Trade synchronization and social ties in stock markets

Abstract

Previous studies suggest that individuals sharing similar characteristics establish stronger social relationships. This motivates us to examine what combinations of socioeconomic investor attributes are more likely to be associated with joint trading behavior. We use a unique data set on actual social ties between investors and find that similarities in investors’ age, geographical location, or length of the co-employment can affect trade synchronization under certain circumstances. Our findings have implications for the analysis of investor networks.

1 Introduction

Information is a key resource in the stock markets. Informed investors trade securities based on their expectations of the dividend streams and discount rates [1–3]. When new information arrives, investors revise their expectations, and consequently, the stock price changes due to shocks in supply and demand. While public information is an important factor that shapes the market dynamics and is widely used in asset pricing with various factors [4, 5], private information also plays a vital role in stock markets [6]. The problem, however, is that, by definition, private information is not publicly observable, which makes its research challenging. Nevertheless, the diffusion of private information and its consequences have been investigated from different points of view with direct and indirect observations. There is evidence of a strong association between day traders’ instant messaging and trade synchronization [7], inside information transfer and illegal trading [6], and investor’s centrality in an investor network and its relation to profit-making [8, 9]. The strength of the investor network links and, at the same time, information channels are affected by investors’ socioeconomic attributes, such as age, language, and geographical distance (see, e.g., [6, 10, 11]). Overall, the extant literature provides strong evidence on the existence and use of private information in stock markets (see also [12, 13]).

While there is research about investor trade synchronization (see, e.g., [14–18]), and, in turn, trade synchronization can signal information exchange [8], less is known about what socioeconomic attributes increase the likelihood of trade synchronization between investors. To this date, a significant limitation of the research on investor networks is caused by the lack of ground truth observations about the actual social connections. We use a unique combination of an observable social network between company insiders and their complete trading history. The proxy for the social network is constructed from simultaneous co-employments. Because there are insiders who sit on the boards of multiple companies, we obtain a connected network of Finnish company insiders. Hereafter, we refer to investors with ties to multiple companies as Connectors. Importantly, even if we extract the social network links from the data on insiders’ co-employment, we do not analyze insider trading per se.

In this paper, we analyze whether trade synchronization is associated with specific attributes of social ties. We hypothesize that attributes associated with stronger social connections are more likely to be observed for those pairs of socially connected investors who are found to synchronize their transactions than for those who trade differently. Particularly, we test whether socially connected investors who synchronize their trades (i) are more similar in age, (ii) are located more closely to each other geographically, and (iii) have worked longer together than the pairs who do not trade synchronously.

Similarly, to understand the effect of socioeconomic attributes for a pair of disconnected investors who synchronize their trades, we test whether socially connected investor pairs on the shortest paths between them ($\mathrm{i}^{*}$) are more similar in age, ($\mathrm{ii} ^{*}$) are located more closely to each other geographically, and ($\mathrm{iii} ^{*}$) have worked together longer than other socially connected investors.¹

Our research question is related to the concept of homophily, which is defined as a tendency for individuals to establish and prefer connections to others similar to them [19, 20]. Social network studies observe, among other characteristics, stronger social ties for people with similar age, profession, and geographical proximity. For example, Fischer [21], Marsden [22], and McPherson et al. [19] find that interactions in relationships with a stronger age homophily tend to be more personal, longer lived, and frequent. Geographical proximity is a strong predictor on how often friends get together to socialize [23]. Proximity induces social interactions as it is easier to connect, socialize and maintain relationship with the local contacts [19, 23–25]. Spacial proximity enables spreading of peer influence [26]. Furthermore, ties that are involved into regular business interactions survive much longer than ties of individuals not sharing the same professional role title [27]. In addition, prior co-employment facilitates social tie formation [28], persistence and decay [29]. Longer lasting relationships in work environment induce friendships and information exchange, because people with the same education background and occupation are more likely to confide in each other [19, 27]. Moreover, Barone and Coscia [30] find that businesses tend to connect with similar businesses, and interestingly, business partnerships exhibit tax fraud homophily.

We focus our analysis on the insiders of 150 companies listed in the Helsinki Stock Exchange (HSE). We combine (a) historical data about company insiderships, (b) insiders’ mandatory notification of trades, and (c) an investor-level transaction data with complete trading history of all investors who traded in HSE. Typically, in the existing empirical research, real investor social relationships are neither observable nor can be determined from the trading data. Similarly to Wong et al. [31] and McEvily et al. [32], we use information about simultaneous insiderships to derive our proxy for the investor social network. By combining data sets (b) and (c), we gain access to insiders’ full trading history on all the securities they traded in the HSE. Our research relies on a two layer network:

• An observable proxy for a social network between 6318 insiders who share insider positions in the same company. Insiders of different companies are linked through Connectors, who hold insider positions in multiple companies.

• An investor network with 1756 nodes, where a link between a pair of investors is based on the level of trade timing similarity, as introduced in Tumminello et al. [33].

Our research contributes to understanding the effect of socioeconomic attributes on the financial decision-making in investor networks. Differently from existing studies on information transfer in insider networks (see, e.g., [6]), our study broadens the investigation of private information in financial markets, not limiting the analysis to insider trading. We do this at a cost by making some strong assumptions. First, we assume that the network derived from the co-employment records is a valid proxy for the investor social network. Second, when interpreting the results from the point of view of private information diffusion, we consider the trade synchronization network as a proxy for the information network [8]. To the best of our knowledge, this paper is the first to analyze a trade synchronization network inferred from shareholder registration data together with an observable proxy of a social network.

2 Methods

With an increasing interest in network science applications in the financial domain (see, e.g., [34–36]), several techniques have been introduced to identify trade and portfolio similarities between investors [8, 9, 16, 33, 37]. Among $\mathcal{O}(N^{2})$ investor pairs, one would want to focus only on meaningful similarities. To filter out spurious trade co-occurrences, the links are usually statistically validated against a chosen null model with a selected statistical significance threshold.

In this paper, we use Statistically Validated Network (SVN) method [14] that identifies non-random trade co-occurrences using hypergeometric distribution. Applying SVN, we project the bipartite system of investors connected to their trading days into a monopartite investor network. A link in this network represents investor trade co-occurrence. The statistical significance of trade co-occurrence between investors is estimated by leveraging the hypergeometric test. The set of statistically significant trade co-occurrences yields the trade synchronization network. Though this method does not allow to determine the direction of influence between two investors, it is sufficient for our analysis purposes. The method is presented below in more detail.

