Rationing of excessive demand on crowdinvesting-platforms

Rationing of excessive demand on crowdinvesting-platforms Oliver Mäschle Universität Rostock February 2012 Abstract On crowdinvesting-platforms non-publicly traded companies can offer equity to private investors. Platforms like Crowdcube.com in Great Britain or Seedmatch.de in Germany are using a mechanism for the allocation of available shares best described by the phrase first come, first served at the moment. In this paper it is argued, that this kind of allocation of shares or rationing of excessive demand is not optimal. It is described here, which characteristics rationing of excessive demand has to imply to protect the interests of involved parties in an appropriate manner. A recommendation for a concrete practical implementation is offered as well.

Contents Contents... I 1. Introduction... 1 2. Criteria of an optimal rationing mechanism... 4 2.1 Realization of benefits implied by a broad and diffuse investor base... 4 2.1.1 Increased liquidity on the secondary market... 4 2.1.2 Protection of the control of the initial entrepreneurial team... 6 2.2 Protection of informational disadvantaged investors... 9 2.3 Compensation of initial investors... 11 2.3.1 Costs of initial investors... 11 2.3.2 Positive external effects by initial investments... 12 3. Conflicting implications of mentioned criteria... 17 4. Rationing mechanisms for practical purposes... 18 4.1 Practical features of an optimal rationing mechanism... 18 4.1.1 A Zero-Rationing-Threshold... 18 4.1.2 Investor base maximizing rationing beyond the Zero-Rationing-Threshold... 19 4.1.3 Soft-Ending of the financing period... 20 4.2 Illustrating example for a practically applicable rationing mechanism... 21 5. Upcoming research... 23 6. Conclusion... 25 Literature... II I

1. Introduction Increasing importance of the internet has changed the financial sector in several ways and at the same time it has increased the number of investment opportunities. One recent deployment was the creation of crowdinvesting-platforms. On these platforms private investors can buy shares of nonpublicly traded companies guaranteeing investors a right to receive a certain share of upcoming profits and on some platforms voting-rights. In the area of investment opportunities the shares traded on crowdinvesting-platforms fill a gap between classical public equity, that is stocks, and private equity. The terms public and private discriminate classes of equity depending on the type of information investors have about these assets. The information of owners of public equity is not exclusive to them, but it is public. The information of private equity owners, for example venture capitalists, stays private. If a company sells equity on a crowdinvesting-platform, it makes information about the company public. But once enough investors have been acquired, no more public trading takes place, implying the end of further information flows to the public. So equity sold on these platforms can be seen as temporarily public equity. What are the motives of entrepreneurs selling public, private or temporarily public equity? Selling public equity on an international stock exchange has got several advantages. First, there is the obvious advantage of acquiring new capital to finance further investments or to diversify the portfolios of initial owners. Second, being listed on an international stock exchange increases the degree of public perception. The resulting increased reputation can recruit new customers as well as new employees. But since the listing standards of international stock exchanges are quite restrictive and imply a certain amount of costs, this kind of selling equity is only reserved to relatively mature and big companies. Private equity is very attractive for young and fast growing firms excluded from stock exchanges. This kind of capital is often offered by venture capitalists. These financial companies usually do not just invest money, but they support their companies using their experience and competence as well. This fact motivated some economists like Schafer and Schilder (2009) to denominate this kind of financial support smart capital 1. But of course investors holding an informational advantage compared to other potential investors will have some bargaining power undesirable for the entrepreneur. Venture capitalist can use this bargaining power for example by naming conditions for further necessary investments. Equity sold on crowdinvesting-platforms seems to be a compromise between the two classical forms of equity. Even though the supply of information on such a platform might imply some costs, these costs should be negligible compared to the costs implied by a listing on a stock exchange. At the same time it is quite unlikely that external investors obtain the same bargaining power like a classical private equity investor, protecting the interests of the initial entrepreneurial team. So equity sold on these 1 Schafer, Schilder (2009): p.163 1

platforms still allows for access to new capital and diversification, but without the same degree of disadvantages implied by classical types of external equity. On crowdinvesting-platforms entrepreneurs describe their business ideas and choose a fixed amount of capital as an investment target. At the same time an entrepreneur has to describe, which share of corporate profits and voting rights are sold in return for the fixed amount of money. If the investment target is completely funded within a fixed time period (on Crowdcube.com this period is 90 days 2 ), the raised capital less pre-specified charges is handed out to the entrepreneur. If the investment target is not reached within this time period, the already invested capital is given back to the private investors 3. This paper exclusively focuses on the scenario, when the investment target is funded completely. Once 100% of the investment target is reached, Crowdcube.com immediately stops the financing period and transfers the money to the entrepreneur 4. But it is probably misleading, if you assume that a successful funding on a crowdinvesting-platform is the result of a Walrasian equilibrium price implying supply equals demand. Instead the following assumption is chosen for the rest of this paper: 100% of the investment target can only be funded, if the price per share is lower than the market clearing price of a Walrasian equilibrium. That is, a successful funding necessarily implies excessive demand for shares. This assumption coincides with evidence of initial public offerings (IPOs). In an IPO corporate equity is sold to external investors, just as it is the case on crowdinvesting-platforms. Stocks initially sold to the public predominantly have been underpriced on all international stock exchanges in the last decades 5. This underpricing is usually measured as the difference between a stock s price at the end of the first day of trading minus the stock s issue price 6. This initial price increase can only be achieved, if the issue price implies some degree of excessive demand for the asset. Equity issues are multiply oversubscribed most of the times 7. So if some degree of excessive demand is a necessary condition for a successful issue of shares on an international stock exchange, the same should be true for issues realized on crowdinvestingplatforms. One problem of the allocation procedure of crowdinvesting-platforms at the moment is that excessive demand cannot be observed, if platforms close the financing period immediately once the investment target is reached. If you close the financing period immediately once the investment target is reached, the demand of all the investors still willing to invest, but run late, will be completely rationed. A reason, for an investor 2 http://www.crowdcube.com/pg/crowdcube-faq-20#howlong (11/19/2011) 3 http://www.crowdcube.com/pg/crowdcube-faq-20#howlong (11/19/2011) 4 http://www.crowdcube.com/pg/crowdcube-faq-20#howlong (11/19/2011) 5 For example Ljungqvist (2007): Figure 2 on p.383 shows that 4079 IPOs conducted on European stock exchanges have been underpriced on average. Despite national differences the mean underpricing is positive for every national stock exchange. Figure 1 on p.382 shows the mean underpricing of US-stocks in 172 quarters between 1960 and 2003. Only in 13 of these quarters the mean issue price was overrated. 6 Ljungqvist (2007): p.381 7 For example Brennan and Franks (1997) on p.398: 46 IPOs in Great Britain between 1986 and 1989 had a mean Demand-Supply-Ratio of 18.77. 2

