Why do we need Venture Capitalists? The Role of Competent Intermediaries in the Creation Process. David Mas, Annick Vignes
∗†
September 29, 2006
Abstract In this paper, we study the influence of human capabilities on the efficiency of venture capital as a means of financing innovation. We show that although competence is indispensable to a venture capitalist it is not sufficient. We demonstrate that efficient screening can only take place within a market with a large number of potential start-ups. We also show that global performance benefits greatly from the independence of the evaluation made by the venture capitalists. This echoes Richardson’s thesis that, within the context of an imperfect market, complementary interaction between the market and the competence of the firm can improve efficiency. Here, the market imperfection is due to the type of goods involved which engenders Knightian uncertainty. These results are demonstrated by a theoretical model and simulation. They are based on stylized facts obtained through an empirical analysis. keywords: Venture capital, screening, competence, agent-based model J.E.L. codes: G24, L22, C15
∗
ERMES-CNRS - Universit´e Paris II, 12 place du Panth´eon, 75231 Paris Cedex 05, contact:
[email protected],
[email protected] † The authors thank CO3 (Common Complex Collective Phenomena in Statistical Mechanics, Society, Economics and Biology), European targeted project, for financial support.
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“I have argued that the efficiency of an economic system will depend, in the long run, not only on the quality of the allocation of resources achieve relative the existing estimates, but also on the quality of the estimates themselves...” Richardson (1953)
1
Introduction
In the last 25 years, venture capital has grown from an industry worth less than $1 billion to one worth over $100 billion (a growth that has far surpassed any other class of investment products). Venture capital is actually considered a very efficient means of financing innovation. Kortum & Lerner (2000) claim that “a dollar of venture capital could be up to ten times more effective in stimulating patenting than a dollar of traditional corporate R&D”. The question we ask in this paper is that of the utility of venture capital. Venture capitalists are intermediaries between fund owners (banks, pension funds, insurance companies, etc.) and start-ups. Do they play a simple role of coordination? Why is this role of coordination so important? According to Carlsson & Eliasson (2003) the function of venture capital is to select and finance the most promising start-ups and to bring the successful ones to industrialization. How efficient selection is achieved, however, is something these authors leave in the dark. Some economists have focused on the question of how entrepreneurs choose their investors (see Leshchinskii (2003)); as far as we know, few studies explore the question of how investors screen the startups in which they choose to invest (see Tyebjee & Bruno (1984) for a good description of the investment process). A venture capitalist has to invest in firms with a huge level of uncertainty (in biotechnologies, for example, positive returns are not expected before 10 years) and there is a wide asymmetry of knowledge between entrepreneurs and investors 1 . Numerous articles consider venture capital as an answer to a typical agency problem between start-ups and institutional moneylenders. The mainstream of theoretical analysis in this field is based on the seminal work of Aghion & Bolton (1992), Dewatripont & Tirole (1994) and Admati & Pfleiderer (1994). These studies focus on the optimal contract between the venture capitalist and the entrepreneur. But these approaches seem to ignore the fact that the financed enterprises deal with new products (venture capital essentially invests in radical innovation), and that entrepreneurs have myopic beliefs about the level of uncertainty concerning the expected success of their own product (success depends not only on the technical characteristics but also on other environmental factors, such as the ability of the product to match a new market demand). Therefore, instead of asymmetry of information it would be more appropriate to consider a double uncertainty, both on the supply side (moneylenders) and on the demand side (start-up founders). Kaplan & Stromberg (2001) distinguish three main roles for venture capitalists, which are contracting, monitoring, and screening. We believe that in a context of double uncertainty a contract is not sufficient to reduce the risk, and screening is therefore essential to favor a successful investment. To be efficient, the screening must be done by competent investors. We use the term ‘competence’ in 1
See essentially Gompers & Lerner (2004) for a very complete study of the venture capital industry, but also Sahlman (1990) for a concise and precise analysis of venture capital organization.
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the sense defined by Foss & Knudsen (1996), i.e. “a typically idiosyncratic knowledge capital that allows its holder to perform activities, and typically to perform them more efficiently than others”. In the case of venture capital, we assume that the concept of competence concerns the ability of the venture capitalist to recognize the right products for investment, in other words the start-ups of high quality, the ones with high expected returns. This level of competence is seen as a determinant of their long-term competitive advantage (Penrose 1959). Even if the literature recognizes the importance of screening in reducing uncertainty, the capacities required to screen and the conditions in which the screening takes place are rarely considered. In this paper we make the original assumption that a competent investor is someone who is able to measure the risk, and we propose to explore the link between his competence and the results of the screening. As a first step, we empirically analyze a huge database which gives, for a certain number of venture capitalists, the number of funds raised (between 1990 and 2005) and, for each fund, the number of start-ups financed together with the characteristics of these start-ups (means and period of exit, field of production concerned, etc.). In order to find empirical evidence of the role of competence in the efficiency of the screening, we estimate the influence of competence on the probability of success of an investment. This competence is evaluated through the intrinsic characteristics of venture capitalists and their adopted strategy (more or less risky investment decisions). We show that this competence is vertically differentiated and that it is reasonable for heterogeneous venture capitalists to adopt different investment strategies. In a second step, we build an original theoretical agent-based model of venture capital : we consider a system of interacting competent venture capitalists on one side and start-up projects of heterogeneous quality on the other side. Within this framework, we focus on the influence of competence on the results of the venture capital market. Following the results of our first step analysis, we postulate that a more competent venture capitalist reduces risk by a better evaluation of the quality of startup projects, and hence by better screening. We therefore show under what conditions the market structure of venture capital allows for an efficient exploitation of this competence. We emphasize the role of information structure and the influence of the intensity of the screening. The paper is structured as follows. Section 2 presents the empirical evidence on which our model is based. Section 3 describes the model. Section 4 is dedicated to the results of simulation. Section 5 concludes.
