"Human Swarming" Amplifies Accuracy and ROI when Forecasting Financial Markets

Abstract

Many social species amplify their decision-making accuracy by deliberating in real-time closed-loop systems. Known as Swarm Intelligence (SI), this natural process has been studied extensively in schools of fish, flocks of birds, and swarms of bees. The present research looks at human groups and tests their ability to make financial forecasts by working together in systems modeled after natural swarms. Specifically, groups of financial traders were tasked with forecasting the weekly trends of four common market indices (SPX, GLD, GDX, and Crude Oil) over a period of 19 consecutive weeks. Results showed that individual forecasters, who averaged 56.6% accuracy when predicting weekly trends on their own, amplified their accuracy to 77.0% when predicting together as real-time swarms. This reflects a 36% increase in forecasting accuracy and shows high statistical significance (p<0.001). Further, if investments had been made according to these swarm-based forecasts, the group would have netted a 13.3% return on investment (ROI) over the 19 weeks, compared to the individual's 0.7% ROI. 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 and ROI of financial forecasts.

Full text

©2019 IEEE International Conference on Humanized Computing and Communication (HCC 2019)
“Human Swarming” Amplifies Accuracy and ROI
when Forecasting Financial Markets
Hans Schumann
Unanimous A.I.
San Francisco, CA, USA
hans@unanimous.ai
Louis Rosenberg
Unanimous A.I.
San Luis Obispo, CA, USA
louis@unanimous.ai
Gregg Willcox
Unanimous A.I.
San Francisco, CA, USA
gregg@unanimous.ai
Niccolo Pescetelli
Massachusetts Institute of Technology
Cambridge, MA, USA
niccolop@mit.edu
Abstract— Many social species amplify their decision-making
accuracy by deliberating in real-time closed-loop systems. Known
as Swarm Intelligence (SI), this natural process has been studied
extensively in schools of fish, flocks of birds, and swarms of bees.
The present research looks at human groups and tests their ability
to make financial forecasts by working together in systems
modeled after natural swarms. Specifically, groups of financial
traders were tasked with forecasting the weekly trends of four
common market indices (SPX, GLD, GDX, and Crude Oil) over a
period of 19 consecutive weeks. Results showed that individual
forecasters, who averaged 56.6% accuracy when predicting
weekly trends on their own, amplified their accuracy to 77.0%
when predicting together as real-time swarms. This reflects a 36%
increase in forecasting accuracy and shows high statistical
significance (p<0.001). Further, if investments had been made
according to these swarm-based forecasts, the group would have
netted a 13.3% return on investment (ROI) over the 19 weeks,
compared to the individual’s 0.7% ROI. 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 and ROI of financial forecasts.
Keywords— Swarm Intelligence, Artificial Swarm Intelligence,
Collective Intelligence, Wisdom of Crowds, Human Swarming,
Artificial Intelligence, Financial Forecasting, Human Forecasting.
I. INTRODUCTION
Extensive prior research has shown that groups of human
forecasters can outperform individual forecasters by aggregating
estimations across groups using simple statistical methods [1-3].
Often referred to as the Wisdom of Crowds (WoC) or Collective
Intelligence (CI), this phenomenon was first observed over a
century ago and has been applied to many fields, from predicting
financial markets to forecasting geopolitical events. The most
common methods involve polling a population of individuals for
self-reported estimations and then aggregating the collected
input statistically as a simple or weighted mean [4].
In recent years, a new method has been developed that is not
based on aggregating data from isolated individuals, but instead
involves groups of forecasters working together as real-time
systems, their interactions moderated by AI algorithms modeled
on the natural principle of Swarm Intelligence.
Known as Artificial Swarm Intelligence (ASI) or simply
“Human Swarming,” this method has been shown in numerous
studies to significantly amplify the accuracy of forecasts
generated by human group [5-11]. For example, in a recent study
conducted at Stanford University School of Medicine, groups of
radiologists were asked to forecast the probability that patients
are positive for pneumonia based on a reviews of their chest x-
rays. When forecasting together as a real-time swarm, diagnostic
errors were reduced by over 30% [12].
While prior studies have shown ASI systems to significantly
amplify the predictive accuracy of human groups across a range
of tasks, from forecasting sporting events to predicting sales
volumes of new products, the present study was conducted to
assess whether swarm-based forecasts of financial markets can
achieve similar improvements. To address this, a nineteen-week
study was conducted that tasked groups of financial traders with
making weekly forecasts regarding the change in price of four
financial indices – the S&P 500 (SPX), the price of gold (GLD),
the price of gold mining stocks (GDX), and the price of crude
oil (CRUDE). The objective was to assess whether a significant
improvement would be measured when comparing individual
forecasts to swarm-based predictions. Swarm performance was
also compared with traditional “Wisdom of Crowd” aggregation
methods. In this way, the present study compared three
forecasting methods – as Individuals, Crowds, and Swarms.
II. SWARMS VS CROWDS
In crowd-based forecasting methods, participants provide
input in isolation, usually via polling, for statistical aggregation.
In swarm-based methods, groups of human participants forecast
together in real-time systems modeled after biological swarms.
The present study uses Swarm AI technology, which is modeled
largely on the dynamic behaviors of honeybee swarms.
The decision-making process that governs honeybee swarms
has been researched since the 1950s and has been shown at a
high level to be quite similar to decision-making in neurological

