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Abrupt rise of new machine ecology
beyond human response time
Neil Johnson
1
, Guannan Zhao
1
, Eric Hunsader
2
, Hong Qi
1
, Nicholas Johnson
1
, Jing Meng
1
& Brian Tivnan
3,4
1
Physics Department, University of Miami, Coral Gables, Florida 33124, U.S.A.,
2
Nanex LLC, Evanston, Illinois, U.S.A.,
3
The MITRE
Corporation, McLean, VA 22102, U.S.A.,
4
Complex Systems Center, University of Vermont, Burlington, VT 05405, U.S.A.
Society’s techno-social systems are becoming ever faster and more computer-orientated. However, far from
simply generating faster versions of existing behaviour, we show that this speed-up can generate a new
behavioural regime as humans lose the ability to intervene in real time. Analyzing millisecond-scale data for
the world’s largest and most powerful techno-social system, the global financial market, we uncover an
abrupt transition to a new all-machine phase characterized by large numbers of subsecond extreme events.
The proliferation of these subsecond events shows an intriguing correlation with the onset of the
system-wide financial collapse in 2008. Our findings are consistent with an emerging ecology of competitive
machines featuring ‘crowds’ of predatory algorithms, and highlight the need for a new scientific theory of
subsecond financial phenomena.
A
s discussed recently by Vespignani
1
, humans and computers currently cohabit many modern social
environments, including financial markets
1–25
. However, the strategic advantage to a financial company
of having a faster system than its competitors is driving a billion-dollar technological arms race
6–9,16–19
to
reduce communication and computational operating times down to several orders of magnitude below human
response times
26,27
-- toward the physical limits of the speed of light. For example, a new dedicated transatlantic
cable
18
is being built just to shave 5 milliseconds (5 ms) off transatlantic communication times between US and
UK traders, while a new purpose-built chip iX-eCute is being launched which prepares trades in 740 nanose-
conds
19
(1 nanosecond is 10
29
seconds). In stark contrast, for many areas of human activity, the quickest that
someone can notice potential danger and physically react, is approximately 1 second
26,27
(1 s). Even a chess
grandmaster requires approximately 650 ms just to realize that she is in trouble
26,27
(i.e. her king is in checkmate).
In this paper we carry out a study of ultrafast extreme events (UEEs) in financial market stock prices. Our study
is inspired by the seminal works of Farmer, Preis, Stanley, Easley and Cliff and co-workers
2,3,6–9
who stressed the
need to understand ultrafast market dynamics. To carry out this research, we assembled a high-throughput
millisecond-resolution price stream across multiple stocks and exchanges using the NANEX NxCore software
package. We uncovered an explosion of UEEs starting in 2006, just after new legislation came into force that made
high frequency trading more attractive
2
. Specifically, our resulting dataset comprises 18,520 UEEs (January 3rd
2006 to February 3rd 2011) which are also shown visually on the NANEX website at www.nanex.net. These UEEs
are of interest from the basic research perspective of understanding instabilities in complex systems, as well as
from the practical perspective of monitoring and regulating global markets populated by high frequency trading
algorithms.
Results
We find 18,5 20 cr ashes and spikes with durati ons less than 1500 ms in our dataset, with examples of each
given in Fig. 1A (crash) and 1B (spi ke). We define a crash (or spike) as an occurrence of the stock price
ticking down (or up) at le ast ten times before tic king up (or dow n) and the pric e change exceeding 0.8% of
the initial price, i.e. a fractional change of 0.008. We have checked that our main conclusions are robust to
variations of these definitions. In order to have a standardized measure of the size of a UEE across stocks, we
take the UEE size to be the fractional change between the price at the start of the UEE, and the price at the
last tick in the sequence of price jumps in a given dire ction. Since both crashes and spikes are typically more
than 30 standard deviations larger than the average price movement either side of an event (see Figs. 1A and
1B), they are unlikely to ha ve arisen by chance since, in that case, their expected number would be essentially
zero whereas we observe 18, 520.
