Journal of Financial Intermediation 11, 9–36 (2002) doi:10.1006/jfin.2001.0319, available online at http://www.idealibrary.com on IPO Auctions: English, Dutch, . . . French, and Internet∗ Bruno Biais Université de Toulouse, IDEI, Place Anatole France, 31200 Toulouse, France and Anne Marie Faugeron-Crouzet Université de Paris Val de Marne, 61, avenue du Général de Gaulle, 94010 Créteil Cedex, France Received December 6, 1999 Unseasoned shares are sold through the Book Building process in the United States and the United Kingdom, fixed price offerings in several countries, uniform price auctions in Israel or the new internet-based Open IPO mechanism, and an auction-like mechanism called the Mise en Vente in France. We analyze and compare the performance of these various IPO mechanisms within the context of a unified theoretical model. Fixed price offerings lead to inefficient pricing and winner’s curse. Dutch auctions can also lead to inefficiencies, to the extent that they are conducive to tacit collusion by investors. The Book Building and Mise en Vente can lead to optimal information elicitation and price discovery. We document empirically the similarity between the Book Building and the Mise en Vente. We discuss the implications of our analysis for the design of optimal Internet IPO auctions. Journal of C 2002 Elsevier Science (USA) Economic Literature Classification Numbers: G24, G3, D82. ∗ Many thanks to Tom Chemmanur and the two referees for helpful comments, and to the Paris Bourse for financial support, access to data, and many insights, especially Jacky Billard, Martine Charbonnier, Didier Davydoff, Dominique Leblanc, Bernard Mirat, Alain Morice, and Pascal Samaran. We are also grateful for helpful discussions with Michael Fishman, Jean–Pierre Florens, Julian Franks, Sylvain Friedrich, David Goldreich, Richard Green, Michel Habib, Shmuel Kandel, Kjell Nyborg, Pegaret Pichler, Jean Charles Rochet, Chester Spatt, Bill Wilhelm, Luigi Zingales, and seminar participants at the University of Chicago, the London Business School, the London School of Economics conference on trading markets for smaller companies, the Utah Winter Conference, the CEPR Summer Symposium on Financial Economics, the conference “Raising Capital in Different National Markets” in Frankfurt, the 2000 Meetings of the American Finance Association and the Journal of Financial Intermediation Conference on New Technologies, Financial Innovation and Intermediation at Boston College. 9 1042-9573/02 $35.00 c 2002 Elsevier Science (USA) All rights reserved. 10 BIAIS AND FAUGERON-CROUZET 1. INTRODUCTION One of the major benefits of public listing on stock exchanges is the rich flow of information, about the firm’s prospects and the investors’ willingness to hold its shares, that is reflected in prices and trades in the secondary market. Prior to the IPO very little such information is available. Consequently, the task of finding the IPO price is a difficult one. The auction by which the unseasoned shares are sold can therefore play an important role in eliciting information from the market participants about their valuation of the stock. Yet IPO auction mechanisms vary quite significantly across countries, and their ability to elicit information revelation from investors is likely to also vary (see Loughran et al. (1994) and Sherman (1999)): • In the United States and the United Kingdom, in the Book Building method, the investment banker elicits indications of interest from institutional investors and uses these indications to set the IPO price and allocate the shares (see Benveniste and Spindt (1989), Benveniste and Wilhelm (1990 and 1997), Spatt and Srivastava (1991), Hanley (1993), Hanley and Wilhelm (1993), and Cornelli and Goldreich (1998)). • In Singapore, Finland, and the United Kingdom, fixed price offers are used, whereby investors submit demands at the fixed price, and (possibly random) rationing rules are used to allocate the shares (see Koh and Walter (1989), Levis (1990), and Keloharju (1993)). • In Israel, IPOs are conducted according to the standard uniform price, market clearing, Dutch auction, whereby the price is set to equate supply and demand (see Kandel et al. (1997)). • In the Mise en Vente, an auction-like IPO method commonly used in France, investors submit limit orders and then the auctioneer sets the price as a function of aggregate demand (the name of this auction procedure has been recently changed to Offre a Prix Minimum, but its workings have not been altered). In this IPO mechanism the price does not clear the market, and prorata rationing is used. For descriptions and analyses of this IPO method see Belletante and Palliard (1993), Derrien and Womack (1999), Dubois (1989), Husson and Jacquillat (1989), Jacquillat and Mac Donald (1974), Jacquillat et al. (1978), Leleux (1993), and Mirat (1983, 