Commodity Future Money Flows Trading Strategies Based on HMM

Transcription

1 Inernaonal Journal of Sascs and Probably; Vol. 6, No. 4; July 2017 ISSN E-ISSN Publshed by Canadan Cener of Scence and Educaon Commody Fuure Money Flows Tradng Sraeges Based on HMM Jshan Ma 1 & Yuanbao Zhang 2 1 Fnance Deparmen of Inernaonal Busness School, Jnan Unversy, Zhuha, Chna 2 Elecrcal And Informaon College, Jnan Unversy, Zhuha, Chna Correspondence: Jshan Ma, Jnan Unversy, No.206, Qanshan Road, Xangzhou Dsrc, Zhuha, Chna. E-mal: @qq.com Receved: May 4, 2017 Acceped: May 24, 2017 Onlne Publshed: June 7, 2017 do: /jsp.v6n4p16 URL: hps://do.org/ /jsp.v6n4p16 Absrac Ths paper ams o esablsh a quanave radng sraegy of commody fuures based on marke money flows. Frsly, we use Accumulaon/Dsrbuon ndex o respecvely consruc he CMF ndex whch represens he rao of oal capal flows o oal volume, and he CHO ndex whch represens he exponenal movng average of he cumulave capal flows. In vew of he dfferen flows of money beween buyers and sellers, he esablshmen of he ransacon ne volume ndex VTL s used o descrbe respecvely he flow of money beween buyers and sellers. On hs bass, he HMM model s nroduced, and he above hree knds of ndexes are combned o choose he me, a whch we execue he sop-loss operaon and rsk conrol. Fnally, all performance ndex values of he sraegy are as follows: he rae of nal capal reurn s %, he annual rae of reurn s 99.86%, he maxmum reracemen rae s 15.73%, he Sharpe rae s 2.05 and he prce earnngs rao s Keywords: money flows, HMM model 1. Inroducon Money flows ncludes he flow drecon and volume of money, whch s a sandard echncal ndex, reflecng he excess demand or supply on one sock of curren marke. Vewng he acve buyng of a sock as a capal nflow and he acve sellng as a capal ouflow, f he dfference s posve, an excess demand wll be formed and f s negave, an excess supply wll be formed. The value of money flow s ha reflecs no only he excess supply and demand of he curren sock, bu also he excess supply and demand of fuure socks. Tha s, n heory, he money flow ndex s no only correlaed wh he rae of reurn on he curren socks, bu also he rae of reurn on fuure socks. In he fuures markes, because of he exsence of shorng mechansm, we canno drecly use he money flow formula of he sock marke o depc he real money flow rules of fuures conrac. For example, he prce for a fuures conrac s down, probably resulng from money nflows or ouflows. Ths paper akes no accoun he facors such as he amoun of holdng and he urnover and he flucuaon of he prce, o depc he flow drecon of money of he fuures producs. Many foregn researchers have done grea research on money fow. Clark (1974) proposed Mxure Dsrbuon Hypohess (MDH) and hough every day here was an unpredcably ha wen no he sock marke and had an mpac on sock radng. Andersen (1996) mproved he MDH heory by sudyng he mcrosrucure of he marke and go he Modfed Mxure Dsrbuon Model (MMM). Km (2000) ook use of he money flow daa p fnd he mbalance of order had a negave predcve effec on sock reurns. Chan and Lakonshok (1995) consdered ha money flows were posvely correlaed wh hsorcal yelds. However, Benne and Sas (2001) found ha he flow of money was relaed o he ncome of same perod and he flow of hsorcal funds could predc fuure flows. Frazzn and Lamon (2008) used muual fund flows as a measure of ndvdual nvesors' senmen oward dfferen socks, hey found ha he curren hgh senmen led o lower sock reurns n he fuure. Cambell and Ramadora (2009) hough ha he agency day order sream has a negave effec on he fuure earnngs of he sock, especally he negave effec of he commsson sells orders. The domesc exploraon of money flow sared lae bu also acheve ceran resuls. Wehua Zhu (2009) proposed ha hrough guaraneeng he compleeness and susanably of nformed radng regulaon and mprovng he corporae governance, mprovng he sysem of nvesor proecon, buldng lawful nsder radng marke and dsclosure sysem and so on we could mprove he regulaon effcency of nformed radng. Qmng Tang and Zhang Yun (2009) hough nformed radng could smulae he nformaon asymmery of company level, causng he radng volume flucuaons. 16

