Improvement and Test of Stock Index Futures Trading Model Based on Bollinger Bands

Transcription

1 Internatonal Journal of Economcs and Fnance; Vol. 9, o. 1; 2017 ISS X E-ISS Publshed by Canadan Center of Scence and Educaton Improvement and Test of Stock Index Futures Tradng Model Based on Bollnger Bands Xao-Xu Yan 1, Yuan-Bao Zhang 1, 2, Xn-Kun Lv 1 & Z-Yu L 1 1 Innovaton Practce Base of Mathematcal Modelng, Electrcal and Informaton College of Jnan Unversty, Zhuha, Chna 2 Key Laboratory of Product Packagng and Logstcs of Guangdong Hgher Educaton Insttutes, Jnan Unversty, Zhuha, Chna Correspondence: Yuan-Bao Zhang, Innovaton Practce Base of Mathematcal Modelng, Electrcal and Informaton College of Jnan Unversty, Zhuha , Chna. E-mal: zybt@jnu.edu.cn Receved: October 26, 2016 Accepted: ovember 17, 2016 Onlne Publshed: December 14, 2016 do: /jef.v9n1p78 URL: Abstract Bollnger Bands tradng model s an mportant strategy n program tradng. But n practce, the trade model based on the tradtonal Bollnger Bands theory has great flaws such as over-senstve flaw, ncomplete transacton stop-loss, and the adaptablty of the model s basc parameters s poor. In ths paper, the emprcal research method s used to analyze the shortcomngs of the tradtonal Bollnger Bands transacton model and put forward mproved methods. Accordngly, we ntroduce the prce speed, mprove the stop-loss rules, and adjust the basc parameters to mprove the model. The mproved tradng model s tested wth the data of Shangha and Shenzhen stock ndex futures. The result showed that the modfed Bollnger Bands transacton model has strong proftablty and low rsk, whch s nstructve to the practce of stock ndex futures. Keywords: bollnger bands, stock ndex futures, program tradng, flaws, mproved methods 1. Introducton 1.1 Introduce the Problem Stock ndex futures refers to the stock ndex as the subject matter of standardzed futures contracts, the two sdes agree upon a specfc date n the future and follow the pre-determned sze of the stock prce ndex for the sale of the underlyng ndex. Snce Kansas Futures Exchange has developed a value ndex futures contract n February 1982, Stock ndex futures have been ncreasngly valued by all knds of nvestors, the scale of the transacton has been expandng rapdly and the varety of tradng has been ncreasng. At present, the stock ndex futures have become the world s largest futures tradng varetes. Shangha and Shenzhen 300 stock ndex futures (CSI300) market has been runnng n Chna for more than sx years. It s actve durng these years and provdes researchers wth lots of real and valuable market data. Wth the rse and gradual development of the stock ndex futures market, n order to obtan greater profts and hedgng, the major tradng nsttutons and nvestors began to conduct n-depth research and focus on dscoverng more complex tradng strateges. However, the mplementaton of most tradng strateges must rely on the mplementaton of programmatc transactons. In foregn markets, as the man tradng mode n the securtes market, programmatc transactons have gradually replaced ordnary artfcal tradng. Due to the backward development of Chna s fnancal market, there s a certan gap on the development of program tradng between Amerca and European countres. Development of programmng tradng can not only help to acheve the rsk management and optmze nvestment combnaton, but make full use of the advantages of speed n the process of tradng to mprove the market effcency. Accordng to the transacton mechansm, the programmed tradng strategy model s dvded nto techncal ndcator model and forecastng model. The techncal ndcator model has wder applcaton because of ts hgh accuracy. Among them, the Bollnger Bands model has become one of the most wdely used tradng models n the captal market because of ts flexblty and adaptablty. It plays an mportant role n the practce of Chneese and nternatonal securtes exchange market.the Bollnger Bands model has beed wdely ued for about 30 years. However, n the practce of dfferent markets, some defects of tradtonal model appeared gradually. Tradtonal 78

