Artificial Swarm Intelligence amplifies accuracy when predicting financial markets

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AUTHOR DRAFT (pre publication)
Artificial Swarm Intelligence Amplifies Accuracy
when Predicting Financial Markets
Louis Rosenberg
Unanimous AI
San Francisco, CA, USA
Louis@Unanimous.ai
Niccolo Pescetelli
University of Oxford
Clarendon, UK
niccolo.pescetelli@chch.ox.ac.uk
Gregg Willcox
Unanimous AI
San Francisco, CA, USA
gregg@Unanimous.ai
Abstract— Across the natural world, many species have
evolved methods for amplifying their decision-making accuracy
by thinking together in real-time closed-loop systems. Known as
Swarm Intelligence (SI) in the field of biology, the process has
been deeply studied in schools of fish, flocks of bird, and swarms
of bees. The present research looks at human groups and tests
their ability to make financial predictions by forming online
systems modeled after natural swarms. Specifically, groups of
financial traders were tasked with predicting the weekly trends
of four common market indices (SPX, GLD, GDX, and Crude
Oil) over a period of 14 consecutive weeks. Results showed that
individual participants, who averaged 61% accuracy when
predicting weekly trends on their own, amplified their accuracy
to 77% when predicting together as real-time swarms. These
results reflect a 26% increase in financial prediction accuracy
and show high statistical significance (p=0.001). This suggests
that enabling groups of traders to form real-time systems online,
governed by swarm intelligence algorithms, has the potential to
significantly increase the accuracy of financial forecasts.
Keywords— Swarm Intelligence, Artificial Swarm Intelligence,
Collective Intelligence, Human Swarming, Artificial Intelligence.
I. INTRODUCTION
Artificial Swarm Intelligence (ASI) has been shown to
amplify the intelligence of human groups by connecting users
into real-time systems modeled after biological swarms [1, 2].
Prior studies have shown that “human swarms” can produce
more accurate predictions than traditional “Wisdom of Crowd”
methods such as votes, polls, and surveys [3]. For example, a
2015 study tested the ability of human swarms to forecast the
outcome of college football games. A swarm comprised of 75
amateur sports fans was tasked with predicting 10 college bowl
games. As individuals, the participants averaged 50% accuracy
when predicting outcomes against the spread. When thinking
together in real-time swarms, those same participants achieved
70% accuracy against the spread [2]. Similar increases have
been found in other studies, including a long-term test that
required participants to predict a set of 50 soccer matches in
the English Premier League and showed a 31% increase in
accuracy when participants were connected in swarms [4].
While prior studies have documented the ability of artificial
swarms to amplify the predictive ability of human groups when
forecasting sporting events, political races, and media awards
such as the Oscars and Grammys, no formal study has been
performed to assess whether swarm-based predictions of
financial markets can achieve similar improvements. To
address this need, a fourteen-week study was conducted that
tasked human swarms of financial traders with making weekly
predictions regarding the change in four financial indices
(SPX, GLD, GDX, and Crude Oil). The objective was to assess
whether a statistically significant improvement would be
measured when comparing individual predictions to swarm
predictions. In addition, swarm performance was compared
with the traditional “Wisdom of Crowd” method of using the
most popular prediction across the participant pool as the group
forecast. Thus, the present study compared the predictive
abilities of three cases – Individuals, Crowds, and Swarms.
II. SWARMS AS INTELLIGENT SYSTEMS
The primary difference between “crowds” and “swarms” is
that in crowd-based methods, individual participants provide
their input in isolation (for statistical aggregation after the fact),
while in swarm-based methods, groups “think together” as
real-time systems governed by intelligence algorithms and
converge on solutions in synchrony. The swarming process is
generally modeled after biological systems such as schools of
fish and swarms of bees. The present research uses Swarm AI
technology from Unanimous A.I. Inc, which is modeled largely
on honeybee swarms. This model was chosen for the current
study because honeybee swarms are known to significantly
amplify the accuracy of critical decisions by enabling members
to form real-time systems – i.e. “hive minds” – that can solve
problems as a unified and amplified intelligence.
