Tick-by-Tick Analysis and the Retur n Efficiency Theor y for Financial Mar kets
Vladimir Pr elov, Ph.D.
Russian Academy of Sciences, IMASH RAN,
RUSSIAN FEDERATION 101990 MOSCOW
Maliy Kharitonievskiy per., 4
Tel.: +7(499)135-7771, Fax: +7(495)624-9800
prelov@iitp.ru
ABST R AC T
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different global financial markets. We have investigated official tick-by-tick records and results of market participants (speculators & investors) trading activity
such as an average rate of at-the-moment return for the decade period starting with 1999 and up-to-date.
We have exploited a dealing rate of return at-the-moment (profitability) r, to design an alarm parameter, so-called Efficiency, E, of financial market transactions as
a standard mean for the ratio r/R over k periods, where R was observed as the theoretically available floating maximum for the trading period in question. During
tick data processing we noticed the asymptotic stability phenomenon in the E behavior over all the financial instruments at both the global and emerging markets.
Investigating this, we established some relations in E with Shannon's entropy and Maxwell distribution and proved our result should be stated as a financial
PDUNHW¶VIXQGDPHQWDOLQYDULDQW:HDSSOLHGVRPHWKHRUHWLFDOQXPEHULGHDVHQIRUFHGZLWKD/DUJH6\VWHPWKHRU\WRSUHVHQWDQDV\PSWRWLFK\SRWKHVLVDQGJXHVVD
behavior of so-called E-waves for show that waves ranges are restricted not only with inverse exponent, 1/e=0.367880, and the constant of the famous Fibonacci
retracement target, 0.381966, which is rather popular within the global financial market traders, but as well are corresponded with )LERQDFFLQXPEHU¶V LQWHUYDO
bounds [1/3,1/2] under some wide assumptions.
We realize a theory of E-waves and present a family of E-curves as new sensitive toolset for both operational and market-making activity, which are of a special
interest for both portfolio- and risk managers and for regulators at the global financial markets, as well, while a post-crisis reality.
PRESENTATION
A lot of approaches to foresee any fatal, including financial markets, event are based on the concept of the precursor - a sharp
change in the local dynamics of some parameters given. W e propose a new approach to the "precursor" as to a special, multi-level
structure that reflects the complexity of the classical concept. Variations of the market environment are reflected in the signals of
finance- information field &%¶V interventions, investments, speculations, rumors). The aim of any research on this point is to
interpret the anomalies of financial fields (tick flows, level of activity of market makers, dynamics of the trading system
applications, etc.), bearing both permanent and casual character. The goal of this paper is to show a deep two-sided, so called
³EHIRUHDIWHU´ interlink extracted over time for some transformation of operational parameters of the financial environment in
order to obtain the reliable proof for the strength\weakness of the market and the potential risks, financial and economic threats
inspired with activity of operators E\ PHDQV RI QHZ (ZDYHV¶ DQG (FXUYHV¶ WKHRU\ W e start with the Russian Ruble show in a
form of the plane E-curves extracted out of the Moscow Interbank Currency Exchange (MICEX) tick database official records for
the beginning of 2012.
Fig.1. Impact and Reflected E-waves in a form of self-intersecting E-curves junction done for 926489 ticks of Russian Ruble at MICEX in 2012 (real dealing rate
of return normalized and vectorized for the period given, the Central Bank of Russian Federation intervention volumes included, % scale).
Detailed analysis done for these E-waves allow us to conclude that financial markets are not what they seem. It is easy to see after
some routine mathematical transformations that a period for assets targeting with intervention tools is restricted with a cumulative
th
volume. Starting with a total tick volume accumulated with different market assets by the early 2000 , fulfilling the %ROW]PDQQ¶V
limit conditions of the Large System Theory, we have a self-organized system of the chaos controlled by now when the monetary
tools period is coming to be over. It is understandable if we consider the geometry probabilistic interpretation for an entropy as a
standard measure of chaos. The %ROW]PDQQ¶VHQWURS\IDFWRUIRUSODQHFXUYHVDERYHLVMXVW>@ *[22.5;47.5]=9/80=11.25%!!!
So, we have now to present
THE MAIN STATEMENTS
·
·
The global financial markets institution has established itself as a full self-completed chaos controlled IT-system.