coming too late, might be a comparatively long evaluation process due to a lack of investment experience. This exclusion from buying shares is even more severe than in case of an IPO on stock exchange, since publicly traded stocks can easily be bought on the secondary market, while there is no formal secondary market for equity initially sold on crowdinvesting-platforms. In the following chapters the weaknesses of the current rationing or allocation mechanism will be highlighted and criteria of an optimal mechanism will be identified. Moreover a concrete recommendation for a practical implementation of a mechanism fulfilling the named criteria is articulated. These platforms are a very young appearance. The first successful funding has been realized in 2011 on Crowdcube.com as well as Seedmatch.de. Consequently academic literature related to this topic is very rare. But in developing the following argumentation the so called IPO-underpricing -literature has been helpful. Useful surveys of this literature are the articles of Ljungqvist (2007) or Ritter and Welch (2002). This literature is useful for developing a rationing mechanism for crowdinvesting-platforms, since the theories of this finance discipline explicitly describe the motives of the parties, involved in an IPO, to create excessive demand as well as the benefits arising from excessive demand. An optimal rationing mechanism of a crowdinvesting-platform has to incorporate these aspects associated with excessive demand. The paper is structured in the following way. Chapter 2 specifies the criteria an optimal rationing mechanism should fulfill. Chapter 3 discusses the tradeoffs implied in the implementation, since certain criteria recommend conflicting measures. Chapter 4 delivers an example of a practically applicable mechanism. Possible questions and goals of future research are discussed in chapter 5, while chapter 6 concludes. 3

2. Criteria of an optimal rationing mechanism The following chapter includes four criteria an optimal mechanism has to fulfill. The realization of benefits implied by a broad and diffuse investor base is desirable for two reasons. First, it increases the liquidity of shares in the secondary market. Second, it offers some protection of the initial entrepreneurial teams control. The protection of investors with informational disadvantages is a third criterion, while an appropriate compensation of initial investors is a fourth criterion. 2.1 Realization of benefits implied by a broad and diffuse investor base Several benefits arise, if rationing of excessive demand is performed in a way, that the number of investors is maximized. The emitter gets some additional and desirable scope of action absent in a situation of equal demand and supply for assets. First, the liquidity of post-emission trade will be maximized, if the number of investors is maximized implying a higher price per share in the informal secondary market. Second, a diffuse ownership structure can avoid the emergence of big blocks of external investors, protecting the initial owners of the company and reducing the probability of a hostile takeover. 2.1.1 Increased liquidity on the secondary market The term liquidity describes the conditions of availability of a trade partner, when you want to buy or sell an asset. High liquidity is given, if you can trade an asset in a short time and with low associated costs. For example if you want to trade an asset on a dealer-market the bid-ask-spread, that is the difference between the offer and the bid price, describes the trading costs implied by an immediate trade. That is why Amihud and Mendelson (1986) interpret the bid-ask-spread as a measure of illiquidity of the underlying asset 8. Buying an asset generating a known cash-flow an investor will incorporate the costs of selling the asset in the future already in the moment of the purchase. Looking at two assets generating identical cash-flows an investor will be willing to pay a bigger price for the asset with higher liquidity. So the market value of an asset is positively related to its liquidity 9. The described relationship between an asset s market price and liquidity motivated Booth and Chua (1996) to develop a model of emitters using IPO-underpricing to optimize the resulting after-market liquidity of their companies shares. In this model entrepreneurs deliberately choose an underrated issue price to attract a multitude of investors. The resulting excessive demand allows them to allocate the fixed supply of shares in an investor base maximizing way. The diffusion of assets will maximize the price per share in the secondary market. More formally: the increased number of involved 8 Amihud and Mendelson (1986): p.223 9 Amihud and Mendelson (1986): Proposition 2 on p.228 4

investors n should increase the expected market value of the asset in the aftermarket E[V(n)], that is there is appositive relationship between E[V(n)] and n with d E[V(n)]/dn > 0 and d² E[V(n)]/dn² < 0 10. In the model of Booth and Chua (1996) firms are faced by a number of uninformed investors with different costs of information production. It is assumed that only informed investors will buy issued shares and will trade the firm s assets in the secondary market 11. In this model the aggregated profits of the investors implied by underpricing (E[V(n)] - ) have to equal the aggregated costs of information production C(n). While Booth and Chua (1996) assume a convex function of aggregate costs of information production, a concave function seems to be more plausible in case of crowdinvesting-platforms 12. In their model investors produce information simultaneously and consequently one investor cannot draw conclusions from the information production of other investors. But the sequential information production and investment process on crowdinvesting-platforms allows individual investors to make use of the evaluations of preceding investors. So an aggregate function of information production with dc(n)/dn > 0 and d²c(n)/dn² seems more realistic. Assuming an entrepreneur knows the optimal number of investors n*, he will choose the issue price, so the following equality holds 13 : [E(V(n*)) - ] C(n*) = 0. (1) For a given rationing mechanism the necessary degree of underpricing will be positively related to the number of investors that should be attracted. But if you treat the rationing mechanism as endogenous, it is decisive that this mechanism implies a maximal dispersion to minimize the required underpricing. The rationing mechanism for example used by Crowdcube.com does not fulfill this criterion. There are also several rationing mechanisms used by international stock exchanges, which do not optimally spread the investor base. The random balloting method implies that the individual demand of randomly chosen investors is met completely, while the individual demand of other investors is rationed completely 14. The resale of shares of non-publicly traded firms is not just important for the topic of liquidity, it also an important topic in the literature about venture capitalists 15. These financial institutions are usually planning a so called exit, that is a strategy to resell the assets in the future for example via an IPO or a takeover, already in the moment of the purchase. Knowing this, it is a good advice to entrepreneurs selling equity on a crowdinvesting-platform to include an exit-strategy in their business plan. But 10 Booth and Chua (1997): p.295 11 Booth and Chua (1996): p.294. The authors actually assume informed investors are just more likely to trade on the secondary market. The simplification here that only informed investors are allowed to trade on the secondary market is of course a stronger but an illustrating assumption. 12 Booth and Chua (1996): p.294 13 Booth and Chua (1996): Formula (2) on p.295. The notation of the issue price OP has been changed to. 14 Koh and Walter (1989): Description of random-balloting rationing on p.253. 15 For example Bscha and Walz (2001) 5

