Syndication network associates with specialisation and performance of venture capital firms

The Herfindahl Index, also known as Herfindahl–Hirschman Index (HHI), was first proposed to measure the competition between companies based on the market share of each firm [32]. With a similar formalisation, HHI later got adopted to evaluate the degree of specialisation of VC firms, which is the sum of the squares of the percentage of all previous investments of a VC firm in each industry [6] or in each investment stage. For example, if a VC firm i (VC_i ) invests in α industry with a fraction $p^{\alpha}_i = n_i^{\alpha} / \sum_{\alpha = 1}^{m_i} n_i^{\alpha}, \alpha = 1, 2, \dots, m_i$, where $n_{i}^{\alpha}$ is the number of investments the VC_i makes in α industry, m_i is the total number of industries VC_i entered (which can be different across VC firms), and $\sum_{\alpha} n_i^{\alpha}$, is the total number of investments the VC_i has made. The counting of investment numbers is illustrated in figure 1(a). Then its HHI of industry, $\textrm{HHI}_i^\textrm{ind}$, is

$$\begin{equation} \textrm{HHI}_i^\textrm{ind} = \sum_{\alpha=1}^{m_i} \left(p_i^\alpha\right)^2. \end{equation} \tag{ 1 }$$

The most specialised VC firms ($m_{i} = 1$) have $\textrm{HHI}_i^\textrm{ind} = 1$, and the most diversified or generalised ones have $\textrm{HHI}_i^\textrm{ind} = 1/m_{i}$, which corresponds to the situation with equal number of investments $n^{\alpha}_{i}$ for each industry $\alpha = 1, 2, \dots, m_{i}$. The formalisation for the HHI of investment stage $\textrm{HHI}_i^\textrm{stage}$ is the same as equation (1) with $p^{\alpha}_{i}$ the fraction of investments in a certain stage α.

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Evaluating and predicting financial investment performance lies at the heart of VC research [6, 11]. However, accurately assessing this performance remains a challenging task. The optimal method for evaluating a VC firm's financial performance involves using the return on investment of each deal or internal rate of return of each fund. Unfortunately, obtaining such data is often difficult due to proprietary business concerns.

VC firms typically generate significant profit or achieve higher valuations of invested start-ups when investments exit through IPOs, M&As, or by securing the next round of investment. Other exit types usually yield less favorable results [11]. Consequently, we define a VC firm's success rate as the proportion of investments resulting in IPOs, M&As, or the attainment of the next round of investment, relative to the firm's overall investment portfolio, following the approaches of [11, 13].

The Moran's Index (Moran's I) is widely used to measure the spatial autocorrelation of concerned variables [33–35], and here we adapt it to measure autocorrelation between the variables of VC firms in the syndication network. The Moran's I for a variable with N observations x_i is defined as:

$$\begin{equation} I = \frac{\sum\limits_{i=1}^{N}\sum\limits_{j=1}^{N}w_{ij}(x_{i}-\bar{x})(x_{j}-\bar{x})}{|{\mathbf{\textsf{W}}}|\sigma_{x}^{2} }, \end{equation} \tag{ 2 }$$

where N is the number of VC firms in the syndication network; x_i is the variable of interest of node i (e.g. it can be HHI of stage $\textrm{HHI}^\mathrm{stage}$ or HHI of industry $\textrm{HHI}^\mathrm{ind}$, or success rate of a VC firm); $\bar {x} = \frac{1}{N}\sum_{i = 1}^{N}x_{i}$ is the mean of x; $\sigma_{x}^{2} = \sum\nolimits_{i = 1}^{n}(x-x_{i})^2 / N$ is the variance of that variable. w_ij is the spatial weight between nodes i and j and $w_{ii} = 0$. The sum is $|{\mathbf{\textsf{W}}}| = \sum_{i = 1}^N\sum_{j = 1}^N w_{ij}$. We can define a spatial weight matrix ${\mathbf{\textsf{W}}}$ with entries w_ij . Literature, especially in geosciences, use this measurement to identify the geographic difference in or characterise the regional variations of the variables of interest. It is a measurement that combines both relational information (i.e. how close the two entities are) and non-relational information (i.e. feature of an entity). Moran's I ranges from −1 to 1, and a higher positive value of Moran's I indicates a more clustering scenario where entities with similar feature is closer to each other, and a smaller negative value of Moran's I indicates a more dispersed scenario where entities with contrasting feature are closer to each other, and a zero value corresponds to a random situation [33–35]. This Moran's I is a global indicator for evaluating the average autocorrelation of the whole study area, in this work, we simply denote the global Moran's I as I.