1984). The diversity of unseasoned shares selling mechanisms has actually even increased in the recent past as new, internet-based IPO auctions have been recently proposed (see Wilhelm (1999)): • Open IPO offers to sell unseasoned shares through a Dutch auction. In its advertising (for example on its website: www.openipo.com) it emphasizes that the use of this standard uniform price, market clearing auction ensures that “IPO offfering prices are set by the market” and reflect “what people are truly willing to pay for the stock.” It also advises that “investors should make a bid at the maximum 11 IPO AUCTIONS TABLE 1 IPO Selling Mechanisms in Different Countries U.K. U.S. Wit capital Singapore Finland U.K. Israel Open IPO France Dutch (uniform price) auction after Mise en Vente after Institution Book building Price set before of after demand Price clears market Rationing rule after Fixed price auction before no no yes no discretionary prorata or random — prorata price at which they are comfortable owning shares of the issue.” In fact, Open IPO has sometimes been presented as an alternative for the standard Book Building process, potentially more efficient than the latter, thanks to the use of the Dutch auction mechanism. • Wit Capital follows a somewhat more standard strategy. It seeks to entice individual investors to bid in IPOs, but does not contribute in a major way to the price discovery mechanism. The latter is in large part operated by the lead managers of the IPOs in which Wit Capital participates. These lead managers, which are major investment banks such as Goldman Sachs, Morgan Stanley, or Merrill Lynch, determine the IPO price based on the traditional Book Building process, which is more focused toward large institutional investors. The overall diversity of IPO auction formats (summarized in Table 1) raises the following issues: • What is the optimal IPO mechanism in terms of expected proceeds, price discovery, and information elicitation from informed investors? How should IPO prices be set, in response to investors’ demand? Is the frequently used fixed price method optimal? • Or is the a priori appealing Dutch auction the optimal selling mechanism? • How do different auction-like IPO procedures, such as the Book Building, the Mise en Vente, and Dutch auctions compare? • How should Internet-based IPO auctions be designed? These questions are of interest to finance and economics scholars aiming to understand price formation and the workings of auctions. They are also very relevant in practice for investors, shareholders, and investment bankers, whose profits can be significantly affected by the nature and efficiency of the IPO mechanisms. 12 BIAIS AND FAUGERON-CROUZET To address these issues, this paper develops a unified theoretical model to analyze the workings of the different IPO mechanisms listed above: the Book Building method, the fixed price auction, the Mise en Vente, and the uniform price market clearing auction. The participants in the IPO process are the sellers, financial intermediaries, and potential investors. In the model presented in Section 2 we assume the sellers seek to maximize the proceeds from the IPO, and the financial intermediary acts in their best interest. Some investors are large, strategic, institutional investors, with private information about the valuation of the stock in the secondary market. For simplicity, we assume that only the investors have private information, and abstract from the important problems arising when the sellers have private information (see, e.g., Allen and Faulhaber (1989), Grindblatt and Hwang (1989), Welch (1989), and Chemmanur (1993)). In addition to the large investors, there are smaller, and uninformed, but rational, investors. The funds available to these small investors are limited, hence they cannot absorb the whole issue. In Section 2, in the line of Benveniste and Spindt (1989), Benveniste and Wilhelm (1990), and Spatt and Srivastava (1991), we consider the optimal direct mechanism, and its implementation within the context of the Book Building method. In Section 3, we show that, in the fixed price auction, since prices cannot adjust to demand, winner’s curse problems, as in Rock (1986), lead to severe underpricing. Since the winner’s curse effect reflects the absence of adjustment of prices to demand it is natural to expect that the market clearing uniform price auction should perform better. Yet, we show that this auction can be conducive to tacit collusion between bidders, as in Wilson (1979), leading to large underpricing. This provides an alternative interpretation for the underpricing empirically evidenced by Kandel et al. (1997) in IPOs in Israel. In contrast, we show that the Mise en Vente can be structured to implement the optimal mechanism and to rule out tacit collusion, in contrast with the uniform price