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私設取引システムの市場特性について

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MIMSカフェセミナー(2012年3月7日)

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私設取引システムの市場特性について

  1. 1. 私設取引システムの市場特性について 1 Mitsuru KIKKAWA (吉川満) (Graduate School of Advanced Mathematical Sciences, Meiji University) THIS FILE IS AVAILABLE AT http://kikkawa.cyber-ninja.jp/ MIMSカフェセミナー 7 Mar., 2012
  2. 2. Today’s Talk 2 Examine 1) PTS’s properties (Price discovery (価格発見), the statistical properties of order book) 2) Interaction between Tokyo Stock Exchange and PTS (Order aggressiveness)
  3. 3. In my Ph.D thesis • To formulate a financial market with the trader’s strategic behavior. • Focus on the order book (板情報) , which is the outcome of it. • Formulate a limit order market (指値市場) as a double auction. • Only one market • Two prices : the execution price and Walras equilibrium (clearing price) 3【MOVIE】
  4. 4. 東証 Market Impact View • ある銘柄の注文状況は売り買いどちらに偏っ ているのかを直感的に把握 • 板が厚く、値段が動きにくい(流動性が高い) 銘柄をピックアップ 4 2012年1月 サービス開始
  5. 5. This field • Market microstructure … the study of the process and outcomes of exchanging assets under explicit trading rules. • The microstructure literature analyses how specific trading mechanisms affect the price formation process. • Liquidity (流動性), institution, • information, volume (出来高) 5 Finance Economics Empirical Analysis
  6. 6. Classical Mathematical Financial Theory • Random walk, Brownian motion • Stochastic differential equation, Ito calculus • The price formation process is a “black box”. ⇒ Market microstructure 6
  7. 7. 1. INTRODUCTION 7
  8. 8. What is “PTS” ? • PTS … Proprietary Trading System (私設取引システム) (SBI Japannext, Co., Ltd. Chi-X Japan, U.S. … Alternative Trading System, Europe … Multilateral Trading Facilities) PTS is notable for 1. Advanced trading system 2. Tick size 3. Cost effective 4. Long trading hours 5. Sophisticated trading methodology, liquidity supply 8
  9. 9. Technological Innovations • high-speed, low-cost electronic trading systems dramatically changing the structure of financial markets. EX. ) Smart Order Routing (SOR)…can constantly scan available execution venues (primary and alternative markets) for best available price, and then execute optimally based on various internal and market rules. 9
  10. 10. SOR (SBI Sec. Inc.)[Youtube] 10
  11. 11. Foucault and Menkveld (2008) • They examined smart routers that investors use to benefit from liquidity supply in multiple markets. • They showed its importance to the existence of the alternative market and the development of smart routing technologies. 11 Primary market dominates Markets coexist O Alternative market dominates 1 Transaction cost in alternative market The proport ion of smart routers
  12. 12. Algorithmic Trading (AT) • AT is the use of electronic platforms for entering trading orders with an algorithm deciding on aspects of the order such as the timing, price, or quantity of the order, or in many cases initiating the order without human intervention. Ex ) 1. Investor 1 submits a market order to buy 10000 shares 2. Investor 2 uses co-location service to buy 10000 shares and then sells them at a higher price immediately. 3. Investor 1 will buy them at a higher and investor 2 will make profit. [Hypothesis] PTS is related with AT. It is difficult to execute the above example in TSE where the market depth is large. The market depth in PTS is smaller than that in TSE. (→ order aggressiveness) 12
  13. 13. PTS : Turnover Share 13 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 2010年1月 2010年2月 2010年3月 2010年4月 2010年5月 2010年6月 2010年7月 2010年8月 2010年9月 2010年10月 2010年11月 2010年12月 2011年1月 2011年2月 2011年3月 2011年4月 2011年5月 2011年6月 2011年7月 2011年8月 2011年9月 2011年10月 2011年11月 日本証券クリアリング機 構が決済履行を保証 The data source : PTS Information Network Mitsubishi UFJ (8306): 12.5%, Nissan (7201): 10.7% % The SBI SOR Arrowhead (TSE) Chi-X Japan