OPEN
SUBJECT AREAS:
SCIENTIFIC DATA
NONLINEAR PHENOMENA
STATISTICAL PHYSICS
APPLIED PHYSICS
Received
19 November 2012
Accepted
22 August 2013
Published
11 September 2013
Correspondence and
requests for materials
should be addressed to
N.J. (njohnson@
physics.miami.edu)
SCIENTIFIC REPORTS | 3 : 2627 | DOI: 10.1038/srep02627 1
Figure 2 shows that as the UEE duration falls below human res-
ponse times
26,27
, the number of both crash and spike UEEs increases
very rapidly. The fact that the occurrence of spikes and crashes is
similar (i.e. blue and red curves almost identical in Fig. 1C and in
Fig. 2) suggests UEEs are unlikely to originate from any regulatory
rule that is designed to control market movements in one direction,
e.g. the uptick regulatory rule for crashes
16,17
. Their rapid subsecond
speed and recovery shown in Figs. 1A and 1B suggests they are also
unlikely to be driven by exogenous news arrival. We have also
checked that using ‘volume time’ instead of clock time, does not
simplify or unify their dynamics. The extensive charts at www.na-
nex.net, of which Figs. 1A and 1B are examples, show that the total
volume traded within each UEE does not differ significantly from
trading volumes during typical few-second market intervals, nor do
the UEEs originate from one large but possibly mistaken trade.
The horizontal green lines in Fig. 1C show that the UEEs started
appearing at different times in the past for individual stock, but then
escalated in the build-up to the 2008 global financial collapse (black
curve). Moreover, these escalation periods tend to culminate around
the 15 September bankruptcy filing of Lehman Brothers. Indeed, the
ten stock with the most UEEs (solid green horizontal lines) are all
major banks with Morgan Stanley (MS) first, followed by Goldman
Sachs (GS). Figure 2 in the SI shows explicitly the escalation of UEEs
in the case of Bank of America (BAC) stock. For each stock shown in
Fig. 1C, the start and end times of the escalation period (i.e. hori-
zontal green line) are determined by examining the local trend in the
arrival rate of the UEEs. In determining these start and end times, we
checked various statistical methods such as LOWESS and found
them all to give very similar escalation periods to those shown in
Fig. 1C. We also find that the occurrence of UEEs is not simply
related to the daily volatility, price or volume (see SI Fig. 2 for the
explicit case of BAC). Figure 1C therefore suggests that there may
indeed be a degree of causality between propagating cascades of
UEEs and subsequent global instability, despite the huge difference
Figure 1
|
Ultrafast extreme events (UEEs). (A) Crash. Stock symbol is ABK. Date is 11/04/2009. Number of sequential down ticks is 20. Price change is
20.22. Duration is 25 ms (i.e. 0.025 seconds). The UEE duration is the time difference between the first and last tick in the sequence of jumps in a
given direction. Percentage price change downwards is 14% (i.e. crash size is 0.14 expressed as a fraction). (B) Spike. Stock symbol is SMCI. Date is 10/01/
2010. Number of sequential up ticks is 31. Price change is 1 2.75. Duration is 25 ms (i.e. 0.025 seconds). Percentage price change upwards is 26% (i.e.
spike size is 0.26 expressed as a fraction). Dots in price chart are sized according to volume of trade. (C) Cumulative number of crashes (red) and spikes
(blue) compared to overall stock market index (Standard & Poor’s 500) in black, showing daily close data from 3 Jan 2006 until 3 Feb 2011. Green
horizontal lines show periods of escalation of UEEs. Non-financials are dashed green horizontal lines, financials are solid green. 20 most susceptible stock
(i.e. most UEEs) are shown in ranked order from bottom to top, with Morgan Stanley (MS) having the most UEEs.