When generalising the traditional Moran's I into the network setting, the main difference lies in measuring the distance between nodes w_ij , which defines the weight matrix $\mathrm{dist}$. In the geography setting, every entity is embedded into a Euclidean space, and their adjacency can be well described by a spatial lattice network, and their Euclidean distance is easy to calculate; while in the network setting, the adjacency between entities can be quite heterogeneous, and shortest path length between two nodes characterises how 'close' they are. To make further investigation on the impacts of topological distance on the autocorrelation of variables, we define four different weight matrices ${\mathbf{\textsf{W}}}$ based on different levels of neighbourhood: considering the nearest neighbours (i.e. first-order neighbourhood), further integrate the second-order, third-order, and all reachable neighbours, respectively. The detailed definitions are:

$$\begin{align} {\mathbf{\textsf{W}}}_{ij}^{(1)} &= {\mathbf{\textsf{A}}}_{ij}^{(1)},\phantom{+ \frac{1}{2}{\mathbf{\textsf{A}}}_{ij}^{(2)} + \frac{1}{3}{\mathbf{\textsf{A}}}_{ij}^{(3)} + \frac{1}{4}{\mathbf{\textsf{A}}}_{ij}^{(4)} + \cdots+ \frac{1}{L}{\mathbf{\textsf{A}}}_{ij}^{(L)},} \end{align} \tag{ 3a }$$

$$\begin{align} {\mathbf{\textsf{W}}}_{ij}^{(2)} &= {\mathbf{\textsf{A}}}_{ij}^{(1)} + \frac{1}{2}{\mathbf{\textsf{A}}}_{ij}^{(2)},\phantom{+ \frac{1}{3}{\mathbf{\textsf{A}}}_{ij}^{(3)} + \frac{1}{4}{\mathbf{\textsf{A}}}_{ij}^{(4)} + \cdots+ \frac{1}{L}{\mathbf{\textsf{A}}}_{ij}^{(L)},} \end{align} \tag{ 3b }$$

$$\begin{align} {\mathbf{\textsf{W}}}_{ij}^{(3)} &= {\mathbf{\textsf{A}}}_{ij}^{(1)} + \frac{1}{2}{\mathbf{\textsf{A}}}_{ij}^{(2)} + \frac{1}{3}{\mathbf{\textsf{A}}}_{ij}^{(3)},\phantom{+ \frac{1}{4}{\mathbf{\textsf{A}}}_{ij}^{(4)} + \cdots+ \frac{1}{L}{\mathbf{\textsf{A}}}_{ij}^{(L)},} \end{align} \tag{ 3c }$$

$$\begin{align} {\mathbf{\textsf{W}}}_{ij}^{(L)} &= {\mathbf{\textsf{A}}}_{ij}^{(1)} + \frac{1}{2}{\mathbf{\textsf{A}}}_{ij}^{(2)} + \frac{1}{3}{\mathbf{\textsf{A}}}_{ij}^{(3)} + \frac{1}{4}{\mathbf{\textsf{A}}}_{ij}^{(4)} + \cdots+ \frac{1}{L}{\mathbf{\textsf{A}}}_{ij}^{(L)}, \end{align} \tag{ 3d }$$

where L is the diameter of the network and

$$\begin{equation} {\mathbf{\textsf{A}}}_{ij}^{(n)} = \left\{\begin{matrix} 1 & i \neq j \ \textrm{and with a shortest path}\ l_{ij}=n\\ 0 & \textrm{otherwise} \end{matrix}\right. \end{equation} \tag{ 4 }$$

represents the non-zero entry of nth order of adjacency, for example, ${\mathbf{\textsf{A}}}_{ij}^{(1)}$ is the ordinary adjacency matrix of the network, and ${\mathbf{\textsf{A}}}_{ij}^{(2)} = 1$ indicates there is at least one shortest path with a path length $l_{ij} = 2$ between node i and j.