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Empirical Evidence
Our empirical results are based on the study of a database provided by Dow Jones Venture Source. This database accurately describes the functioning of the venture capital market. A venture capitalist raises successive funds from institutional investors and invests them in different start-ups. Venture capitalists usually spread their investment in start-ups over successive rounds, following the development of the firm. Venture capitalists also often syndicate their investment, each round usually involving more than one investor. The investors distinguish five main stages of development, which we group into two main categories, early stages (start-up, product development, product in beta
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Fund A1
...
Fund Ai
Fund B1
...
Venture Capitalist A
...
...
Fund Bi
...
Venture Capitalist B
Rounds
Start−up 1
...
Start−up i
...
Start−up j
...
Start−up k
...
Exit ?
BK − Bankruptcy
MA − Acquired
IPO − Public
Figure 1: The architecture of the venture capital financing system test) and later stages (shipping product, profitability). The figure 1 below describes this functioning.
2.1
The data
For each venture capitalist, the database provides the successive funds it has raised between 1990 and 2005, and the characteristics of the start-ups in which it has invested. For each start-up, we know the financing rounds it has received and the venture capitalists involved in each round. We also know the amount of the investment for each round, and the stage of development of the start-up when the round occurs. Finally, we know the industry in which the start-up is operating (Information Technologies (IT), Retail and consumers, buyer product, services (RETAIL) and Healthcare (HEALTH) or OTHER) and its current status at the end of the observation time (bankruptcy, private or exit). In the case of exit, we know the method of exit - Initial Public Offering (IPO) or Merger and Acquisition (M&A). If an IPO exit is usually considered as a clear success, the consequences of an M&A exit are more complicated to estimate. If some acquisitions are made at very high prices with a positive profit for the investor, others can be made with losses. Unfortunately, there is a lack of information on M&A outcomes, which prevents us from discriminating between successful and unsuccessful exits. For our study, we use data on 10824 first investments in 4544 firms, made by 663 venture capitalists between 1990 and 1998. We only consider the first investment because venture capitalists always take part in the following rounds when they first invest in a start-up. Thus, the first investment is where the decision to invest is made. We observe firms up until the year 2005, but since we are interested in the fate of the firm, we have to give them a sufficient amount of time to exit. We focus exclusively on firms and venture capitalists in the United States. In the database, investors are of many types (Venture Capital, Other Private Equity, Corporate, SBIC, Investment
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Bank, Public, Angel Investor, Others). To insure some homogeneity in our analysis, we decided to study only the Venture Capital type which designates independent venture capital firms. They represent 48% of the investors in the database, but 72% of the investments. Table 5 in annex describes the variables used in the following regressions.
2.2
The properties of early stage investment
As we have already explained, we propose in this paper to measure the influence of venture capitalists’ competence on the efficiency of the market. We postulate that greater competence leads to better screening, and consequently to a better choice of start-ups in which to invest. As Gompers (1998) and Sorensen (2004) note, and because of the lack of information on returns, M&A can be considered an ambiguous means of exit: we therefore make the simplifying assumption that a successful investment is one that leads to an IPO. With this definition, to be considered as competent, an investor has to invest in start-ups that exit more often through IPO. Hence, he has to screen successful enterprises, i.e. enterprises which will be able to exit on the financial market. We can ask the following question: does the success of an investment depend on strategic variables? We measure in table 1 the influence of different variables on the probability of success of the investment. We observe that most of the selected variables are significant. For example, investing in the health sector (HEALTH) is more successful than investing in the information technologies sector (IT) or in the retail sector (RETAIL). We believe this phenomenon is essentially due to the Internet bubble, which mainly affected IT and RETAIL. This regression also confirms that investing in the early stages is more risky than in the later stages. The probability of success for the mean investment drops from 19% to 16% when we move from later to early stages. In table 2 we now estimate the return of IPO exit (see Annex B for a description of how these returns are calculated). We observe that each variable that positively influences the probability of success negatively influences the return of IPO, and vice versa. Here, we find the evidence that the riskier the investment, the higher the return. In particular, the yearly log return for the mean investment raises from 194% for a later stage investment to 210% for a early one.
2.3
Competence and investment strategy
We have now seen that a venture capitalist can invest in different ways, with different results. The possibility of strategic choices are multiple, through the field of investment, the amount invested, the stage of development of the enterprise. We have confirmed, above, that the choice of the stage is particularly important. The issue we address now is the question of strategic decisions. Do venture capitalists strategically choose the stage of investment? In other words, do they decide to invest in a more or less risky stage depending on their competences? In figure 2 we select the venture capitalists that have invested in more than 10 start-ups between 1990 and 1998. For each of them, we measure the proportion of investments made in the early stages and consider the distribution of this proportion (i.e investors are ranked according to their ability to
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Table 1: Early Stage investment are riskier Success of a first investment in a start-up by a venture capitalist Estimate Std. Error z value Pr(>|z|) (Intercept) −1.365 0.09546 −14 2.112e−46 *** Early stage −0.1914 0.04608 −4.2 3.285e−05 *** amount 0.03026 0.003567 8.5 2.219e−17 *** nb.inv 0.1542 0.01065 14 1.634e−47 *** HEALTH 0.2893 0.05082 5.7 1.258e−08 *** RETAIL −0.06021 0.07245 −0.83 0.4059 OTHER 0.08607 0.1518 0.57 0.5707 I XXXX yes *** Null deviance 13112 Residual deviance 12233 Pseudo R2 0.0667 Signif. codes: 0 ’***’ 0.001 ’**’ 0.01 ’*’ 0.05 ’.’ 0.1 ’ ’ 1 note: we explain the success of 10824 first investments made in the US between 1990 and 1998 by 663 venture capitalists in 4544 different start-ups with a logit model.