www.nature.com/scientificreports
SCIENTIFIC REPORTS | 3 : 2627 | DOI: 10.1038/srep02627 2
in their respective timescales. Although access to confidential trade
and exchange information is needed to fully test this hypothesis, at
the very least Fig. 1C demonstrates a coupling between extreme
market behaviours below the human response time and slower global
instabilities
2,5
above it, and shows how machine and human worlds
can become entwined across timescales from milliseconds to
months. We have also found that UEEs build up around smaller
global instabilities such as the 5/6/10 Flash Crash: although fast on
the daily scale, Flash Crashes are fundamentally different to UEEs in
that Flash Crashes typically last many minutes (?1s) and hence
allow ample time for human involvement. Future work will explore
the connection to existing studies such as Ref. 28 of market dynamics
immediately before and after financial shocks.
Having established that the number of UEEs increases dramat-
ically as the timescale drops below one second, and hence drops
below the human reaction time, we now seek to investigate how
the character of the UEEs might also change as the timescale drops
– and in particular, whether the distribution may become more or
less akin to a power-law distribution. Power-law distributions are
ubiquitous in real-world complex systems and are known to provide
a reasonable description for the distribution of stock returns for a
given time increment, from minutes up to weeks
13–15
. Our statistical
procedure to test a power-law hypothesis for the distribution of UEE
sizes, and hence obtain best-fit power-law parameter values, follows
Clauset et al.’s
29
state-of-the-art methodology for obtaining best-fit
parameters for power-law distributions, and for testing the power-
law distribution hypothesis on a given dataset. Following this pro-
cedure, we obtain a best estimate of the power-law exponent a, and a
p-value for the goodness-of-fit, for the distribution of UEE sizes.
Specific details of the implementation, including a step-by-step
recipe and documented programs in a variety of computer languages,
are given in Ref. 29.
Figure 3 shows a plot of the goodness-of-fit p-value, and the cor-
responding power-law exponent a, for the distribution of sizes of
UEEs having durations above a particular threshold. As this duration
threshold decreases, the character of the UEE size distribution exhi-
bits a transition from a power-law above the limit of the human
response time to a non-power-law below it -- specifically, the good-
ness-of-fit p falls from near unity to below 0.1 within a small time-
scale range in Figs. 3B and 3C. This loss of power-law character at
subsecond timescales suggests that a lower limit needs to be placed
on the validity of Mandelbrot’s claim that price-changes exhibit
approximate self-similarity (i.e. approximate fractal behavior and
hence power-law distribution) across all timescales
30
. It can be seen
that the transition for crashes is smoother than for spikes: this may be
because many market participants are typically ‘long’ the market
16
and hence respond to damaging crashes differently from profitable
spikes. Not only is the crash transition onset (650 ms) earlier in
Fig. 3B than for spikes in Fig. 3C, it surprisingly is the same as the
thinking time of a chess grandmaster, even though individual traders
are not likely to be as attentive or quick as a chess grandmaster on a
daily basis
26,27
. This may be a global online manifestation of the ‘many
eyes’ principle from ecology
6
whereby larger groups of animals or
fish may detect imminent danger more rapidly than individuals.
Figures 4 and 5 show further evidence for this transition in UEE
size character as timescales drop below human response times.
Figure 4 shows that the cumulative distribution of UEE sizes for
the example of spikes, exhibits a qualitative difference between
UEEs of duration greater than 1 second, where p 5 0.91 and hence
there is strong support for a power-law distribution, and those less
than 1 second where p , 0.05 and hence a power-law can be rejected.