Apart from the global Moran's I, we can scrutinize the feature clustering effect at a local level using the local Moran's I of a node i in networks $I_i^{\,\mathrm{local}}$, which is defined as:

$$\begin{align} I_{i}^{\,\mathrm{local}} &=\frac{N}{|{\mathbf{\textsf{W}}}|}\frac {x_{i}-{\bar {x}}}{\sigma_{x}^{2}} \sum _{j=1}^{N}w_{ij}(x_{j}-{\bar {x}}), \end{align} \tag{ 5a }$$

$$\begin{align} I &= \frac{1}{N}\sum_{i=1}^N I_i^{\,\mathrm{local}}. \end{align} \tag{ 5b }$$

The VC industry originated after World War II and matured in the late 1970s [11]. There have been several boom-and-bust cycles in the VC industry decades ago in the western world [36]. However, VC is still a relatively newly emerging industry in China, where government policies keep changing, the governance structure is immature, and information asymmetry always bothers investors [37, 38]. Nevertheless, the Chinese VC industry has undergone fast growth in the recent decades, especially after 2013 (see figure 1(b)). Although a drastic decrease in active VC firms happened after 2017, the number of start-up companies that receive VC investments remains high (see figure 1(b)).

We split our dataset into two parts: 1985–2013 and 2014–2020. We use investment data before 2014 to construct syndication network, and use exit events data from 2014 to 2020 to make better evaluations on the outcome of previous investments. The duration of the second part is seven years and is long enough to observe the results of investments made before 2014. As a start-up company needs time to grow or to mature, VC investments generally requires several years to exit [13].

The number of investments of individual VC firms, $\sum_{\alpha = 1}^{m_{i}}n_{i}^{\alpha}$ exhibits a power law (see figure 1(c)), which indicates that most VC firms only make a few investments, and only a notable small fraction of VC firms making many investments. However, since the slope −1.8 is larger than −2, the investments made by this small fraction of VC firms might take up the majority of VC investments in the whole market, because the average number of investments is determined by the tail of the distribution. The number of VC investments received by each start-up company also exhibits a power-law tail, implying some start-up companies receive a much larger number of investments from VC firms (see figure 1(d)). However, the distribution of investments made by VC firms are more heterogeneous as indicated by a flatter exponent compared with figure 1(d), reflecting that the probability of a VC firm has a large number of investment activities is higher than the probability of a start-up company receiving lots of investments. We find that the number of IPOs of VC firms exhibits a power law (see figure 1(e)). Similar behaviour is observed for the number of M&As, the number of investments that are not closed yet but receive a next round of investment, and unsuccessful exits (see appendix figures A1(a)–(c)). Again, these power-law like investment distributions indicate the heterogeneous nature of the VC market.

Making investment decisions requires a versatile knowledge and resources depending on different industries and stages. Thus, being specialised is typically a sensible choice for VC firms to guarantee long-lasting and reproducible successful investments [6, 7].

According to the categories given by the Industrial Classification of National Economic Activities (ICNEA), there are seventeen industries in the first level classification, therefore, the range of the HHI of industry ($\textrm{HHI}^\mathrm{ind}$) is within the interval $\left[1/17, 1 \right]$ (see the distributions of HHI of VC firms in figure A3 in appendix).

Except for the well-understood industry entry barriers [39], we would like to further explain the four different investment stages of VC investments. In each stage, apart from providing capital support, VC firms need to assist the start-up on various aspects with different focuses. During the seed stage, the VC investors focus on helping the start-up to prove the idea, polish its products, and build the team. In the initial stage, dissecting market opportunities and finding the target markets would generally be the focus, which is also referred to as product-market fit. In the expansion stage, VC firms needs to help scale the business or diversify and differentiate product lines. And at last, in the mature stage, VC firms prioritise how to go public. The four stages gives the range of HHI of stage ($\textrm{HHI}^\mathrm{stage}$) $\left[1/4, 1 \right]$ (see the distributions of HHI of VC firms in figure A3 in appendix). The financing stage of each investment is documented in the database, which is classified as seed, initial (may also be named as early stage), expansion, and mature (may also be termed as mezzanine stage or bridge stage or pre-public stage), and we incorporate this classification in our analysis. In some criterion, there might be five stages with a pre-seed stage, and we just adopt the classification provided by the dataset.

Even though the Chinese VC market undergoes viral growth after 2013, the fraction of VC investments in 2020 in different investment stages (see figure 2(a)) and industries (see figure 2(b)) remains quite close to the 2013 snapshot. Most VC investments fall into the expansion stage and into 'manufacturing' (code C of ICNEA) and 'information transmission, software and information technology service' (code I of ICNEA), with a slight decrease in manufacturing and an increase in the information industry.