First, for each investor i and her/his traded security k on the trading day t, we calculate the scaled net-volume as

$$\begin{aligned} &{v}_{ikt}= \frac{{V}^{b}_{ikt}-{{V}}^{s}_{ikt}}{{V}^{b}_{ikt}+{{V}}^{s}_{ikt}}, \end{aligned}$$

(1)

where ${V}^{b}_{ikt}$ and ${V}^{s}_{ikt}$ are the total daily buy and sell volumes observed from the shareholder registration data. Next, investors’ buy and sell trading states are defined using the scaled net-volume as follows:

$$\begin{aligned} \textstyle\begin{cases} b \text{ -- buying state, when } {v}_{ikt} > \theta , \\ s \text{ -- selling state, when } {v}_{ikt} < {-\theta}, \end{cases}\displaystyle \end{aligned}$$

(2)

where $\theta > 0$. In this paper, we use $\theta = 0.10$. Net scaled volumes that fall between −θ and θ indicate a day-trading pattern, for which we do not assign a trading state. Using the hypergeometric test we assume that trading days are homogeneous in terms of investor trading activity. Similarly to [14], we find that the distribution of trading state occurrences in different trading days has a bell shape on the log-scale with a fluctuation of approximately one decade around the mean. We conclude that the limited heterogeneity should not undermine the use of the hypergeometric null model.

The null hypothesis is that the trading state co-occurrences for two investors are random. We define $T_{ijk}$ as the length of the joint trading period of security k for investors i and j. The probability of observing X co-occurrences in $T_{ijk}$ observations is estimated by the hypergeometric distribution, i.e.,

$$ H \bigl(X\mid T_{ijk}, N_{ik}^{P}, N_{jk}^{P} \bigr) = \frac{\binom{N_{ik}^{P}}{X}\binom{T_{ijk} - N_{ik}^{P}}{N_{jk}^{P} - X}}{\binom{T_{ijk}}{N_{jk}^{P}}}. $$

(3)

Here, P is one of the trading states, i.e., $P \in \{b, s\}$, and $N_{ik}^{P}$ is the number of days investor i was in the trading state P for the security k. In turn, the probability of having at least $N_{ijk}^{P}$ trading state co-occurrences by chance is calculated as follows:

$$ p\bigl(N_{ijk}^{P}\bigr) = \operatorname{Prob} \bigl(Y \geq N_{ijk}^{P} \bigr) = 1 - \sum _{X=0}^{N_{ijk}^{P}-1}H \bigl(X\mid T_{ijk}, N_{ik}^{P}, N_{jk}^{P} \bigr). $$

(4)

Using Eq. (4), we estimate p-values for our one-sided tests, $p_{ijk}^{P} := p(N_{ijk}^{P})$, for all pairs of investors who traded at least once on the same day. We separately calculate and retain the minimum p-value for each unique pair of investors across multiple trading states (buy and sell sides) and securities, i.e.

$$ p_{ij} = \min \bigl(p_{ijk_{1}}^{b}, p_{ijk_{1}}^{s}, p_{ijk_{2}}^{b}, p_{ijk_{2}}^{s}, \dots \bigr), $$

(5)

where security $k_{(\cdot )}$ does not belong to a company where investor i or investor j is an insider.² The link is validated for investors i and j, i.e., investors have synchronized trading, if $p_{ij} < \alpha$, where α is a chosen statistical significance threshold. To investigate the sensitivity of our results, we vary α thresholds. Optionally, this procedure is combined with the multi-test correction (MTC) to reduce the type I errors. We present some results with Bonferroni multiple test correction [38].

3 Data

3.1 Data sets

This paper introduces a new worldwide-unique data set of an insider network representing insiders and related parties from 153³ publicly listed companies in the HSE coupled with complete histories of their trading behavior for 22 years.⁴ The list of insiders⁵ contains all persons who have access to inside information⁶ and who are working for the issuer under a contract of employment or otherwise performing tasks which give them access to inside information. Among other, the insider list includes members of the board of directors, senior company executives, and other employees with access to insider information. Related parties include spouses, other relatives, minors under guardianship, and controlled or influenced companies. Data set is comprised of three information sources:⁷

• (i) Shareholder registration data (SRD) from all the individual Finnish investors and companies. This includes data for more than 1.5 million investors, provided by Euroclear Finland. The data contains information about transaction date, price, volume, security ID, the postal code, year of birth, and gender of the investor. These data have been extensively used in the literature over two decades [9, 16, 40, 41].

• (ii) Insiders’ mandatory notifications of trade in the HSE from 2005 to 2010 and from 2013 to 2018 for 153 companies. The data include information about family members and trading companies associated with the insiders. This data set is provided by Euroclear Finland’s insider register service (SIRE).

• (iii) Insiders’ assignments and positions in Finnish companies obtained from Finnish Patent and Registration Office (Virre⁸). This data is used for reconstructing the insider network.

More details about the three data sources can be found in Appendix A. The time spans for the collected data sets and the empirical analysis period of this paper are shown in Fig. 1. By matching data sets (i) and (ii), we have been able to track all transactions over all the securities made by a part of the insiders in the HSE. The matching procedure is described in more detail in Sect. 3.2.

Figure 1

Timeline of the analyzed data sets. The observations in the Virre data set are available starting from April 1962 until November 2019. SIRE data was collected over two non-overlapping periods. The first one covers the period between July 2005 and February 2010, while the second is between March 2013 and September 2018. SRD data set is available for the period between January 1995 until December 2016. The investigated period in the empirical part of this paper ranges between January 2005 and December 2009. In the SRD data from 2010 onwards, the transactions are net aggregated under the registration date, making the estimation of scaled net-volume (Eq. (1)) impossible

3.2 Data preprocessing

First, we construct the observable insider network by combining both Virre and SIRE data sets. The social insider network is a dynamic network, constructed on a daily basis. A pair of insiders have a link on the day t if they both were insiders in the same company on this day. Over the union of all daily network snapshots the network contains $13{,}932$ nodes that represent insiders (see Fig. 2 and Table 1).

Figure 2

The matched data set is composed of insiders observed in the Virre and SIRE data sets. Overall, the temporal insider network is composed of $13{,}932$ insiders and their related parties. The $12{,}925$ insider observed in the Virre data set are complemented by 1007 insiders that have been included in the SIRE data set, and were matched with their trading accounts in Euroclear data set. 245 of them belonged to insiders’ family members, 310 belonged to related company’s accounts, and 452 belonged to insiders that were not recorded in Virre data set

Table 1 Summary statistics for insider data over all the years from April 1962 and November 2019 and the analyzed period between January 2005 and December 2009

The history of co-employment establishes a potential social relationship that can be used to share information. Because not all co-employment relationships are equivalent, our analysis is specifically focused on determining which attributes of the co-employment relationships are more likely to be associated with trade synchronization.

Second, to unveil the entire trading history in the insiders’ accounts over all the securities, we match reported insiders’ trades in SIRE data with the anonymized trading data in the SRD data set. The matching is done by looking up the reported insider’s own company trades in the SRD data set based on the trading date, trade direction, traded volume, traded security ID, the initial and closing balance, and the birth year of the account holder. In some cases, there were no trades executed and reported during the five year period, but we could match the accounts by the balance of the shareholdings reported in the SIRE data set. Once an insider is matched with his/her account in the SRD data set, we obtain access to information about all his/her transactions, i.e., the transactions in own company and all other transactions executed in HSE between 1995 and 2016. Hereafter, we will refer to the insiders with matched trading accounts as matched insiders.