A similar conclusion holds for crashes. Figure 5 shows the cumulat-
ive distribution of sizes for UEEs in different duration windows, with
the distribution for the duration window 1200–1500 ms showing a
marked change from the trend at lower window values. The follow-
ing quantities that we investigated, also confirm a change in UEE
character in this same transition regime: (1) a Kolmogorov-Smirnov
two-sample test to check the similarity of the different UEE size
distributions within different duration time-windows (see SI
Fig. 5); (2) the standard deviation of the size of UEEs in a given
window of duration (see SI Fig. 6); (3) the average and standard
deviation in the number of price ticks making up the individual
UEEs which lie in a given duration window (see SI Fig. 7); (4) a test
for a lognormal distribution for UEE durations (see SI Fig. 8). Figure
9 of the SI confirms that using different binnings for the UEE dura-
tions does not change our main conclusions.
Discussion
Inspired by Farmer and Skouras’ ecological perspective
6
, we analyze
our findings in terms of a competitive population of adaptive trading
agents. The model is summarized schematically in Fig. 1 of the SI
while Refs. 31, 40 and 41 provide full details and derivations of the
quoted results below. Each agent possesses several (s . 1) strategies,
but only trades at a given timestep if it has a strategy that has
performed sufficiently well in the recent past. The common informa-
tion fed back to the agents at each timestep is a bit-string encoding
the m most recent price movements
31–35
. The key quantity is
g~2
mz1
=
N corresponding to the ratio of the number of different
strategies (i.e. strategy pool size which is 2
m 1 1
in our model
31,33
)to
the number of active agents N. For g . 1, there are more strategies
than agents, which is consistent with having many human partici-
pants since individual humans have myriad ways of making deci-
sions, including arbitrary guesswork, hunches and personal biases.
Hence g . 1 is consistent with having many active human traders,
which in turn is consistent with longer timescales (.1 s) since this is
where humans can think and act. The g . 1 output, illustrated in
Fig. 6B (right panel), does indeed reproduce many well-known fea-
tures of longer timescale price increments
31
. The chance that many
Figure 2
|
Number of UEEs as a function of UEE duration. The UEE
duration is the time difference between the first and last tick in the
sequence of jumps in a given direction. UEE crashes are shown as red curve,
UEE spikes as blue curve. Since the clock time between ticks varies, two
UEEs having the same number of ticks do not generally have the same
durations.
www.nature.com/scientificreports
SCIENTIFIC REPORTS | 3 : 2627 | DOI: 10.1038/srep02627 3
Figure 3
|
Empirical transition in size distribution for UEEs with duration above threshold
t
, as function of
t
. (A) Scale of times. 650 ms is the time for
chess grandmaster to discern King is in checkmate. Plots show results of the best-fit power-law exponent (black) and goodness-of-fit (blue) to the
distributions for size of (B) crashes, and (C) spikes, as shown in the inset schematic.
Figure 4
|
Extent to which the cumulative distribution for UEE spikes
follows a power-law, for the subset having durations greater than 1
second (upper panel) and less than 1 second (lower panel). For durations
more than 1 second, there is strong evidence for a power-law ( p-value is
0.912). For durations less than 1 second, a power-law can be rejected. Black
line shows best-fit power-law.
Figure 5
|
Cumulative distribution for UEE spikes with durations within
a given millisecond range, having a size which is at least as big as the
value shown on the horizontal axis.
www.nature.com/scientificreports
SCIENTIFIC REPORTS | 3 : 2627 | DOI: 10.1038/srep02627 4
agents simultaneously use the same strategy and submit the same
buy or sell order, is small if g . 1, hence there are very few extreme
price-changes -- exactly as observed in our data for . 1 s. Reducing
g below 1 corresponds to reducing the strategy pool size below the
number of agents, which is consistent with a market dominated by
specific high-frequency trading algorithms. As the trading timescale
moves into the subsecond regime, the number of pieces of informa-
tion that can be processed by a machine decreases since each piece of
information requires a finite time for manipulation (e.g. storage and
recall), which is consistent with a reduction in m and hence a
decrease in g since g~2
mz1
=
N.