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As mentioned in the section 1, evidence shows that both specialisation and generalisation can be beneficial to investment performance [6, 11, 22]. Why do we have this seemly contradictory phenomenon? We need new perspectives to comprehensively quantify the impacts of networking on specialisation and investment performance.

To study the network influences, we build the syndication network of VC firms based on their investment activities. In the syndication network, nodes are VC firms, and edges signify joint-investments in the same start-up company at the same time, see figures 1(a) and 3(a). To make a better illustration, we take the example in figure 1(a), as VC firm i and j invested in the same startup C₁ at the same time t₁, thus in the syndication network presented in figure 3(a), nodes i and j are connected. VC firms j, k, and l invested in the start-up company C₂ at time t₂ and thus these three nodes are linked in the syndication network (see figure 3(a)). In contrast, at a later time t₃, nodes k and m jointly invested in start-up company C₂, resulting in node m being connected only to node k and not to nodes j and l. We do not regard the investments at different stages as joint-investment since the investments between different rounds are not necessarily direct collaboration. For example, some VC institutions that make investments in earlier stages may exit in later rounds. The joint-investment network of VC firms in the Chinese market has grown quite dense with the emergence of many hub nodes that maybe of great importance (see figure 3(b)). There is not a strong correlation between the success rate and the number of investments. A similar pattern can be observed when considering the degree (refer to the figure A2) in appendix. Recent advance indicates that so called h-index can reveal the importance of a node in the network [41]. The node centrality h-index measure is defined to be the maximum value h such that there exists at least h (nearest) neighbours of degree larger than or equal to h. If a node has h-index 5, it has 5 neighbours with degree larger than or equal to 5 but does not have 6 neighbours with a degree larger than or equal to 6 [41]. We find that the distribution of the h-index also exhibits a power-law tail (see figure 3(d)). There is also a profound community structure in the Chinese VC market (see figure 3(e)), where VC firms within the same community would have denser connections with one another than with others outside that community [40, 42, 43].

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As suggested by previous literature [11, 20, 22], for a VC firm, collaborating with others generally brings more information and knowledge, which is needed when entering an unfamiliar industry or stage. However, there is no quantitative analysis on the relation between networking (i.e. making joint-investments with others) and specialisation and, eventually, the performance of the VC firm. Here, we scrutinize the investment sequence of each VC firm to see if there is a higher probability for VC firms to enter a new stage or industry with others, especially with new friends who might have new knowledge, skills, or other resources.

In figure 4, we take an anonymous VC firm as an illustration. It enters three new stages (indicated by squares), one of which is joint-investment with others (indicated by filled symbols). We calculate the fraction of joint-investment out of all first-investment when entering a new industry for all VC firms, and find such a fraction is generally higher than 50% (see figure 4(b)). The same procedure is applied to analysis of investments when entering a new industry (see figure 4(d)), and very similar results are obtained (see figure 4(f)). This suggests that when a VC firm enters either a new stage or industry, it would have a high chance of making collaboration. This phenomenon most likely occurs because VC firms employ collaboration to complement knowledge and skills against uncertainty. However, given the frequency and the size of collaboration, the fraction of joint investment is lower than the randomised null model, where we randomly assign each of their joint-investment partners to an investment event (see table A1 in appendix for the randomisation process).

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Furthermore, for all joint-investments entering a new stage or industry, we analyse the fraction of joint-investments with new friends, i.e. the ones that have no collaboration before. The fractions are quite high, around 90% for both entering a new stage and industry (see figures 4(c) and (f)), and it is also much higher than the random configurations in the null model. This indicates that collaborations with new friends generally happen with a denser concentration and suggests that there are certain mechanics other than randomness driving joint-investments with new friends when entering unfamiliar situations. One of the possible reason is that new friends might be crucial for bringing in new information and resources, another explanation is that 'collaboration' with new friends is not intended, yet just a consequence of entering new stage or industry where the VC firm has few old friends.

By analysing the relationships between degree of the joint investment networks and the HHIs, we discover that when a VC firm has more friends (i.e. a larger degree in the syndication network), their level of specialisation on both investment stages (see figure 5(a)) and industries (see figure 5(b)) decrease (i.e. they are becoming more like a generalist), and the trends of deceasing become stronger when the degree is roughly beyond eight for both cases, which might be also fundamentally related to branching processes in networks [44].