The decision-making processes that govern the behavior of
honeybee swarms have been studied since the 1950s and have
been shown to be remarkably similar to the decision-making
processes in neurological brains [5,6]. Both employ large
populations of simple excitable units (i.e., bees and neurons)
that work in parallel to integrate noisy evidence, weigh
competing alternatives, and converge on decisions in
synchrony. In both, outcomes are arrived at through a real-time

AUTHOR DRAFT (pre publication)
competition among sub-populations of excitable units. When
one sub-population exceeds a threshold level of support, the
corresponding alternative is chosen. In honeybees, this enables
the group to converge on optimal decisions, picking the best
solution to complex problems (i.e. selecting a new home
location) over 80% of the time [7,8,9].
The similarity between “brains” and “swarms” becomes
even more apparent when comparing decision-making models
that represent each. For example, the decision process in
primate brains is often modeled as mutually inhibitory leaky
integrators that aggregate incoming evidence from competing
neural populations [10]. A common framework for primate
decision is the Usher-McClelland model in Figure 1 below.
Fig. 1. Usher-McClelland model of neurological decision-making
This neurological decision model can be directly compared
to swarm-based decision models, for example the honey-bee
model represented in Figure 2 below. As shown, swarm-based
decisions follow a very similar process, aggregating input from
sub-populations of swarm members through mutual excitation
and inhibition, until a threshold is exceeded.
Fig. 2. Mutually inhibitory decision-making model in bee swarms
When viewed in this context, it becomes apparent that,
while brains are systems of neurons structured so intelligence
emerges, swarms are systems of brains structured so amplified
intelligence emerges. Thus, the objective of the current study
is to connect human financial traders into synchronous systems
that are structured so that an amplified intelligence emerges.
III. ENABLING “HUMAN SWARMS”
Unlike many other social species, humans have not evolved
the natural ability to form closed-loop systems that enable real-
time swarming. That’s because we lack the subtle connections
that other organisms use to establish high speed feedback-loops
among members. Schooling fish detect vibrations in the water
around them. Flocking birds detect subtle motions propagating
through the population. Swarming bees use complex body
vibrations called a “waggle dance.” To enable real-time
swarming among groups of networked humans, specialized
user interfaces, intelligence algorithms, and networking
paradigms are required to close the loop among all members.
To address this need, a technology called Swarm AI was
developed to enable human groups to congregate online as
real-time swarms, connecting synchronously from anywhere in
the world. It was first deployed in 2015 in an online platform
called UNU that allow distributed groups of users to form
closed-loop swarms using standard web-browsers [1]. Modeled
after the decision-making process of honeybee swarms, the
online system allows groups of distributed users to work in
parallel to (a) integrate noisy evidence, (b) weigh competing
alternatives, and (c) converge on decisions in synchrony,
while also allowing all participants to perceive and react to the
changing system in real-time, thereby closing a feedback loop
around the full population of participants.
As shown in Figure 3, swarms answer questions by moving
a graphical puck to select among a set of alternatives. Each
participant provides input by manipulating a graphical magnet
with a mouse or touchscreen. By positioning their magnet with
respect to the moving puck, real-time participants express and
impart their personal intent on the swarm as a whole. The input
from each user is not a discrete vote, but a stream of vectors
that varies freely over time. Because the full population of
users can adjust their intent continuously in real-time, the
swarm moves, not based on the input of any individual, but
based on the dynamics of the full system. This enables a
complex negotiation among all members at once, empowering
the group to collectively explore the decision-space and
converge on the most agreeable solution in synchrony.
Fig. 3. A human swarm answering a question in real-time

AUTHOR DRAFT (pre publication)
It is important to note that participants do not only vary the
direction of their intent, but also modulate the magnitude of
their intent by adjusting the distance between their magnet and
the puck. Because the puck is in continuous motion across the
decision-space, users need to continually move their magnet so
that it stays close to the puck’s outer rim. This is significant,
for it requires participants to be engaged continuously
throughout the decision process, evaluating and re-evaluating
their intent as they convey their contribution. If they stop
adjusting their magnet with respect to the changing position of
the puck, the distance grows and their applied sentiment wanes.
Thus, like bees vibrating their bodies to express sentiment
in a biological swarm, or neurons firing activation signals to
express conviction levels within a biological neural-network,
the participants in an artificial swarm must continuously update
and express their changing preferences during the decision
process, or lose their influence over the collective outcome. In
addition, intelligence algorithms monitor the behaviors of all
swarm members in real-time, inferring their implied conviction
based upon their relative motions over time. This reveals a
range of behavioral characteristics within the swarm population
and weights their contributions accordingly, from entrenched
participants to flexible participants to fickle participants.