entrepreneurs and investors should be interested in liquid trade before an exit as well. If a limited liability company does not grow fast enough to realize an exit via an IPO, the shareholders should be particularly interested in having a diffuse investor base implying a comparatively high liquidity. A broad investor base will increase the probability of an internal sale of shares to another shareholder. So the marginal effect of increased liquidity on the firm s market value should be even bigger than the marginal effect of liquidity in case of a publicly traded company. If there is an excessive demand for shares sold on a crowdinvesting-platform, an optimal rationing mechanism should fulfill the following criterion: Criterion 1: The rationing mechanism of a crowdinvesting-platform should imply a maximal dispersion of shares to maximize the liquidity of shares in the informal secondary market. 2.1.2 Protection of the control of the initial entrepreneurial team A young entrepreneur trying to finance his firm via a crowdinvesting-platform faces a tradeoff. On the one hand, the entrepreneur needs capital, which he is not willing or able to raise in a traditional way, like a bank loan. On the other hand, he wants to stay in control of his company. The reason for this conflict of interest is the fact, that external equity implies voting rights for the investors. If an entrepreneur sells more than 50% of his company s equity, it is possible that external investors enforce a new management against the will of the entrepreneur. The entrepreneur has two opportunities to avoid this scenario for sure. First, the entrepreneur could sell non-voting shares. But these shares are less attractive for investors, since they increase the scope of the manager and founder of the firm to maximize private benefits instead of shareholder value. Consequently investors will only be willing to pay a lower price for equity guaranteeing a fixed share of profits. This discount on non-voting shares is well known from international stock exchanges. For example Zingales (1994) using data from the Milan Stock Exchange found out, that the market price of stocks with voting rights is 81.5% bigger than otherwise equal non-voting stocks 16. The disadvantage of missing voting rights is a reason for many institutional investors to abstain from buying such shares 17. Even though there are platforms, like Seedmatch.de, selling exclusively non-voting shares, it seems obvious, that voting shares are much more attractive to investors 18. And also the emitter should be interested in not being forced to use even more underpricing to compensate investors for their missing voting rights. Second, an entrepreneur could just sell less than 50% of his company s equity. But in some special cases this might imply, that the planned investment has to be detruncated to a suboptimal level. Another way to realize the optimal investment amount is to sell shares overpriced increasing the probability of not getting any investment at all. 16 Zingales (1994): p.131 17 Brennan and Franks (1997): p.395/396 18 https://www.seedmatch.de/faq (15/2/2012) 6

For the following analysis it assumed, that an entrepreneur will not sell non-voting shares and that he is forced to sell more than 50% of his company s equity. So the entrepreneur keeps less than 50% of the shares that is < 0.5. In such a situation the entrepreneur could be forced to leave the company s management by external investors. But this will only happen, if the non-managing shareholders think, that a change of the management will increase the shareholder value significantly. It is assumed here, that a shareholder value increasing change of management will not voluntarily be realized by the founder of the firm, since he realizes so called benefits control. These benefits of the entrepreneur s role as a manager work as an overcompensation for losses due to potentially suboptimal management of the entrepreneur, that is > -. The variables and describe the value of the firm under new management and under the management of the entrepreneur. Benefits of control can arise for example through the wage of the manager but also through non-monetary benefits like prestige 19. Transferring the argumentation of Shleifer and Vishny (1986) the probability of an entrepreneur being removed from the management particularly depends on the monitoring incentives of the biggest external investor. Shleifer and Vishny (1986) use the simplifying assumption that a change of management can only be realized if an external investor owns at least 50% of a firm s equity 20. So in their model two conditions must be fulfilled to realize a change of management: First, the biggest external investor must perform costly monitoring verifying suboptimal management by the entrepreneur, and second, the biggest external investor must own at least 50% of the shares. The expected utility from monitoring of an investor, initially not involved in the company s management, is 21 : E[ (I, )] = I[0.5( - ) (0.5 - ) ( ) - - ] (2) Formula (2) describes the expected utility from monitoring-intensity I to the biggest external investor owning < 0.5 before the takeover. The monitoring intensity I can be interpreted as the probability, that a systematic management mistake is detected resulting in the removal of the entrepreneur from the management. 0.5( - ) describes the expected payoff to the biggest external investor from taking over the company and replacing the management. This investor can only form expectations about potential profits from changing the management, since the actual 19 For example Moskowitz and Vissing-Jorgensen (2002): pp.771 ff. describe several monetary and nonmonetary returns of entrepreneurial activity besides pure dividends, which seem to be the motivation for becoming an entrepreneur. 20 Shleifer and Vishny (1986): on p.465 the authors assume, that only the biggest external investor has access to the monitoring technology. So the outcome of the assumption formulated here and the assumption in the source is essentially the same. 21 Shleifer and Vishny (1986): Formula (3) on p.469. Since expectations only need to be formed about variable Z, the formula has been changed in this way. Moreover here was assumed that E[ (I, )] can be negative. Besides that monitoring costs, mentioned in Vishny and Shleifer (1986) on p.465, were also included in the formula. 7

appreciation of value is not definite before the beginning of monitoring 22. The variable ( ) describes the minimal premium in excess of the value per share under the old management of the entrepreneur. Buying more shares to increase his share of the firm to 50%, the biggest external investor has to pay this price premium, since other external (atomistic) investors anticipate the future appreciation of value. Shleifer and Vishny (1986) assume that the price premium ( ) is negatively related to, since the bargaining power of the biggest investor should increase with 23. The fixed costs of a takeover are illustrated by, including legal and administrative costs. Variable displays the costs of monitoring. Now it is decisive to understand, that the marginal net benefit of increased monitoring is positively related to : = 0,5E(Z) (0,5 - ) ( ) - - - I = 0 (3) The marginal gross benefit of monitoring is 0,5E(Z) = 0.5( - ) and the marginal costs of monitoring are (0,5 - ) ( ) - - - I. So you can see that the marginal net benefits of monitoring are inversely related to the size of (0,5 - ) ( ). The term (0,5 - ) displays, how much percent of the firm s equity must be sold by the biggest external investor, to realize a change in management. So obviously (0,5 - ) is inversely related to. As we have seen the term ( ) is inversely related to. So as you can see, the marginal net benefit of monitoring will increase with growing. So formula (3) says that the probability of the entrepreneur losing his role as the lead manager of the firm is positively related to the share of the biggest external investor. But since the entrepreneur is interested in his benefits of control, it is decisive for him, that a crowdinvesting-platform implements a rationing mechanism, that maximizes the dispersion of shares among investors or at least avoid the formation of big blocks of external investors. Shleifer and Vishny (1986) portray a high degree of monitoring as generally positive. But it is obviously not in the interests of the old management. This motivated Brennan and Franks (1997) to develop an underpricing theory, where firms going public use underpricing to generate excessive demand to realize a dispersed ownership structure. So managers of these firms use underpricing, to protect their control. The same might be true for firms selling equity via crowdinvesting-platforms. So if entrepreneurs faced with a fixed rationing mechanism use underpricing as a tool to dispersed external ownership and protection of their control, then consequently a rationing mechanism implying maximal dispersion of shares will lower the required underpricing. This line of argumentation might be dubious to some readers. If you assume, that entrepreneurs do not realize any benefits of control, an optimal strategy of an entrepreneur would be attracting just one 22 Shleifer and Vishny (1986): p.456/466. The appreciation of value caused by the replacement of the management Z = + is drawn from the cumulative distribution function F(Z) limited to the interval (0, ]. 23 Shleifer and Vishny (1986): Lemma 1 on p.468. 8