The ideal match is when all mandatory trade notifications lead to one anonymized owner ID in the SRD data set. In some cases, even though some transactions in the SRD or the mandatory notifications were missing, we could uniquely match accounts based on account balances. Moreover, in some cases, to confirm an account match when not all trades or account balances have been matched, we used information about insiders’ year of birth, gender, geographical location, nationality, and language to decide the account match.

We are not able to match insiders with their trading accounts either because the investors (1) do not trade at all and therefore do not have trading accounts; (2) they trade but have not traded companies where they need to make mandatory trade notifications, which makes their trading account identification impossible; or (3) we are not able to uniquely match their accounts. The latter can be related to identical trades in terms of volume, price, and direction executed by multiple investors on the same day. If neither the account balances nor the socioeconomic attributes help to identify the account holder, we cannot match the account without observing additional transactions.

Out of 3514 insiders who have reported their transactions, we were able to match 2711 with their trading accounts in SRD data (a success ratio of 77%). The matched accounts include 2156 insiders, 245 family member accounts, and 310 accounts of other related third parties. The complementary cumulative distribution function of the ratio between the matched insiders and all insiders in a company is shown in Fig. 8 for all 153 companies. Appendix B provides more detailed descriptive statistics about the data set.

3.3 Analyzed data

In the empirical part, we limit our analysis between 2005 to 2009 for two reasons. First, SIRE data are not available prior to 2005. Second, from 2010 onwards the transactions in SRD data are net aggregated under the registration date. This makes the estimation of scaled net-volume (Eq. (1)) impossible after 2010. During this period, 6402 individuals were part of the insider network, composed of eight disconnected components. The largest connected component contains 6318 investors, while the size of the second-largest component is only 20 investors. The size of the remaining six components varies from 18 to two investors.

We focus our analysis on the largest connected component of the network, which is composed of insiders from 150 companies. The social investor network is defined as $\mathcal{G}= (\mathcal{I}, \text{CON})$, where $\mathcal{I}$ is the set of investors, and CON is the set of co-employment connections. We denote a link between investors $i \in \mathcal{I}$ and $j \in \mathcal{I}$ as $(i, j)$, and say that they are linked in the social network, i.e., $(i, j) \in \text{CON}$ if both of them have been insiders in the same company at the same time. In total, there are $|\mathcal{I}|= 6318$ insiders and $|\text{CON}| = 500{,}766$ connections in the analyzed social network. The average degree $\langle k \rangle = 158.52$, and the network’s diameter $d = 8$.⁹ The distribution of the number of insiders per company is shown in Fig. 14. We report the summary statistics for the analyzed network in the Appendix C.

Out of $|\mathcal{I}| = 6318$ investors (nodes), $|\mathcal{I}^{m}| = 1756$ are matched with their transactions in the SRD data over all securities. Even if the majority of the investors are not matched with the shareholder registration data, they are important for our analysis. Note that unmatched investors can trade both their own and other company shares. Insider network with all insiders and the network with only matched insiders are shown in Fig. 3 (a) and Fig. 3 (b).

Figure 3

Subfigures illustrate the (a) network with all insiders and (b) the insider network only with matched insiders. The node colors differentiate insiders’ companies except for the dark blue color which identifies the Connector nodes, i.e., investors serving as insiders in multiple companies

4 Results

4.1 Trade synchronization and social distance

In this section, we investigate the association between trade synchronization and social distance for matched insiders. We start by retrieving investor trade synchronization network applying the SVN method [33] for a set of 30 most traded securities among the investors in the analyzed network (see Appendix Table 7). Here, we do not validate the links. Instead, we define the score that measures the level of synchronization for investors i and j,

$$ \mathrm{SCORE}_{ij} = 1-p_{ij}, $$

(6)

where $p_{ij}$ is the minimum p-value obtained with Eq. (5). For investor pairs that have no overlapping trades we set $\mathrm{SCORE}_{ij} = 0$.

Generally, a p-value is a probability of having empirical observations under randomness – $P(\text{data}|\text{null model})$. We can say that the lower (higher) probability, the less (better) the random model explains an observed overlap between the transactions, and the more (less) abnormal the observed overlap is. From this point of view, the p-value, can be used to measure the strength of synchronization. Particularly, $\mathrm{SCORE}_{ij}$ is defined by the probability that the observed synchronization is not generated by the random null model, which assumes independence between traders.

Next, we calculate the social distances $d_{ij}$ using our proxy for the investor social network. The social distance between two investors is defined as the length of the shortest path between them. The two most distant matched insiders are seven links apart.¹⁰ Finally, we calculate $\langle \mathrm{SCORE}_{ij} \mid d_{ij}\rangle$ which defines the average trade synchronization score for investor pairs separated by $d_{ij}$ social connections. Figure 4 shows that the highest scores of trade synchronization are between the directly connected nodes. There is a clear decay of the scores as the distance increases, suggesting, that synchronized trading may actually be associated with social proximity. We evaluate the significance in the decrease of the score with one-side independent two-sample test with unequal variance and sample sizes (Welch’s t-test). The decreasing average score is statistically significant comparing scores at social distances 1 and 2, 2 and 3, and 6 and 7 (see Table 2). However, we observe a local peak at the social distance five. It can imply that information travels via roughly five links before both nodes at the ends of the chain act on it. Intuitively, in case of illegal information exchange, investors close to the source of information may be wary of acting on it due to the higher probability of being monitored for the abuse of insider information. For example, Ahern [6] finds that buy-side managers and analysts act as the tippers as they receive information in the fourth and later links. The results are robust with the Jaccard coefficient as the trade synchronization score, see Table 8 and Fig. 17 in Appendix F.

Figure 4

Average trade synchronization score for different social distances between investors. Here, the social distance is the number of links between a pair of investors in the observable insider network. The light blue bands mark the Standard Error of the Mean region

Table 2 One-sided independent two-sample Welch’s t-test on the difference in trade synchronization score for pairwise consecutive social distance. Here, $\mathrm{D}_{k}$ is the set of the synchronization scores between investors at the distance k

4.2 Are investors more similar to their neighbors with whom they synchronize their trades?

In this section, we start to analyze the effects of investor socioeconomic attributes on the trade synchronization between socially connected investors. Here, we aim to understand why investors trade more similarly with some of their social connections. The underlying hypothesis is that investors are more similar to their social contacts with whom they synchronize their transactions. We investigate the strength of a tie between investors through three attributes: age, postal code, and investor’s insidership periods. In particular, we hypothesize that a stronger similarity of investor attributes such as (i) smaller age difference, (ii) closer geographical proximity, and (iii) longer time of joint co-employment in the same company (co-insidership) facilitates trade synchronization.