2 jef.ccsenet.org Internatonal Journal of Economcs and Fnance Vol. 9, o. 1; 2017 Bollnger Bands model needs to be mproved to adapt to dfferent markets. 1.2 Descrbe Relevant Scholarshp At present, the research on Bollnger Bands tradng model s relatvely mature n the world. Bollnger Bands theory was frst proposed by John Bollngern the 1980s to measure the level of stock prces (John, 2001). Then the research on Bollnger Bands has become popular around the world, and the research scope s very extensve.after comparng the proftablty of the movng average and Bollnger Bands model were compared, Joseph Man-Joe Leung and TerenceTa-Leung Chong fnds that Bollnger Bands model s more capable to capture sudden prce fluctuatons, but the proftablty s lower than the movng average model (Joseph & Terence, 2003). Accordng to OD Wllams (2006), Bollnger Bands could capture the abrupt fluctuaton of the prce level and profts level of the model could be affected by the adjustment of ts nput. Accordng to Lento (2007), by testng the proftablty of the Bollnger Bands model, she found that the proftablty of the Bollnger Bands model mght not be as good as the strategy of buyng and holdng when the transacton costs were adjusted. Then, Bollnger Bands model was put forward to be appled to forecast stock prce trend wdely and ts applcaton value was proved (K. Senthamara, 2010). Basng on the prevous research, some scholars began to propose the strategy to mprove the tradtonal model. Bouble-Bollnger Bands theory compensated the defects of the tradtonal Bollnger Bands model and could more accurately judge the runnng trend of the securty prce (Kathy, 2015). The research on Bollnger tradng model s few n Chna, scholars manly analyzed the theory framework of the Bollnger Bands and put forward the use of ths ndex n Chna s securtes market.the scentfc rgor of the Bollnger Bands ts use lmtatons n Chna s securtes market were frst explaned n 2001 (Deng, 2001). Accordng to Shenjun, Qng and Yunbo (2011), the K lne and Bollnger Bands could be used as the basc tool to determne and predcte the Xamen real estate cycle fluctuatons and prce trends. As the Chnese markets are qute dfferent from the foregn, some scholars attempted to evaluate the valdty of the Bollnger Bands based on the Shangha Composte Index.The results shows that the Bollnger Bands model s effectve n Chnese market (Jusheng, Yxuan, & We, 2014). As we can see, the domestc and foregn scholars manly pay attenton to the proftablty of Bollnger Bands theory and ts applcaton research. The study on the mprovement of Bollnger tradng model and the applcaton of Bollnger Bands tradng model n stock ndex futures are few. 1.3 Frame of Paper Ths paper frst bulds the Bollnger Bands transacton model based on the tradtonal Bollnger Bands theory, then analyzes ts shortcomngs and fnds out the mprovement strategy. Fnally, we use the one-mnute K-lne data of CSI300 market from 2010 to 2013 to test the mproved Bollnger Bands model and put forward the ratonalzaton suggeston accordng to the practce of Chna s stock ndex futures market. 2. Bollnger Bands Model and Its Shortcomngs 2.1 Theory of Bollnger Bands Bollnger Bands was frst desgned by the stock analyst John Bollnger n USA n the actual transacton based on statstcal prncples. It s one of the techncal ndcators commonly used n the captal market. Bollnger Bands s put forward accordng to the phlosophy of relatvty, Bollnger argued that stock prces were relatve rather than absolute, so he set a channel (consstng of upper, mddle and lower tracks), whch the prce of stock fluctuates around. He hoped that through ths channel on the stock prce, relatvely hgh and low of the prces could be defned. That s to say when the stock traverses the trajectory, the stock prce s relatvely hgh. On the contrary, when the stock prce fell below the trajectory, the stock prce s relatve low. Therefore, the ratonalty of channel desgn ratonalty s the key to the ratonalty of the desgn of Bollnger bands. Weghted movng average, movng Average, and exponental smoothng average lne, etc. can be used as the trajectory of Bollnger