2 hp://jsp.ccsene.org Inernaonal Journal of Sascs and Probably Vol. 6, No. 4; 2017 Gao L and Wedong Fan (2002) hrough he cash flow esmaon of he sock marke n Chna, analysed he nfluence of he macro capal srucure change caused by he source of funds, he capal srucure and so on n he sock marke on he marke behavor of macroeconomc man body. Luq Lang (2008) dd he research on aded compuer analyss sysem of he secures funds flow from he perspecve of compuer engneerng, compuer. 2. Model Preparaon Hdden Markov Model s a sascal model used o descrbe a Markov process wh mplc unknown parameers. Fgure 1 s a a hree-sae Hdden Markov Model sae ranson dagram, where x represens mpled condon, y represens observable oupu, a represens sae ranson probably, b represens oupu probably. a12 a23 b1 x1 x2 x3 a21 b2 b3 y1 y2 y3 Fgure 1. Hdden Markov Model Sae Transon Dagram For HMM, has hree mporan assumpons as follows: assumpon 1: he Markov hypohess (The sae forms a frs order Markov chan)... P X X X P X X assumpon 2: mmobly hypohess(the sae has nohng o do wh he me) P X X P X X,, j 1 j1 j assumpon 3: oupu ndependence hypohess(the oupu s only relaed o he curren sae) There s a probably on he relaonshp beween hdden and observable saes, assumed for P(O1 H). If here are hree knds of observable sae, hen P O H P O H P O H In hs way, we can ge confuson marx. The conen of he marx s he probably ha a hdden sae s observed respecvely o several dfferen observable saes. For example, Index1 Index2 Index3 Sae Sae Sae Fgure 2 reflecs he evoluon of he model, where he box represens he hdden sae, he crcle represens he observable sae, and he arrow ndcaes he probably of dependency beween saes. 17

3 hp://jsp.ccsene.org Inernaonal Journal of Sascs and Probably Vol. 6, No. 4; 2017 S A S A S A S A S B B B K K K K K Fgure 2. The Evoluon of The Model Wh he collecon N, M,, A, B represenng he HMM model, n he model, N s he number of hdden saes, whch s known or by speculaon, M s he number of observable saes, whch can be obaned from he ranng se, s he probably of nal sae, A a j s he ranson marx of hdden sae Pr x x 1 j B b k represens he probably of he sae whch can be observed due o he hdden sae a one me, namely he confuson marx Pr o x j. Each probably n he sae ransfer marx and he confuson marx s me-ndependen, ha s, when he sysem evolves, hese marces do no change over me. The HMM model for fxed N and M, we use, AB, as s parameer. In he operaon process of hs algorhm, he HMM canno be judged drecly, and for a gven sequence of observable saes O, we canno accuraely fnd ou he opmal parameer o make PO be he larges, so we use forward-backward algorhm (also known as Baum-Welch algorhm) o seek he opmal soluon. Frsly we defne wo auxlary varables, whch are respecvely he probably of sae a me and he probably of sae j a me +1, namely The formula s equal o, j Pq, q j O, 1, j P q, q 1 j O, P O Make use of he precedng varable and he backward varable, he above formula can be represened as j 1 jo 1, j N N 1 j1 j b j b j 1 jo 1 The second varable s defned as he poseror probably, whch s he probably of sae a me n a gven observaon sae sequence and HMM, namely Pq O, Make use of he precedng varable and he backward varable, he above formula can be represened as, and 18

