Decoding Social Influence and the Wisdom of theCrowd in Financial Trading NetworkWei PanYaniv AltshulerAlex (Sandy) PentlandMIT Media LabCambridge, MA 02139Email: [email protected] Media LabCambridge, MA 02139Email: [email protected] Media LabCambridge, MA 02139Email: [email protected]—In this paper, we study roles of social mechanismsin a financial system. Our data come from a novel on-line foreignexchange trading brokerage for individual investors, which alsoallows investors to form social network ties between each otherand copy others’ trades. From the dataset, we analyze thedynamics of this connected social influence systems in decisionmaking processes. We discover that generally social tradesoutperform individual trades, but the social reputation of the toptraders is not completely determined by their performance due tosocial feedback even when users are betting their own money. Wealso find that social influence plays a significant role in users’trades, especially decisions during periods of uncertainty. Wereport evidences suggesting that the dynamics of social influencecontribute to market overreaction.I. I NTRODUCTIONRecently the interests on social influence and social dynamics are growing with the rise of Computational SocialScience [1]. We see increasing research efforts in measuringand understanding different social dynamics systems: onlinesystems like Twitter, and real living systems ranging fromdiscussion groups [2], a dormitory community [3] to a NewEngland town [4], to name a few.One particularly interesting type of social systems are thefinancial systems. Though financial systems have been analyzed dominantly with physics stochastic calculus (i.e. randomwalk) models such as Black-Sholes [5], they are with no doubtdriven by the collective behavior of humans. Key aspects ofsocial science, such as the existence of social influence and thetopology restrictions on information flow, are rarely discussedby finance researchers [6]. By adopting social theories into theanalysis of different financial systems, this approach may beable to better explain the many mysterious phenomena in themarkets, such as overractions and market crash.On the other side, financial systems are among the bestquantitatively documented systems, with datasets of transactions in mill-second resolution. Though many of the data arestill only about trades rather than networks, researchers areable to infer the network properties of financial systems withnewly developed tools [7] [8] to understand the underlyingconnectivity from individual trades. In addition, new financial data with explicit social relationships are also becomingavailable [6].In this work, we demonstrate how the study of financialsystems, from the Computational Social Science point ofview, can lead to interesting results for some general socialscience questions. We also demonstrate that the understandingof financial systems with social science perspectives can beturned into profitable hedging and trading strategies.Our work is based on a novel retail online brokerage knownas ”eToro” ( eToro provides users easytools to trade in foreign exchange and commodity markets.The most important feature of eToro is that users can alsolook at other users and follow others’ trades. We will discussthe detail of our eToro dataset in Section II. Based on thisdataset, we will demonstrate how two fundamental challengesin social science are also the fundamental challenges insidethe eToro financial system:The first challenge is whether we can elicit optimal decisions from the wisdom of the crowd. From the literatureone may expect that financial systems are among the bestcrowd wisdom systems, as researchers believe that real cashincentive is the driving force behind optimal rational crowdwisdom [9] [10] [11]. We analyze the performance of thecrowd of eToro users in predicting experts( i.e. those whowill make the most money in the future), and we discuss thepotential causes of our observations. Our results suggest thatgenerally the crowd does much better than individuals. Still,the eToro crowd is subject to social influence dynamics ratherthan complete rational thinking even under strong monetaryincentives. The detail is in Section III.The second challenge is to understand how social influence alters the dynamics of the crowd. Many social scienceresearchers have studied social influence dynamics on networks [7] [12], and naturally we expect such social influencedynamics to exist in financial systems. With the eToro data,we are able to closely examine how social influence changesdecision making process. We discover strong evidence thatsocial influence stimulates speculations and overreactions infinancial markets. The results are shown in Section IV.Readers may argue that eToro is a special type of financialmarkets, and our results may not be representative. We believethat in the real financial world while market participants canusually trade with any other participant in open platforms suchas NYSE, information flow, opinions and influence from otherpeers, and the eventual trading decisions are often largelyconstrained by the network connections of traders in a mannersimilar to the eToro user network.