Bands. Bollnger valdated these dfferent methods through statstcal methods. The results show that the weghted average lne and the exponental smoothng average lne are more complex, but ther promoton to grasp the prce trends s not obvous. So, the trajectory of the Bollnger Bands s generally defned by the movng average. The man lne of tradtonal Bollnger Bands s decded by the 20-day movng average. Of course, nvestors n the practcal applcaton can change the tme parameter accordng to the actual stuaton. The wdth of the Bollnger channel s determned by the standard devaton. The upper trajectory s a multple of the standard devaton of the stock prce, and the lower trajectory s the same multple of the standard devaton of the stock prce mnus the trajectory. From a statstcal pont of vew, when the multples of 2, the probablty of the stock prce between the upper and lower trajectory s more than 95%. In other words, when the stock prce s outsde the trajectory, we beleve that the correspondng hgh or low stock prce s reasonable. Ths 79

3 jef.ccsenet.org Internatonal Journal of Economcs and Fnance Vol. 9, o. 1; 2017 shows that the desgn of Bollnger channel s reasonable. The relatonshp between Bandwdth and statstcal probablty s shown n Table 1. Table 1. Relatonshp between bandwdth and statstcal probablty wdth of Bollnger Bands statstcal probablty 1.7 tmes the standard devaton More than 90% 2 tmes the standard devaton More than 95% 2.3 tmes the standard devaton More than 97% 2.2 Basc Indcators of Bollnger Bands Calculaton of -mnute movng average: MA= Where, s the perod of the movng average, C s the closng prce of the -th mnute. Calculaton of -mnute of standard devaton of the prce. 1 c (1) Calculaton of the trajectory, SD 1 ML MA ( c MA) UP MB K SD 2 LW MB K SD (3) Where, ML s the man lne or the mddle trajectory, UP s the upper bands, LW s the lower bands, SD s standard devaton of the prce, K represents bands wll be K standard devatons above or below the man lne. 2.3 Desgn of Tradng Strategy of Tradtonal Bollnger Bands Model Admsson Rules Sell and open a poston: When Prce breaks the upper lne, t ndcates stock ndex futures prces are overvalued and have more possblty of correcton. In order to avod rsks and gan profts, we wll sell and open a poston. Buy and open a poston: When Prce breaks the lower lne, t ndcates stock ndex futures prces are undervalued and have more possblty of reboundng. In order to avod rsks and gan profts, we wll buy and open a poston Departure Rules Buy and close a poston: when the prce fall down to the man lne from the peak, t ndcates the stock ndex futures prces have more possblty of rsng. In order to avod rsks and gan profts, we wll buy and close a poston. Sell and close a poston: when the prce rses up to the man lne from the bottom, t ndcates the stock ndex futures prces have more possblty of fallng. In order to avod rsks and gan profts, we wll sell and close a poston Scalng Rules To smplfy the transacton process and explan the basc prncples of transactons, ths artcle does not consder the scalng rules. In the study, the transactons are sngle-handed transactons, that s, when you open a poston, you have to close the poston before a new trade Prncples of Profts When stock ndex futures prce rse to the upper lne, we have the bearsh outlook, sell the contract and open a poston. We wll buy the contract and close a poston when prce falls down to the man lne. Therefore, we could gan the profts because of the dfference n prce.just lke that, we can also buy the contract and open a poston when stock ndex futures prce fall to the lower lne, and then sell the contract and close a poston when (2) 80