The %ROW]PDQQ¶V WKHRU\ FRQILUPV WKDW D SDJH IRU PRQHWDU\ FRQWUROOHG ILQDQFLDO PDUNHWV LV WXUQHG RYHU XQGHU WKH
GLVSXWDEOHDVVXPSWLRQWKDWERWK*OREDO)LQDQFLDO0DUNHWV¶LGHRORJ\DQGWKHVKRZPXVWJRRQ
INTRODUCTION
The above figures have visualized some of joint E-waves followed tick data of FX and stock sections at MICEX provided below.
Fig.2. Direct\Indirect E-waves done for 926489 ticks of USDRUB in 2012, and E-waves averaged for Russian blue chips in 2007 and for Russian FX in 2011.
Rapid IT stream opens a wide spectrum of new opportunities and set new requirements for market-making and trading efficiency
as well as for both financial markets forecasting and risk-management. E-ZDYHV?FXUYHV¶ WKHRU\ LOOXVWUDWHV QHZ PHWKRG IRU
estimating the risk. We follow a cross-disciplinary paradigm in approaching this complex scientific problem, and use some new
non-statistical forecasting methods to detect patterns hidden in catalogues of recorded transactions data.
First of all, we suppose that all records collected at tick-by-tick database reflect the processes at an open dynamical system which
is chaotic in both standard and systemic time. Then, we suppose that every financial spurt has a set of precursors, related in both
time scales, leading to the self-organized criticality which triggers the event. The challenge is to use these data to create a logical
procedure to identify precursors for turmoils as well as to filter out false events. New opportunities to collect the trading info and
to analyze the data flows let us rely on solving the problems such as crucial events forecasting, the problem of short-term takeprofit & stop-loss control in a real-time mode. Both general practical and theoretical results obtained with analytical processing of
catalogues are illustrated below. For example, an entropy method could be applied to reduce a complexity of FX targets
forecasting problem.
DATA COLLECTION
We have deal with an official dataset of Russian blue chips and FX (Russian and Global) presented at this table
LKOH
1999
2000
2001
2002
2003
2004
2005
2006
2007
Total tick #
18178
64748
275196
474730
905194
1576935
2646763
4686483
4188999
Cumulative tick #
18178
82926
358122
832852
1738046
3314981
5961744
10648227
14837226
MICEX, Mb
5237 Mb zipped
UTS, Mb
33 Mb zipped
22
36
60
94
133
141
345
447
1,6 blns of ticks
Stock Section
3
3
3
2
2
3
4
4
2008
2009
2010
2011
2012
SBER
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
6225467
9371378
7235391
9426456
1109598
Total tick #
40597
86071
72817
202693
186916
406064
401691
945860
2618297
8596686
25646567
21062693
30434071
37669462
47 095 918
Cumulative tick #
40597
126668
199485
402178
589094
995158
1396849
2342709
4961006
13557692
39 204 259
592
1103
1018
1098
148
FX Interbank
2001 Q1
2001 Q2
2001 Q3
2001 Q4
2002 Q1
2002 Q2
2002 Q3
2002 Q4
7
11
17
27
7
USDJPY
241750
345791
298994
216762
798556
280526
409394
557083
EURUSD
252512
285498
237869
181777
440269
174908
347536
322319
TOTAL ticks
3 148 856
2 242 688
We use here a standard notations as LKOH = Lukoil (RF), SBER = Sberbank (RF) etc.
A cumulative effect for LKOH and SBER total tick number approximation is shown at Fig.A5 in Appendix.