To test Hypotheses (i)–(iii), we conduct one-side Welch’s t-tests. We create an experiment set and a reference set of investor pairwise relationships. We remind that pairs of investors linked in the social network $\mathcal{G}$ belong to the set CON. Social connections between investors with matched accounts are defined as $\text{CON}^{m} = \{(i, j): (\exists i, j \in \mathcal{I}^{m})[(i, j) \in \text{CON}]\}$. Next, we denote pairs of investors who synchronize their trades as SYNC and define it as

$$ \text{SYNC}= \bigl\{ (i,j)\mid p_{ij} < \alpha \cap i,j \in \mathcal{I}^{m} \bigr\} , $$

(7)

where α is a chosen statistical significance threshold and $p_{ij}$ is the p-value obtained with Eq. (5). Note that investors who synchronize their trades do not necessarily have a direct link between them. However, as we are analyzing a connected network, there is a path between each pair of investors.

The experiment set is the set of investor pairs who are both socially connected and synchronize their trades, defined as

$$ \text{CON}\text{-}\text{SYNC}= \text{CON}\cap \text{SYNC}= \bigl\{ (i, j) \mid (i, j) \in \text{CON}\cap (i, j) \in \text{SYNC}\bigr\} . $$

(8)

We find a relatively small number of social links that exhibit trade synchronization. For example, there are $|\text{CON}\text{-}\text{SYNC}| = 336$ social links out of $|\text{CON}^{m}| = 18{,}027$ social links between investors with matched accounts. This observation is, in fact, inline with the social networks literature. Specifically, it has been observed that usually the interaction with neighbors in a social network is low [42] and only a few social links are actively exploited for communication [43].

To understand whether there is a qualitative difference between the social connections over which investors synchronize and do not synchronize their trades, we define the reference set of links as

$$ \text{CON}\text{-}\text{NSYNC}= \bigl\{ (i, j) \mid \bigl(\exists k \in \mathcal{I}^{m}\bigr)\bigl[(i, k)\in \text{CON}\text{-} \text{SYNC}\cap (i, j) \in \text{CON}\backslash \text{SYNC}\bigr]\bigr\} . $$

(9)

The reference set $\text{CON}\text{-}\text{NSYNC}$ includes pairs of investors where one of the investors synchronizes trades with at least one social connection and the second investor is socially connected to the said investor but does not synchronize trades with him/her. For the illustration of the test and reference sets, see Fig. 16 (b) in Appendix E.

Table 3 (Panel A) summarizes the results of one-sided Welch’s t-tests when the statistical link validation threshold $\alpha = 0.01$. We do not find evidence to support the Hypothesis (i), as the age difference is statistically insignificant comparing $\text{CON}\text{-}\text{SYNC}$ and $\text{CON}\text{-}\text{NSYNC}$, but we provide evidence for Hypotheses (ii) and (iii). Particularly, the geographical distance is significantly shorter in $\text{CON}\text{-}\text{SYNC}$ than in $\text{CON}\text{-}\text{NSYNC}$. Therefore, we reject the null hypothesis in favor of the alternative (Hypothesis (ii)). Thus socially connected insiders are more likely to synchronize trading if their geographical distance is shorter. This observation is inline with the findings in Baltakys et al. [11], that investors located closer to each other tend to synchronize their trades more than those who are farther away. The novelty of our results is that we establish this association between individuals with observable social connections. Moreover, in favor of the alternative Hypothesis (iii) we find that the length of the co-insidership is significantly longer for relationships in the set $\text{CON}\text{-}\text{SYNC}$ than $\text{CON}\text{-}\text{NSYNC}$. In other words, the longer the work relationship is, the more likely it is for the colleagues to synchronize their trading.

Table 3 One-sided Welch’s t-test on the difference in age, length of co-insidership and geographical distance between $\text{CON}\text{-}\text{NSYNC}$ (Eq. (9)) and $\text{CON}\text{-}\text{SYNC}$ (Eq. (8)) sets (Panel A), and $\text{CON}\text{-}\text{NSYNC}^{*}$ (Eq. (10)) and $\text{CON}\text{-}\text{SYNC}$ sets (Panel B). Trade synchronization between investors is validated at the significance level of $\alpha = 0.01$. Here, $H_{A}$ is the direction of the alternative hypothesis. The units for the co-insidership are trading days, age difference in years, and geographical distance in kilometers

For the robustness check we restrict the set of links by considering only those investors who have their trading accounts matched, i.e.,

$$ \text{CON}\text{-}\text{NSYNC}^{*} = \bigl\{ (i, j) \mid i \in \mathcal{I}^{ \text{CON}\text{-}\text{SYNC}}\cap j \in \mathcal{I}^{m}\cap (i, j) \in \text{CON}\backslash \text{SYNC}\bigr\} . $$

(10)

We repeat the Welch’s t-tests using $\text{CON}\text{-}\text{NSYNC}^{*}$ as a reference set, see Table 3 (Panel B). The geographical distances are no longer statistically significantly shorter than in the reference set $\text{CON}\text{-}\text{NSYNC}^{*}$.

To see if the findings are generally true with various link validation threshold levels α, we run another robustness check. We take 100 threshold levels α equally spaced on a log scale between 10⁻¹⁰ and 1. At each threshold level α, a pair of investors $i, j$ is said to be synchronizing their trades ($(i, j) \in \text{SYNC}$), if the p-value obtained with the hypergeometric test (Eq. (4)) is less than $p_{ij} < \alpha$. The results are reported in Fig. 5 (a) and (b) for the reference sets $\text{CON}\text{-}\text{NSYNC}$ and $\text{CON}\text{-}\text{NSYNC}^{*}$, respectively. We observe that across different validation thresholds the socially connected and synchronized investor pairs ($\text{CON}\text{-}\text{SYNC}$) exhibit stronger similarity of geographical distance (Hypothesis (ii)) and the length of co-insidership (Hypothesis (iii)). Figure 5 (b) shows that, in fact, the results for the geographical distance in general support Hypothesis (ii), even if results with higher threshold levels, such as $\alpha = 0.01$, are insignificant. At the same time, this analysis confirms that there is no statistically significant difference in terms of the age difference whether the socially connected investors synchronize their transactions or not. Overall, we provide strong evidence on Hypothesis (iii), partial evidence on Hypothesis (ii), and no evidence on Hypothesis (i).