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Given the heterogeneous nature the joint-investment syndication network, to further quantify the relation between networking and specialisation and investment performance, we adapt Moran's I in geoscience (see section 2) to study correlation between network measurements and the non-network properties of VC firms. In spatial analysis, the level of adjacency (i.e. the weight matrix ${\mathbf{\textsf{W}}}$ in equation (3)) between entities can be defined based on different Euclidean distance threshold [34] or other criteria [45]; on networks, we can specify the different level of adjacency and we define four types of weight matrices. The first one is the ordinary adjacency matrix (${\mathbf{\textsf{W}}}_{ij}^{(1)} = {\mathbf{\textsf{A}}}_{ij}$), i.e. if two VC firms have joint-investment, then $w_{ij} = 1$, otherwise, $w_{ij} = 0$ (see equation (3a )). As information and trust can spread on networks, we further integrate the second-order neighbours (${\mathbf{\textsf{W}}}_{ij}^{(2)}$), but with a smaller weight for them: $w_{ij} = 1/2$ if there exists a shortest path between i and j with $l_{ij} = 2$ (see equation (3b )). We further accumulates third-order neighbours (${\mathbf{\textsf{W}}}_{ij}^{(3)}$), and all reachable neighbours (${\mathbf{\textsf{W}}}_{ij}^{(L)}$, where L denotes the diameter of the network) in the same way, see equations (3c ) and (3d ), respectively.

The global Moran's I for different weight matrices ${\mathbf{\textsf{W}}}$ are summarised in table A2 in appendix. We find that for all measurements p-value $\lt0.001$, which demonstrate the significance of the local clustering of the concerned measurement (e.g. specialisation or performance). It is also worth noting that the global Moran's I for HHI of stage and industry are all high. Such clustering phenomenon suggests the trend that VC firms tend to make joint-investment with others alike. Moreover, there is a clear pattern of negative correlation between the global Moran's I and different level of adjacency (see figure 6). When considering the weighted adjacency with three-order neighbours, the global Moran's I becomes much smaller for all three measurements ($\textrm{HHI}^\mathrm{ind}$, $\textrm{HHI}^\mathrm{stage}$, and success rate), which suggest that at a larger range, the autocorrelation is much weaker, and the clustering effect is only obvious within second-order (e.g. for $\textrm{HHI}^\mathrm{ind}$ and $\textrm{HHI}^\mathrm{stage}$) or even just first-order (e.g. for success rate) neighbourhood (see figure 6). Such a discovery is also consistent with previous findings on VC firm syndication patterns that the syndication probability drops quite fast when the distance between two VC firms are larger than two [31].

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However, counter-intuitively, this global gathering pattern cannot represent the local similarity patterns, and the three variables ($\textrm{HHI}^\mathrm{ind}$, $\textrm{HHI}^\mathrm{stage}$, and success rate), distribute on the networks heterogeneously. The specialisation level ($\textrm{HHI}^\mathrm{ind}$ or $\textrm{HHI}^\mathrm{stage}$) or success rate of each node and their local Moran's I is shown in figure 7. Given the fact that there are many small VC firms with a high specialisation level due to a limited number of investment activities (see figure A3 in appendix), it is nontrivial to observe that specialists have small local Moran's I values, while generalists typically have larger local Moran's I values, which indicates a strong local clustering in their neighbourhoods. Additionally, we can find a clear decreasing trend of averaged local Moran's I along with the increase of HHI of both industry and stage. This indicates that when a VC firm becomes more specialised, their neighbours tend to be more random, i.e. with both similar and dissimilar neighbours around.

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Compared to clustering of specialisation, the local Moran's I on success rate is not that high (see orange line in figure 7), indicating weak dependence of success level on local Moran's I. The local patterns of VC firms with higher success rate is within the error bar of the null model (except for the success rate 1). In other words, co-investing with successful investors will not guarantee a successful investment. However, the averaged local Moran's I is higher than the null model for most nodes with a low success rate (see the zoom-in figure in figure 7). This suggests that VC firms of poor performance may have a stronger clustering, while the performance of neighbours around relative successful VC firms are more random. Our results take new measurements of Moran's I, which is not considered by the previous study, such as [46]. Their conclusion that the better networked VC firms perform better is based on the regression of network measurements and the VC performance, which overlooked the local patterns.