auction. In this auction, investors with good signals submit large demands, this drives prices up and thus enhances price discovery. In Section 4, we present empirical evidence from Mise en Vente auctions consistent with our theoretical result that it can implement the optimal mechanism, similar to the Book Building method. Hanley (1983) showed that, consistent with the implications from Benveniste and Spindt (1989) and Benveniste and Wilhelm (1990), prices somewhat underreact to demand; i.e., the covariance between price adjustment and underpricing is positive. This is also the case empiricaly in the Mise en Vente. Cornelli and Goldreich (1999) show empirically that, in the Book Building method, prices are set deliberatey below the market clearing level and that, anticipating this, investors inflate their demand. This also arises in the Mise en Vente. Conclusions emerging from our analysis are the following: • Efficient price discovery in IPOs requires some adjustment of prices to demand. Consequently, fixed price selling methods are inefficient. This is consistent IPO AUCTIONS 13 with the empirical finding by Loughran et al. (1994) that auction-like mechanisms lead to more efficient pricing than fixed price offers. • Yet, prices should not adjust to demand too strongly, lest this should spur tacit collusion. Consequently, the standard market-clearing uniform price (or Dutch) auction is not the optimal mechanism. In this auction, bidders can tacitly collude by placing demand functions such that the market clearing price is very low, and such that, any attempt to bid more aggressively, to gain market share, would push prices too high to be attractive. In the Mise en Vente, in contrast, since prices underreact to demand, tacit collusion on low prices can be unravelled. Indeed, underreaction implies that, if the other bidders were to bid at low prices, one investor could gain a large market share, without impacting the price too much. • In spite of obvious differences in institutional characteristics, two auctions, the Mise en Vente and the Book Building method, can be designed to implement the optimal IPO mechanism. From a theoretical perspective, it is not unnatural that different institutions can be used to implement the same optimal direct mechanism. From an empirical perspective, it is interesting that, consistent with our theoretical finding that the two institutions are comparable, data generated by the Book Building method in the United States or the United Kingdom and by the Mise en Vente in France, exhibit the same observable patterns, in particular underreaction of prices to demand and oversubscription. • This analysis has implications for the design of Internet-based IPO auctions. While the Dutch auction format proposed by Open IPO seems a priori attractive, our theoretical model shows that it can lead to tacit collusion on the part of bidders, and in that case it can be quite inefficient. In these collusive equilibria, the optimal strategy of the investors is to shade their bids rather than to “make a bid at the maximum price at which they are comfortable owning shares of the issue” as advised on Open IPO’s website. In fact, our analysis suggests that, in contrast with the Dutch auction, it can be optimal to let prices underreact to demand. Note that, in a recent IPO (Andover.net, Inc.), Open IPO actually set the IPO price at a significant discount relative to the market clearing price, more in line with the rules governing the book building or the Mise en Vente than with those of the Dutch auction. A challenge facing internet IPO auction designers is to translate into explicit computer algorithms the rather implicit rules that map demand into prices in the Mise en Vente or the Book Building method. 2. MODEL There are S unseasoned shares for sale. The seller faces N large, strategic, institutional investors with private information about the valuation of the firm by the market and large bidding capacity, and a fringe of small, retail investors who are uninformed and cannot absorb the whole issue. All agents are rational and 14 BIAIS AND FAUGERON-CROUZET risk neutral, and this is a common value auction. The objective of the seller is to maximize the proceeds from the sale. Each large investor can buy the whole issue and observes a private signal si , i = 1, . . . N . The signals are identically and independently distributed and can be good (g), with probability π, or bad (b) with the complementary probability. The value v of the shares on the secondary market is increasing in the number of good signals n and its realization is denoted vn . The retail investors, as a whole, can purchase up to S(1 − k) shares, with k ∈ [0, 1]. The financial intermediary is assumed to act in the best interest of the seller. She is in contact with the large institutional investors, and she has a