Figure 5

Welch’s t-statistic on the differences in age, length of co-insidership and geographical distance between (a) $\text{CON}\text{-}\text{NSYNC}$ (Eq. (9)) and $\text{CON}\text{-}\text{SYNC}$ (Eq. (8)) sets, and (b) $\text{CON}\text{-}\text{NSYNC}^{*}$ (Eq. (10)) and $\text{CON}\text{-}\text{SYNC}$ sets. The statistic is reported for 100 log-spaced α thresholds used for the validation of investors’ trade synchronization. The dotted vertical line marks the Bonferroni validation threshold

4.3 Similarity on the shortest paths between synchronized investors

We continue our analysis of the effects of investor attributes’ on trade synchronization. Here, our focus is on the shortest paths between investors who synchronize their trades but are not directly connected in the social network. This synchronization may partially result from information exchange and be driven by intermediate investors, i.e. Connectors. However, we do not expect investors to act on information each time they receive it. In fact, some of the private information may be classified, therefore acting on it would be illegal. Ahern [6] finds that on average, inside tips travel along three links in the network before they are acted upon. In this case, instead of acting on an inside tip, an investor may choose to pass it further along in the network, possibly to win favor with other investors. Therefore, it is plausible that Connectors can enable trade synchronization even if they do not trade themselves. On average, there are 3.3 hops in the shortest paths between the insiders with trading similarities who do not have a direct social link in our network.¹¹ Interestingly, Ahern [6] finds that on average, inside tips travel along three links in the network before they are acted upon.

In this section, our hypothesis is that trade synchronization of two indirectly linked investors is more likely to occur with a stronger similarity of attributes between Connectors. In particular, we expect that the social connections on the paths between investors who synchronize their trades are associated with ($\mathrm{i}^{*}$) smaller age differences, ($\mathrm{ii} ^{*}$) closer geographical proximity, and ($\mathrm{iii} ^{*}$) longer time of joint co-insidership.

To test Hypotheses ($\mathrm{i}^{*}$)-($\mathrm{iii} ^{*}$), we conduct one-side Welch’s t-tests. First, we denote the set of investor pairs who synchronize their trades but are not directly connected in the social network as $\text{NCON}\text{-}\text{SYNC}= \text{SYNC}\backslash \text{CON}$. The length of the shortest path between investors $i,j \in \text{NCON}\text{-}\text{SYNC}$ is denoted as $d_{ij}$. The set of all the shortest paths between investors i and j is defined as

$$ \text{PATH}_{ij} = \bigl\{ \bigl((k_{0}, k_{1}), \ldots , (k_{d_{ij}-1}, k_{d_{ij}})\bigr) \mid k_{0} = i\cap k_{d_{ij}} = j\cap (k_{l}, k_{l+1}) \in \text{CON} \bigr\} , $$

(11)

where $0 \leq l \leq d_{ij}-1$. Then the set of all links on the shortest paths between investors i and j is defined as

$$ \mathbf{P}_{ij} = \bigl\{ (k, l) \in \text{CON}\mid (\exists \text{path} \in \text{PATH}_{ij})\bigl[(k, l) \in \text{path}\bigr]\bigr\} , $$

(12)

Our experiment set includes all the links on shortest paths between investors who synchronize their trades but are not directly connected, defined as

$$ \text{PATH}\text{-}\text{SYNC}= \bigl\{ (k, l) \mid \bigl(\exists (i, j) \in \text{NCON}\text{-}\text{SYNC}\bigr)\bigl[(k, l) \in \mathbf{P}_{ij} \bigr] \bigr\} . $$

(13)

The reference set includes all remaining social connections except links between investors who are directly socially connected and synchronize trades,

$$ \text{NPATH}\text{-}\text{SYNC}= \text{CON}\backslash (\text{PATH}\text{-} \text{SYNC}\cup \text{CON}\text{-}\text{SYNC}). $$

(14)

For the illustration of the test and reference sets, see Fig. 16 (c) in the Appendix E.

Table 4 (Panel A) summarizes the results of one-sided Welch’s t-tests when the statistical link validation threshold $\alpha = 0.01$. Note that differently from the experiment described in the previous section, here we investigate social connections on the shortest paths between investors who are not directly socially connected. We provide evidence for Hypotheses ($\mathrm{i}^{*}$) and ($\mathrm{ii} ^{*}$) that investor pairs with smaller age differences and shorter geographical distances are more likely to be located between investors who synchronize their trades. This result may signal a favorable setting for information transfer. At the same time, we find no evidence in support of Hypothesis ($\mathrm{iii} ^{*}$). In fact, if the one-sided Welch’s test on the length of co-insidership were formulated in the other way around, the results would be highly significant. Given that trade synchronization results from information flows, this could be explained as follows. Even if Connector nodes participate in information transfer, they do not necessarily trade themselves. Their motivation for information transfer can be quite different. As Ahern [6] points out, one of the motives for information transfer is to gain favor. Therefore, information may travel through acquaintances in order to establish and strengthen relationships. The joint working history is important in considering whether you act on trading tips yourself or just pass them on to others. When you receive trading tips from a colleague you have known for a short time only, you are more likely to distribute information to others rather than act on it yourself.

Table 4 One-sided Welch’s t-test on the differences in age, length of co-insidership and geographical distance between $\text{NPATH}\text{-}\text{SYNC}$ (Eq. (14)) and $\text{PATH}\text{-}\text{SYNC}$ (Eq. (13)) sets (Panel A), and $\text{NPATH}\text{-}\text{SYNC}^{*}$ (Eq. (16)) and $\text{PATH}\text{-}\text{SYNC}^{*}$ (Eq. (15)) sets (Panel B). Trade synchronization between investors is validated at the significance level of $\alpha = 0.01$. Here, $H_{A}$ is the direction of the alternative hypothesis. The units for the co-insidership are trading days, age difference in years, and geographical distance in kilometers

For the robustness check we restrict the set of links further, by considering only those investors who have their trading accounts matched. The experiment set is redefined as

$$ \text{PATH}\text{-}\text{SYNC}^{*} = \bigl\{ (k, l) \mid (k, l) \in \text{PATH}\text{-}\text{SYNC}\cap k,l\in \mathcal{I}^{m}\bigr\} , $$

(15)

and the reference set as

$$ \text{NPATH}\text{-}\text{SYNC}^{*} = \bigl\{ (i, j) \mid (i, j) \in \text{NPATH}\text{-}\text{SYNC}\cap i, j\in \mathcal{I}^{m}\bigr\} . $$

(16)

These results are reported in Table 4 (Panel B). The results for age differences become insignificant.

In addition, we apply 100 threshold levels for the validation of investor trade similarities equally spaced between 10⁻¹⁰ and 1, see Fig. 6. The Welch’s t-statistic for the age difference fluctuates around zero, yet is significant with $\alpha = 0.01$. At the same time, the difference in the length of the co-insidership is consistently negative and significant. The difference in the geographical distance is negative and significant with different thresholds α in the baseline analysis, but fluctuates closer to zero with low α values for robustness checks that include only matched investors.