4 jef.ccsenet.org Internatonal Journal of Economcs and Fnance Vol. 9, o. 1; 2017 a correcton sent prces s up to the man lne. 2.4 Tradtonal Bollnger Bands Model Analyss of Tradtonal Bollnger Bands Transacton Model s Defects Wth MATLAB software, we wrote a program and used the tradtonal Bollnger Bands model to have a back test to fnd ts shortcomngs. The date was1 mnute K-lne transacton data n CSI 300 ndex market from In ths quanttatve strategy operaton, the closng prce of the stock ndex futures transacton was taken every 1 mnute. We took the 20-cycleclosng prce to calculate the average prce as a pont of the man lne. As the cycle shfts one unt, we would get a new pont, and connect these ponts to get movng average lne, that s, the man lne. Upper bands would be 2 tmes standard devatons above the man lne, and the lower would be below. The test results are shown n Fgure 1 and Table 2 below. Fgure 1. The cumulatve profts curve of the tradtonal Bollnger bands model Table 2. Test results of tradtonal Bollnger bands model Statstcal ndcators Results Fnal profts Yuan Accumulated maxmum profts Yuan Wnnng rate Maxmum retracement Yuan Transacton number 9129 beneft-to-rsk rato Fgure 1 shows that the model only gans profts at the begnnng of the transacton and then have a substantal declne, the transactons are at a loss. Table 2 shows the number of transactons s up to 9129 tmes, the ultmate loss of s up to 2.35 mllon Yuan, and the maxmum retracement of s up to 2.36 mllon Yuan, whle the cumulatve maxmum profts are only Yuan. Though the wnnng rate s relatve hgh, the fnal ncome s negatve, ndcatng that the amount of transactons to acheve proftablty s very small. The beneft-to-rsk rato s negatve ndcates the trade losses are serous. It shows that the tradtonal Bollnger Bands model fals n the test and has serous flaws. It s found that the defects of the tradtonal Bollnger Bands transacton model are manly emboded n several aspects, such as over-senstve and transacton stop-loss, and the adaptablty of the model s basc parameters s poor Over-Senstve Defects As shown n Fgure 2, we extract the test process from mnutes to mnutes for a total of 20 mnutes and get the Bollnger Bands plot. In accordance wth the tradtonal Bollnger band tradng strateges, at the pont A, when the stock prce rses to the upper band, we wll sell the contract and open a poston and then buy the contract back and close a poston when a correcton sent prces down to the man lne. Through the transacton, we wll gan profts. However, accordng to Fgure 2,we can see the prce stll rse above pont A to pont B. In practce, we sell the contract and open a poston at pont A and have a bearsh outlook, resultng n a large loss. Actually, the tme when prce s at the pont B or close to the pont B, t s the best opportunty to deal. At ths tme we can lead to smaller losses and obtan hgher profts. 81

5 jef.ccsenet.org Internatonal Journal of Economcs and Fnance Vol. 9, o. 1; 2017 Fgure mnute tradng of tradtonal Bollnger bands model The above analyss shows that the tradtonal Bollnger Bands tradng strategy has the problem that the model transacton s excessvely senstve and does not take the nfluence of prce trend nto account. When the stock prce breaks man lne, upper bands, or lower bands, the stock prce may stll contnue to run along the orgnal trend. At ths tme, f we open a poston, t wll reduce the profts and even close out the open postons at a loss to stop the loss.in order to solve ths problem, t s necessary to confrm whether the orgnal trend has ended when the stock prce breaks the bands. We beleve that, n most cases, before changng the orgnal trend, stock prces wll stll run n accordance wth the orgnal trend for some tme. Stock prces wll eventually reverse untl the falure of the orgnal trend. We call ths nature of stock prce nerta of stock prce. Therefore, accordng to the tradtonal tradng strategy, we defne the orgnal trend s about to reverse when the stock prce break. Ths does not meet the logc of the stock prce movement --- stock prce nerta Stop-Loss Defcences Stop loss s one of the basc concepts of nvestment. The settng of stop-loss durng a programmed tradng s called the soul of a programmed transacton. Some stop-loss strateges such as Tme stop-loss, spreads stop-loss, trackng stop-loss and lmt stop-loss are common n practce. Futures tradng have the delvery date and a leverage effect because of the characterstcs of ts margn tradng. If the loss can t be stopped n tme, we wll face the rsk beng forced to cut postons