II. DATASETSOur data come from eToro (See,an on line discounted retail broker for foreign exchangesand commodities tradings with easy-to-use buying and shortselling mechanisms as well as leverage up to 400 times. Inother words, eToro makes trading accessible and fun, as itallows any user to take both long and short positions, witha minimal bid of a few dollars. eToro also magnifies risks intrades, as it allows user to be leveraged. As a result sometimestraders do lose more than 100% of their position value in asingle transaction.(a) Social Trading Landing Page(b) Public Profile for a UserFig. 1. We show the screenshots for the eToro social trading platform here:a) The general landing page showing the current trades by other users and topranked traders. Users can click any trade to copy; b) A public profile page fora eToro user (images and names removed), which contains his current trades,messages and most importantly the number of followers mirroring his trades.However, among all new features, the most interestingfeature of eToro is that it provides a social network platform(known as The Open Book) for all traders. We illustrate themain social trading interface in Fig. 1. Users can easily lookup other users’ trades, portfolios, and past performance. Userscan place three types of trades in eToro. Single trade: Users can place a normal trade by themselves. Copy trade: This mechanism allows a user to place a tradeexactly as another user’s one single trade. In the followingdiscussion, we will refer to this type of copying as ”copytrade”. As shown in Fig. 1(a), users can review all currentreal-time trades, and choose any one to copy. Mirror trade: This mechanism allows a user to pick anexample user. For every trade the example user makes,eToro automatically executes the same trade on behalfof the user. In the following discussion, we will refer tothis type of copying as ”mirror trade”. Fig. 1(b) showsa user’s profile page, where other users can follow andmirror all the trades of this user in his profile page. Theword ”follow” and ”mirror” in the following content isinterchangeable.Our data are composed of over 5.8 million trades fromAugust 2010 to January 2012 (social trading features werelaunched at early 2011). Among them 3 million trades arenon-social independent trades, and around 2.7 million tradesare automatically executed ”mirror trades” for each user bycopying trades from the people the user follows. The rest are”copy trades” that users manually copied from other users’trades.Like many other crowd-sourcing tasks, the truth is in thehands of the few. Overall most investors in eToro are losingtheir investments. Though we have to recognize that thisperiod is the most difficult time for our financial systems,it should be noted that eToro provides both long and shortmechanisms. Therefore, many successful traders can still profitfrom shorting the market and other market neutral strategies.We first look at some statistics of all transactions: on averageeach trade lost 2.8% in its position size, with σ 40%. Theoverall total transaction in our datasets is over 47 millionsUSD, and the total loss from users is around 2 millions USD.User-wise, of all the users who have traded at least once, only16% users were able to make a profit during the time periodin the dataset. This matches the common belief that in crowdsystems there usually exists a very small portion of elites [13].Nevertheless, the promise in eToro lies in its social features:In Fig. 2, we plot average daily ROI (Return On Investment)of EUR/USD on all the trades of different categories. We findthat different types of trades lead to different levels of returns(ANOVA p 1e 10), and mirror trades actually generate apositive return (t-test, p 0.005). At a first look, followingother users in the crowd seems to be a simple way to makemoney, and social trades do outperform single trades. In thispaper, we will take a deep look into the crowd wisdom todecode how social mechanisms alter crowd behaviors in theeToro financial system.In the following content, we only focus on one singlesecurity, EUR/USD, which is the most liquid instrument oneToro and counts for over 82% of all transactions on eToro.III. E LICITING C ROWD W ISDOM FOR B EST T RADERSWhile people do recognize the power of human computingin certain tasks that machines are simply not able to do, itis still unclear if a crowd can provide better predictions anddecisions about future events [10]. Many researchers defendcrowd prediction by suggesting that real money incentives areimportant, and urge governments to allow real cash flow inprediction market [9]. Financial systems provide the exact