Figure 6

Welch’s t-statistic on the difference in age, length of co-insidership and geographical distance between (a) $\text{NPATH}\text{-}\text{SYNC}$ (Eq. (14)) and $\text{PATH}\text{-}\text{SYNC}$ (Eq. (13)) sets, and (b) $\text{NPATH}\text{-}\text{SYNC}^{*}$ (Eq. (16)) and $\text{PATH}\text{-}\text{SYNC}^{*}$ (Eq. (15)) sets. The statistic is reported for 100 log-spaced α thresholds used for the validation of investors’ trade synchronization. The dotted vertical line marks the Bonferroni validation threshold

4.4 Are synchronizing investors more similar if they are socially connected?

In this section, we investigate whether investors who synchronize their trades are more similar in age and geographical location if they are socially connected in the co-employment network. We select two sets: the test set $\text{CON}\text{-}\text{SYNC}$ (defined by Eq. (8)) constituting of investor pairs who are both connected in the social network and synchronize their transactions, and the reference set $\text{NCON}\text{-}\text{SYNC}$ comprised of the insider pairs that are not directly connected but synchronize their trades. Our hypothesis is that investors who synchronize their trades are ($\mathrm{i}^{**}$) more similar in age, and ($\mathrm{ii} ^{**}$) geographically closer if they are also socially connected. Since by construction, investor pairs in $\text{NCON}\text{-}\text{SYNC}$ are not socially connected, they also do not have a co-insidership attribute.¹² Therefore, we only look into the Welch’s t-test for age difference and geographical distance. For the illustration of the test and reference sets, see Appendix Fig. 16 (d).

Assuming that information travels between investors who synchronize their trades, those investor pairs that are not socially connected ($\text{NCON}\text{-}\text{SYNC}$) can either have a social connection that we do not observe or exchange information indirectly through other investors. Suppose the main test set links ($\text{CON}\text{-}\text{SYNC}$) do not exhibit stronger ties quantified through attributes than the links in the reference set. In that case, we have a reason to suspect that we have missing observations for the social links between investors who synchronize their trades but are not socially connected. Otherwise, we anticipate that disconnected but synchronizing investors use the observable social network to acquire valuable information indirectly through other investors.¹³

Table 5 summarizes the results of one-sided Welch’s t-tests when the statistical link validation threshold $\alpha = 0.01$. We provide evidence for Hypotheses ($\mathrm{i}^{**}$) and ($\mathrm{ii} ^{**}$) that the age differences are smaller and geographical distances are shorter between investors who synchronize their trades and are socially connected. In addition, as a robustness check, we apply 100 threshold levels for the validation of investor trade similarities equally spaced between 10⁻¹⁰ and 1, see Fig. 7. The results are rather consistent with different levels of α, especially regarding geographical distance.

Figure 7

Welch’s t-statistic on the difference in age and geographical distance between $\text{NCON}\text{-}\text{SYNC}$ and $\text{CON}\text{-}\text{SYNC}$ sets. The statistic is reported for 100 log-spaced α thresholds used for the validation of investors’ trade synchronization. The dotted vertical line marks the Bonferroni validation threshold

Table 5 One-sided Welch’s t-test on the differences in age and geographical distance between $\text{NCON}\text{-}\text{SYNC}$ and $\text{CON}\text{-}\text{SYNC}$ sets. Trade synchronization between investors is validated at the significance level of $\alpha = 0.01$. Here, $H_{A}$ is the direction of the alternative hypothesis. The units for the co-insidership are trading days, age difference in years, and geographical distance in kilometers

5 Discussion and conclusions

In this paper, we provide evidence of statistical relation between the characteristics of social ties and investor trading behavior using three attributes: differences in age, geographic proximity, and length of joint co-employment. We show that investors that are closer in the social network also have a stronger trading similarity. We indicate that trade synchronization between an investor pair is more likely to happen when investors have worked together (serving as insiders) in the same company longer. This is an intuitive finding, because the time spent together could give more ground for more frequent interactions. This could be related to the development of trust over time. Moreover, partial evidence is provided that geographical proximity explains trading synchronization. In addition, partial evidence is provided that investors of the similar age are more likely to be found on the paths between investors who synchronize their trades.

One of the limitations of our study is that the observable social network is only a proxy of the complete social network between the investors in our analysis. While we observe the relationships between insiders that arise from co-employment, we do miss other types of social relationships. In this regard, alternative proxies for the social network and different investor socioeconomic attributes should be investigated. The other limitation is that we are not able to uniquely identify trading accounts for all investors in our social network proxy. To remedy this we have performed robustness checks to consider only investors with matched accounts.

A trade synchronization network could be used as a proxy for the information network [8]. From this point of view, one could conclude that our results reveal patterns in mutual information transfer between investors, but, possible implications to information trading should be considered with caution. In particular, trading decisions can be independent even if the information is shared between two investors. Moreover, if two investors synchronize their transactions, it does not necessarily mean that they have been exchanging information. For example, both investors can react to public news similarly [9], they may have developed similar trading strategies or consult the same financial advisors.

In our future research, we will analyze investors’ positions in the insider network and how they relate to their stock market performance. Moreover, predictive analysis about investors’ trading behavior using information about their social connections is in our interest.

Appendices

Appendix A: Data sources

1.1 A.1 Euroclear shareholder registration data set (SRD)

This section describes the shareholder registration data set in more detail. This data contains complete trading records from all Finnish investors on publicly traded stocks in HSE along with the background information on traders’ transactions and their attributes from 1995 to 2016. Each transaction in the data set is characterized by the investors’ anonymized ID, trade and registration dates, security identifier (ISIN), traded volume, investor’s sector code, postal code, and investor’s birth year and gender for household investors. We use this data set not only to match insiders’ IDs, but we also use it to analyze insider trade synchronization.¹⁴ More information about the Euroclear data set can be found in other research publications (see, e.g., [9, 11, 16, 44–49]).

1.2 A.2 Insider register data and mandatory notification of trades (SIRE)

The Euroclear Finland’s insider register service (SIRE) data set contains information about mandatory notifications of trade by 3514 company insiders. It covers information from 153 companies listed in the HSE. The data set was manually collected from SIRE insider registry for two disjoint periods of roughly five years, from July 2005 to February 2010 and March 2013 to September 2018. The SIRE register reports historical data for the previous five years of insider holdings and transactions for the publicly listed companies. The data contains a list of insiders names and surnames and a list of third parties related to them, e.g., family members or related companies. Information on insiders includes their nationality, spoken language, the dates and the basis for considering them an insider in given companies. Each trade notification comes with an identifier, both for traded stocks and derivative instruments, trading date and volume, and information about whether the transaction was executed by himself/herself or by his/her family member or by a related third-party company account. If an insider did not trade their own company shares, s/he might not be included in this data set. In some cases, individuals who disclosed their trades in the SIRE data sets and, therefore, are considered insiders, were not included in the Virre data set. A part of those insiders and related parties, who’s mandatory notifications of trade were successfully used to match them with their complete trading histories in Euroclear data set, is used to complement the insider network constructed from the Virre data (see Fig. 2). Out of 3514 insiders in SIRE data set 2711 were matched with their trading accounts in Euroclear data set (reaching 77% matching success ratio). 1007 of them were not found in the Virre data set, and were added to the set of nodes in the temporal insider network. The bigger part of them (555) belong to family members and related companies.