and lead to serous losses. Tradtonal Bollnger Bands tradng strategy stops loss manly rely on the breakout of the man lne to select the tme to close a poston, whch has great lmtatons n the volatle, frequent changes market. As shown n Fgure 3, we extract the test process from 712mnutes to 812 mnutes for a total of 100 mnutes and get the Bollnger Bands graph. Fgure mnute tradng of tradtonal Bollnger bands model As shown n Fgure 3, In accordance wth the tradtonal Bollnger Bands tradng model, the program wll sell and open a poston at pont C when the prce rses to the upper lne. At ths pont, the CSI s 3192 ponts. In tradtonal Bollnger Bands model, f you do not set a stop-loss pont properly, you need to carry untl the prce fall to the ntersecton of the prce lne and the man lne at pont D. You won t buy and close a poston untl the pont D. However, accordng to the transacton rules n Stock ndex futures market, you wll suffer catastrophc 82

6 jef.ccsenet.org Internatonal Journal of Economcs and Fnance Vol. 9, o. 1; 2017 losses. Therefore, n addton to takng nto account the stock prce nerta, choose the rght tme to trade, we also need to set a reasonable stop-loss strategy to avod tradng rsk caused by the excessve prce fluctuatons Lack of Basc Parameters Applcablty Because of the complexty, varablty and perodc characterstcs of the stock ndex futures market, thebasc parameters of the tradtonal Bollnger Bands model are dffcult to adapt to the changng market. In practce, t s necessary to adjust the basc parameters of the Bollnger Bands model accordng to the dfferent types of stages of the transactons to desgn dfferent tradng strateges, whch are more n lne wth the actual transactons. 3. Improvements of Bollnger Bands Model 3.1 Improvement of Over-Senstve Defects The above analyss of defects has ponted out that when the stock prce breaks through the Bollnger Bands, we determne the orgnal trend s about to reverse, whch does not meet the stock ndex prce logc stock prce nerta. Takng nto account ths stuaton nto account, we set rules that when the stock prce breaks the Bollnger Bands, the program wll not make reverse transactons mmedately, but determne whether the orgnal trend has changed through a seres of condtons. When the change n the trend s confrmed, the program wll open or close a poston. Referrng to the results of prevous research (Tng, 2013) on the stock ndex futures prce trend, ths paper uses the prce ndex of stock ndex futures to judge the prce trend. (y t, t=1, 2 ) are regarded as prce seres of stock ndex futures. That means y t represents the t tme of the stock ndex futures prce t=1 s regarded the as the frst mnute stock ndex futures closng prce. Prce seres econometrc model are establshed as follows. Y X t Where, Y s the closng prce n recent mnutes, ε s an error term wth a ndependent dentcally dstrbuted varance σ 2 and mean 0. yt1 1 1 y t2, 2 Y X, 2 (5) yt Y y, X (6) t The coeffcents of the regresson model are estmated usng the least squares estmator: x and y are defned as follows 1 t 1 t ( X x )( Y y ) x X 2 Substtutng nto the calculaton, we can get the result. Where, S t s defned the prce speed at the t mnute., ( X x) 2 t y 1 Y 1 y t 6 t, 3 2 t t, t t 1 t 1 t 1 s ( y y) (10) Where, S t >0 means futures prces have rsng trend, S t <0 means futures prces have downward trend. S t =0 means the prces were flat.as seen from the formula of prce speed, the speed can be defned as the weghted average of stock prce centerng. For a certan tme t and a fxed number of observatons, the weght ncreases wth the ncrease of the prce. That s, the closer to tme t, the greater the weght of the prce. The prncple s consstent wth the vew that the actual prce s strongly nfluenced by the recent prce. When the futures prce breaks the bands and S t >0, there s a bg possblty to keep the rsng trend. When S t =0, there s a bg possblty that the orgnal upward trend s over. Makng transactons at ths tme can ncrease revenue a lot. In general, the (4) (7) (8) (9) 83