IV. FINANCIAL PREDICTION STUDY
To assess the ability of human swarms to amplify their
accuracy in financial predictions, a study was conducted over a
fourteen week period using groups of volunteers who were
unaffiliated with the research team. The participants were all
self-identified as “active traders” who follow the financial
markets daily and make financial trades regularly. Each
weekly group consisted of between 7 to 36 participants. To
establish a baseline, all participants provided their weekly
forecasts as individuals using a standard online survey. The
group then congregated online as a real-time swarm using the
UNU swarming platform to make synchronous forecasts.
Across the fourteen week period, predictions were made for
the following financial indices: (a) the S&P 500 (SPX), (b) the
gold shares index fund (GLD), (c) the gold miners index fund
(GDX), and (d) the crude oil index (CRUDE). The forecasts
were generated every Tuesday at market close. The participants
were asked to predict if each index would be higher or lower
from the current price at market close on Friday (i.e. 72 hours
later). Predictions were recorded first from individuals on
private surveys, then from swarms working together as a
system. In addition, participants were asked to qualify the
expected change in price by indicating if the predicted move
would be “by a little” or “by a lot.” This was included as a
means for evoking participant confidence in their directional
forecast rather than as a true predictor of magnitude.
Figure 4 shows a snapshot of a human swarm comprised of
24 participants in the process of predicting a weekly change in
GDX price. As shown in the figure, the swarm is given four
options to choose from, enabling the swarm to identify which
direction the index will move, as well as express a general
sense of magnitude. The magnitude indicator is helpful as it
causes the swarm to split into multiple different factions and
then converge over time on a solution that maximizes their
collective confidence and conviction. It’s important to note
that Figure 4 shows an instantaneous snapshot of the swarm as
it moves over time towards a final answer. The full process of
converging upon a solution generally required between 10 and
30 seconds of real-time interactions within the swarm.
Fig. 4. Snapshot of a human swarm predicting GDX in real-time
A process called Faction Analysis has been developed to
help researchers visualize how the participants in a human
swarm adjust their support over time and converge upon the
answer they can best agree upon. Figure 5 shows a faction
analysis plot for the swarm above, the colors indicating how
the swarm was initially split (at t=0.0) and then converged over
the time upon the “down a little” option (at t=12.5), which in
this case was an accurate prediction.
Fig. 5. Faction Analysis for human swarm predicting GDX
V. ANALYSIS AND RESULTS
For each of the fourteen weeks in the testing period, a set of
predictions were made for each of the four market indices
(SPX, GLD, GDX, CRUDE), providing 56 sets of predictions.
Results were generated indicating: (a) Individual Accuracy –
computed as the average performance across the pool of human
subjects, (b) Crowd Accuracy – computed by taking the most
popular prediction from the participant pool and using that to
compute accuracy over time, and (c) Swarm Accuracy –
computed by assessing the accuracy of the predictions made by
the swarms each week.

AUTHOR DRAFT (pre publication)
To assess whether the human swarms predicted the
directional change in market indices more accurately than
individuals, we compared swarm performance with individual
performance using a bootstrapping procedure. For each of the
four investment categories (SPX, GLD, GDX, CRUDE) and
each prediction week, we selected the answer provided by an
individual sampled at random among the individuals who
provided a response for that particular week and investment
type. Answers were averaged across the four investment types
and the 14 weeks to obtain a percentage accuracy measure. The
procedure was repeated 10,000 times in order to obtain a
distribution of probabilities for making a correct prediction.
The distribution, shown in Figure 6 as a probability density
function, represents the probability of an individual making a
correct prediction when responses are randomly sampled from
the individual answers provided. With a median accuracy of
61%, the individuals were moderately better than random
guessing when predicting the directional change in these
market indicators. The red line in Figure 6 shows the empirical
performance of the swarms, which at 77% accuracy was
significantly higher performing as compared to individuals.
The probability of individuals scoring better than the swarm,
using a random sampling procedure, was extremely low
(p=0.002) indicating a highly significant result.
Fig. 6. Individual Accuracy vs Swarm Accuracy when predicting the
directional change in all four indices in the subsequent 72-hour period.
A similar analysis was done using the more traditional
“Wisdom of Crowd” method of taking the most popular
predictions across the pool of individuals as the forecast. This
is shown as the blue line in the figure above. At 66% accurate,
the crowd was significantly lower performing than the swarm.