mean daily return: Simple vs. Mirror0.040SimpleSocialreturn0.03 0.01 0.030top5*top10*top50**top100*** 0.04Sharpe ratio: Simple vs. Mirror 0.050.2 0.06 0.07mirror tradescopy tradessingle tradesratioaverage ROI per trade (with 95% confidence)ROI for different types of trades0.01SimpleSocial0.150.10.05Fig. 2. The mean ROI for all trades of the three types. The returns aresignificantly different from each other (ANOVA p 1e 10), and mirrortrades generate significant positive return(t-test, p 0.005).unique perspective in understanding the crowd wisdom, as realmoney incentives are always involved.In eToro, one of the best strategies for users is actuallyto mirror other traders’ strategies as seen in Fig. 2. UserA can choose to mirror a more sophisticated user B, andeToro will automatically copy and execute user B’s all futuretrades on behalf of user A. Naturally this mirroring behaviorimplies strong trust in user B from user A, and users whoare mirrored and followed the most are likely to be the besttraders. We observe in Fig. 2 that mirroring actually generatesprofit. However, we still would like to know how well thecrowd is performing in selecting its leaders to follow.We study this problem by constructing trading strategiesusing the wisdom of the crowd. We here construct twoportfolio strategies rebalanced daily. The first strategy, referredas the Simple Best strategy, is constructed by looking at thetop t users on eToro platforms. On each day, we rank eachuser by their accumulated continuously compounded returnup to this day, and execute the same trades of the top t usersby evenly dividing possessed capital among these users in thisday. If none of the top t users is trading on a particular day, wedon’t trade either. We construct the second social strategy byanalogy to the first Simple Best Strategy. Everything remainsthe same except we rank users by their numbers of followersrather than their return performance. The intuition behind thisstrategy is that the best users recognized by the crowd are thebest users on the platform. We execute the same trades of thetop t mirrored users by evenly dividing capitals. We refer tothis strategy as the Social Best strategy.In Fig.3, we plot the mean return and Sharpe Ratio for boththe Simple Best and Social Best Strategies. Sharpe ratio isdefined as the mean return divided by the risk (i.e. varianceof the return), which is a common financial metric for riskadjusted return [14]. It seems that the crowd did select areasonable set of trusted traders to follow, as their returnis significantly above average. Also, for both the top 5 and0top5*top10*top50**top100***Fig. 3. The mean daily ROI and Sharpe Ratio for both the Simple Beststrategy and the Social Best strategy. (*: Both returns are significantly abovezero in t-test with p 0.01; **: only the Simple Best strategy return issignificantly above zero; ***: neither strategy is significantly above zero withp 0.1.)the top 10 strategies, we notice that the performance of thecrowd and the performance of the simple best strategy arealmost equivalent. However, the Sharpe ratio of the crowd isslightly higher. We suspect that this is due to the fact thatcrowds are more risk averse. However, when we extend ourportfolio to top 50 users using both strategies, we notice thatthe performance of the crowd drops significantly.Fig. 3 provides a lot of information: it seems that it ispossible to profit from the top users, but there are very few ofthem. Increasing the diversity of the selected users beyond top10 will immediately reduces profitability. Another interestingobservation is that the crowd performs really well in selectingits top leaders, but fails to outperform a simple algorithm whenbeing asked to select more experts.To answer this problem, we also plot from the top 20%users the distributions on their accumulated returns and theirnumbers of followers in Fig. 4(a) and Fig. 4(b) respectively.It is clear that for performance, very few users exhibit strongtrading skills, and the distribution suggests an exponential decaying distribution. However, the number of followers followa power-law long tail distribution, and unlike trading skills,the distribution is much flatter.A. DiscussionOur results match very well with a well-known culturalmarket study [15], in which the crowd votes for the best songson an artificial online music sharing website where previoususer votes are recorded and displayed. The sharing websitehas multiple independent universes to attend for repeat studies.Researchers discovered that the ”best” songs always rank atthe top, but most songs had uncertain ranking outcomes indifferent universes. In eToro, the top 10 best traders recognized