7 jef.ccsenet.org Internatonal Journal of Economcs and Fnance Vol. 9, o. 1; 2017 probablty of events that prce rse to the upper bands and fall to the lower bands are small. Though t happens, the futures prces are very hgh or very low and the trends are not stable. At ths pont the msjudgment of the tmng of transactons wll result n huge losses. In order to accurately determne the tmng of the transacton wthout causng too much loss, when the prce of the prce changes n the range of [-a, a], futures prces are n a flat state and close to the peak pont. The best tradng opportunty s n ths perod of tme. Ths paper tested and found that when a s between 0-0.1, the effect of transacton s better. In practce, t can be adjusted accordng to transacton needs. Prces close to the man lne are n the mddle and fluctuant. When the prce of the prce changes n the range of [-b, b], futures prces are n a relatve flat state and close to the peak pont. The best tradng opportunty s n ths perod of tme. We tested and found that when b s between , the effect of transacton s better. Also, n practce, the parameters can be adjusted. 3.2 Improvement of the Tradng Stop Defect From the analyss of the stop-loss trade, t s necessary to set the stop-loss n the process of tradng. Stop-loss strateges such as tme stops, spreads stops, trackng stop-loss and lmt stops are common and wdely appled. Ths artcle draws on the vew of La Xangqun (2008), and uses the method of lmt stop to set stop-loss rules. Assumng the prncpal s one unt, after the transacton of n tmes, the prevous (n-1) tmes are at a loss, the last tme we get profts, then at ths tme our amount of money can be expressed by the followng formula. n1 Rn (1 ) (1 x) ( n 2) (11) From the above formula, the profts and loss of the transacton are determned by a sngle tme stop loss β, profts and loss rato x and the wnnng rate v. Due to the prevalng wnnng rate n the exstng procedural tradng model s about 1/3, settng a sngle stop loss of 0-5% s approprate. In practce, accordng to the needs of the transacton, t can be adjusted. The optmal stop loss s a mathematcal concept that has mportant reference value, t helps to acheve the lowest possble rsk to obtan the maxmum profts n the transacton. Stock ndex futures nvestment s an art, the program tradng model need to set the necessary transacton profts and loss rato and stop loss and resolutely mplement. So for the above defects, we make the followng mprovements. When the closng prce breaks through the upper bands, we may choose a tme to open and sell postons. At the same tme, we set γ tmes the prce as a stop-loss pont. When the closng prce n the future does not reach the rght tme to buy open, and the closng prce has reached the γ tmes as much as the open prce, the program mmedately buy and close a poston to prevent greater losses. Smlarly, when the closng prce breaks through the lower prce, we may choose a tme to open and buy postons. At the same tme, we set ω tmes the prce as a stop-loss pont. When the closng prce n the future does not reach the rght tme to open and sell a poston, and the closng prce ω tmes below the open prce of buyng tmes, the program mmedately sell and close a poston to prevent greater losses. And the value γ and ω can be adjusted accordng to tradng practces. 3.3 Adjustment of Basc Parameters The tradng model should be desgned accordng to the dfferent transacton types and tradng phases. The adjustment of the basc parameters of the Bollnger Bands model s more n lne wth the actual transacton, thus reducng the rsk and ganng more profts. 4. Emprcal Testng We mprove the desgn of tradng strategy accordng to the above prncples and test the mproved model wth 1 mnute K-lne transacton data n CSI 300 market from agan. 4.1 Desgn of Improved Bollnger Bands Model Basc Parameters The parameters of the Bollnger Bands n actual transacton can be set accordng to dfferent actual condtons. Consderng the model appled to Chna s stock ndex futures market has ts partcularty, we make some adjustments to the basc parameters. After lots of tests, we fnd that when =14 and k=17, the transacton ndcators of the model are deal. In the followng, the specfc parameters n the tradng rules are also adjusted Admsson Rules Sell and open a poston: When Prce breaks the upper bands, t ndcates stock ndex futures prces are overvalued and have more possblty of correcton. At the same tme, the prce speed S t1 changes n [ , ], futures prces are n a relatve flat state and close to the peak pont. The best tradng opportunty s n 84