4 hp://jsp.ccsene.org Inernaonal Journal of Sascs and Probably Vol. 6, No. 4; 2017 N 1 The formula s he expecaon of sae a any momen, namely he expecaon of ransfer from he sae o he observed sae o expecaon. In he same way, he formula s also he expecaon of ransfer from sae o sae j, so we defne relaonshp beween he wo varables for N j1, j,1 N,1 T In he parameer learnng process of forward-backward algorhm, updaes he HMM parameers consanly o make PO be he larges. Assumng ha he nal HMM parameer s, AB,,respecvely calculae he forward varable, backward varable and expecaon, updae he HMM parameers based on he followng hree heavy esmae formulas, and erae over. Thus consanly revalung he HMM parameers, and afer many eraons we can ge a maxmum lkelhood esmaes of he HMM model, whch s a local opmal soluon. 3. Index Consrucon 3.1 Accumulaon/Dsrbuon,(A/D) Index 1 T 1,1 N 1 1, o k T 1, j 1 j,1 N,1 j N T 1 T j bjk,1 j N,1 k M j Accumulaon/Dsrbuon (A/D) ndex s an ndex based on radng volume, whch measures he cumulave raffc flow or money flow of flowng no and ou of he produc. In he classcal A/D formula A / D Close Low Hgh Close Hgh Low Volume In hs formula, Hgh, Low, Close respecvely ndcaes he hghes, lowes and closng prce of he K-lne, and Volume ndcaes he correspondng radng volume. When he dfference beween he closng prce and he lowes prce s greaer han he dfference beween he hghes prce and he closng prce, he closng prce s greaer han half he prce of he hghes and he lowes, namely I s now seen as money flowng no he varey; Close Hgh 2 Low When he dfference beween he closng prce and he lowes prce s less han he dfference beween he hghes prce and he closng prce, he closng prce s less han half he prce of he hghes and he lowes, namely Close I s now seen as money flowng ou of he varey. Hgh 2 Low The amoun of money nflows or ouflows n he prce range can be expressed as 19

5 hp://jsp.ccsene.org Inernaonal Journal of Sascs and Probably Vol. 6, No. 4; 2017 Close Low Hgh Close Hgh Low Is range from -1 o 1. The absolue value of he value s closer o 1, ndcang he greaer he amoun of money nflows or ouflows. The classc A/D formula s he amoun of capal nflow/ouflow n he weghed volume of he ransacon, reflecng he overall flow drecon of capal. To furher mprove he classcal A/D formula, add he A/D value of he prevous perod o he A/D value of he curren perod, and ge he classcal ncremen formula Close Low Hgh Close A / D Volume A / D1 Hgh Low Add he exsng A/ D, we can ge he oal capal flows of n perods n 1 A/ D Replace he molecules n he classcal ncremen formula wh he dfference beween he closng prce and he openng prce, and ge anoher represenaon of he A/D formula In he formula, 3.2 CMF Index Close Open A / D Volume A / D1 Hgh Low Open s he openng prce of he K-lne Esablsh money flow ndex accordng o he classc A/D formula 2Close Low Hgh MFV Hgh Low * Volume The CMF ndex s he rao of he sum of capal flows n recen perods o oal radng volume n recen perods MFV CMF Volume Take 30 days for a perod, 0.1as he upper and lower hreshold, and apply o all producs. When he CMF value s greaer han he hreshold we should be gong long, bu when he CMF value s less han he hreshold we should be gong shor. 3.3 CHO Index Esablsh money flow ndex accordng o anoher represenaon of he A/D formula 1 Close Open VAR * Volume Hgh Low Add he VAR 1 from nal perod o curren perod, we can ge accumulave capal sumvar 1. Make exponenal movng average o accumulae capal respecvely on 12 days and 20 days as a perod o form he shor-erm EMA and long-erm EMA. When a shor-erm EMA upward cross a long-erm EMA, forms a gold fork and we should be gong long. On he conrary, when forms a deah fork we should be gong shor. 3.4 Transacon Ne Volume Index VTL The game of buyers and sellers resuls n he fuures marke o ncrease or decrease. The fgure 3 smulaes he endency of he fuures prces change every mnue n 10 mnues. We can see he prces go down n perod AB and CD, FG, GH, IG, suggesng ha he curren marke s he seller's marke and he sellng volume s greaer han he buyng volume, so 20