  14. 14. 2. RELATED LITERATURES 14
  15. 15. Related Literatures 15 Empirical findings (Huang, 2002, Barclay et al. 2003, Conrad et al, 2003, Fink et al, 2006, Brandes and Domowitz, 2010, O’Hara and Ye, 2011 and so on): 1. bid-offer spreads tighten 2. trading costs reduce 3. overall market turnover increase 4. increased liquidity 5. more efficient markets 6. price improvements deliver better trading outcomes
  16. 16. 3. EMPIRICAL ANALYSIS 16
  17. 17. 3. 1. PRICE DISCOVERY 17
  18. 18. Data set 18 SONY (6758) in TSE on Dec. 26, 2011, the execution price at 1-second intervals. 1375 1380 1385 1390 1395 1400 9:00:00 9:10:05 9:20:08 9:30:10 9:40:09 9:50:04 9:59:54 10:09:44 10:19:32 10:29:27 10:39:26 10:49:32 10:59:34 11:09:33 11:19:28 11:29:27 12:39:32 12:49:41 12:59:44 13:09:44 13:19:46 13:29:47 13:39:59 13:49:53 14:00:00 14:09:59 14:20:00 14:29:59 14:40:03 14:50:05
  19. 19. Data set 19 SONY (6758) in PTS on Dec. 26, 2011, the execution price at 1-second intervals. 1375 1380 1385 1390 1395 1400 9:00:00 9:10:05 9:20:08 9:30:10 9:40:09 9:50:04 9:59:54 10:09:44 10:19:32 10:29:27 10:39:26 10:49:32 10:59:34 11:09:33 11:19:28 11:29:27 12:39:32 12:49:41 12:59:44 13:09:44 13:19:46 13:29:47 13:39:59 13:49:53 14:00:00 14:09:59 14:20:00 14:29:59 14:40:03 14:50:05
  20. 20. Cointegration Tests of Phillips-Ouliaris 20 → cointegration relationship. 1375 1377 1379 1381 1383 1385 1387 1389 1391 1393 1395 1397 1399 0.375 0.375763889 0.376527778 0.377303241 0.37806713 0.378842593 0.379606481 0.38037037 0.381134259 0.381886574 0.382662037 0.383425926 0.384189815 0.384965278 0.385717593 0.386469907 0.387222222 0.387986111 0.38875 0.389502315 0.39025463 0.391006944 0.391747685 0.392511574 0.393275463 0.394050926 0.394826389 0.395590278 0.396354167 0.397118056 0.397881944 0.398645833 0.399398148 0.400162037 0.400902778 0.401666667 0.402418981 0.403171296 0.403923611 0.404675926 0.405428241 0.40619213 0.406944444 0.407696759 0.408449074 0.409201389 0.409953704 0.410706019 0.411446759 0.412199074 0.412951389 0.413703704 0.414444444 0.415196759 0.4159375 0.416666667 0.417395833 0.418148148 0.418900463 0.419641204 0.420393519 0.421134259 0.421886574 0.422638889 0.42337963 0.42412037 0.424849537 0.425590278 0.426331019 0.427071759 0.427824074 0.428564815 0.42931713 0.430069444 0.430810185 0.4315625 0.432303241 0.433055556 0.43380787 0.434560185 0.4353125 0.436076389 0.436828704 0.437581019 0.438333333 0.439074074 0.439814815 0.44056713 0.441342593 0.442118056 0.442881944 0.443645833 0.444398148 0.445173611 0.4459375 0.446689815 0.447453704 0.448263889 0.449039352 0.449791667 0.450555556 0.451319444 0.452083333 0.452847222 0.453611111 0.454363426 0.455115741 0.45587963 0.456643519 0.457407407 0.458159722 0.458923611 0.459675926 0.460439815 0.46119213 0.461944444 0.462696759 0.463460648 0.464212963 0.464976852 0.465740741 0.466493056 0.46724537 0.467997685 0.468738426 0.469490741 0.470243056 0.47099537 0.471747685 0.472511574 0.473275463 0.474027778 0.474780093 0.475520833 0.476284722 0.477048611 0.477800926 0.478553241 0.520983796 0.521747685 0.522523148 0.523287037 0.5240625 0.524826389 0.525590278 0.526354167 0.527118056 0.527893519 0.528657407 0.52943287 0.530208333 0.530972222 0.531736111 0.532511574 0.533287037 0.534039352 0.534814815 0.53556713 0.536331019 0.537106481 0.537881944 0.538645833 0.539409722 0.540162037 0.540925926 0.541678241 0.54244213 0.543206019 0.543969907 0.544722222 0.545474537 0.546226852 0.546990741 0.547743056 0.54849537 0.549259259 0.550023148 0.550787037 0.5515625 0.552326389 0.553078704 0.553842593 0.554606481 0.555358796 0.556111111 0.556875 0.557638889 0.558402778 0.559166667 0.559930556 0.56068287 0.561446759 0.562199074 0.562962963 0.563715278 0.564479167 0.565266204 0.566030093 0.566805556 0.567581019 0.56837963 0.569166667 