8 jef.ccsenet.org Internatonal Journal of Economcs and Fnance Vol. 9, o. 1; 2017 ths perod of tme. Buy and open a poston: When Prce breaks the lower bands, t ndcates stock ndex futures prces are undervalued and have more possblty of reboundng. At the same tme, the prce speed S t1 changes n [ , ], futures prces are n a relatve flat state and close to the peak pont. Then, we wll buy and open a poston to gan profts Departure Rules Buy and close a poston: when the prce fall down to the man lne from the peak, t ndcates the stock ndex futures prces have more possblty of rsng. At the same tme, the prce speed S t2 changes n [ , ], futures prces are n a relatve flat state and close to the peak pont. Then, we wll buy and close a poston to gan profts. Sell and close a poston: when the prce rse up to the man lne from the bottom, t ndcates the stock ndex futures prces have more possblty of fallng. At the same tme, the prce speed S t2 changes n [ , ], futures prces are n a relatve flat state and close to the peak pont. Then, we wll sell and close a poston to gan profts Stop-Loss Rules When the prce breaks through the upper bands, we may choose a tme to open and sell postons. We may choose a tme to open and buy postons. At the same tme, the program wll choose the pont that s 2.11% hgher than the prce of CSI 300 as a stop-loss pont. When the closng prce n the future does not reach the prce of buyng, and the closng prce has reached a pont whch s 2.11% hgher than the sellng prce, the program wll mmedately buy and open a poston to prevent greater losses. Smlarly, when the prce breaks through the lower bands, we may choose a tme to open and buy a poston. At the same tme, the program wll choose the pont that s 2.11% lower than the prce of CSI 300 ndex as a stop-loss pont. When the closng prce n the future does not reach the prce of sellng, and the prce falls to the 98.74% of the buyng prce, the program wll mmedately sell and close a poston to prevent greater losses. 4.2 Analyss of the Test Results There are lots of data of the results, the man performance results are shown n Table 3 and Fgure 4. Fgure 4. Profts curve of mproved Bollnger bands Table 3. Test results of mproved Bollnger bands model Statstcal ndcators Results Fnal profts Yuan Accumulated maxmum profts Yuan Wnnng rate Maxmum retracement Yuan Transacton number 3510 Beneft-to-rsk rato Fgure 4 shows that the model at the begnnng of the transacton s at a loss, and then after the cumulatve profts wth the transacton, the total profts curve volatlty rses, fnally turnaround and acheves a hgher level of proftablty. Table 3 shows the number of transactons s 3510 tmes, compared wth the tradng model before 85

9 jef.ccsenet.org Internatonal Journal of Economcs and Fnance Vol. 9, o. 1; 2017 the mprovement, there s a sgnfcant reducton n the number of transactons. That means the transacton costs wll be greatly reduced, and there s more profts margns. We can see that the transacton over-senstve defects have mproved. The maxmum retracement s 45,600 Yuan, whch s about 1/60 of the tradtonal tradng strategy model. Therefore, the rsk of mproved model declned dramatcally. We can see the over-senstve and tradng stop defects have mproved a lot. For wnnng rate, t s smlar to the tradtonal model. The proftablty of the mproved model unt transacton s greatly mproved, the fnal ncome reaches 374,800 Yuan, and the profts-to-rsk rato s up to Generally speakng, when profts-to-rsk rato s greater than 2, we beleve that the model has practcal value. Therefore, the mproved model can be appled to actual market operaton and s hghly lkely to be proftable. Ths mprovement method s scentfc and feasble. 