Remarkably, decreasing g continually in our model generates a
visually abrupt transition in the output with frequent extreme price-
changes now appearing (Fig. 6B, left panel), which is exactly what we
observed in the data for , 1s.g , 1 implies more than one agent per
strategy on average: crowds of agents frequently converge on the same
strategy and hence simultaneously flood the market with the same
type of order, thereby generating the frequent extreme price-change
events. Although it is quite possible that there are other models that
couldreproduceagradual change in the instability as g decreases, the
task of reproducing a visually abrupt transition as observed empir-
ically in Fig. 3 (particularly Fig. 3C) is far harder. In addition, our
model predicts (1) that the extreme event size-distribution in the
ultrafast regime (g , 1) should not have a power law, exactly as we
observe; (2) that recoveries as in Figs. 1A and 1B, can emerge endo-
genously in the regime g , 1 (see Fig. 6C, left panel), again as we
observe; and (3) that extreme events can be diverted by momentarily
increasing the strategy diversity. To achieve this latter effect, agents
simply need to be added with complementary strategies -- shown as
complementary colors in the right panel of Fig. 6C -- thereby partially
cancelling the machine crowd denoted in red. The fact that the actual
model price trajectory can then bypass the potential extreme event
(green dashed line in left panel of Fig. 6C) therefore offers hope of
using small real-time interventions to mitigate systemic risk.
Although the simplicity of our proposed minimal model necessar-
ily ignores many market details, it allows us to derive explicit analytic
formulae for the scale of the fluctuations in each phase, and hence an
indication of the risk, if we make the simplifying assumption that the
number of agents trading each timestep is approximately N (see Refs.
31, 40 and 41 for details). For g . 1, the scale is given by
N
1
2
1{ 2
{ mz1ðÞ
N
1
2
for general s, while for g , 1 it abruptly adopts
a new form with upper bound 3
{
1
2
2
{
m
2
N 1{2
{2 mz1ðÞ
1
2
and lower
bound 3
{
1
2
2
{
mz1ðÞ
2
N 1{2
{2 mz1ðÞ
1
2
for s 5 2. This predicted sud-
den increase in the fluctuation scale from being proportional to N
1
2
for
g . 1, to proportional to N for g , 1, is consistent with the observed
appearance of frequent UEEs at short timescales, and specifically the
visually abrupt transition that we observe in Fig. 3.
More detailed investigation of the properties of UEEs, and the
potential implications for financial market instability, will require
access to confidential exchange data that was not available in the
present study. However a remarkable new study by Cliff and
Cartlidge
36
provides some additional support for our findings. In
controlled lab experiments, they found that when machines operate
on similar timescales to humans
36
(longer than 1 s), the ‘lab market’
exhibited an efficient phase (c.f. few extreme price-change events in
our case). By contrast, when the machines operated on a timescale
faster than the human response time
36
(100 milliseconds) then the
market exhibited an inefficient phase (c.f. many extreme price-
change events in our case).
Figure 6
|
Theoretical transition. (A) Timescales from Fig. 3A. (B) Our model’s price output for the two regimes, using same vertical price scale. g is ratio
of number of strategies to number of agents (g~2
mz1
=
N).g , 1 implies more agents than strategies, hence frequent, large and abrupt price-changes
as observed empirically for timescales , 1s.g . 1 implies less agents than strategies, hence large changes are rare. (C) Large change with recovery from
our model, similar to Fig. 1A on expanded timescale. Right panel shows schematic of our model: Machines in g , 1 regime unintentionally use same
red strategy and hence form a crowd. Adding agents with different strategies (blue and green, schematic) prevents UEE (green dashed line indicates
modified price trajectory).
www.nature.com/scientificreports
SCIENTIFIC REPORTS | 3 : 2627 | DOI: 10.1038/srep02627 5
While our crowd model offers a plausible explanation of the
observed transition in Fig. 3, we stress that our purpose in this paper
was not to explain the details of the price changes during individual
UEEs, nor was it to unravel the underlying market microstructure
that might provoke or exacerbate such UEEs. A recent preprint by
Golub et al.