brains [13,14]. Both employ populations of simple excitable
units (i.e., neurons and bees) that work in parallel to integrate
noisy evidence, weigh competing alternatives, and converge on
decisions in real-time. In both brains and swarms, outcomes are
arrived at through 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 hundreds of scout bees to work in
parallel, collecting information about their local environment,
and then converge together on a single optimal decision, picking
the best solution to complex multi-variable problems [15-17].
The similarity between “brains” and “swarms” becomes
even more apparent when comparing decision-making models
that represent each. The decision process in primate brains is
often modeled as mutually inhibitory leaky integrators that
aggregate incoming evidence from competing neural
populations [18]. 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 compared to
swarm-based decision models, for example the honey-bee
model represented in Figure 2. As shown below, 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
Thus, while brains and swarms are very different forms on
intelligence, both are systems that enable optimized decisions to
emerge from the interactions among collections of processing
units. The goals of the present study are twofold – (i) to assess
if groups of financial traders can form swarm-based systems that
can “think together” as unified intelligence, and (ii) to compare
accuracy of swarm-based forecasts with financial forecasts
generated by individual members or by statistical groups
aggregated using traditional Wisdom of Crowd techniques.
III. SWARMING SOFTWARE
In the natural world, swarming organisms establish real-time
feedback-loops among group members. Swarming bees do this
using complex body vibrations called a “waggle dance.” To
enable real-time swarming among groups of networked humans,
Swarm AI technology was developed. It allows distributed
groups of users to form closed-loop systems moderated by
swarming algorithms [5-7]. Modeled on the decision-making
process of honeybees, Swarm AI 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, networked human groups can answer
questions as a “swarming system” by collaboratively 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, participants impart their personal
intent on the system as a whole. The input from each user is not
a discrete vote, but a stream of real-time vectors that varies
freely. Because all 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
It is important to note that participants freely modulate both
the direction and 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 adjust their magnet so that it stays near the puck’s
outer rim. This is significant, for it requires participants to
remain continuously engaged throughout the decision process,
evaluating and re-evaluating the strength of their opinions 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 imparted 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 FORECASTING STUDY
To assess the ability of human swarms to amplify their
accuracy in financial predictions, a study was conducted over a
nineteen 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 Swarm
platform to make synchronous forecasts.
Across the nineteen 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 an ASI system (i.e. a “human swarm”)
comprised of 24 participants in the process of forecasting a
weekly change in GDX price. It’s important to note that this is
a snapshot of a single moment time, as it generally takes between
10 and 60 seconds of deliberation for the system to converge
upon a solution. As shown in the figure, the group is given four
options to choose from, enabling the set of human forecasters 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. Figure 5 shows a time-
integrated of the deliberation as a heat map, the brightness
representing the level of support imparted for each option.
Fig. 4. Snapshot of a human swarm predicting GDX in real-time
Fig. 5. Support Density heatmap of swarm predicting GDX in real-time
V. ANALYSIS AND RESULTS
For each of the nineteen weeks in the testing period, a set of
predictions were made for each of the four market indices (SPX,
GLD, GDX, CRUDE), providing 76 sets of four 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.