0.569918981 0.570671296 0.571423611 0.572199074 0.572951389 0.57369213 0.57443287 0.575185185 0.575925926 0.576678241 0.577453704 0.578217593 0.578981481 0.579756944 0.580543981 0.581296296 0.582060185 0.582835648 0.583599537 0.584363426 0.585127315 0.58587963 0.586631944 0.587384259 0.588136574 0.588900463 0.589652778 0.590405093 0.591168981 0.591921296 0.592673611 0.593425926 0.594189815 0.594953704 0.595729167 0.596481481 0.59724537 0.597997685 0.59875 0.599502315 0.600243056 0.601018519 0.601770833 0.60255787 0.603310185 0.604074074 0.604837963 0.605601852 0.606377315 0.60712963 0.607893519 0.608657407 0.609421296 0.610185185 0.6109375 0.611701389 0.612476852 0.613240741 0.613993056 0.614756944 0.615509259 0.616273148 0.617037037 0.617789352 0.618564815 0.619328704 0.620104167 0.620868056 0.621631944 0.622407407 0.623159722 0.623935185 0.624710648
  21. 21. Price Discovery (価格発見) • The price discovery is the process of determining the price of an asset in the marketplace through the interactions of buyers and sellers. • Which markets have a price discovery role ? (Hasbrouck, 1995) • Objection : future market, index, ETF, ECNs • Huang (2002) : ECNs are important contributors to price discovery. 21
  22. 22. Vector Error Correction Model • Hasbrouck (1995) recommended a reduced-form model for prices in multiple markets: where, if is the price in market i=1,2 at period t, is the error correction term, and for i=1,2 is the return. The error terms and may be contemporaneously correlated. : the execution price in TSE : the execution price in PTS 22 ,1 1 ,2,21 1 ,1,11111 t K k ktk K k ktktt dadazd        ,2 1 ,2,22 1 ,1,21122 t K k ktk K k ktktt dadazd        itp ttt ppz 21  t1 t2 1p 2p
  23. 23. Information Share • Hasbrouck (1995) proposed a measure of the contribution to the price discovery process, which he called the information share (IS) of a market. His definition is where • IS1=0.63, IS2=0.38. • ⇒ TSE has a price discovery role. 23             , ,2 2 2 221211 2 1 2 2211 tttt iti tt iti i VarCovVar Var Var Var IS         1, 21 2 1 1 2      
  24. 24. 3. 2. STATISTICAL PROPERTIES OF ORDER BOOKS 24
  25. 25. Average volume of the queue in the order book 25 Bouchaud et al. (2002) found that the statistics of incoming limit order prices, follows a power-law around the currentt price with a divergining mean. (Potters and Bouchaud (2003), Zovko and Farmer (2002))
  26. 26. The Order Book ( Bid (sell)) Price (Ask (buy)) ----------------------------------------------- 30000 502 ----------------------------------------------- 20000 501 ----------------------------------------------- 4000 500 --------------------------------------------- 499 8000 ---------------------------------------------- 498 30000 ---------------------------------------------- 497 25000 The center column gives the prices, the second column from the left shows the volume of individual offers (sell). The right hand side of the table represents the bid side (buy). 26
  27. 27. Statistical Properties 27 0 5000 10000 15000 20000 25000 30000 35000 40000 45000 1 2 3 4 5 6 7 8 0 5000 10000 15000 20000 25000 30000 1 2 3 4 5 6 7 8 0 200 400 600 800 1000 1200 1400 1 2 3 4 5 0 200 400 600 800 1000 1200 1 2 3 4 5 The seller’s submissions in TSE The buyr’s submissions in TSE The seller’s submissions in PTS The buyer’s submissions in PTS
  28. 28. 3. 3. ORDER AGGRESSIVENESS 28
  29. 29. Order Aggressiveness 29 Biais et al. (1995), Ranaldo (2004) 1) the most aggressive order: as a large market order and large limit order within the previous quotes 2) the second type of aggressive order: a small market order and small limit order within the previous quotes that demands less volume than a given constant, 3) the third type of aggressive order: limit order at the prevailing quotes, 4)the least aggressive category: withdrawing an existing order.