Table 2: Early stage investment are more profitable Returns from IPO to a first investment in a start-up by a venture capitalist Estimate Std. Error t value Pr(>|t|) (Intercept) 1.3 0.1402 9.3 3.801e−20 *** Early stage 0.1579 0.03117 5.1 4.396e−07 *** amount −0.01181 0.00196 −6 1.965e−09 *** nb.inv −0.02254 0.006215 −3.6 0.0002941 *** HEALTH −0.2913 0.03366 −8.7 9.01e−18 *** RETAIL 0.07088 0.05084 1.4 0.1634 OTHER −0.229 0.121 −1.9 0.05853 . yes *** I XXXX E XXXX yes *** R2 0.3754 Adjusted R2 0.3682 Signif. codes: 0 ’***’ 0.001 ’**’ 0.01 ’*’ 0.05 ’.’ 0.1 ’ ’ 1 note: we explain the annualized rate of return to IPO from 2471 first investment rounds made in the United States between 1990 and 1998 and leading to IPO. These rounds are made in 776 different firms by 418 venture capitalists. To compute the returns we need the amount invested and postvalue for each round from initial investment to IPO. The numerous missing information explain the smallness of this sample.
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40 0
20
Frequency
60
80
Distribution of investors
0.0
0.2
0.4
0.6
0.8
1.0
Proportion of investments in early stages
Figure 2: Distribution of investors by proportion of investment in early stages. note: The three types of investors are highlighted : in the lower quartile, ranging from 0% to 33% of early stage investment, we find “later stage investors”, in the upper quartile, ranging from 62,5% to 100% we find the “early stage investors”, in the middle range we find investors with a mixed strategy. invest in risky assets)2 . An investor in the upper quartile of the distribution will be called an “early stage investor”, an investor in the lower quartile of the distribution will be called a “later stage investor”. In table 3 we evaluate the influence of the chosen strategy (Early, Mixed, or Later) on the probability of success of a first investment in four different settings. The first two regressions are run on all the investments, with a control for the stage of development in the second one. The third and fourth regression are run respectively on the investments made in early and later stages of development. Early investors are significantly more successful than others, no matter what the setting. As we have noted, early investments are more risky, so early investors must be more competent to be more successful. This competence allows them not only to make successful early investments but also to be more efficient in the later stages.
2.4
The influence of learning
Learning can improve the level of competence of a venture capitalist, i.e. the efficiency of its investment. Sorensen (2004) uses an experience variable, defined as the number of previous investments, as a proxy for venture capitalists’ competence. In the above section, we have already shown that investors have different levels of competence, which influence their strategic choices and their probability of success. 2
We rank the venture capitalists according to the proportion of the number of investment and not of the amount invested because investments in early stages are usually smaller than the later ones
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Table 3: Investors specialised in early stages are more competent Success of first investment in a start-up by a venture captalist All stages Early Stages Later Stages (Intercept) −1.488 *** −1.359 *** −1.486 *** −1.54 *** Early VC 0.1945 *** 0.2344 *** 0.1863 * 0.2692 ** 0.07569 0.02868 −0.06536 0.02614 Later VC amount 0.03188 *** 0.03125 *** 0.01866 *** 0.04365 *** nb.inv 0.1624 *** 0.1584 *** 0.1748 *** 0.1451 *** HEALTH 0.2328 *** 0.2699 *** 0.5396 *** −0.1436 . RETAIL −0.01978 −0.05237 −0.2704 . −0.06477 OTHER 0.04826 0.03781 0.2006 −0.01114 I 1991 0.1895 0.1842 0.2254 0.1772 I 1992 0.303 ** 0.2913 * 0.05955 0.5621 *** I 1993 0.0002313 −0.0149 −0.1045 0.1211 I 1994 −0.1548 −0.1593 −0.304 . 0.02755 I 1995 −0.07812 −0.08815 −0.09352 0.02223 I 1996 −0.2252 * −0.2372 * −0.3759 ** −0.004265 I 1997 −0.6489 *** −0.6645 *** −1.004 *** −0.3104 * −0.8004 *** −0.8109 *** −1.333 *** −0.3575 * I 1998 Early Stage −0.2214 *** Null deviance 11708 11708 5708 5982 Residual deviance 10930 10911 5138 5648 2 Pseudo R 0.06642 0.06806 0.09989 0.05595 Signif. codes: 0 ’***’ 0.001 ’**’ 0.01 ’*’ 0.05 ’.’ 0.1 ’ ’ 1 note: we explain the success of 9514 first investments made in the US between 1990 and 1998 by 289 investors in 4181 different firms with a logit model. The explaining variables are the strategy of the investor (Early VC, Later VC, Mixed VC), the amount of the investment, the number of investors taking part in the round, the industry of the firm (IT, HEALTH, RETAIL or OTHER) and the year of the round (I XXXX).
