos s. Bes Combina ions o Long Po olios 38 Figu e 5.1: Ne and G oss Re u ns o Bes Long po olio. In conclusion, he bes pa ame e s combina ion o long po olios in a buying s a egy in ol es ope a ing wi hin a bull ma ke , using a high con idence le el, and employing a ime-weigh ed end- ollowing s a egy. The g ow h me ics and PCA me hod should be applied, wi h lexibili y in he lookback pe iod, al hough la ge uni e ses end o yield be e pe o mance. In his sec ion, 8100 combina ions o sho po olios a e analyzed o de e mine he op imal pa ame e con igu a ion o selling s a egies. The esul s e eal ha he bes con igu a ion appea s in a bea ma ke . This con igu a ion achie es he highes Sha pe a io and APL, al hough i does su e om he highes ku osis. The chosen s a egy is a end- ollowing app oach wi h a ime- weigh ed po olio, which e ec i ely cap u es ma ke ends and manages isks. In e ms o uni e se selec ion, he uni e se is educed using SVM me hodology. SVM p o es o be supe io o e all, despi e exhibi ing highe skewness and ku osis. This sugges s ha while SVM may in oduce some addi ional isk, i s o e all pe o mance bene i s ou weigh hese d awbacks. Re u ns a e he p e e ed me ics in his analysis, consis en ly pe o ming be e ac oss he boa d. Pe o mance shows a clea end o imp o emen as he size o he uni e se dec eases despi e esul ing in highe maximum d awdowns and wo se skewness. Fo he lookback pe iod pa ame e , longe ime ames demons a e be e pe o mance o e all, sugges ing ha an ex ended his o ical iew aids in iden i ying mo e eliable ends. Amongs he sho po olios, his app oach anks 10 h in e ms o mean P&L and 29 h a e accoun ing o ansac ion cos s. Bes Combina ions o Sho Po olios 39 Figu e 5.2: Ne and G oss Re u ns o Bes Sho po olio. In conclusion, he bes pa ame e combina ion o sho po olios in a selling s a egy in ol es ope a ing wi hin a bea ma ke employing a end- ollowing s a egy wi h a ime-weigh ed po olio. The SVM me hod should be used o educe he uni e se, wi h a ocus on e u ns and keeping uni e se size low. Longe ime ames should be u ilized o enhance pe o mance. Wi h a ocus on iden i ying he mos e ec i e con igu a ions o a ying ma ke condi ions, 5400 combina ions o each ma ke class a e analyzed. The le el o con idence pa ame e shows a posi i e co ela ion wi h he pe o mance me ics sugges ing a s onge eliabili y on ma ke ends. The analysis consis en ly shows ha sho po olios a e he op pe o me s in all ma ke classes. This inding highligh s he e ec i eness o sho selling s a egies. In bull ma ke s, end- ollowing ime-weigh ed po olios exhibi sligh ly be e pe o mance compa ed o momen um po olios. The end- ollowing app oach, especially when used wi h a ime-weigh ed po olio, is adep a cap u ing upwa d ends, leading o be e e u ns. The weigh ed aspec o he s a egy allows o a mo e nuanced and esponsi e app oach o ma ke mo emen s (see Appendix D). The pe o mance gap be ween s a egies widens in he neu al ma ke , wi h ime- weigh ed end- ollowing po olios signi ican ly ou pe o ming momen um po olios. In hese ma ke condi ions, whe e he di ec ion is no clea ly de ined, he adap abili y o end- ollowing s a egies p o es ad an ageous (see Appendix E). Du ing bea ma ke s, he end- ollowing ime-weigh ed po olio s ands ou as he supe io choice. This s a egy no only deli e s be e e u ns bu also manages isk mo e e ec i ely in declining ma ke s. Ac oss all ma ke classes, he use o SVM and a smalle uni e se size is a common heme. This me hodological choice ensu es ha he s a egy is applied o a well-selec ed subse o c yp ocu encies, enhancing o e all pe o mance. The SVM me hodology aids in iden i ying he mos ele an and high-po en ial c yp ocu encies, while he educed uni e se size main ains a ocus on quali y o e quan i y. Momen um me ics a e p e e ed in ma ke classes expe iencing subs an ial shi s. These me ics a e e ec i e a quickly cap u ing and exploi ing apid changes in he Bes Combina ions pe Ma ke Class 40 ma ke , p o iding an edge in highly dynamic en i onmen s. G ow h me ics a e employed in he neu al ma ke , emphasizing s abili y and consis en pe o mance. These me ics a e less eac i e o sho - e m ola ili y, which is c ucial in a ma ke whe e clea ends a e absen . The impo ance o he lookback pe iod a ies ac oss ma ke condi ions. In bull ma ke s, sho e lookback pe iods a e a o ed as hey help in quickly iden i ying and capi alizing on upwa d ends. Con e sely, in bea ma ke s, longe lookback pe iods a e p e e ed. They o e a comp ehensi e iew o long- e m downwa d ends, aiding in mo e s a egic decision-making. Figu e 5.3: Bea Ma ke Op imal Combina ion Flow 5.1.3. Top Ranked Combina ions Analysis In his sec ion, he op 20 pe cen o combina ions anked by APL, accoun ing o 3240 combina ions a e analyzed. This subse ep esen s he mos p o i able and p omising pa ame e con igu a ions, o e ing aluable insigh s in o he ac o s con ibu ing o hei success. When examining he op combina ions, i is c ucial o analyze he pe cen ages o use o each pa ame e and s a egy. Among he op combina ions, SVM eme ges as he p e e ed me hod, being u ilized 60% o he ime. 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Jou nal o Asse Managemen , 15(4), 261-278. h ps://doi.o g/10.1057/jam.2014.25 51 Appendix A Appendix B Appendix C Appendix D Lookback T ades Sha pe So ino MDD APL Ku osis Skewed Coun 4 2330 -1.8623 -0.0501 -0.8469 -0.000890 21.3508 -0.3753 5400 12 2329 -0.8744 -0.0243 -0.7899 -0.000370 20.0291 0.1157 5400 24 2328 -1.1593 -0.0304 -0.8042 -0.000518 19.6678 -0.2197 5400 S a egy T ades Sha pe So ino MDD APL Ku osis Skewed Coun Momen um 2329 -1.8570 -0.0491 -0.8256 -0.000849 27.3525 -0.4492 5400 T end 2329 -1.1472 -0.0313 -0.8119 -0.000518 16.7198 -0.0361 5400 T end Weigh ed 2329 -0.8918 -0.0244 -0.8034 -0.000410 16.9754 0.0061 5400 Ma ke T ades Sha pe So ino MDD APL Ku osis Skewed Coun Bea 2258 -1.5059 -0.0378 -0.8497 -0.000834 27.1663 -0.1143 5400 Bull 3175 -1.3971 -0.0334 -0.9092 -0.000499 17.1102 -0.1734 5400 Neu al 1553 -0.9929 -0.0337 -0.6820 -0.000444 16.7713 -0.1915 5400 52 Appendix E 53