big investor, because the maximized monitoring will maximize the shareholder value. This motivated Stoughton and Zechner (1998) to develop a model contrary to Brennan and Franks (1997). In their model of IPO-underpricing firms use underrated issue prices to attract one big investor implying maximal monitoring. Nonetheless in the context of crowdinvesting-platforms it is plausible to assume, that a major motivation for young entrepreneurs is the realization of benefits of control. This is in line with empirical evidence. Neuberger, Räthke and Bruder (2007) have conducted a survey showing that the main motivation to become an entrepreneur is the implied independence of being your own boss. By implementing a rationing mechanism that does not protect this elementary motive the participation of entrepreneurs on these platforms is jeopardized. This makes the protection of the benefits of control of the entrepreneurs a decisive participation constraint and leads to following criterion 2: Criterion 2: The rationing mechanism of a crowdinvesting-platform should imply a maximal dispersion of shares to reduce the probability of a loss of control of the initial entrepreneurial team. 2.2 Protection of informational disadvantaged investors It is plausible to assume that not all investors, who buy shares on crowdinvesting-platforms, have got access to the same information. Some investors might have informational advantages for example because they got superior knowledge about a certain industry or geographical area. It is well known that there is informational heterogeneity among investors participating in IPOs. An experienced institutional investor should have an informational advantage compared to an inexperienced retail investor. Rock (1986) tries to illustrate this situation by assuming two types of investors participating in an IPO: informed and uninformed investors. Informed investors can observe the true value of a firm, while uninformed investors can only form uncertain expectations. Another central assumption of Rock (1986) is that the emitter is also uninformed. The justification for this assumption is that the emitter loses his initial informational advantage by disclosing all information in the context of the IPO. Without an precise knowledge of the true value of his firm, the emitter has to form expectations as well when choosing the issue price. Consequently the chosen issue price could be higher or lower than the price implied by the true firm value. The behavior of an informed investor in this setting is trivial. If the issue price is higher than the true value, an informed investor will not buy any shares. But if the issue price is lower than the true value, he will buy shares. But this kind of behavior has a negative impact on uninformed investors. When an uninformed investor wants to buy underpriced shares, the probability of being rationed is comparatively high. The reason for this is the fact, that underpriced shares are not just demanded by uninformed investors, but by informed investors as well. So the probability of excessive demand and required rationing is comparatively high. When an uninformed investor applies for overpriced shares, the probability of rationing is comparatively low, since informed investors abstain from buying these shares. 9

The expected utility of an uninformed investor from participating in an initial equity offering is 24 : = p( > ) E[U( ( - )) > ] (4) + p( ) E[U( ( - )) ] with <. The realized utility of an uninformed investor implied by allocation depends on the difference between the true value V and the issue price. The variables p( > ) and p( ) display the probabilities that the (estimated) true value of a share is stricty bigger or less (or equal) than. Variables and are the estimated probabilities of an uniformed investor receiving an allocation of underpriced or overpriced shares. It is decisive to understand, that the disadvantage of uniformed investors does not arise from rationing in general, but from the bias in rationing, that is from the fact that < 25. If uninformed investors were rationed equally in case of underpriced and overpriced issues, the profits and losses were balanced. But the problem here is that in an extreme scenario uninformed investors applying for overpriced shares are possibly not rationed at all ( = 1), while uninformed investors applying for underpriced shares are completely rationed ( 0). The consequence will be that uninformed investors will abstain from buying shares in an initial offering at all. In Rock s (1986) model the participation of uninformed investors is necessary to guarantee the successful conduct of equity issues, since informed demand is not big enough to absorb the whole supply of assets 26. So emitters have to choose an issue price, low enough to compensate uninformed investors for the allocation bias. Implementing this underpricing strategy optimally, uninformed investors should realize zero-profits from participating in the issue market. There is convincing evidence for the theory of Rock (1986). Levis (1990) examined 123 IPOs conducted at the London Stock Exchange between 1985 and 1988. An investor hypothetically buying shares worth 500 in each IPO would have earned an excessive return of 8.14%, if you assume a rationing of 0% in every IPO 27. But accounting for the actual allocation probabilities of each IPO such a hypothetical investor only earned 1.67% 28. So the empirical results are in line with the theory, that underpricing is chosen, to guarantee the participation of uninformed investors. Further empirical articles, like Koh and Walter (1989), Amihud, Hauser and Kirsh (2002) or Keloharju (1993) have conducted analogous studies using data from other stock exchanges without getting results in stark contrast to Rock s (1986) theory. 24 Rock (1986): Equation (3) on p.193. The notation of Rock (1986) has been modified to be match the notation used in the rest of this paper. Moreover I have assumed that uninformed investors do not have an outside option of buying riskless assets, implying that an uninformed investor does not realize positive utility in case of rationing. 25 Rock (1986): p.194 26 Rock (1986): Assumption 3 on p.191. 27 Levis (1990): p.81. The initial excessive returns describe the relative price increase per share minus the market return. 28 Levis (1998): p.84. 10