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Table 4: Learning and strategic choice influences on success rate are independent Success of a first investment in a startup by venture capitalist reference strategic choice learning both (Intercept) −1.309 *** −1.359 *** −1.4 *** −1.477 Early VC 0.2344 *** 0.25 Later VC 0.02868 0.1006 0.001987 *** 0.00211 experience amount 0.0301 *** 0.03125 *** 0.02939 *** 0.03024 nb.inv 0.1575 *** 0.1584 *** 0.1591 *** 0.16 0.2885 *** 0.2699 *** 0.3002 *** 0.2848 HEALTH RETAIL −0.06665 −0.05237 −0.05669 −0.04699 OTHER 0.01983 0.03781 0.04915 0.06682 I 1991 0.1925 0.1842 0.1778 0.1697 I 1992 0.3003 ** 0.2913 * 0.2857 * 0.2766 I 1993 −0.00588 −0.0149 −0.03763 −0.04796 I 1994 −0.1552 −0.1593 −0.1898 −0.1957 I 1995 −0.09003 −0.08815 −0.1283 −0.1308 I 1996 −0.2338 * −0.2372 * −0.2656 * −0.273 I 1997 −0.6608 *** −0.6645 *** −0.7058 *** −0.7142 −0.8013 *** −0.8109 *** −0.8596 *** −0.8733 I 1998 Early stage −0.182 *** −0.2214 *** −0.1933 *** −0.2236 Null deviance 11708 11708 11708 11708 Residual deviance 10929 10911 10899 10880 2 0.06657 0.06806 0.06904 0.07073 Pseudo R Signif. codes: 0 ’***’ 0.001 ’**’ 0.01 ’*’ 0.05 ’.’ 0.1 ’ ’ 1
*** *** *** *** *** ***
* . ** *** *** ***
note: we explain the success of 9514 first investments made in the US between 1990 and 1998 by 289 investors in 4181 different firms with a logit model. The explaining variables are the strategy of the investor (Early VC, Later VC, Mixed VC), the general experience of the VC, the amount of the investment, the number of investors taking part in the round, the industry of the firm (IT, HEALTH, RETAIL or OTHER) and the year of the round (I XXXX).
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We now verify the importance of learning through four regressions presented in table 4 below. Starting with a reference model with no proxy of competence, we build three models which take into account respectively strategic choices, experience and both of them. We observe that experience and the choice of an early strategy both positively and significantly influence the probability of success. The fact that the coefficients remain stable from one regression to another one indicates that the influence of these two variables is independent3 . This analysis confirms the positive impact of experience and learning on the efficiency of investment decision. But our results go a little bit further, clearly pointing out that learning is not the only component of competence. We observe that venture capitalists who choose an early investment strategy are more efficient than the others. But our last analysis shows that this effect is independent of the effect of learning. It seems that to be competent, a venture capitalist needs something more than learning.
3
The model
We have defined a competent investor as someone who is able to measure risk. Investors choose between different strategies according to their own level of competence. Their competence and their level of learning influence their choice of investment strategies and surely their screening. It is actually impossible to statistically evaluate the influence f the screening on the results of the market. For this purpose , to explain the influence of venture capitalists competence on the results of the market, we use an agent-based model. Hence we postulate that a more competent venture capitalist reduces risk by a better evaluation of the quality of startup projects, and hence by better screening. In what follows, we concentrate on the screening phase of venture capital and show under what conditions the screening will be efficient. Two types of agent operate in the market, venture capitalists and start-ups. Each start-up is characterized by a level of quality, and each venture capitalist is characterized by a level of competence. We describe a one-period model in which each venture capitalist screens a finite set of start-up projects and finances one of them.
3.1
The start-ups Hypothesis - 1: The return on investment For an initial investment I in a start-up i the expected profit is: E(πi ) = (pi g − 1) I
(1)
Hypothesis (1) models the “hit or miss” characteristic of venture capital investment. A start-up is reduced to an investment that may succeed with probability pi or fail. Financing a start-up means investing an amount I with a risky outcome. In the event of success, the start-up generates a gain of g times the investment, otherwise the investment is a pure loss. 3
We checked for colinearity issues in the forth regression.
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Hypothesis - 2: The quality of start-up projects Start-ups projects are heterogeneous in quality. The quality of each startup project determines the probability of its success if undertaken. For each start-up project i, the probability of success pi is given by: pi = qi p¯
(2)
With the mean quality of start-up projects q¯ = 1. Among the factors explaining the success of a start-up, the main ones are the technological feasibility of the new product, the as-yet-unknown market demand for it, and the capability of the management team. For simplicity, we condense all these factors into one unique quality level. And we choose a very simple linear relationship between quality and the probability of success. With such a linear relationship, if we assume that the mean start-up project quality is equal to 1, then p¯ is exactly the mean probability of success for the population of start-up projects. Thus, the choice of the distribution for q parametrizes the dispersion of the quality of the start-up projects and p¯ the mean probability of success. The simplest distribution for q would be a uniform distribution in [0; 2], but we can choose any other distribution of mean 1.