SKETCH OF METHOD
The best way to check up the result of our efforts is to see Fig.A1 in Appendix done for Russian Ruble at MICEX for the period
since 01.01.2007 to 30.06.2009 (about 610 trading days and 730000 ticks processed) with a 86'58%¶VGHYDOXDWLRQSHULRG
included. We arrange so-called Efficiency Waves (or E-waves) on the basis of the tick volumes distribution dynamics over the
period in question. Histogram for Cumulative Wave at this Figure shows that first alarm we had 10.07.2008, i.e. 6 days before the
USDRUB minimum, 23.1255, occurred (16.07.2008). The next alarm we got 05.02.2009, i.e. 14 days before the final local
devaluation target was done in USDRUB, i.e. maximum value of 36.4629 in CBRF official rate (19.02.2009). We introduce EWaves as follows. If we consider the volume distribution over the trading range [p0,p1] in question V([p0(t),p1(t)],t)=V(t),
W « 1VHHVDPSOHDW)LJWKHQ(ZDYHVGHILQHGDVIXQFWLRQVRIIORDWLQJ9WLH(W (9>@WDV1WHQGVWRLQILQLW\
Fig.3. LKOH as of 01/01/2000 and SBER as of 01/01/2007 tick volume distribution samples
We have to note that E-waves are very sensitive to the database quality. This follows the brief analysis of the E distortions inspired
with Internet data incompleteness (MICEX, intraday records for 19.07.2011) provided in the short Table below
Official MICEX Data
as of 20110719 [a]
EUR_RUB__TOM
Free Internet Data
20110719 [b]
USD000000TOD
Free Internet Data
20110719
USD000UTSTOM
Free Internet Data
20110719
r
0,202672
R
0,434536
E=
= r/R
46,64092
0,335364
0,629907
53,24025
0,246627
0,785925
31,38054
0,18587
0,307198
0,229568
0,434536
0,622773
0,785925
Sources:
[a]. EOD official records (MICEX data for 19.07.2011), http://rts.micex.ru
[b]. Free Internet database, see for example http://www.mfd.ru
42,77429
49,3275
29,20986
# Ticks
total
940
937
2535
7086
Database
Completeness
+3
99,6809
2540
+5
7111
+25
99,8031
99,6484
Distortion
in E
9,04%
7,93%
7,43%
Our methods operate with financial interpretations [1-9] for a benchmark of the %ROW]PDQQ¶V/DUJH6\VWHP7KHRU\>@
Let us consider, without loss of generality, one trading period
series
pik = p0k + i, i = 0...N k , N k ® ¥ ,
Sk
for the financial market with unit step in quoting a price and
where we use a notation
p0k and p Nk k = p 0k + N k
for daily prices of the asset
Dk be the total number of two-side anonymous deals done with the asset during Sk .
t j = ( pt j ,Vt j , Tt j ), j = 1...Dk ± VWDQGDUG vectorized record for every transaction done for the
under consideration. Let
Def.1. Tick
pt j , Vt j , Tt j ±WLFNSULFHYROXPHDQGWXUQRYHUUHVSHFWLYHO\
Def.2. Cash and volume turnover
T Sk
and
V Sk
rk = T
Def.5. At-the-moment Efficiency
E = lim
Sk
k® ¥
are
T
Rk = N k
Def.3. Nominal rate of at-the-moment return
Def.4. Profitability at-the-moment
Sk
for given
¦
¦
k
p ik V i k
Ek
Sk
p 0k
=
¦ Tt
.
, where
Vi k =
j
¦
,
V
Sk
=
¦
Vt k
j
asset given, where
.
Vt kj d ( p ik ) , i = 0...N k
.
Our result is formulated as a
THEOREM-1 FOR INTERNATIONAL FINANCIAL MARKETS
The Efficiency of the transactions at the global markets asymptotically tends to the value of
E » 37 ,8 %.
This result depends neither on asset nor market in question.
SKETCH OF PROOF
Let us assume that
Sk
is over and omit index k. Let cash and volume turnovers T and V be fixed now. To get the key parameter,
we have to obtain the
additional conditions
Vi
distribution of the maximal probability, i.e. we meet problem to minimize
¦ p V = T , ¦V = V
i
with the well known %ROW]PDQQ¶V UHVXOW
i i
i i
¦V
Vi = ae - bp
i
i
i
ln Vi
under
, L «1, where
a , b - const, b  [0;1]. It is easy to see that E follows the normalization in the unit cube and we estimate E from the averaging
formula
³
[ b N - ln
e b N +1
2
( b ( p - N ) + ln
e b N +1
2
- e - b N ln
e b N +1
2
]
+ 1 ) - e - b N ( b ( p + N ) + 1 - ln
e b N +1
2
)
dW
Data processing with Russian blue chips shows that we have some troubles with recalculating the targets due to the huge amount
of information and, moreover, we can apply this approach only for the long-term analysis to fulfill the %ROW]PDQQ¶V FRQGLWLRQ
N> T/V-p at real financial market transactions flows.
NUMERICAL VALUE
E ( p, N , b ) ~
[36 ( N + 4 p )
(N + 4 p )
p / 18
2
3
Ÿ E ~
Note that our E flirts with the Golden Mean
157
1080
+
25
18
+ 12 ( N + 4 p ) N 2 b + ( N 2 - 18 Np - 24 p 2 ) N 2 b
ln 5 -
26
9
2
]
ln 2 » 0 . 37827562 .
j = 1 - ( 5 - 1) / 2 » 0.381966 and the inverse exponent 1 / e » 0.367880 (Fig.2).