6 hp://jsp.ccsene.org Inernaonal Journal of Sascs and Probably Vol. 6, No. 4; 2017 he marke s n a sae of money ouflow; conrarly, he prces go up n perod BC, DE, EF, ndcang ha he buyers are engaged and he buyng volume s greaer han he sellng volume, so he marke s n a sae of money nflow. F E I G C G H A B D Fgure 3. Prce Smulaon Pah Ignore he small flucuaons n prce changes, and he prce change suaon afer smplfcaon s shown n fgure 4 F G A B Fgure 4. Prce Pah afer Smplfcaon Consruc he ndex V Volume Hgh Low*2 ABS Close Open When he closng prce s greaer han he openng prce, shown by fgure 4,he componens of he prce pah nclude perod AB Open Low, BF Hgh Close. The oal volume of money nflow/ouflow s Hgh Low, FG Hgh Low *2 ABS Close Open The ndex V reflecs he urnover of he un money flow, he greaer he V, he more acve he marke. In Fgure 4, he buyng volume s correspondng o he perod BF, for 21

7 hp://jsp.ccsene.org Inernaonal Journal of Sascs and Probably reflecng he buyer s flow drecon of money; Vol. 6, No. 4; 2017 V * Hgh Low and he sellng volume s correspondng o he perod AB+FG, for V * Hgh Close Open Low reflecng he seller s flow drecon of money. When he closng prce s less han he openng prce, he drecon of money flow of he buyers and sellers shall be expressed separaely for V * Hgh Open Close Low V * Hgh Low The dfference beween he money flow of he buyers and sellers s he ne volume of he ransacon, whch s represened by nev. The VTL ndex dfferenaes he flow of money beween buyers and sellers, makng up for he shorcomng n he prevous arcles. nev from nal perod o curren perod and ge he cumulave ransacon ne volume of sequence sumnev, whch s used o buld dfferen ypes of ndexes such as cloh Bollnger Band, SMA, Psychologcallne. Add he Through he comparson, ulmaely choosng EMA when gold fork and deah fork o choose he me plays he bes effec. Make exponenal movng average o sumnev respecvely on 12 days and 20 days as a perod o form he shor-erm EMA and long-erm EMA. When a shor-erm EMA upward cross a long-erm EMA, forms a gold fork and we should be gong long. On he conrary, when forms a deah fork we should be gong shor. 4. Correlaon Predcon Informaon Coeffcen(IC), represens he coeffcen of cross secon correlaon beween he facor value of seleced varees and he nex yeld of sock. Through he IC value, we can judge he predcve ably of he facor value on nex yeld of sock. Usually IC s consdered o be more effcen when he IC value s greaer han 0.2 or less han Selec wo varees of Cu and Ta randomly and calculae he IC value respecvely beween CMF ndex, he CHO ndex, he VTL ndex and he fuure yeld of correspondng varees. Fgure 5. The IC value of he CMF ndex of he Cu varey 22

8 hp://jsp.ccsene.org Inernaonal Journal of Sascs and Probably Fgure 6. The IC value of he CMF ndex of he Ta varey Fgure 7. The IC value of he CHO ndex of he Cu varey 23 Vol. 6, No. 4; 2017

9 hp://jsp.ccsene.org Inernaonal Journal of Sascs and Probably Vol. 6, No. 4; 2017 Fgure 8. The IC value of he CHO ndex of he Ta varey Fgure 9. The IC value of he VTL ndex of he Cu varey 24