In addition, the probability of an individual scoring better than
the crowd was less conclusive (p=0.164). For these reasons,
the results suggest that real-time swarming is a significantly
more accurate and more reliable method for amplifying the
intelligence of a human population when making financial
forecasts. Looking at the results as a percentage increase, the
swarms, on average, were 26% more accurate when predicting
the directional movement in the financial indices than the
individual financial traders who comprised those swarms.
In addition to analyzing the predictive accuracy across all
four indices in aggregate (as shown in Figure 6 above), it is
also instructive to assess performance with respect to each of
the four financial categories in isolation. This is shown in
Figure 7 below. Across 14 weeks, the swarm outperformed the
individual traders and the crowd-based forecasts in all four
instances. Of particular interest is the performance of the
swarm when predicting GDX, as we see the crowd
underperformed the individual traders while the swarm
significantly over-performed the individual traders. This
suggests that while crowds can amplify errors, swarms are
more resistant, converging on correct results in instances when
the majority of participants selected an incorrect prediction.
Fig. 7. Individual Accuracy vs Swarm Accuracy when predicting the
directional change in each individual index in the subsequent 72-hour period.
Focusing specifically on the ability of swarms to amplify
the accuracy of human forecasters and thereby enable more
accurate financial predictions, the accuracy improvements for
each of the four indices above are summarized in Table 1
below. As shown, the swarm amplified the accuracy of the
participants by differing amounts across the four financial
categories. The largest accuracy increase was recorded in crude
oil predictions, which registered an impressive 28% point net
gain, corresponding to a 43% amplification in total accuracy.
Table 1. Individual Accuracy vs Swarm Accuracy across each index
In addition to assessing the ability to predict the directional
trend of each financial index, it is also instructive to assess the
ability of individuals, crowds, and swarms to qualify their
predictions further by indicating if the weekly change would be

AUTHOR DRAFT (pre publication)
“by a little” or “by a lot.” While these are loose metrics, each
was tied to a specific threshold. For example, when predicting
GDX, the threshold was defined for the participants as a 4%
change, meaning if the index changed by less than 4% it was
classified as “by a little” and if the index changed by more than
4% it was classified as “by a lot.” Because all participants
were required to provide this additional qualifier when
predicting on the survey and in the swarm, the same analysis
can be performed for the primary results above.
Figure 8 below shows a probability density function that
represents the probability of an individual making a correct
prediction (in both direction and value) across all fourteen
weeks and all four market indices. With a median accuracy of
44%, the individuals were less accurate with this additional
qualifier added. The red line in Figure 8 shows the empirical
accuracy of the swarms, which at 57% accuracy, was still
significantly higher performing as compared to individuals.
The probability of individuals scoring better than the swarm,
using a random sampling procedure, was extremely low
(p=0.01) indicating a highly significant result.
Fig. 8. Individual Accuracy vs Swarm Accuracy when predicting the
direction and value change in all four indices in the subsequent 72-hour period.
As also shown in Figure 8 above, the swarm predictions
were more accurate than the crowd predictions, which at 46%
accurate was not statistically better than the individual
forecasts (p=0.32). Thus, even with the added constraint of
predicting if the weekly move would be “by a little” or “by a
lot” (which increased difficulty), the swarm demonstrated
significant benefits over both individual and the crowd-based
forecasts. This suggests that swarm-based forecasting is not
only a benefit when the individuals are most often correct (as
in Figure 6), but also a benefit when the individuals are most
often incorrect (as in Figure 8), further supporting robustness.
VI. CONCLUSIONS
Can real-time swarms of financial traders outperform the
predictive accuracy of individual traders? The results of the
current study suggest that swarms can significantly increase
prediction accuracy when forecasting the directional movement
of certain financial metrics. The results also show that the
swarming process is more accurate and more repeatable than
traditional crowd-based forecasting. Additional research is
warranted to further validate the benefits of Artificial Swarm
Intelligence for financial forecasting applications. Of particular
interest is the ability of swarms to amplify prediction accuracy
in longer term predictions, as the current study used a relatively
short 72-hour forecasting window. Other topics recommended
for ongoing research include exploring swarms of larger sizes,
comparing participants of varying expertise levels, and testing
improved swarming algorithms.
ACKNOWLEDGMENT
Thanks to Chris Hornbostel and David Baltaxe for their
efforts in coordinating the weekly swarms of financial traders
that generated predictions. Also, thanks to Unanimous A.I.
for the use of the unu.ai platform for this ongoing work.
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