distribution of users accumulated return0evolutionary human cognitive structure [17].15 21010 410data 610exponential fit y eax: a 1.23 810 1010 5051010accumulated return1050 5 10(a) Distribution of Returndistribution of mirror trades no. of followers 110 15datapower law fit: α 1.5Prob(no. of followers x)accumulated returnProb(accumulated return x)10 210050100150200250rank by no. of followers300350Fig. 5. We plot the accumulated return for the top 300 most followed users ineToro. Except for the top ones, most users’ performance seems to be irrelevantof their ranking. 310 410 510010110210341010no. of followers5106IV. S OCIAL I NFLUENCE IN F INANCIAL D ECISION M AKING10(b) Distribution of Number of FollowersFig. 4. From the top 20% users the distributions on both (a) the accumulatedreturn and by (b) the number of followers are plotted here. The distribution offollowers show strong power-law pattern, but the accumulated return followsan exponential accumulated performance and crowd choices generatecomparable return. However, when we further diversify ourportfolio by including more top followed users, we start torealize that the crowd’s selected experts have less certain skills,just like many top ranked songs in the cultural market study.We suspect that the process of expert eliciting on eTorois similar to a preferential attachment model [16], becausein eToro users are also provided with the information of thenumber of followers about another user. We notice that thenumber of followers in Fig. 4(b) forms a distribution close toa power-law curve rather than the exponential distribution ofuser performance in Fig. 4(a), which is a strong indicator forpreference attachment behavior [16]. In other words, users areheavily affected by the existing number of followers whenmaking mirroring decisions, even when eToro completelydiscloses trading performance and ranks. Under a fully rationalmodel, users’ preference should always match the traders’performance. However, we examine the performance of thetop 300 most followed users in the system (Fig. 5), and wefind that ranking doesn’t correlate with the performance. Ourfinding contradicts the common view for collective intelligenceresearchers who argue that strong monetary incentives inducemore rational decisions [11], and we argue that social feedback does sometimes overweight individual rational thinking.We believe the reason lies in the fundamental basis of theBesides mirroring other users, eToro also allows users tocopy a single trade rather than every trade from another user(the copy trade type). Users can log into the Open Book tolook for other users’ trades, and click to copy one trade. If auser copies a trade, it implies that the user has come to theOpen Book and consulted other users’ trades. He/she made thedecision based on his/her own judgment as well as the socialinfluence from others. It should be mentioned that copyingtrades are less common ( 2% of all transactions) in eToro.There is a long line of research studying the effects on socialinfluence in different domains, such as health [4], purchasebehavior [18] [19], to name a few. eToro datasets provide usan unique opportunity to unveil social influence in financialtrading behavior, and our paper is the first one on this topicas far as we know. Most of the time researchers are unable toknow exactly what information and influence a trader receivesbefore making trades, while in eToro we know that all copytrades are clearly under social influence.We define the following notation: for each day d, wecompute the percentage of long trades among all single tradesdenoted as sd , and the percentage of long trades among allcopy trades as cd . We also refer to sd as single marketperspective, and cd as crowd market perspective.We here plot sd and cd in Fig. 6. Our discovery is surprising:while individual beliefs in buys and sells are fairly stable, thespeculations in copy trades are a magnitude more volatile (σ 2 :0.006 vs. 0.03, F-test p 10 36 ). Therefore with explicitsocial inputs, users tend to become more extreme rather thanconverge. Social influence seems to play an important role indriving market volatility.We plot (sd , cd ), d on a 2-d space, and the results areillustrated in Fig. 7. Fig. 7 clearly suggests that a linear correlation with slope 1.37. In other words, the explicit exposure

daily percentage of long and shortall longcorrelation between long copy trades and market trend0.1single tradescopy trades1 day average3 day average7 day average14 day average0.05correlation coefficient0even 0.05 0.1 0.15 0.2 0.25all shortMar 11 0.3Jun 11 Sep 11 Dec 11 0.35 3 2 10shifts in days123crowd market perspectiveFig. 6. Daily single market perspective and daily crowd market perspective.1.5Fig. 8. The correlation coefficient between cd and tid of different windowsize i shifted from -3 days to 3 days. The largest correlation occurs whenmarket trend is one day after, with an average window size of 7 and 14 days.datafit: slope 1.37, r 0.6210.5000. market perspective1Fig. 7. The single market perspective versus the crowd market perspectivefor all trading others’ trades drives the market further from parity. Forexample, when 60% of the crowd individually decides to shortthe stock, exposing the crowd to others trading behaviors willlikely push 80% of the crowd to short. If we believe that theaverage individual opinion of the market is the best price of themarket, then social influence seems to encourage overreactionand to