To assess whether the human swarms predicted the
directional change in market indices (i.e. UP or DOWN) more
accurately than individuals, the swarm’s performance was
compared with the individuals’ 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 19 weeks to
obtain a percentage accuracy measure. The procedure was
repeated 1,000 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 mean accuracy of 56%,
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 that the swarm and the crowd were more accurate
than individuals due to random chance was calculated using a
bootstrapping procedure, and was found to be extremely low
(p<0.001) indicating a highly significant result.
Fig. 6. Individual vs Swarm vs Crowd 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. The
crowd in this study achieved a 66.2% accuracy, shown as a blue
line in the figure above. The probability that the swarm
performed better than the crowd due to random chance was low
(p=0.022), indicating that we can be confident that the swarm
significantly outperformed the crowd in aggregate in this study.
Looking at the results as a percentage increase, the swarms,
on average, were 36% 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 5 above), it is also
instructive to assess performance with respect to each of the four
financial categories in isolation, shown in Figure 7 below.
Across 19 weeks, the swarm outperformed or matched the
individual traders and the crowd-based forecasts in all four
instances.
Fig. 7. Individual Accuracy vs Swarm Accuracy when predicting the
directional change in each individual index in the subsequent 72-hour period.
Focusing on the ability of swarming to amplify the accuracy
of financial predictions, the improvements for each of the four
assets above are summarized in Table 1 below. As shown, the
largest accuracy increase achieved by swarm-based forecasting
was recorded in SPX predictions, which showed an impressive
26.6 percentage point gain over the individuals, corresponding
to a 43% amplification in accuracy. The swarm-based forecasts
also outperformed the crowd-based forecasts, achieving an
average increase of 10.8 percentage points across the four assets
tested. This corresponds to a net 16% amplification in total
accuracy for swarm-based forecasts vs crowd-based forecasts.
Table 1. Individual Accuracy vs Swarm Accuracy across each index
A paired t-test was used to calculate the likelihood that the
swarm was more accurate than the crowd at predicting the
direction of stock movement due to random chance alone. The
results of this test, as shown in Table 2 below, reveal that we can
be confident that the swarm outperforms individuals in each
index (p<0.05 for each individual index), and we can also be

confident that the Swarm outperformed the crowd on average
(p=0.022) and the crowd when predicting SPX only (p=0.010).
Table 2. Significance between Swarm and Crowd or Individual Directional
Forecast Accuracy
To make the difference in accuracy between these predictive
methods more concrete, a financial simulation was conducted to
calculate the financial impact of investing using the guidance of
swarms versus individual forecasts and the crowd’s average
forecast. In this simulation, each forecasting method started with
a $1000 bankroll, and invested 100% of its bankroll each week
evenly across the four predicted indexes. If the forecasting
method predicted the index would increase in price, a “long”
position was taken, while if the method predicted a decrease in
price, the index was “shorted”. The net bankroll was tallied at
the end of each week, accounting for the position that was taken
and the decrease or increase in the price of each of the assets that
week, and the new bankroll was then re-invested according to
the next week’s predictions. The final return on investment of
the forecasting method was calculated as the final bankroll
divided by the initial bankroll ($1000).
The results of this simulation are shown in figure 8 below
and summarized in table 3. The swarm again outperforms the
crowd, ending the 19-week simulation with a 13.28% ROI,
while the crowd ends with an 8.87% ROI. The individuals were
the lowest performers, ending with a positive, but lower 3.60%
ROI. To put these results into perspective, the performance that
would have resulted from simply investing “long” (i.e. buy and
hold without trading) in the four assets is plotted in red and ends
up with a 1.96% ROI. Clearly, both the crowd and the swarm
were able to predict weekly price swings to some degree, and as
a result outperform the market in the long term in this study.
Fig. 8. Simulated Bankroll by Week for each Forecasting Method
Table 3. Simulated Bankroll by Week for each Forecasting Method
To color these results further, the probability that the swarm-
based ROI outperformed the crowd-based ROI and the average
Individual’s ROI by random chance is calculated using a
bootstrapping test. In this test, the forecasts that each method
makes are resampled 1,000 times, and the average ROI per
dollar investment is calculated. The average ROI per dollar
investment is used instead of the compounded ROI at the end of
the study to mitigate the effect of compounding on the final
results (i.e. to ensure that early-week correct predictions don’t
artificially inflate the outcome). This histogram of bootstrapped
average ROI per dollar investments is shown in figure 9.
The probability that the Swarm outperformed the Market due
to random chance was low (p<0.001), so we can be confident
that this swarm of financial traders over these 19 weeks would
on average outperform the market. The probability that the
swarm outperformed the crowd due to random chance was also
low (p=0.077).
Fig. 9. Histogram of Swarm Average Return per Dollar per Week to Crowd,
Individual, and Market.
VI. CONCLUSIONS
This study explored if real-time swarms of financial traders
could outperform the predictive accuracy of either (i) individual
traders and/or (ii) groups of traders aggregated using traditional
Wisdom of Crowd (WoC) techniques. The results showed that
groups of forecasters, working together in real-time swarms, can
significantly outperform the accuracy of individual traders when
predicting the directional movement of four common financial
assets (SPX, GLD, GDX, and CRUDE).