3.2
Venture capitalists Hypothesis - 3: Competence Competence is approximated by the ability of a venture capitalist to evaluate the level of quality of a start-up project. For each venture capitalist of competence cj , the evaluation of the start-up project quality qi is : q˜ij = cj qi + (1 − cj ) uij
(3)
The mean-preserving mix we choose here is similar to the specification used in Voorneveld & Weibull (2004), except that we use a distribution for q instead of two discrete levels. Here, u is a noise with a distribution identical to q, and (1 − cj ) is the level of noise. With cj equal to 1, the venture capitalist is very competent and has an exact evaluation of the start-up quality. With cj equal to 0, he has no specific competence and the quality he observes is totally uncorrelated with the true quality. Hypothesis - 4: Screening Each venture capitalist invests in a unique start-up. Each start-up is financed by only one venture capitalist. The screening is sequential. Let S be the set of start-up projects, and Sj−1 the start-ups selected by the previous j − 1 venture capitalists. Each venture capitalist finances the best start-up sj according to its evaluation in the set S\Sj−1 : sj = argmaxi∈S\Sj−1 (˜ qij = cj qi + (1 − cj ) uij )
11
(4)
3.3
The Market
The market is defined by the following six variables: the mean probability of success of the start-up projects p¯, the gross return in case of success g, the number of startup projects S, the number of venture capitalists V , the distribution of the quality of start-up projects q and the distribution of competence of the venture capitalists c. Let us now consider q¯s , the average level of quality of the start-ups. From hypotheses ¯ 1 and 2, we obtain E(π) = (¯ qs p¯g − 1) I. Thus the product p¯g allows us to determine the minimum level of average quality required to achieve positive profit: 1 ¯ E(π) > 0 ⇔ q¯s > p¯ g
(5)
We now consider the ratio of the number of start-up projects to the number of venture capitalists l = VS . Since each venture capitalist finances only one start-up, only one out of l projects is financed. Thus, l allow us to determine the intensity of screening, defined as the probability for a start-up project of being financed. The higher l, the lower this probability. Hence, the market is only defined by p¯g, l the screening intensity, q the distribution of the quality of start-up projects, and c the distribution of the competence of venture capitalists.
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Simulation results
In this section, we test both theoretically and through simulation the influence of venture capitalists’ competence and the influence of screening intensity on the efficiency of the venture capital market. To simplify the analysis, we consider that venture capitalists are homogeneous in competence. This simplification allows us to investigate the influence of different levels of competence. A further study should consist in running this model with agents of heterogeneous competence.
4.1
Conditions for positive returns
Proposition 1 The average rate of return of venture capital is an increasing function r¯(l, c) of the competence of venture capitalists c and of the screening intensity l: ∂∂cr¯ > 0 if l > 1 and ∂∂lr¯ > 0 if c > 0 . There exists a frontier of null rate of return r¯(l, c) = 0 which determines the minimum level of competence and screening intensity that ensure positive rates of return to the venture capitalists. To prove proposition 1, let us compute the average rate of return. We first derive an analytic formulation of this function4 . For this purpose, we need to formulate two additional assumptions: • let us first choose a uniform distribution on [0 : 2] for the quality of start-up projects q. 4
We only report here the formulas for each step of the computation, the literal expressions are given in annex C.
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• let us assume furthermore that all the venture capitalists are homogeneous in competence and share the same evaluation of each start-up quality. This allows us to rewrite the hypothesis 3 of our model: q˜ij = q˜i = c qi + (1 − c) ui
(6)
Under these assumptions, the screening operates as a simple truncature of the distribution of the evaluation of quality q˜ as shown in figure 7 in annex. In other words, the screening allows us to determine the minimum level of estimated quality q˜ above which a start-up project will be financed. We first compute this threshold. From a technical point of view, the distribution of the evaluation of quality is a linear combination of two identical uniform distributions q and u (hypothesis 3). Thus, the expression of the density fq˜ is a simple convolution: Z ∞ fc q (t) f(1−c) u (˜ q − t) dt (7) fq˜(x) = −∞
The table 6 in annex shows the exact expression for this density. To find the threshold value q˜ for the truncature we need to compute the repartition function Fq˜ for q˜. This is a simple integration of fq˜. The expression of Fq˜ is given in table 7 in annex. Z x fq˜(t)dt (8) Fq˜(x) = 0
The proportion of projects that are financed is 1 − Fq˜(˜ q ). This proportion is also V 1 equal to S or l . Thus q˜ is the solution of the equation 9. This threshold is a function of l and c. The exact expression is given in table 8 in annex. 1 V = (9) S l There are six different expressions of q˜ depending on the value of c and l. This splits the map (c, l) into six different areas, where the final expression of r¯(c, l) is different. These areas are drawn on figure 8 in annex. P (x > q˜) = 1 − Fq˜(˜ q) =
We have determined the distribution of the evaluation of quality of the selected start-ups. But the returns will depend on their real quality, not on the evaluation. We therefore need to compute the expected quality of a start-up with an evaluation q˜ : E(q|˜ q ). This depends on the probability P (q|˜ q ) that can be computed from Bayes’ rule. The exact expressions for P (q|˜ q ) and E(q|˜ q ) are given respectively in table 9 and 10 in annex. E(q|˜ q) =
Z
2
q P (q|˜ q ) dq =
0
Z
0
2
P (˜ q |q) P (q) q dq P (˜ q)
(10)
And now we can finally compute the mean quality of the selected start-ups. q¯s = E(q|˜ q > q˜) =
Z
2 q˜
P (˜ q) E(q|˜ q) d˜ q=l∗ P (˜ q > q˜)
Z
2
E(q|˜ q ) P (˜ q ) d˜ q
(11)
q˜
This final expression is given in table 11 in annex. The average rate of returns r¯(c, l) can be computed easily using equation 12 between the average quality and the average rate of return:
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E(π) = (g p¯ q¯s − 1) (12) I It is easy to verify that the partial derivatives of this function are positive. The figure 3 shows the average rate of return computed with p¯g = 0.75.(l and c vary and q is a uniform distribution) The average rate of return is increasing with the screening intensity l and with the competence of venture capitalists c. An interesting result is the frontier of null return that splits the map (l, c) into two regions. Negative rates of return are found on the top left, positive rates of return on the bottom right. These frontiers give insightful information about market efficiency. Here, there is an absolute minimum screening intensity of l = 1.5 required to achieve positive returns. This corresponds to a proportion of financed start-up projects of 32 . At this intensity, the minimum required level of competence is c = 0.4. Lower levels of competence can also achieve positive rates of return, but only for an higher screening intensity l, increasing while c decreases. The effect of the screening intensity can explain the result of Gompers & Lerner (2000) that an important inflow of money in venture capital can lower its performance. Indeed, if more money is provided, venture capitalists will finance more start-up projects. This means that the screening intensity will be lower and the average rate of return will diminish. r¯ =
Turning to simulation allows us to draw the average rate of return function under less drastic assumptions. For instance, we can change the distribution of start-up quality q from a uniform distribution in [0 : 2] to a normal distribution N (1, 0.3). This allows us to consider a population of start-up projects of less heterogeneous quality and thus harder to discriminate between. These simulations are run with V = 100 venture capitalists and the average rate of return is computed over a hundred independent simulated screenings. The figure 4 shows the function r¯(l, c) in this case. The main effect of changing the distribution of start-up project quality to a normal distribution is to lower the average rate of return for each value of competence c and of screening intensity l. In this situation a venture capitalist needs to be more competent and/or to be in a more competitive environment (higher screening intensity) to achieve positive returns.