37
claims that a majority of all UEEs carry the label of ISO
(Inter-market Sweep Order
37
). However this claim does not affect the
validity of our findings. Moreover, Ref. 37 does not uncover or
explain the visually abrupt transition that we observe in Fig. 3, nor
does it invalidate our own crowd model explanation. Irrespective of
the underlying order identities, every UEE is the result of a sudden
excess buy or sell demand in the market, and our model provides a
simple explanation for how sudden excess buy or sell demands are
generated, not how they get fulfilled. Indeed it is a common feature of
our model output that a large imbalance of buy or sell demand can
suddenly appear, producing a UEE as observed empirically. We also
note that Golub et al.
37
make several strong assumptions in their
attempts to label the UEEs, each of which requires more detailed
investigation since the resulting identifications are neither unique
nor unequivocal. Whether the visually abrupt transition in Fig. 3 is
a strict phase transition in the statistical physics sense, also does not
affect the validity of our results. The extent to which UEEs were
provoked by regulatory and institutional changes around 2006, is a
fascinating question whose answer depends on a deeper understand-
ing of the market microstructure along the lines started by Golub et
al.
37
. It may be that ISOs are particularly problematic, but this is still
unclear because of the assumptions made in Ref. 37. Once this has
been resolved, it should be possible to make definite policy recom-
mendations based on our findings, as well as expanding the study to
connect to systemic risk
38
and derivative operations
39
.
Methods
The power-law analysis that we use to obtain our main result in Fig. 3, follows the
state-of-the-art testing procedure laid out by Clauset et al.
29
. Our accompanying
crowd model considers a simple yet archetypal model of a complex system based on a
population of agents competing for a limited resource with bounded rationality. This
model has previously been shown to reproduce the main stylized facts of financial
markets
31
. Its dynamics are based on the realistic notion that it is better to be a buyer
when there is an excess of sellers or vice versa when in a financial market comprising
agents (hu mans or machines) with short-term, high-frequency trading goals. The
formulae given above for the scale of the fluctuations in each phase, are derived
explicitly in Ref. 40, and also Refs. 31 and 41.
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Acknowledgments
NJ (Neil Johnson) gratefully acknowledges support for this research from The MITRE
Corporation and the Office of Naval Research (ONR) under grant N000141110451. The
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SCIENTIFIC REPORTS | 3 : 2627 | DOI: 10.1038/srep02627 6
views and conclusions contained in this paper are those of the authors and should not be
interpreted as representing the official policies, either expressed or implied, of the above
named organizations, to include the U.S. government. We thank Amith Ravindar, Joel
Malerba, Zhenyuan Zhao, Pak Ming Hui, Spencer Carran, D avid Smith, Michael Hart and
Paul Jefferies for discussions surrounding this topic and help with assembling datafiles and
parts of figures.
Author contributions
All authors participated in discussions of the research, its findings, and the content of the
manuscript. NJ (Neil Johnson), GZ and BT wrote the manuscript. NJ (Neil Johnson), EH
and BT designed the research. NJ (Neil Johnson) GZ, EH, HQ, NJ and BT analysed the
empirical data. GZ, HQ and JM did the numerical calculations while NJ (Neil Johnson)
completed the analytical derivations.
Additional information
Supplementary information accompanies this paper at http://www.nature.com/
scientificreports
Competing financial interests: The authors declare no competing financial interests.
How to cite this article: Johnson, N. et al. Abrupt rise of new machine ecology beyond
human response time. Sci. Rep. 3, 2627; DOI:10.1038/srep02627 (2013).
This work is licensed under a Creative Commons Attribution-
NonCommercial-NoDerivs 3.0 Unported license. To view a copy of this license,
visit http://creativecommons.org/licenses/by-nc-nd/3.0
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