drive the market to extreme.Now we know that social influence has effects on tradingbehaviors, we continue to investigate that if such influence isconsistent all the time. We first define the market trend tid .tid pd avg(pd i:d ),(1)where pd is today’s price, and avg(pi d:d ) is the average pricefrom the previous i days, with i as the average window size.The price trend is to eliminate high frequency noise from themarket trend. If tid is positive, the market has a up-going trend;otherwise the market tends to go down.We correlate both sd and cd with different values ofi {1, 3, 5, 7, 14, 20}, and shift the trend days forwardand backward to check if eToro users’ market perspectivepredicts or follows the market trend. We find that there isno significant correlation between market trend and individualsd (r 0.02, p 0.10). However, we observe a strongcorrelation between the crowd market perspective and the nextday’s price trend (r 0.35, p 0.1). The results are shownin Fig. 8 for different window sizes for market trends anddifferent shifts.We clearly see Fig. 8 that the strongest correlation is ati 10 with tomorrow’s market trend. As a result, social copytrades can actually be used to predict tomorrow’s market trend.Also notice that the coefficient in Fig. 8 is negative, whichmeans that the more long social trades are today (long tradesimply expectation of market recovery), the more likely themarket is going down tomorrow with respect to its weeklyaverage. We plot both the sd and tid (shifted by one day) withi 14 in Fig. 10, and it is pretty visible to notice that whensd goes extreme in one direction, tid usually goes the oppositedirection.Surprisingly, such observation connects well with one ofthe most popular hedge funding trading strategy: the meanreversion strategy [20], which argues that all aggressive marketreaction is overreaction, and the market will correct it quickly.The mean reversion strategy then bets on the opposite directionof today’s stock trends the next day or so. In our results,the negative correlation suggests that aggressive copy tradingsoften lead to market overreaction, and the market quicklycorrects in the near future.A. Social Reversion StrategyWe can use similar ideas from the mean reversion strategyto construct a trading strategy. We balance the portfolio daily.If we notice a day with strongly biased copy trades (cd 0.65or cd 0.35), we will long or short the security with 0.5 cdfraction of the total capital we have, which is merely betting

mean daily ROI (95% confidence)researchers have long been aware of the fact of marketoverreaction and often profit from it [20], and there exist a lotof theories to explain the overreaction [21]. However, eToro0.06data has provided us a unique view on the social influencebehavior of traders: The mere fact that a trader looks up onother traders’ records will increase trading strategy volatility0.04and market overreaction. We believe that this is an importantmechanism for the dynamics of financial systems.0.02What also surprises us is the result demonstrated in Fig. 8and Fig. 10. which suggests that social trading can be used as aprediction signal while individual trades can not. We think that0each user may have different speculation tendency at differenttimes, and therefore the parameter a is dynamic rather than 0.02static. When the market is full of uncertainty and users are1*2*3*45more likely to speculate, users are more vulnerable to externaldays between rebalancing (*:significant above zero) influence in decision making processes and tend to overreact.On the other hand, when users are more certain about theFig. 9. The mean daily ROI for our mean reversion strategy based on copymarket, the external influence plays a less important role in thetrades overreaction. We plot the daily ROI with different holding periods, andwe discover that holding 2 to 3 days for market correction provides the bestdecision making process. Therefore, the strong signals frompositive return (*: significantly positive with t-test p 0.01).social copy trades can be a measure of overreaction as well asmarket uncertainty, which usually indicates a potential changein market direction.against the crowd market perspective. The stronger the bias,To better illustrate this point, we also look at the ratiothe more weights we put into our bets. We then hold thebetween the daily number of copy trade transactions andposition for a certain number of days. Fig. 9 shows the meanthe number of single trade transactions. We correlate theROI for different holding periods, and it seems that waiting 2ratio of daily single trades over copy trades with the maror 3 days for market to correct is the most profitable. Sinceket daily volatility computed using a exponential smootherforeign exchange prices move slowly, in this example weλ 0.80 for computing the exponentially weighted volatilityincrease leverage to 30 .risk metric [22] for EUR/USD. The results are shown in