4.2
Horizontal Variety
Proposition 2 The global performance is better when each venture capitalist has an independent evaluation of start-up quality We now abandon the assumption that the evaluation q˜ is shared by all the venture capitalists, and consider that they have a private independent evaluation. They are still homogeneous in competence, but they now differ in their evaluation of the quality of a start-up project. This means that hypothesis 3 can now be rewritten as: q˜ij = c qi + (1 − c) uij
(13)
The figures 5 and 6 show the corresponding simulated average rate of return, with the same setting of parameters as before, respectively with a uniform and a normal distribution of start-up quality. In these figures, the lower dashed line allows a direct comparison with the previous cases (figure 3 and 4) It appears clearly that the performance is better with private,
14
Average rate of return with g = 10, p = 0.075
0.5 0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3
0.5 0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3
returns < 0 0 0.2
returns > 0 0.4
c: competence
0.6 0.8 1 1
2
3
4
5
6
7
8
9
10
l: screening intensity
Figure 3: Average rate of return as a function of competence c and of the ratio of the number of new start-up to the number of venture capitalists l with an uniform distribution for q and shared evaluation. At the bottom the frontier of null rate of return divides the space in a region of positive and a region of negative rate of returns. (theoretical derivation)
Average rate of return with g = 10, p = 0.075
0.5 0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3
0.5 0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3
0
returns < 0
0.2 0.4 c: competence
returns > 0 0.6 0.8 1 1
2
3
4
5
6
7
8
9
10
l: screening intensity
Figure 4: Average rate of return as a function of competence c and of the ratio of the number of new start-up to the number of venture capitalists l with a normal distribution N(0, 3) for q and shared evaluation. The line at the bottom is the frontier of null rate of return. (simulation)
15
Average rate of return with g = 10, p = 0.075
0.5 0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3
0.5 0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3
returns < 0
0 0.2
returns > 0
0.4 c: competence
0.6 0.8 1 1
2
3
4
5
6
8
7
9
10
l: screening intensity
Figure 5: Average rate of return as a function of competence c and of the ratio of the number of new start-ups to the number of venture capitalists l with an uniform distribution for q and private evaluation. At the bottom two frontiers of null rate of return are drawn. The solid line corresponds to the current function, the lower dashed corresponds to the previous case of a shared evaluation. (simulation)
Average rate of return with g = 10, p = 0.075
0.5 0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3
0.5 0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3
returns < 0
0 0.2
returns > 0
0.4 c: competence
0.6 0.8 1 1
2
3
4
5
6
7
8
9
10
l: screening intensity
Figure 6: Average rate of return as a function of competence c and of the ratio of the number of new start-ups to the number of venture capitalists l with an normal distribution for q and private evaluation. As above the two frontiers of null rate of return corresponds to the current function (solid line), and to the case of a shared evaluation (lower dashed line). (simulation) 16
independent evaluation than it is with a shared evaluation. To understand this result it might be useful to consider the information structure of the market. The shared evaluation case corresponds to a situation where the information is common knowledge (they are homogeneous in competence), whereas the private evaluation case corresponds to a market with decentralized information. The result we find here echoes the claim of Carlsson & Eliasson (2003) that venture capital requires horizontal variety to be efficient, i.e. many venture capitalists of different backgrounds and specializations. They justify their claim by the need to avoid type II errors (‘missing a good project’) rather than type I (‘financing a bad project’). In this case, Sah & Stiglitz (1986) indeed claim that polyarchy would be more efficient than hierarchy. Our analysis is in line with these results: we show here that when investors are homogeneous in competences, the market environment influences the efficiency of the screening, through the structure of information.