While Rock (1986) justifies the necessity of the participation of uninformed investors, by assuming the informed demand is not big enough to absorb the whole supply, this assumption is not appropriate for crowdinvesting-platforms. But as was shown in the preceding chapter 2.1 there are major benefits of a broad investor base. To realize these benefits it is necessary to make sure, that informational disadvantaged investors participate on such platforms as well. The used rationing mechanism of Crowdcube.com for example is not able to achieve this goal. The reason for undesirable discrimination of informational disadvantaged investors is that an experienced investor observing underpriced shares can buy all available shares triggering a stoppage of the financing period. If the informational advantage of these investors takes the form of a quicker evaluation process, this scenario is quite likely. The problem is even more severe, if informational advantaged investors are on average wealthier. This assumption is plausible, because you are only able to develop superior investment experience, if you have got more money to invest. So if wealthier and more experienced investors with superior information invest faster, informational disadvantaged investors will no longer participate in the market, since all the corporate shares left over for them will be overpriced. A strategy of random bidding by informational disadvantaged investors as a respond to their comparatively slow evaluation process, will not generate nonnegative profits if a critical number of bad projects reach the investment target making their investment binding. The main argument of Rock (1986) was that for a given rationing mechanism emitters have to underprice their shares to make sure, informational disadvantaged investors participate. But if you have to choose a rationing mechanism instead, you should implement a mechanism not discriminating against informational disadvantaged investors, who should be comparatively small and slow investors. This leads to the following criterion: Criterion 3: The rationing mechanism of a crowdinvesting-platform must not discriminate against comparatively small and slow investors, to guarantee their participation. 2.3 Compensation of initial investors These investors, who are first to invest on a crowdinvesting-platform, differ from the successive investors in two aspects. First, these investors are faced by bigger costs of information production. Second, initial investors have a comparatively big impact on the probability of a successful funding, since their investment implies a positive external effect on other investors. 2.3.1 Costs of initial investors In the beginning of a financing period on a crowdinvesting-platform investors are faced with a problem. Every investor has to decide whether the sold shares are good or bad, that is whether they are underpriced or overpriced. To answer this question, investors will incur a time-consuming evaluationprocess. 11

In a way investors are faced with a free-rider problem. As an investor you could choose a strategy to exclusively invest in projects that have been positively evaluated by other investors identifiable by the investments of preceding investors. This kind of strategy would eliminate or at least reduce the individual costs of information production. Assuming it is individually optimal to leave the costly evaluation process to other investors an equilibrium with no information production and no investment at all will evolve. To overcome this socially undesirable equilibrium it is necessary to create some incentives to produce information. One possible incentive would be a preferential allocation of shares to an initial investor. It was shown in chapter 2.1.1 that the aggregate costs of information production C(n) should be an increasing function with decreasing slope. This implies the highest individual costs of information production for the first investor with > > >. Assuming underpriced shares and consequently excessive demand for shares, the expected profit of the first investor is: E( ) = E[ ( - )] - (5) Again describes the probability that the initial investor receives the desired allocation of the company s equity. The problem is: If E( ) < 0, no potential investor will produce information. To create incentives for information production, you could guarantee initial investors a fixed allocation compensating them for their disproportionately high costs of information production. In this case, the expected utility of an initial investor would rise to E( ) as a consequence of the preferential treatment: E( ) = E( - ) + E[ )( - )] - with (6) The fixed allocation does not mean that initial investors get an allocation for free. The variable just says that a certain amount of initial investors demand is not rationed in case of excessive demand. For example =10% implies the individual demand of investors contributing the first 10% of the investment target will not be rationed up to this threshold. If this threshold is reached by five investors each contributing 2% of the investment target, these investors are not rationed at all. If one individual investor contributes for example 20% > of the assets first, then one half of his demand will not be rationed, while the other half will be rationed like the individual demands of successive investors. 2.3.2 Positive external effects by initial investments The following chapter 2.3.2 will describe the comparatively high importance of investment pioneers for a successful funding. In this context it is important to understand, that there are not just monetary motives for investment, but non-monetary motives as well. Initial investors increase the probability that successive investors will satisfy both kinds of motives. These positive external effects justify a preferential treatment of initial investors. 12

Positive external effects on investors with monetary motives An initial investor creates an incentive for successive investors with monetary motives to invest as well. This incentive arises for two reasons. First, an initial investment includes some positive information about a firm s return prospects. Assume there are two entrepreneurial projects trying to raise funds on a platform with an identical investment target and the same time left until the end of the financing period. Then an investor will plausibly assume that the project, that has been able to attract more investors so far, will be more attractive implying a higher expected return. So an investor, who is indifferent after independently evaluating two projects, will decide to invest in the project that attracted more investors so far. The second positive externality on successive investors with monetary motives arises, because the investment of the initial investor might actively change the return-risk-profile of a supported company. As we have seen in chapter 2.1.2 external investors have disciplining impact on the firm s management 29. The reason for that is the fact, that external investors will scrutinize the management s decisions. The inclusion of external investors can even increase a firm s human capital, if the initial entrepreneurial team is willing to use the investors knowledge. For example an experienced lawyer investing in a firm with a young entrepreneurial team could reduce the legal cost of this firm. So if the parties manage to make an external investor an internal member of the firm, an initial investment will not just imply a positive evaluation of the pre-issue firm, but it might also improve the prospects of the post-issue firm. So the described external effects of initial investors should increase the willingness of successive investors to buy shares as well. Consequently, initial investors should be treated preferentially in case of excessive demand to account for their disproportionately high positive impact. Positive external effects on investors with monetary motives To explain the positive external effect on investors with non-monetary motives implied by initial investments, it is necessary to include an excursion about science and practice of charitable funding now. Excursion: Behavior of individuals in the course of donation campaigns Comparing the entrepreneurial projects trying to raise money on crowdinvesting-platforms like Crowdcube.com with the noncommercial projects trying to raise money on charitable crowdfundingplatforms like Mysherpas.com you might be surprised of the lack of differences. On these last named donation platforms for example artists, musicians or caterer are trying to attract financial support. Assuming a world of individuals with exclusively monetary investment motives, it is puzzling that some 29 Chapter 2.1.2 used the argumentation of Shleifer and Vishny (1986), that external investors will monitor the management. 13

projects on these platforms have ever been able to realize a successful funding. This is puzzling, because the financial support takes place in the absence of financial rewards for investors. Human behavior in the course of donation campaigns is illustrated in the academic literature by analyzing private individual contributions to a public good. A pure public good is characterized by two characteristics, namely no rivalry in consumption and non-excludability from the consumption of this good. A classical example of a pure public good is environment protection. Now the behavior of individuals in course of donation campaigns is explained by illustrating the theoretical model of Andreoni (1998) in a formally simplified way. Assume there are two individuals i and j owning identical endowments =. Each of these individuals can use its endowment to contribute or to the public good. Andreoni (1998) assumes that the public good only generates utility if a certain threshold is passed. The utility individual i derives from the consumption of the private good and the public good G is 30 : = (7) Formula (7) says that each individual realizes a positive utility by consuming its private good or and the public good G. But the public good will only generate a positive utility, if the threshold passed. is Understanding the further analysis requires the understanding of two further variables. First, the variable, which is the biggest value of resulting in individual i being willing to provide the threshold of the public good on his own. That is, even if individual j does not contribute anything, individual i would make an individual contribution big enough to pass. Formally this means that id the solution of the following equation 31 : ( -, ) (,0) (8) Formula (8) says that individual i is indifferent between contribution, resulting in G =, and a contribution of 0 resulting in G = 0. The difference of the endowment and the individual contribution is the individual consumption of the private good. The second important variable is, which is only relevant in sequential contribution games. Assume a sequential two-staged game with individual j making a contribution in the first stage and individual i making a contribution in the second stage. The is the lowest contribution of individual j on the first stage guaranteeing that individual i on the second stage will make a contribution sufficient to pass the threshold. That is, is the solution of the following equation 32 : 30 Andreoni (1998): The illustrated formula is a combination of the optimization problem of an individual on p.1191 and the distinction of cases for public goods with threshold on p.1192. 31 Andreoni (1998): p.1193 32 Andreoni (1998): p.1196 14