1.3 A.3 Insiders’ assignments and positions data (Virre)

The primary source of information about the insider network structure comes from the Virre data set acquired from the Virre Information Service. The data set contains information about historical insider positions in Finnish companies. Virre data set contains the information about most company insiders, irrespectively of whether they have traded or not own company shares. The data includes the name of the company, the name and the surname of the insider, his/her role in the company, e.g., board members, auditors, legal representatives, and other key employees, and all start and end dates of the insiderships. Virre data alone best represents the complete insider network. The whole data set contains information about $12{,}925$ insiders. When we construct the insider network, we connect by links individuals indicated as insiders in the same companies. The ties last as long as the connected nodes are both considered insiders in the same company. However, the data does not include information about family members and controlled companies of the insiders. Virre data set spans between 1962 and 2019 and contains information about 148 companies.

Appendix B: Descriptive statistics

The list of company insiders is mainly comprised of employees in higher positions and board members. Typically key employees do not change too often, and board members can serve multiple terms. The stability of corporate structure allows us to have a sufficiently high coverage of insiders who trade in the stock market, even outside the two five-year periods for which SIRE data was collected.

In particular, in 2005, the start of the first SIRE data collection period, we were able to match 752 insiders, which corresponds to 22% of all insiders in the network at that moment (see Table 6). Looking at the network snapshots in 2000 and 2003 we observe only a marginal decrease in the fraction of matched insiders, correspondingly 14% and 19%. Figure 8 shows the complementary cumulative distribution function of the ratio between the matched insiders and all insiders in a company.

Figure 8

The figure illustrates the complementary cumulative distribution function of the % of insiders with matched trading accounts over all 153 companies. Here we exclude family members and related company accounts. The percentage for each company is calculated by taking the ratio between the number of company insiders that have their trading accounts matched and the number of all insiders in the company. On average, 37% of a given company’s insiders have their trading accounts identified (dashed red line). The average match ratio is higher than a global match ratio 19% (2711 matched accounts divided by 13,932 investors), because it is calculated as a mean of matching ratios for each company. Matched Connector insiders can be counted multiple times if they are insiders in more than one company

Table 6 Global statistical properties of the insider network calculated on January 1st in a corresponding year t. The years were selected in order to illustrate network properties over the whole span of the SRD data as well as SIRE insider trade data set collection periods (see Fig. 1). Here, $N_{t}$ denotes the number of nodes, $N_{\text{MATCHED}, t}$ – number of matched insiders, $N_{\text{MATCHED}, t} /N_{t}$ – ratio of matched insiders to all insiders in the network, $L_{t}$ – number of links, $\langle k_{t} \rangle$ – average degree, $\langle k_{t} \rangle /N_{t}$ – normalized average degree $N_{t}$, $N_{c,t}$ – number of nodes in the maximal connected component, $N_{c,t}/N_{t}$ – fraction of nodes belonging to the maximal connected component

The insider network is dynamic, with daily snapshots between 1995 and 2016. Each snapshot on a day t contains a set of $N_{t}$ nodes which represent insiders and related third parties as well as $L_{t}$ links that represent relationships between them (see Table 6 for the global network statistics). The relationship between two nodes can indicate either both of the nodes being insiders in at least one same company, or one of them being an insider in some company and the other being a third party related to the insider (mostly leaf nodes), e.g., a family member, or a company, where s/he exerts control or has a significant influence on its investment decisions. Insiders with positions in multiple companies connect different insiders from different companies.

2.1 B.4 Number of insiders and board members

The daily number of insiders $N_{t}$ and board members in our temporal network between 1995 and 2016 over all companies is shown in Fig. 9. The number of all insiders in the insider network (the blue solid curve) ranges from 1810 to 3798, while the number of matched insiders (the orange solid curve) ranges from 211 to 1636. For comparison, the dashed blue line shows the total number of board members in the insider network, ranging from 776 to 1044, and matched board member IDs ranging from 132 to 706 are shown by the orange dashed line. Note that we could only identify those insider accounts that traded own company stock within the two five-year periods (indicated by two grey colored bands in Fig. 9). This does not necessarily mean that other insiders were inactive investors, as they could have traded other stocks without being obliged to report them. While their trades are recorded in the SRD data set, we do not have sufficient information to identify those accounts.

Figure 9

Daily number of company insiders, matched insiders, board members, and matched board members. Solid lines represent insiders, while the dashed lines mark company board members. Grey bands mark two periods of SIRE data set. The difference between the blue and the orange solid (dashed) curves indicates the number of insiders (board members) that did not trade shares of their own securities during the observed period, i.e. the number of insiders and board members for which we had no data in order to match them with a trading account from the SRD data set. The difference is smaller when looking only at board members. This means that there are fewer unmatched board members than other kinds of unmatched insiders

In our data set, there are approximately 26.2 (±2.4) insiders and 6.9 (±2.3) matched insiders¹⁵ on average per company in a year (Fig. 10 (a)). The blue dashed line shows the average number of insiders per company in a year, ranging from 21.5 to 29.7 insiders. The orange dashed line in Fig. 10 (a) shows the average number of matched insiders and ranges from 3.2 to 9.6. Similarly, the average board size per company is composed of 8.5 (±0.8) board members in a company in a year, out of which on average we identified around 4.4 (±1.3) matched board members (Fig. 10 (b)).

Figure 10

Number of insiders and board members. (a) Median and average number of insiders and matched insiders per company in a year. (b) Median and average number of board members and matched board members per company in a year. The bands around the medians are filled between 1st and 3rd quantiles

2.2 B.5 Age of insiders and board members

The average age of an insider is around 48.8 (±0.6) years, rising from 47.5 years in 1995 to 50.3 years by 2017 (see Fig. 11 (a)). The average age of a board member is around 51.8 (±1.3) years, rising from 49.9 years in 1995 to 54.0 years in the end of 2016 (the green line of the Fig. 11 (a)). At the end of the insider network data period, the average age of an insider (board member) was 50.5 (54.2) years, while the average age of male (female) investors was 55 (57) years and Finland’s population age was correspondingly 41 (44) years [50]. This means that an average insider is younger than an average investor and older than an average Finn, while the average board member is very close in age to the average Finnish investor. Based on the average board member age in the data set, we can suspect that the older board-members from the 1995-2005 period retired and were not captured in the matched data sets during the collection period between 2005 and 2010, and 2013 and 2018. This can be seen by a rapidly increasing red line until 2005 (Fig. 11 (a)). Age preferences for different companies are shown on Fig. 11 (b). We chose the year 2007 as the mid point of our empirical analysis.