Now, if NBD (No Bad Deals) assumption is valid, i.e. all the transactions are profitably closed, then, as a side result of the both
crisis and just post-crisis tick-by-tick data processing we have proved and present a
THEOREM-2 FOR INTERNATIONAL FINANCIAL MARKETS
Under NBD assumption an asymptotic behavior of the global financial markets is ruled with two functions of r ±
F1 is valid for up-trends, F2 for down-trends, and r as above.
As mentioned above, a huge amount of information gives problem to fulfill %ROW]PDQQ¶V FRQGLWLRQ >@ DW UHDO ); DQG RWKHU
ILQDQFLDOPDUNHWV: HKDYHWRFRQVLGHUVRPHFUHDWLYHPHWKRGVWRUHGXFHWKHFRPSOH[LW\±IRUH[DPSOHIRUWKHVKRUWWHUPDQDO\VLV
we recommend to apply another interdisciplinary point of view [11]. This number-theoretical and entropy combined method
applied for Efficiency (under the direct trading rules) gives us a number-theoretical
THEOREM-3 FOR INTERNATIONAL FINANCIAL MARKETS
Efficiency is well approximated with an integral-differential combined formula as follows
d
dq
­
® q
¯
s1
s
–
2
j=1
1 - q s3 +
1 - q j
j
½
¾ ˜
¿
³
­
® q
¯
b1
b
–
2
j=1
1 - q b3 +
1 - q j
j
½
¾ dq
¿
APPENDIX
Figures below present new results of tick database processing to comment the statement of E-Theory via E-waves/-curves
presented above for different classes of trading ranges, for different financial markets of the high liquidity level.
Fig.A1. USDRUB_TOM dynamics and some E-Waves for the period since 01.01.2007 as of 30.06.2009.
Fig.A2. Two types, Aggregand and Segregand, of E-waves (USDJPY Q1-2001, global FX dealing) for R=9,87%.
Fig.A3. Long- and short-term E-waves at Russian interbank dealing (USDRUB_TOM 2011, RTS-MICEX) for R=21,23%.
Fig.A4. The same phenomenon in E-waves for the Russian blue chips (Gazprom 2007, MICEX) for R=61,42%.
Fig.A5. Russian blue chips, LKOH and SBER, polynomial approximation for cumulative tick number as of 2011.
CONCLUSION REMARK ON EARLY WARNING SYSTEMS
We have omitted all proofs of Theorems for short here. Our goal at-the-moment is to complete a parallel processing of
official tick-by-tick data collections from different financial markets (RTS-MICEX, NYSE, LIFFE, ICE, FX etc.) and
to present a new tools for forthcoming crises early alarm system based on Theorems for E-Waves as well as a new
paradigm for both high frequency trading and open market operations efficiency control. This reason is a strong
motivation to launch the joint international research project for global crises forecasting and control methods design
on the basis of data processing opportunities all over the world.
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[1] P r elov V.V. ± The New Financial Theorem: Russian Blue Chips and Global Commodities Evidence.//ISSN 1931-0285 CD, v.
3, No. 2, 2008, pp. 39-43.
[2] P r elov V.V. ± On the Efficiency Theorem.// ISSN 1931-0285 CD, v. 4, No. 2, 2009, pp. 88-91.
[3] P r elov V.V. ± Data Mining and Crisis Forecasting Opportunities.// ISSN 1931-0285 CD, v. 4, No. 2, 2009, pp. 60-64.
[4] P r elov V.V. ± Large Systems Theory and Crisis Precursors.// ISSN 1931-0285 CD, v. 5, No. 1, 2010, pp. 94-97.
[5] P r elov V.V. ± Information Analysis and Target Simulation.// ISSN 1931-0285 CD, v. 5, No. 1, 2010, pp. 98-104.
[6] P r elov V.V. ± Some Remarks on Crisis Forecasting.//BAI P roceedings CD , 2008.
th
[7] P r elov V.V. ±2Q*DXVV4SRO\QRPLDOVDQG(IILFLHQF\(YDOXDWLRQRI7UDGLQJ Operations.//VI Intern. Conference on Ma th.
Simula tion P roceedings: Yakutsk, 2011, pp. 102-103 (in Russian).
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4, pp. 11-17 (in Russian).
[9] P r elov V.V., M a k h u tov N.A.±$QDO\VLVDQG)RUHFDVWLQJRIWKH)LQDQFLDOTurmoils.//Sa fety a nd Emergencies P roblems , 2004,
v. 2, pp. 47-57 (in Russian).
[10] Boltzm a n n L .±W ien. %HU%GV±
[11] An d r ews G .E .±7KH7KHRU\RI3DUWLWLRQV$GGLVRQ: HVOH\Publ. Comp., 1976.