  30. 30. Order aggressiveness in PTS • The frequencies of the different order submission 30-minutes intervals in PTS. 30 1375 1380 1385 1390 1395 1400 9:00:00 9:00:48 9:01:36 9:02:25 9:03:13 9:04:01 9:04:50 9:05:39 9:06:27 9:07:15 9:08:03 9:08:51 9:09:39 9:10:27 9:11:15 9:12:03 9:12:52 9:13:41 9:14:29 9:15:17 9:16:03 9:16:51 9:17:39 9:18:26 9:19:15 9:20:03 9:20:50 9:21:37 9:22:24 9:23:11 9:23:58 9:24:46 9:25:34 9:26:23 9:27:12 9:28:00 9:28:49 9:29:37 9:30:25 9:31:14 9:32:02 9:32:50 9:33:38 9:34:25 9:35:13 9:36:00 9:36:48 9:37:35 9:38:23 9:39:10 9:39:58 9:40:45 9:41:32 9:42:19 9:43:07 9:43:55 9:44:43 9:45:30 9:46:18 9:47:05 9:47:52 9:48:40 9:49:26 9:50:14 9:51:02 9:51:49 9:52:35 9:53:23 9:54:11 9:54:57 9:55:45 9:56:32 9:57:19 9:58:06 9:58:53 9:59:38 10:00:25 10:01:11 10:01:58 10:02:45 10:03:32 10:04:19 10:05:06 10:05:53 10:06:41 10:07:28 10:08:15 10:09:02 10:09:48 10:10:35 10:11:22 10:12:07 10:12:54 10:13:41 10:14:27 10:15:14 10:16:01 10:16:48 10:17:36 10:18:23 10:19:10 10:19:57 10:20:44 10:21:31 10:22:18 10:23:06 10:23:53 10:24:40 10:25:28 10:26:15 10:27:03 10:27:51 10:28:38 10:29:26 10:30:12 10:31:00 10:31:46 10:32:33 10:33:20 10:34:08 10:34:55 10:35:45 10:36:34 10:37:22 10:38:10 10:38:58 10:39:45 10:40:34 10:41:21 10:42:10 10:42:58 10:43:45 10:44:35 10:45:25 10:46:14 10:47:02 10:47:50 10:48:38 10:49:26 10:50:14 10:51:02 10:51:51 10:52:39 10:53:26 10:54:13 10:55:01 10:55:49 10:56:37 10:57:25 10:58:13 10:59:01 10:59:49 11:00:36 11:01:24 11:02:11 11:03:00 11:03:47 11:04:34 11:05:22 11:06:10 11:06:57 11:07:45 11:08:33 11:09:21 11:10:08 11:10:57 11:11:44 11:12:31 11:13:18 11:14:05 11:14:53 11:15:40 11:16:27 11:17:15 11:18:02 11:18:49 11:19:37 11:20:25 11:21:13 11:22:00 11:22:48 11:23:35 11:24:22 11:25:09 11:25:58 11:26:46 11:27:34 11:28:21 11:29:09 11:29:57 12:30:44 12:31:32 12:32:21 12:33:09 12:33:59 12:34:47 12:35:35 12:36:23 12:37:11 12:38:00 12:38:48 12:39:35 12:40:24 12:41:13 12:42:02 12:42:51 12:43:39 12:44:27 12:45:16 12:46:04 12:46:52 12:47:41 12:48:29 12:49:17 12:50:06 12:50:54 12:51:42 12:52:30 12:53:18 12:54:07 12:54:55 12:55:44 12:56:31 12:57:19 12:58:06 12:58:54 12:59:42 13:00:30 13:01:18 13:02:06 13:02:54 13:03:42 13:04:29 13:05:17 13:06:05 13:06:51 13:07:40 13:08:27 13:09:15 13:10:03 13:10:51 13:11:38 13:12:26 13:13:15 13:14:03 13:14:52 13:15:39 13:16:27 13:17:15 13:18:03 13:18:51 13:19:39 13:20:26 13:21:14 13:22:02 13:22:50 13:23:38 13:24:27 13:25:15 13:26:02 13:26:50 13:27:38 13:28:25 13:29:13 13:30:01 13:30:49 13:31:36 13:32:24 13:33:13 13:34:03 13:34:50 13:35:39 13:36:28 13:37:16 13:38:07 13:38:58 13:39:46 13:40:34 13:41:21 13:42:09 13:42:56 13:43:44 13:44:32 13:45:19 13:46:06 13:46:53 13:47:39 13:48:27 13:49:14 13:50:01 13:50:48 13:51:37 13:52:26 13:53:14 13:54:02 13:54:51 13:55:41 13:56:29 13:57:17 13:58:05 13:58:53 13:59:41 14:00:30 14:01:17 14:02:06 14:02:54 14:03:41 14:04:29 14:05:16 14:06:04 14:06:50 14:07:39 14:08:26 14:09:14 14:10:01 14:10:49 14:11:36 14:12:24 14:13:12 14:13:59 14:14:46 14:15:35 14:16:23 14:17:11 14:18:00 14:18:48 14:19:35 14:20:23 14:21:10 14:21:58 14:22:45 14:23:32 14:24:19 14:25:07 14:25:55 14:26:43 14:27:33 14:28:21 14:29:08 14:29:56 14:30:44 14:31:33 14:32:21 14:33:10 14:33:57 14:34:45 14:35:33 14:36:22 14:37:10 14:37:58 14:38:45 14:39:33 14:40:21 14:41:09 14:41:58 14:42:46 14:43:34 14:44:21 14:45:10 14:45:57 14:46:45 14:47:33 14:48:21 14:49:09 14:49:56 14:50:45 14:51:34 14:52:22 14:53:10 14:53:58 14:54:46 14:55:35 14:56:23 14:57:11 14:58:00 14:58:48 14:59:37