10 hp://jsp.ccsene.org Inernaonal Journal of Sascs and Probably Vol. 6, No. 4; 2017 Fgure 10. The IC value of he VTL ndex of he Ta varey Accordng o he fgure 5,6,7,8,9,10, we can know Boh radonal CMF, CHO ndex and VTL bul n hs paper, he fuure of commody fuures marke asses yeld has srong ably of explanng, herefore hs paper by usng quanave radng sraegy o each parameer values o consruc n he capure of fuures marke funds flow rule can also oban good reurns. 5. Sraeges Selecon and Reesng For he enry sraegy and sgnal unwndng sraegy based on CMF ndex, ake 30 days for a perod, 0.1as he upper and lower hreshold, and apply o all producs. When he CMF value s greaer han he hreshold we should be gong long, bu when he CMF value s less han he hreshold we should be gong shor. For he enry sraegy and sgnal unwndng sraegy based on CHO ndex, make exponenal movng average o accumulae capal respecvely on 12 days and 20 days as a perod o form he shor-erm EMA and long-erm EMA. When a shor-erm EMA upward cross a long-erm EMA, forms a gold fork and we should be gong long. On he conrary, when forms a deah fork we should be gong shor. For he enry sraegy and sgnal unwndng sraegy based on VTR ndex, make exponenal movng average o sumnev respecvely on 12 days and 20 days as a perod o form he shor-erm EMA and long-erm EMA. When a shor-erm EMA upward cross a long-erm EMA, forms a gold fork and we should be gong long. On he conrary, when forms a deah fork we should be gong shor. Combne he above hree ndexes and nroduce he HMM model. Use 1, 0, -1 respecvely represens he drecon of each ndex sgnal, accordng o he radng sgnals n he dfferen K-lnes of he CMF ndex, he CHO ndex and he VTL ndex, and form he observable sequence. Ths sequence s dvded no pars needng ranng and pars needng no ranng, and when wo or more han wo ndexes gve he same openng sgnal, he mnory s subordnae o he majory, so ha we hnk ha he sequence does no need ranng, namely he openng poson s deermned. The deals are as follows: 25

11 hp://jsp.ccsene.org Inernaonal Journal of Sascs and Probably Vol. 6, No. 4; 2017 Sgnal 1 Sgnal 2 Sgnal 3 Seres Seres Seres Seres Seres Seres Seres Seres Seres Seres Seres Seres Seres Seres Seres Oherwse, we should need o use HMM model o ran, he deals are as follows: Sgnal 1 Sgnal 2 Sgnal 3 Seres Seres Seres Seres Seres Seres Seres Seres Seres Seres Seres Seres Defne he hdden sae vecor Go up Keep fla Go down In he above vecor, sae 1 ndcaes ha he closng prce are up before and afer he sgnal changes and he ncrease s more han wo mes of he handlng charge; sae - 1 ndcaes a declne n he closng prce before and afer he sgnal changes and he decrease s more han wo mes of he handlng charge; sae 0 ndcaes ha he absolue value of he dfference beween he closng prce before and afer he sgnal changes s less han wce of he fee. Use hsorcal daa o rees, oban he sae ranson marx and confuson marx by ranng, use he Verb algorhm, and combned wh he observable sequence furher o ge he openng drecon of hdden condon. 26

12 hp://jsp.ccsene.org Inernaonal Journal of Sascs and Probably Vol. 6, No. 4; Sop-loss Sraegy By nroducng he ATR ndex n he sop-loss sraegy, he mean real wave of he ATR s calculaed as follows: he range beween he hghes and lowes prce of he curren K-lne he range beween he closng prce of he a former K-lne and he hghes prce of he curren K-lne he range beween he closng prce of he a former K-lne and he lowes prce of he curren K-lne The maxmum of he curren K-lne amplude, he dfference beween curren maxmum and he closng prce of a former K-lne and he dfference beween he curren lowes and he closng prce of a former K-lne s he real amplude. Work ou he average movng he real wave of N K-lnes, and now se he parameer N as 10, he formula s ATR MA TR, N TR= max max Hgh Low, ABS REF Close,1 Hgh, ABS REF Close,1 Low Long sop-loss:record he openng prce as Avgprce, when he prce P below he openng prce of 2*ATR, he sop-loss appears,namely P Avgprce 2* ATR Shor sop-loss:record he openng prce as Avgprce, when he prce P ncreases over he openng prce of 2*ATR, he sop-loss appears,namely P Avgprce 2* ATR Long prof-lm:record he openng prce as Avgprce, when he hghes prce ncreases over he openng prce of 4*ATR and he maxmum whdrawal back reach 1.5* ATR, he sop-loss appears,namely Hghesprce Avgprce 4* ATR back 1.5* ATR Shor prof-lm:record he openng prce as Avgprce,when he lowes prce below he openng prce of 4*ATR and he maxmum whdrawal back reach 1.5* ATR, he sop-loss appears,namely Lowesprce Avgprce 4* ATR back 1.5* ATR 5.2 Reesng Resul Selecng he 15mn K-lnes of varous varees, he above four sraeges were reesed on he Auo-Trader plaform, and he resuls were as follows: Fgure 11. CMF ndex sraegy equy curve 27