( + -, ) (, 0) (9) Formula (9) says that individual i will be indifferent between a contribution of = - and zero contribution. Contributing - individual i would consume = - + of the private good, while without a contribution it could use its whole endowment for the consumption of the private good. Now presume a simultaneous contribution game for the moment. If and are strictly smaller than, no individual will make a contribution sufficient to provide the necessary amount of the public good to pass. In such a situation there exists an equilibrium implying that the threshold is not passed. The reason for the existence of this equilibrium is the fact, that it is optimal for individual i not to make any contribution if it expects that individual j will make a contribution smaller than. This socially undesirable equilibrium can definitely be avoided in a sequential game. Assume again that individual j makes its contribution on stage 1, and individual j observes this contribution before choosing its own contribution on stage 2. If individual j chooses a contribution of = it is guaranteed that individual i will contribute the remaining amount to pass the threshold, that is individual i will contribute = - 33. Notice that this could require individual i to make a much bigger contribution than the first contributing individual j as long as > /2. As you can see, the contribution on the first stage, named seed-money by Andreoni (1998), can guarantee that at least the threshold amount of the public good will be provided. That is, seedmoney increases the probability of a successful funding. The behavior of successive donators can be described as conditionally cooperative : Presuming individual j makes a sufficient contribution in stage 1, individual i will also make a contribution as well. The positive influence of seed-money on other individuals is empirically proven. In a field experiment List and Lucking-Reiley (2002) contacted 3000 households, to ask for a donation for the local university. The authors manipulated the call for donations in the following way: In one third of calls for donations it was written that 10%, 33% and 67% of the fixed funding target has already been collected. For example, the increase of seed-money from 10% to 33% increased the share of households making a contribution from 3.4% to 8.4%. At the same time the mean donation amount grew from $11.88 to $35.36 34. End of excursion Donation platforms like Mysherpas.com try to use the positive external effect of seed-money by displaying the share of the funding target that has already been contributed at any time of the funding period. The same is true for crowdinvesting-platforms. By displaying the amount of money that has already been invested you increase the willingness to cooperate of all investors with charitable motives of investment. An example is investors buying shares of a company producing solar 33 Of course this result implies that individual i chooses a contribution in case of the indifference described in equation (9). 34 List and Lucking-Riley (2002): Table 1 on p.221 15

collectors. The motive of such an investment usually is not exclusively the expectation of comparatively high returns, but one main motive seems to be the implied protection of environment. This positive environmental externality can be seen as a public good justifying the preceding analysis. Return to initial investors on crowdinvesting-platforms: If the set of potential investors of a firm includes some investors with non-monetary motives, the investment of initial investors will increase the mobilization of these types of investors. The early investments decrease the probability of a social undesirably free-rider equilibrium to evolve. So since the initial investors have a strong positive impact on the dynamics of a funding, they should be rewarded with a preferential treatment in case of excessive demand and rationing. At the same time the assumption of charitable investment motives makes another characteristic of the market design reasonable. If all investors have got exclusively non-monetary investment motives and you guarantee a fixed allocation of shares to an initial investor, you would force him to make a comparatively high contribution. So to avoid a punishment for first-contributors you should make the fixed allocation optional. Consequently, investors with non-monetary motives will abstain from using that option resulting in lower contribution, while investors with monetary investment motives will make full use of this option to get the maximum of available shares. To sum up: It is difficult to get a funding started for several reasons. This makes the investments of the early investors very valuable to the entrepreneur trying to raise money. This requires offering some preferential treatment to initial investors, leading to the following criterion: Criterion 4: The rationing mechanism of a crowdinvesting-platform must compensate initial investors for their comparatively high costs of information production as well as their disproportionate positive impact on a successful funding. 16

3. Conflicting implications of mentioned criteria The described criteria of an optimal rationing mechanism are meant to protect the interests of the parties involved in the funding process on a crowdinvesting-platform. Unfortunately it is not always possible to realize a maximal protection of one party without violating the interests of another party. This chapter describes arising conflicts and discusses reasonable compromises. The main arising conflict is between the compensation of initial investors on the one hand, and the realization of benefits of a broad investor base. As we have seen, initial investors need preferential treatment in case of excessive demand and rationing, because otherwise investors could be stuck in a an equilibrium with no investment at all, since no individual investor will be willing to incur the highest individual costs of information. But there is a problem, when you treat initial investors preferentially. It is quite plausible to assume that early investors and informational advantaged investors are the same due to a presumably fast evaluation process of informational advantaged investors. So by rewarding informational advantaged investors, you discriminate against informational disadvantaged successive investors. But by discriminating informational disadvantaged investors, you will increase the probability that these investors abstain from the market. If informational disadvantaged investors abstain from the market, the investor base will decrease. But we have seen that a big investor base is particularly important, to increase the liquidity and consequently the resulting market value of a firm s shares as well as protecting the interests of the initial entrepreneurial team. So the goal of protecting informational disadvantaged investors and the realization of a broad investor base coincide and are both in conflict with the reward of initial investors. To get closer to a solution of this problem, you have to take a closer look at the two mainly conflicting criteria, namely the reward of initial investors and the realization of the benefits of a broad investor base. To start the dynamics of a successful funding, initial investors have to be rewarded. But once you triggered the necessary dynamics, there is no further need for compensation of early investors. So you can describe this criterion as a criterion that needs to be satisfied, but not maximized. That is not true for the benefits of a broad investor base. It was assumed that the value of shares traded on the secondary market is positively related to the number of investors. Even though we assumed a decreasing positive slope of the function of this relationship, it remains a growing function. That is, the goal of a rationing mechanism of the platform should be a maximization of this liquidity criterion, instead of a satisfaction. So to summarize this argument, when choosing the design of a rationing mechanism the following rule should be applied: Reward initial investors as much as necessary, and maximize the resulting investor base. 17