5
Conclusion
As far as we know, although economics and management literature on venture capital abounds, few articles study the influence of human capabilities on the efficiency of this mode of financing innovation. In particular, the way the investment decision is taken is rarely considered. Recent real events have shown how the trust of economic actors in this mode of financing is strongly influenced by irrational phenomena such as mimetism, bubbles and myopic beliefs. In this article, we analyze the conditions under which the functioning of venture capital can be efficient and show that this depends on rational variables. Firstly, we provide empirical evidence of the influence of venture capitalists’ competence on the investment’s probability of success. We also prove that if learning positively influences an investment’s probability of success, this effect is independent of the effect of strategic choices, which suggests that competence is something more than learning. Secondly, we show that although competence is indispensable to a venture capitalist for selecting the most promising start-ups, it is not sufficient. Through a theoretical model and simulation we show that the intensity of screening positively influences the return function. In other words, we demonstrate that efficient screening (i.e. screening which results in positive profits for venture capitalists) can only take place within a market where a large number of innovators are seeking funding for their start-ups. Thirdly, we show that each venture capitalist must possess an independent private evaluation of the start-up projects competing for finance. In other words the market benefits from horizontal variety. Finally, our most striking discovery in this paper is that success requires complementarity between venture capitalist competences and market organization. This echoes Richardson’s thesis that, within the context of an imperfect market, complementary interaction between the market and the competence of the firm can improve efficiency. Here, the market imperfection is due to the type of goods involved - new technologies which provide no point of reference in terms of past performance - which engenders Knightian uncertainty. In an economy where start-up projects have difficulties in emerging, even a very competent venture capitalist would not be efficient. Conversely, it would not be useful for an economy to sustain start-up projects in the absence of competent and independent venture capitalists.
17
References Admati, A. & Pfleiderer, P. (1994), ‘Robust financial contracting and the role of venture capitalist’, The Journal of Finance 49(2). Aghion, P. & Bolton, P. (1992), ‘An incomplete contracts approach to financial contracting’, The Review of Economic Studies . Carlsson, B. & Eliasson, G. (2003), ‘Industrial dynamics and endogeneous growth’, Industry and Innovation 10(4). Cochrane, J. (2005), ‘The risk and return of venture capital’, Journal of Financial Economics 75(1). Dewatripont, M. & Tirole, J. (1994), ‘A theory of debt and equity: Diversity of securities and manager-shareholder congruence’, The Quarterly Journal of Economics 109(4). Foss, N. & Knudsen, C. (1996), The emerging competence perspective, in ‘Towards a Competence Theory of the Firm’, London : Routledge. Gompers, P. (1998), The determinant of corporate venture capital success : Organizational structure, incentives and complementarities., Nber working paper, NBER. Gompers, P. & Lerner, J. (2000), ‘Money chasing deals? the impact of fund inflows on private equity valuations’, Journal of Financial Economics 55(2). Gompers, P. & Lerner, J. (2004), The Venture Capital Cycle, 2nd edn, MIT Press. Kaplan, S. & Stromberg, P. (2001), ‘Venture capitalists as principals: Contracting, screening, and monitoring’, The American Economic Review 91(2). Kortum, S. & Lerner, J. (2000), ‘Assessing the contribution of venture capital to innovation’, The Rand Journal of Economics 31(4). Leshchinskii, D. (2003), How should entrepreneurs choose their investors?, in A. Ginsberg & I. Hasan, eds, ‘New Venture Investment : Choices and Consequences’, Elsevier. Penrose, E. (1959), The Theory of the Growth of The Firm, Basil Blackwell Publisher. Richardson, G. (1953), ‘Imperfect knowledge and economic efficiency’, Oxford Economic Paper 5(2). Sah, R. K. & Stiglitz, J. (1986), ‘The architecture of economic systems: Hierachies and polyarchies’, The American Economic Review 76(4). Sahlman, W. (1990), ‘The structure and governance of venture-capital organizations’, Journal of Financial Economics 27(2). Sorensen, M. (2004), How smart is money ? an empirical two-sided matching model of venture capital, Working paper, Department of Economics, Stanford University. Tyebjee, T. & Bruno, A. (1984), ‘A model of venture capitalist investment activity’, Management Science 30(9). Voorneveld, M. & Weibull, J. (2004), Prices and quality signals, Working Paper Series in Economics and Finance 551, Stockholm School of Economics.
18
A
Descriptive statistics Table 5: Descriptive statistics
Quantitave variables min 1st quartile amount 0.000 1.820 nb.inv 1 2
median 3.720 3
Qualitative variables success true 2905
false 6609
3rd quartile 6.620 5
max mean 141.900 5.486 12 3.5679
early stage
true 4773
false 4741
industry
IT 5447
HEALTH 2741
RETAIL 1139
OTHER 187
I 1990 642
I 1991 622
I 1992 751
I 1993 774
I 1995 1091
I 1996 1417
I 1997 1541
I 1998 1902
year of investment
I 1994 774
note: These statistics correspond to 10824 first investments made in the US between 1990 and 1998 by 663 venture capitalists in 4544 different start-ups. “amount” represents the amount invested in million dollars. “nb.inv” represents the number of investor taking part in the round. “success” indicates that the start-up has made an exit trough IPO. “early stage” indicates that the round occured as the start-up was in an early stage of development. “industry” and “year of investment” are self explaining.