13 hp://jsp.ccsene.org Inernaonal Journal of Sascs and Probably Vol. 6, No. 4; 2017 Fgure 12. CHO ndex sraegy equy curve Fgure 13. VTL ndex sraegy equy curve Fgure 14. HMM model sraegy equy curve 28

14 hp://jsp.ccsene.org Inernaonal Journal of Sascs and Probably Vol. 6, No. 4; 2017 Table 1. Sraegc performance ndcaor nal capal reurn rae(%) annual rae of reurn (%) Maxmum whdrawal rae(%) Sharpe rao prce earnngs rao CMF CHO VTL HMM As you can see from able 1, he performance ndcaors of he four sraeges are ranked separaely nal capal reurn rae:hmm>vtl>cho>cmf annual rae of reurn:hmm>vtl>cho>cmf Maxmum whdrawal rae:hmm>vtl>cho>cmf Sharpe rao:hmm>vtl>cho>cmf prce earnngs rao:hmm>vtl>cho>cmf Obvously, The HMM sraegy ranked frs n all performance ndcaors, ndcang ha he sraegy was robus whle mananng hgh reurns. Therefore, we choose he enry sraegy and sgnal unwndng sraegy based on HMM model and he sop-loss sraegy based on ATR ndex as he fnal sraegy combnaon. 6. Rsk Conrol To effecvely conrol he rsk and mnmze he whdrawal, he program lms he number of per ransacon. Mehod one: ge he curren avalable money and he curren dynamc equy of he accoun and calculae average respecvely. Then ake he smaller one, recorded for percash,and ake he bgger one of he openng prce Avgprce and100* ATR, recorded for prce,defnng he ransacon number * percash amoun prce In he formula, s a parameer, whch we can change o conrol he number of per ransacon. Mehod wo: Coun he oal amoun of hsorcal loss money and he rao of he maxmum whdrawal loss amoun o oal losses, namely loss conrbuon rae. Defne he rao of maxmum whdrawal rae o he expeced maxmum whdrawal rae as Rback, se he nal deal hand number as n, and esablsh he dynamc rsk conrol process, so ha he ransacon number can be expressed as he value ha he nal deal hand number scales arge mulple accordng o conrbuon rae: 7. Sraegc Advanage n* amoun Rback Consderng he echncal ndex desgn of he money volume, whch can effecvely capure he game suaon of commody fuures real money, avods he defecs of radonal echncal ndexes frequenly buyng n. By usng he he separaon ndex of buyng volume and sellng volume, we can beer capure he money flow rule of he Chnese commody fuures marke relave o he radonal money flow ndexes. By usng he HMM model o ransfer radng sgnal o observed sae and regard openng poson as a hdden sae, a he same me hrough he machne ranng o reduce he rsk under a ceran reurn and acheve effecve conrol of rsk, he reesng resul s que deal. Parameer opmzaon s no requred, and he over fng phenomenon s avoded. Some research repor wll make nework parameer search for some echncal ndcaors, whch makes he performance of he sraegy n dfferen marke envronmen very nconssen. Bu usng he HMM model for parameer esmaon of each varey, we can effecvely avod he problem of parameer opmzaon. Through opmzng he number of rades o conrol he rsk, he maxmum whdrawal rae was reduced effecvely. 29

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