4. Rationing mechanisms for practical purposes The purpose of the following chapter is to construct a mechanism satisfying the theoretical criteria mentioned in chapter 2. In the first part of this chapter, practical features able to fulfill the mentioned theoretical criteria are listed. In the second part of this chapter an illustrating example is presented. 4.1 Practical features of an optimal rationing mechanism An optimal rationing mechanism for practical purposes must include three features. First, such a mechanism should include a Zero-Rationing-Threshold described later. Second, beyond that threshold the shares should be rationed in way maximizing a firm s ownership structure. Third, a mechanism should include a soft-ending of the financing period. 4.1.1 A Zero-Rationing-Threshold We have seen that an optimal rationing-mechanism should compensate initial investor for their comparatively high individual costs of information production as well as their positive impact on succeeding investors. For that reason a different rationing treatment of initial investors is necessary. Unfortunately the goal of initial investors compensation is in conflict with protection of informational disadvantaged investors and the goal of a maximized investor base. So you have to draw a plausible line between these conflicting goals. One easily traceable implementation is a Zero-Rationing-Threshold already indicated in chapter 2.3.1. This idea can be demonstrated using the before mentioned example of = 10%. This value of implies that the investors contributing the first 10% of the investment target will not be rationed up to this threshold. If the initial investor contributes = 20%, one half of his individual demand will not be rationed at all, while the other half will treated in the same way as the individual demand of any successive investor. If = 10% his individual demand would be completely satisfied. What is a sensible value of in practice? Lacking an appropriate unified model you cannot choose a mathematically optimal Zero-Rationing-Threshold here. Following basic economic rules an optimal threshold will be achieved when marginal benefits of rewarding initial investors equals the marginal costs of their reward. But even with a mathematical model at hand, the practical implementation of this rule would be quite difficult. So some further considerations seem to be more promising in defining a plausible interval for. Since we have seen that an optimal rationing mechanism should protect a company s initial managements control, an upper bound of a threshold of 50% seems plausible. If you assume the extreme scenario of a firm selling 100% of its equity, a threshold strictly smaller than 50% will definitely avoid the situation described by Shleifer and Vishny (1986) where one external investor gets control of more than one half of the company s shares. 18

But it is even harder to find an sensible lower bound for. Since we have seen that investors also have non-monetary motives, the practical donation literature can be useful. An interesting rule of thumb found in an adviser for donation campaigns is the following: Seed-money of at least 20% of the donation target is necessary for a successful funding 35. So it seems as if positive external effects on successive investors with non-monetary motives can only be realized if initial investment is bigger than 20% making this value a sensible lower bound. But of course the implementation of this rule of thumb is far from being academically satisfying. At the same time it remains unclear, whether such a threshold is sufficient compensation for the costs incurred by initial investors. To sum up, an optimal Zero-Rationing-Threshold will be in the interval [0.2; 0.5]. Further research is necessary to get to a more exact specification. 4.1.2 Investor base maximizing rationing beyond the Zero-Rationing-Threshold After allocating the shares inside the Zero-Rationing-Threshold to initial investors, the remaining supply of shares, that is = 1 -, should be allocated in a way implying a maximal diffusion of shares. This feature of a rationing mechanism is meant to realize the benefits of a broad investor base. The first iteration of this allocation process beyond the Zero-Rationing-Threshold is to completely satisfy the smallest individual demand. At the same time the remaining n-1 investors should also receive an allocation of. Of course this is only attainable if the following condition holds: - n = 1 - - n 0. (10) Formula (10) says that the described allocation will only be attainable, if the remaining supply of shares is bigger than the shares necessary for the aggregate allocation n of this iteration. If condition (10) does not hold, implying < n, the remaining supply of shares should be distributed equally to all investors. In such a situation every investors would receive = /n of the company s shares. Remember that initial investors would receive this allocation additively to their shares guaranteed by the Zero-Rationing-Threshold. If condition (10) sill hold holds after the first iteration, the same iteration will be applied for a second time. This implies that the second lowest individual demand will be completely satisfied. So this investor receives a further allocation of - in the second iteration. The same is true for the remaining investors with still positive individual demand. As before, this iteration is only attainable, if: (n 1)( ) = 0. (11) 35 Why you don t need the 800-pound gorilla by Robert F. Hartsook: http://www.allbusiness.com/humanresources/employee-development-leadership/451976-1.html (2/20/2012) 19

If this condition does not hold, the remaining supply will be distributed equally to the remaining n-1 investors still having a positive individual demand. In this scenario every investor, except the smallest investor whose individual demand has been completely satisfied in iteration 1, will receive an additional allocation of = /n = - n )/(n-1). The described allocation mechanism can be continued until all shares are distributed. Taking a look at the formulas of chapter 4.1.2 might create the impression of a complex rationing mechanism, but this not true. As long as possible, the individual demand of the smallest investor with a positive remaining individual demand will be completely satisfied and this allocation will also be given to the other investors. Once this is no longer attainable, the remaining supply of shares is distributed equally to the remaining investors. 4.1.3 Soft-Ending of the financing period As we have seen, another goal of an optimal rationing mechanism is the protection of informational disadvantaged investors to guarantee their market participation. The threat of eliminating informational disadvantaged investors reaches its maximum, if one wealthy informational advantaged investor has the opportunity to buy all shares at once. So if the financing round would end immediately once 100% of the investment target is reached, the elimination of informational disadvantaged investors would be very likely. To make sure the reader understands this argument, an illustrating example is described here. Imagine there are two projects on a crowdinvesting-platform: One project is good implying underpriced shares, while the other one is bad implying overpriced shares. Assume both projects have the same time left until the definite end of the financing period. Assume further the financing round will close once 100% of the investment target is reached. New investors observing the project differ in their speed of evaluation: Informational advantaged investors can evaluate a project faster than informational disadvantaged investors. In the described situation a wealthy informational advantaged investor will use all of his available funds to buy shares of the good project. If he is wealthy enough this will close the financing round immediately. An informational disadvantaged investor can no longer buy underpriced shares now, but he is exclusively faced with overpriced shares. A rational but informational disadvantaged investor will anticipate this situation and will no longer participate in the market 36. This discrimination of informational disadvantaged investors is a result of the hard ending of financing periods implemented by some platforms, for example Crowdcube.com. If you want to protect informational disadvantaged investors, you have to allow them to invest in projects that already have 36 If the informational disadvantage takes the form of a slower evaluation process, these investors could choose a strategy of investing a constant amount in every available firm without an evaluation. But if firms selling overpriced shares are able to reach 100% of their investment target, then this strategy can generate losses on average. 20