B
Return to investment
We computed the return of a round leading to IPO as in Cochrane (2005). For each round i, let Ii be the amount of the investment and P Vi the post-value5 of the firm after the round. Let i be in [0 : IP O], where 0 is the round for which we compute the return, IP O is the exit round and the intermediate i stands for all the rounds in between. The investor initial buys s0 = PIV00 shares for a value of I0 . At exit time, he is entitled to a share of the value of the firm depending on its remaining shares after all the intermediate investments. At each investment i, PIVi i shares are bought for a value Ii . Someone owning si−1 shares before the round thus only owns si = si−1 ∗ (1 − PIVi i ) after the round. This gives the following expression for the gross return to investment R. 5
The post-value is computed on the amount paid per share by the investor. If an investor pays I for s shares the post-value of the firm is P V = s ∗ I
19
IP O sIP O ∗ P VIP O Ii P VIP O Y R= (1 − = ∗ ) I0 P V0 P Vi
(14)
i=1
The gross return R is the ratio of the final on the initial post-value, multiplied by a factor of dilution of the shares due to the intermediate investments (including IPO, which is also an investment). The log-return r = Log(R) is also the rate of return R = 1 + r. We can annualize this rate by dividing it by the number of years between the initial investment and the IPO.
C
Computation of the average rate of return c
1 2
q˜ ∈ [0 : 2c]
q˜ 4c(1−c)
q˜ ∈ [0 : 2(1 − c)]
q˜ 4c(1−c)
q˜ ∈ [2c : 2(1 − c)]
1 2(1−c)
q˜ ∈ [2(1 − c) : 2c]
1 2c
q˜ ∈ [2(1 − c) : 2]
2−˜ q 4c(1−c)
q˜ ∈ [2c : 2]
2−˜ q 4c(1−c)
Table 6: Density function for the evaluation of quality : fq˜
c
1 2
q˜ ∈ [0 : 2c]
q˜2 8c(1−c)
q˜ ∈ [0 : 2(1 − c)]
q˜2 8c(1−c)
q˜ ∈ [2c : 2(1 − c)]
q˜−c 2(1−c)
q˜ ∈ [2(1 − c) : 2c]
q˜−(1−c) 2c
q˜ ∈ [2(1 − c) : 2]
(2−˜ q) 1 − 8c(1−c)
q˜ ∈ [2c : 2]
(2−˜ q) 1 − 8c(1−c)
2
2
Table 7: Repartition function for the evaluation of quality : Fq˜
20
c< l ∈ [1 :
2 (1−c) ] 2−3c
l ∈ [ 2(1−c) : 2−3c l∈
[ 2(1−c) c
2 c (1−c) (l−1) l
l ∈ [1 :
(l−2) (1−c) l
2c l ∈ [ 3c−1 :
1+
2
1 2
c> q
2
2 (1−c) ] c
: ∞]
1 2
1−
q
2 c (1−c) l
l∈
2c [ 1−c
2c ] 3c−1
2
q
2c ] 1−c
2 c (1−c) (l−1) l
1+
: ∞]
2
1−
(l−2) c l
q
2 c (1−c) l
Table 8: Selection threshold on the evaluation of quality : q˜(c, l)
c
1 2
q˜ ∈ [0 : 2c]
c q˜
q˜ ∈ [0 : 2(1 − c)]
c q˜
q˜ ∈ [2c : 2(1 − c)]
1 2
q˜ ∈ [2(1 − c) : 2c]
c 2 (1−c)
q˜ ∈ [2(1 − c) : 2]
c 2−˜ q
q˜ ∈ [2c : 2]
c 2−˜ q
Table 9: Conditional probability of quality given the evaluation of quality : P (q|˜ q)
c
1 2
q˜ ∈ [0 : 2c]
q˜ 2c
q˜ ∈ [0 : 2(1 − c)]
q˜ 2c
q˜ ∈ [2c : 2(1 − c)]
1
q˜ ∈ [2(1 − c) : 2c]
q˜−(1−c) c
q˜ ∈ [2(1 − c) : 2]
4c+˜ q −2 2c
q˜ ∈ [2c : 2]
4c+˜ q−2 2c
Table 10: Expected value of quality given observed quality : E(q|˜ q) 21
c < 1/2 c > 1/2 Probability density 1 2(1−c) 1 2c
0
2
~ q_
2c
2(1−c)
2(1−c)
Quality 2c
Figure 7: Probability density function of the observed quality q˜. According to the value of c, inferior or superior to 21 , the critical values (maximum value, lower and upper bound of the horizontal part) change. The grey area represents the population chosen by the venture capitalists. q˜ is the threshold value of the screening.
5
4.5
l > 2(1-c)/c
l > 2c/(1-c)
l: screening intensity
4
3.5
3
l in [2(1-c)/(2-3c):2(1-c)/c]
2.5
l in [2c/(3c-1):2c/(1-c)]
2
1.5
l in [1:2(1-c)/(2-3c)]
1 0
0.2
l in [1:2c/(3c-1)]
0.4
0.6
0.8
1
c: competence
Figure 8: Segmentation of the map (c, l) determining the expression of the threshold on quality
22
c< l ∈ [1 :
2 (1−c) ] 2−3c
: l ∈ [ 2(1−c) 2−3c
2 (1−c) ] c
: ∞] l ∈ [ 2(1−c) c
1 2
c> 3
l−
1
3
1+
1 l2
2c ] 3c−1
2c ] 1−c
l−
1 c2
1
3
2 2 (1−c) 2 (l−1) 2 3
1 c2
2 − 1l −
1 l2
l (1−c)2 12 c2
3
1
2 2 (1−c) 2 3
l ∈ [1 :
2c : l ∈ [ 3c−1
cl 6 (1−c)
3
2−
3
3
2 2 (1−c) 2 (l−1) 2 1 c2
1 2
2c : ∞] l ∈ [ 1−c
1 l2
2−
Table 11: Expected mean quality in the selection : q¯s (c, l)
23
1
2 2 (1−c) 2 3
1 c2
1 l2
