MIMSカフェセミナー(2012年3月7日)

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. 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. 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. 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. 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. 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. 1. INTRODUCTION
7

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. 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. SOR (SBI Sec. Inc.)[Youtube]
10

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. 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. 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. 2. RELATED LITERATURES
14

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. 3. EMPIRICAL ANALYSIS
16

17. 3. 1. PRICE DISCOVERY
17

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. 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. 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. 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. 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. 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. 3. 2. STATISTICAL PROPERTIES OF
ORDER BOOKS
24

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. 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. 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. 3. 3. ORDER AGGRESSIVENESS
28

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. 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. 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. 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. 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. 4. CONCLUSIONS AND DISCUSSIONS
34

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. 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. 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. 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
• 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