reached the 100% investment target. This gives them the opportunity to wait for positive signals of experienced investors before investing. The question, what is the optimal form of a soft ending of a financing round, cannot be answered academically satisfying here. One idea is to continue the financing period for two weeks once the 100% investment target has been reached. The resulting excessive demand is rationed in a publicly known way. By constructing an optimal mechanism you have to account for the fact, that there are opportunity costs for all the investments contributed so far. So an appropriate soft ending of the financing period should imply a manageable period of time respecting the tradeoff between, protection of informational disadvantaged investors one the one hand, and, opportunity costs on the other hand. 4.2 Illustrating example for a practically applicable rationing mechanism In the following chapter the described desirable features of a rationing mechanism will be illustrated using an example depicted in table1. Investors 1 to 7 successively formulate their individual demand (beginning with investor 1) for perfectly divisible shares each costing 1. Investor 1 transfers 50 to the platform expressing an individual demand for 50 shares. Investor 2 transfers 80 expressing an individual demand for 80 shares. Since the aggregate demand of these two investors exceeds the aggregate supply of 100 shares, the soft ending of the financing round is triggered. The soft ending implies a continuation of the financing period for a pre-specified period of time, for example two weeks. In contrast to experienced investors 1 and 2, the unexperienced investors 3 to 7 wanted to wait for positive signals by the market first. These investors now formulate their individual demand for shares before the ultimate ending of the financing period. The individual demand of these investors varies between 5 and 60 shares. Once the ultimate end is reached, the rationing process begins. First, the initial investor 1 is rewarded for his pioneer investment by receiving = 20 shares implied by the Zero-Rationing-Threshold. The remaining 80 shares are now allocated in an iterative process. The smallest individual demand of investor 6 is = 5. Implementing a rationing mechanism that maximizes the investor base and protects small investors, the individual demand of investor 6 is fulfilled completely. All other investors also receive an allocation of 5 shares in this iteration process. Notice that the initial investor 1 also receives a further allocation of 5 shares, since the remaining individual demand is decisive for this process and not the individual allocation guaranteed so far by the Zero-Rationing-Threshold. In the second iteration the individual demand of the second smallest investor 7, asking for = 15 shares, should be fulfilled completely. But there is a problem: If you want to increase the allocation of every investor by = 10 shares, the remaining supply of = 0.45 percent of the firm s equity is not sufficient to realize this process. This is the trigger of the final iteration process. 21

Table 1: Illustrating example of a rationing mechanism with a Zero-Rationing-Threshold, a soft ending and diffusion of ownership maximizing rationing beyond the Zero-Rationing-Threshold. Investors (in chronological order) Individual demand (number of shares) Received allocations Zero-Rationing- Threshold: = 20% Allocations after the first iteration process Allocations after the second iteration process Allocations after the third iteration process 1 50 20 20+5 = 25 25+10 = 35 25+7,5 = 32,5 2 80 0 5 5+10 = 15 5+7,5 = 12,5 Trigger of the soft ending 3 40 0 5 5+5 = 15 5+7,5 = 12,5 4 60 0 5 15 12,5 5 30 0 5 15 12,5 6 5 0 5 5 5 7 15 0 5 15 12,5 Ultimate End of the financing period Sum 310 20 55 115 > 100 100 Since there are not enough shares to allocate 10 shares to each of the six remaining investors, the still available shares are distributed equally among them. Consequently every investor receives (1 - - 6 /(n - 1) = 7.5 further percents of the firm s equity. The resulting complete individual allocations are depicted in table 1. 22

5. Upcoming research The analysis so far was meant to formulate recommendations for the actual market microstructure of crowdinvesting-platforms based on available academic literature. The topic of this chapter is to describe what a unified mathematical model of a rationing mechanism with the mentioned features had to include and which further research questions arise. A mathematical model depicting the rationing mechanism of a crowdinvesting-platform first of all had to choose an appropriate objective function. The objective of a crowdinvesting-platform is to maximize its expected profit by choosing an optimal rationing mechanism. Assuming a fixed and optimal investment target of each entrepreneurial project trying to raise money on a platform, the objective reduces to a maximization of the probability of successful investments. By maximizing the likelihood of a successful funding, a platform maximizes its expected profits, since these platforms usually ask for a fixed percentage of the investment target as a fee, but only in case of a successful funding. Modeling differing costs of different rationing mechanisms is possible, but is no priority. Such model must be able to depict the calculus of a platform facing different types of investors as well as entrepreneurs. Criterion 2, meant to protect the control of the founders, must be modeled as a participation constraint of entrepreneurs. Criterion 3, meant to avoid an allocation-bias of informational disadvantaged investors, must be modeled as a participation constraint for this type of investors. Criterion 4, meant to reward initial investors, must be modeled as participation constraint for informational advantaged investors. To replicate the described dynamics of a financing period the model has to include at least two stages. On the first stage informational advantaged investors would produce information and make an investment decision. On the second stage informational disadvantaged investors observe the preceding investments and make their investment decision. For the sake of convenience you could assume simultaneous investment on each stage. The complexity of the model will probably be increased severely, if you try to account for investors with non-monetary motives as well. Then you had to include methods able to illustrate the private provision of a public good within the described market microstructure framework. Further questions will arise in such a framework. For example, do investors with charitable motives crowd-out investors with pure monetary motives and informational disadvantages, since the allocation probability will decrease? At the same time, investors with non-monetary motives will dilute the signals of informational advantaged investors, because it is no longer possible to interpret contributed investments as an exclusive signal for promising return prospects. Another important question is: How does a Zero-Rationing-Threshold affect the likelihood of a successful funding? To answer this question, you need to be able, to illustrate the impact of such a threshold on the behavior of informational advantaged investors on the one hand, and informational disadvantaged investors on the other hand. The aggregate demand of both types of investors would 23

depend on their size as well as their financial endowment, making further theoretical assumptions necessary. 24

6. Conclusion The rationing of excessive demand conducted on crowdinvesting-platforms at the moment is not optimal. The used rationing mechanism is best described by first come, first served. This mechanism is not optimal for several reasons, especially for the implied discrimination of informational disadvantaged investors. At the same time this procedure does neither maximize the investor base nor the liquidity of the traded assets. An optimal mechanism has to guarantee the participation on the crowdinvesting market by all involved parties. The interests of the founders hoping to keep the control of their company have to be accounted for, as well as the interest of initial investors facing comparatively high costs of information production and having decisive impact on funding dynamics. The mechanism described here will be a major progress compared to the mechanisms in use at the moment. At the same time further research needs to be done, to develop a unified mathematical framework able to depict the mentioned arguments. Further academic progress will take the form of theoretical and experimental contributions in the near future, since the young age of these platforms avoids immediate empirical applications. 25

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