The results also show that the swarm-based forecasts could
outperform crowd-based forecasts, with the most significant
results being achieved in the prediction of the S&P index fund
(SPX). In addition, the results of this study show that when
investments are made using these swarm-based forecasts, a
significantly higher return on investment (ROI) is achieved
compared to investments made using either (i) individual
forecasts or (ii) crowd-based forecasts.
Additional research is warranted to further validate the
benefits of swarm-based forecasting for financial applications.
Of particular interest is the ability of ASI technology 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
swarm-based forecasting using participant groups 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 AI for
the use of the Swarm platform for this ongoing work. This work
was partially funded by NSF Grant #1840937.
REFERENCES
[1] Galton, F. (1907). Vox Populi. Nature, 75, 450-451.
[2] Steyvers, M., Lee, M.D., Miller, B., & Hemmer, P. (2009). The Wisdom
of Crowds in the Recollection of Order Information. In Y. Bengio and D.
Schuurmans and J. Lafferty and C. K. I. Williams
[3] Philip E. Tetlock and Dan Gardner. 2015. Superforecasting: The Art and
Science of Prediction. Crown Publishing Group, New York, NY, USA.
[4] J Dana, P Atanasov, P Tetlock, B Mellers (2019), Are markets more
accurate than polls. The surprising informational value of “just asking.”
Judgment and Decision Making 14 (2), 135-147
[5] Rosenberg, L.B., “Human Swarms, a real-time method for collective
intelligence.” Proceedings of the European Conference on Artificial Life
2015, pp. 658-659
[6] Rosenberg, Louis. “Artificial Swarm Intelligence vs Human Experts,”
Neural Networks (IJCNN), 2016 International Joint Conference on. IEEE.
[7] Rosenberg, Louis. Baltaxe, David and Pescetelli, Nicollo. "Crowds vs
Swarms, a Comparison of Intelligence," IEEE 2016 Swarm/Human
Blended Intelligence (SHBI), Cleveland, OH, 2016, pp. 1-4.
[8] Baltaxe, David, Rosenberg, Louis and N. Pescetelli, “Amplifying
Prediction Accuracy using Human Swarms”, Collective Intelligence
2017. New York, NY ; 2017.
[9] Willcox G., Rosenberg L., Askay D., Metcalf L., Harris E., Domnauer C.
(2020) Artificial Swarming Shown to Amplify Accuracy of Group
Decisions in Subjective Judgment Tasks. In: Arai K., Bhatia R. (eds)
Advances in Information and Communication. FICC 2019. Lecture Notes
in Networks and Systems, vol 70. Springer, Cham
[10] L. Rosenberg, N. Pescetelli and G. Willcox, "Artificial Swarm
Intelligence amplifies accuracy when predicting financial markets," 2017
IEEE 8th Annual Ubiquitous Computing, Electronics and Mobile
Communication Conference (UEMCON), New York City, NY, 2017, pp.
58-62.
[11] L. Rosenberg and G. Willcox, "Artificial Swarm Intelligence vs Vegas
Betting Markets," 2018 11th International Conference on Developments
in eSystems Engineering (DeSE), Cambridge, United Kingdom, 2018, pp.
36-39
[12] L. Rosenberg, M. Lungren, S. Halabi, G. Willcox, D. Baltaxe and M.
Lyons, "Artificial Swarm Intelligence employed to Amplify Diagnostic
Accuracy in Radiology," 2018 IEEE 9th Annual Information Technology,
Electronics and Mobile Communication Conference (IEMCON),
Vancouver, BC, 2018, pp. 1186-1191.
[13] Seeley T.D, Buhrman S.C 2001 “Nest-site selection in honey bees: how
well do swarms implement the ‘best-of-N’ decision rule?” Behav. Ecol.
Sociobiol. 49, 416–427
[14] Marshall, James. Bogacz, Rafal. Dornhaus, Anna. Planqué, Robert.
Kovacs, Tim. Franks, Nigel. “On optimal decision-making in brains and
social insect colonies.” Soc. Interface 2009.
[15] Seeley, Thomas D., et al. "Stop signals provide cross inhibition in
collective decision-making by honeybee swarms." Science 335.6064
(2012): 108-111.
[16] Seeley, Thomas D. Honeybee Democracy. Princeton Univ. Press, 2010.
[17] Seeley, Thomas D., Visscher, P. Kirk. “Choosing a home: How the scouts
in a honey bee swarm perceive the completion of their group decision
making.” Behavioural Ecology and Sociobiology 54 (5) 511-520.
[18] Usher, M. McClelland J.L 2001 “The time course of perceptual choice:
the leaky, competing accumulator model.” Psychol. Rev. 108, 550–592