Figure 11

Age of insiders and board members. (a) Average age of company insiders, matched insiders, board members, and matched board members. (b) Average age of insiders and board members for 132 companies in 2007

Appendix C: Statistics for the analyzed network

In what follows, we provide the summary statistics on the insiders from the analyzed network. Note that while the subset of investor is restricted to the subset observed between 2005 and 2009, their activity statistics cover their entire data set. Regarding insiders’ trading activity, 1656 out of 1756 matched insider accounts have traded stocks in HSE.¹⁶ An insider traded 20.8 (±32.9) securities on average (Fig. 12 (a)). There were 192 insiders who traded only 1 security, and, at the same time, the investor with the most diversified portfolio traded 923 distinct securities. In our network, the average trading period for an insider network is 9.9 (±5.2) years (Fig. 12 (b)). This number is obtained by taking into account all the observations for the selected 1656 insiders in the entire SRD data set.

Figure 12

Trading statistics for 1656 insiders that have traded in the HSE. (a) The number of the unique traded securities by insiders. (b) The length of trading activity period by insiders in months. The dashed vertical line marks the average

While most serve as insiders for up to two years, the longest observed length of insidership in the Nordic Aluminium company reaches almost 38 years (Fig. 13 (a)). An average insider (board member) insidership length lasts $7.25 \pm 5.26$ ($6.59 \pm 5.3$) years in the analyzed data set and $5.19 \pm 4.46$ ($5.04 \pm 4.59$) years in the entire data set.

Figure 13

Length of insidership in companies of insiders and board members. (a) Length of insidership in a company in years for an insider. The dashed line marks the average length of insidership. (b) The number of unique companies for an insider or a board member in the analyzed data set

Figure 14 shows the distribution of the number of insiders per company. In the analyzed data set, an insider (board member) belongs to 1.3 (1.6) companies on average (Fig. 13 (b)). An insider with the maximum number of companies, worked in 14 companies in total and in seven simultaneously. A board member with the most companies has resided in 13 company boards in total and seven simultaneously. There are 1753 board members in total out of which there are 516 Connector board members, who belonged to more than one company board either changing companies sequentially or being a board member simultaneously in several companies. Out of 516 Connector board members, 400 were simultaneously on more than two companies’ boards. These numbers are limited by the pool of insiders present between 2005 and 2009, but the observations for the selected insiders come from the total period (1962–2019).

Figure 14

Complementary cumulative distribution function for the numbers of insiders in a company. Number of insiders ranges from 2 to 729 per company. The number of companies is 150. Red dashed line marks the average number of insiders per company = 56.25 (±82.89), the mode = 25, and the median = 36

In general, insider networks exhibit the small-world network properties [51, 52] and are comparable to the ones described in Battiston and Catanzaro [53]. More specifically, even if the networks are composed of thousands of nodes, it takes only a small number of leaps between nodes to traverse from any source to any target node. In the insider network, all shortest paths travel through the Connector nodes, i.e., the nodes that have an insider position in two or more companies.

We illustrate the connections between company insiders through the Connector nodes in Fig. 15. Insiders, excluding the family members and third-party accounts, are aggregated into a single node representing the affiliated company. A link between two companies indicates that they have shared at least one insider. We can observe a high connectivity between the company nodes, with the biggest companies in the centre being Nokia and UPM-Kymmene. In the analyzed network, there are 1033 Connector nodes (out of which 575 are matched insiders). There are 200 (19%) women (out of which 104 are matched insiders), and 833 (81%) are men (out of which 471 are matched insiders). Even though gender attribute is available in our data, it is omitted in this study due to high gender class imbalance demonstrated in Fig. 15. Overall, companies are dominated by male insiders, with only four gender-balanced companies. In fact, the male-dominant environment is a favorable setting for the information transfer channels, as both men and women prefer transferring to or receiving information from men [54–56].

Figure 15

Company network. Each node represents a company. Links connect companies that share an insider. The thickness of a link is stronger when the companies share more insiders. For illustration purposes, the full network is reduced to Planar Maximally Filtered Graph. Number of nodes: 150, number of links: 386. The diameter of this network is 6 and the average degree is 5.15. The nodes are scaled per number of insiders in the company. The nodes are colored according to the proportion of male insiders. Percentage of male insiders in the company: - 100, - 90, - 80, - 70, - 60, - 50

Appendix D: Analyzed securities

Table 7 shows 30 most traded securities by the investors analyzed in this paper.

Table 7 Company name and security ID (ISIN)

Appendix E: Investor nodes, investor links, test and reference sets

Here, we elaborate on the types of investor nodes and their notation. We also present different types of links and link sets used in our Welch’s t-tests. Figure 16 illustrates the relationship between different sets of nodes and links used throughout the paper.

Figure 16

Illustration of test and reference sets for statistical tests performed in Sects. 4.2–4.4. (a) illustrates the relationship between different sets of investor nodes. Investors who synchronize their trades with at least one social connection are a subset of investors who synchronize their trades with at least on other investor, which is a subset of investors who have their trading accounts matched which is a subset of all investors in the network, i.e., $\mathcal{I}^{\text{CON}\text{-}\text{SYNC}} \subset \mathcal{I}^{ \text{SYNC}} \subset \mathcal{I}^{m} \subset \mathcal{I}$. (b) illustrates the links that constitute the test and reference sets used in Sect. 4.2. The main test set consists of all pairs of investors who are both socially connected and synchronize their trades (CON-SYNC). The main reference set includes pairs of socially connected investors who do not synchronize their trades, of which at least investors is known to synchronize trades (thus green color squares) with one of its’ direct connection (CON-NSYNC). The robustness reference set ($\text{CON}\text{-}\text{NSYNC}^{*}$) includes only those socially connected investors who have matched trading accounts (thus orange squares, $\text{CON}\text{-}\text{NSYNC}^{*} \subseteq \text{CON}\text{-} \text{NSYNC}$). (c) illustrates the links that constitute the test and reference sets used in Sect. 4.3. The main test set (PATH-SYNC) consists of all pairs of socially connected investors who are on the shortest paths between pairs who synchronize their trades but are not directly connected in the social network. This may include pairs that synchronize (green color) or not (blue and orange color) their trades. The reference set (NPATH-SYNC) includes pairs of investors who are not on shortest paths between directly not connected investors who synchronize their trades. The for the robustness tests we use further restricted sets (indicated with ^∗) with pairs of investors who have matched trading accounts. (d) illustrates the links that constitute the test and reference sets used in Sect. 4.4. The main test set consists of all pairs of investors who are both socially connected and synchronize their trades (CON-SYNC). The reference set (NCON-SYNC) includes pairs of investors who synchronize their trades but are not socially connected

Appendix F: Robustness check for the synchronization score and social distance

Here, we perform a robustness check for the average synchronization score and the social distance estimated with the Jaccard coefficient (Fig. 17 and Table 8).

Figure 17

Average Jaccard similarity score for different social distances between investors. Here, the social distance is the number of links between a pair of investors in the observable insider network. The light blue bands mark the Standard Error of the Mean region

Table 8 One-sided independent two-sample Welch’s t-test on the difference in trade synchronization score for pairwise consecutive social distance. Here, $\mathrm{D}_{k}$ is the set of the synchronization scores between investors at the distance k