Fig.11. It seems that the two curves correlate positively withB. DiscussionR 0.19, p 0.001. This implies that users are less likelyIn Fig. 7, we observe that social influence is increasing to be under others’ influence and trust more in their owntrading reactions. We argue this is an intuitive observation views in the case of strong volatility. Therefore, a very strongwith the following simple model: Assume a user i at time piece of information or a clear market trend actually inhibitsd is likely to buy an instrument at probability p (denoted peer influence and promotes self judgments. As a result, whenas Prob(Xi 1) p) and short an instrument at 1 p social influence effects are strong, the market is usually at an(denoted as Prob(Xi 0) 1 p). If user i consults with uncertain stage, and therefore the crowd market perspective isanother user j sharing a common buy view, the probability of more overreaction over rational estimations.user i buying an instrument will increase by a, 0 a 1.Such social influence assumption is based on the commonV. C ONCLUSIONproperties of adoption models [18]. Vice versa, if j has aWe observe the effects of two social mechanisms in thesell view, the probability of user i buying an instrument will eToro financial system: namely the effects of social feedbackbe decrease by a. Assuming user j has the same distribution in eliciting experts and the effects of social influence whenProb(Xj 1) p, we have:others’ trades are available to users. We find that social trading0.08E(Xi after consulting j) (p a) Prob(Xj 1) (p a) Prob(Xj 0) (p a)p (p a)(1 p) (2a 1)p a.(2)With a slope of 1.37 from eToro, we have a 19%.With the 2008 economic crisis being still vivid in everyone’smind, understanding the vulnerability of the financial systemsbecomes one of society’s most important problems. Financialprovides much better opportunities for profiting compared withindividual trading. We discover that the eToro crowd is makingexcellent but sometimes not optimal decisions in selectingexperts when they can see others’ choices. Our finding shedslight on many crowd wisdom systems which expect users tobe fully rational under strong financial incentives. We arguethat social effects are so strong that they sometimes overridethe rational assumptions. We also discover that users are proneto much riskier behavior when following their peers, and aremuch likely to overreact when their peers are doing so and themarket is uncertain. This may explain the natural fluctuation offinancial markets when there is no external information [23].

EUR/USD: social long trades predicts next day trend0.050.507 day average trend (one day behind)percentage of long in all copy trades10Mar 11Jun 11Sep 11 0.05Dec 11Fig. 10. We plot the crowd market perspective together with the one-day-behind real market trend smoothed by a one-week average window. We notice thatthe crowd market perspective strongly negatively correlates with the next-day market trades and volatility50volatility (smoother λ 0.80)daily ratio: single/copy trades200Mar 11Jun 11Fig. 11.Sep 11Dec 110Volatility of EUR/USD vs. the ratio between single and copy trades.Future works include a more accurate behavioral model fortrading decision making under social influence, and a betterway of hedging and portfolio constructions to leverage thepotential of crowd wisdom at the same time eliminating thenegative effects of social mechanisms on financial systems.Considering the fact that financial systems after all are composed of humans, we believe that this direction of research ispotentially valuable.R EFERENCES[1] D. Lazer, A. Pentland, L. Adamic, S. Aral, A. Barabasi, D. Brewer,N. Christakis, N. Contractor, J. Fowler, M. Gutmann et al., “computational social science,” Science, vol. 323, no. 5915, p. 721, 2009.[2] A. Woolley, C. Chabris, A. Pentland, N. Hashmi, and T. Malone,“Evidence for a collective intelligence factor in the performance ofhuman groups,” science, vol. 330, no. 6004, pp. 686–688, 2010.[3] N. Aharony, W. Pan, C. Ip, I. Khayal, and A. Pentland, “Socialfmri: Investigating and shaping social mechanisms in the real world,”Pervasive and Mobile Computing, 2011.[4] N. Christakis and J. Fowler, “The spread of obesity in a large socialnetwork over 32 years,” New England Journal of Medicine, vol. 357,no. 4, pp. 370–379, 2007.[5] F. Black and M. Scholes, “The pricing of options and corporateliabilities,” The journal of political economy, pp. 637–654, 1973.[6] S. Saavedra, K. Hagerty, and B. Uzzi, “Synchronicity, instant messaging,and performance among financial traders,” Proceedings of the NationalAcademy of Sciences, vol. 108, no. 13, p. 5296, 2011.[7] W. Pan, W. Dong

MIT Media Lab Cambridge, MA 02139 Email: [email protected] Alex (Sandy) Pentland MIT Media Lab Cambridge, MA 02139 Email: [email protected] Abstract—In this paper, we study roles of social mechanisms in a financial system. Our data come from a novel on-line foreign exchange tradin