  31. 31. Volume Effect 31 Volume Effect … the depth at the best quote effects on the order aggressiveness. Parlour (1998) showed that buyers are more likely to be much aggressive to trade when the buyer’s submission are large. On the other hand, sellers are more likely to be much aggressive to trade when the seller’s submissions are larger. (Market follower)
  32. 32. Ordered Probit model • be the order aggressiveness in t. d=B,S, α1, α2 is the coefficient related to the ask and bid volume Ask Vt, BidVt, in TSE. 32 )1(,21, d tt d t dd tn BidVAskVy   )2( .4 ,3,2 ,1 3 1 1 ,              d t d d m d t d m dd t d tn yif myifm yif y    y d tny , Image
  33. 33. Order probit regressions • Regression analysis estimates that the opposite of the volume effect is derived. (Parlour ,1998) • I.e., the buyers in PTS are more likely to be much aggressive to trade when the seller’s submissions are larger in TSE. (consistent with 3.2) • The depth at the best quote in TSE is larger, the order book in PTS will be changed to execute the trade. 33 A “negative” estimated coefficient means that the explanatory variable is positively related to order aggressiveness.
  34. 34. 4. CONCLUSIONS AND DISCUSSIONS 34
  35. 35. Summary 35 1. The execution price at TSE and PTS are a cointegration relationship. 2. PTS does not contribute towards the price discovery role. 3. The order book in TSE is different from that of PTS, the order book in PTS has a typical shape. 4. The depth at the best quote effects in TSE affects the order aggressiveness in PTS. 5. The buyers in PTS are more likely to be much aggressive to trade when the seller’s submissions are larger in TSE. 6. The relationship between TSE and PTS is complement.
  36. 36. Issues • PTS will be popular gradually. However, 1. Integrate into PTSs (PTSの統合) 2. credit transactions (信用取引) 3. 5 % rule (TOB) • An institutional investor will buy in TSE and sell in PTS. 36
  37. 37. Mitsuru KIKKAWA (mitsurukikkawa@hotmail.co.jp) This File is available at http://kikkawa.cyber-ninja.jp/ 37 MY MESSAGES If you want to reduce the transaction cost, I recommend to use PTS.
  38. 38. REFERENCE [1] Bouchaud, J.-P., M. Mezard and M. Potters 2002, “Statistical properties of stock order books: empirical results and models’, Quantitative Finance”, vol. 2, no. 4, pp. 251-256. [2] Foucault, T. and A. J. Menkveld 2008, “Competition for Order Flow and Smart Order Routing Systems,’ The Journal of Finance,” vol. 63, no. 1, pp. 119-158. [3] Hasbrouck, J. 1995, “One Security, Many Markets: Determining the Contributions to Price Discovery,’ The Journal of Finance,” vol.50, no. pp.1175-1199. [4] Huang, R. D. 2002, "The quality of ECN and Nasdaq Market Marker Quotes,' The Journal of Finance", vol.57, no.3, pp.1285-1319. [5] Ranaldo, A. 2004. “Order aggressiveness in limit order book markets,’ Journal of Financial Markets,” vol. 7, no. 1, pp.53-74. [You Tube] mitsurukikkawa’s Channel : http://www.youtube.com/mitsurukikkawa 38
  39. 39. 39 • This research was supported in part by Meiji University Global COE Program (Formation and Development of Mathematical Sciences Based on Modeling and Analysis) of the Japan Society for the Promotion of Science. Acknowledgements

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