5. Conclusons and Recommendatons The tradtonal Bollnger Bands model has serous flaws. In ths paper, we make a seres of mprovements to the exstng defects. Frstly, the tradtonal Bollnger Bands model does not take nto account the stock prce nerta, whch generally exsts n the stock ndex futures market. Before changng the orgnal trend, stock prces wll stll run n accordance wth the orgnal trend for some tme. Stock prces wll eventually reverse untl the falure of the orgnal trend. Ths artcle creatvely ntroduces the prce speed to judge whether the orgnal trend has changed. When the prce speed s close to zero, the change of the trend can be confrmed and t s the proper tme to open or close a poston. Secondly, the set of the stop-loss rules n tradtonal Bollnger Bands model s not perfect. In the mproved model, when the prce rse s up to the upper bands, the program wll choose a proper tme to sell and open a poston whle settng γ tmes the prce of the CSI 300 as a stop pont. When the prce fall down to the lower bands, the program wll choose a proper tme to buy and open a poston whle settng ω tmes the prce of the CSI 300 as a stop pont. Improved stop-loss settngs reduce losses due to trend msjudgments a lot. Thrdly, basc parameters of Bollnger Bands model should be adjusted accordng to the transacton type and the tradng stage to meet the actual transacton, thereby reducng the rsk and get more benefts. In ths paper, based on the revew of the Bollnger Bands model at home and abroad, the paper frst bulds the tradtonal Bollnger Bands transacton model, and then analyzes ts excess senstvty, stop loss and basc parameter adaptablty defects. ext, we mprove the model by ntroducng prce speed to judge the prce trend, mprovng the stop rules and adjustng the basc parameters. Fnally, we use the one-mnute K-lne data of CSI 300 market from 2010 to 2013 to test the mproved Bollnger Bands model. The emprcal results show that the modfed Bollnger Bands transacton model has hgher proftablty and lower rsk. Ths artcle s of great sgnfcance to the practce of stock ndex futures market. In addton, the mproved Bollnger Bands tradng model can be appled not only to the stock ndex futures market, but also a wder range of tradng varetes by learnng the basc deas and adjustng the basc parameters. Acknowledgments Whle remanng responsble for any errors n ths paper, the authors would lke to thank gudance and advce from Tongz Ln who studes n School of Electrcal and Informaton Engneerng n Jnan Unversty on choosng topcs and programmng. References Bollnger, J. (2002). Bollnger on Bollnger Bands. ew York: McGraw Hll. Chuanha, D. (2001). Bollnger prncple and ts applcaton. Statstcs and Decson, (3), Joseph, M. J. L., & Terence, T. L. C. (2003). An emprcal comparson of movng average envelopes and Bollnger Bands. Appled Economcs Letters, Jusheng, S., Yxuan, H., & We, Z. (2014). Study on the Effectveness of Boolean Lne. Statstcs and Decson, (17), K. Senthamara, K., P. Salapath, S., & M. Mohamed, P. (2010). Arumugam. Fnancal Stock Market Forecast usng Data Mnng Technques. Lecture otes n Engneerng and Computer Scence, Kathy, L. (2015). Techncal Strategy: Tradng wth Double Bollnger Bands. Day Tradng and Swng Tradng the Currency Market, Lento, C., Gradojevc,., & Wrght, C. S. (2007). Investment nformaton content n Bollnger Bands? Appled 86

10 jef.ccsenet.org Internatonal Journal of Economcs and Fnance Vol. 9, o. 1; 2017 Fnancal Economcs Letters, Shenjun, Q., Qng, W., & Yuanbo, Z. (2011). Market Trend Forecastng of Real Estate Base on K-lne Theory and Bollnger Bands. Journal of Wuhan Unversty of Technology (Informaton & Management Engneerng), (4), Tng,. (2013). Study of the Stock Index FuturesProgram Tradng Investment Strategy. South Chna Unversty of Technology, Wllams, O. D. (2006). Emprcal optmzaton of Bollnger Bands for proftsablty. Avalable at SSR , Xangqun, L. (2008). Try to comment on the stop-loss settngs. Specal Zone Economy, (3), Copyrghts Copyrght for ths artcle s retaned by the author(s), wth frst publcaton rghts granted to the journal. Ths s an open-access artcle dstrbuted under the terms and condtons of the Creatve Commons Attrbuton lcense ( 87