distribution network, collecting the orders from the retail investors. Consider the following direct mechanism. Each informed investor i sends a message m i ∈ {g, b}. The mechanism maps these N messages into a price and into allocations to the informed agents and the retail uninformed agents. The mechanism is subject to several constraints. First, the price must be the same for all. This is to reflect the constraint, observed in practice, that IPO auctions involve uniform pricing (it should be noted, however, that Benveniste and Wilhelm (1990) show that investment bankers acting in the best interest of the firm could increase expected proceeds by using price discrimination). Second, since we assume the N large traders are ex ante identical, the mechanism is symmetric. Hence the price is simply a function of the total number of investors who report good signals n̂, and is correspondingly denoted p(n̂), while the quantity allocated to informed agent i depends only on her message m i and the number of other informed agents who reported good signals, li . Correspondingly it is denoted q(m i ; li ). Similarly, the quantity allocated to the uninformed agents depends only on n̂, and it is denoted qu (n̂). Third, the allocation must be such that exactly S shares are sold. ∀{m i }i=1,....N , n̂ ∈ {0, . . . N }, N q(m i ; li ) + qu (n̂) = S. i=1 The mechanism opens the possibility to allocate different quantities to investors reporting different signals. Indeed, quantity discrimination is crucial to obtain information revelation from the investors. The program of the mechanism designer is to maximize expected proceeds Maxqi (.;.),qu (..), p(.) E(Sp(n̂)) under the incentive compatibility and participation constraints of the investors. The incentive compatibility constraint of the informed investor i is that she must be better off announcing her true signal than misreporting it, while rationally anticipating 15 IPO AUCTIONS that the others will truthfully report their own signals. When the investor has observed a good signal this amounts to N −1 πl q(g; l)(vl+1 − p(l + 1)) ≥ l=0 N −1 πl q(b; l)(vl+1 − p(l)), l=0 where πl is the probability, from the point of view of the informed investor, that l out the N − 1 other investors have a good signal. We impose the rationality condition in its most demanding form. Investors must still be willing to participate to the mechanism ex post, i.e., after the messages of all the agents are known. This implies that the price set in the optimal mechanism must be lower than or equal to the value of the shares: p(n) ≤ vn . This problem is similar to the problem analyzed by Benveniste and Spindt (1989) and Benveniste and Wilhelm (1990). However, there are three differences. First and most importantly, in the present paper, the uninformed agent participates in the direct mechanism, along with the informed agents; the empirical analysis of the book-building process by Cornelli and Goldreich (1998) is consistent with this view. Considering the game in which both informed and uninformed agents participate enables us to nest in our analysis the study of winner’s curse effects as in Rock (1986) (see the analysis of the fixed price sale in the next section). Second, we do not impose the additive form used in Benveniste and Spindt (1989), where the value of the share is proportional to the number of good signals, which would imply, in our context that vn = αn, where α is a constant. Third, in contrast with Benveniste and Spindt (1989), we assume that each large investor could buy the whole issue. We think this is a reasonable assumption, given the bidding power of the large financial institutions participating regularly to IPOs, compared to the relatively small size of most of these operations. In addition this assumption simplifies the analysis. We discuss below how changing this assumption would alter our results. The optimal mechanism is given in the next proposition, with the proof of this proposition, as well as the following propositions, given in the Appendix. PROPOSITION 1. tics: The optimal direct mechanism has the following characteris- • If all informed investors report a bad signal, the IPO price is equal to the value of the shares: v0 , the amount allocated to the retail investors is maximized, by setting qu (0) = S(1 − k), and the shares which cannot be sold to the retail investors are equally split between the informed investors: q(0; 0) = Sk . N • If there is at least one informed investor reporting a good signal, informed investors reporting a bad signal receive no shares, i.e., q(0, n̂) = 0. • When some informed investors announce good signals, there is underpricing, and correspondingly expected proceeds are lower than the expected value of the 16 BIAIS AND FAUGERON-CROUZET shares: E( p(n)) = E(vn ) − kπ (1 − π ) N −1 (v1 − v0 ). • The optimal mechanism can be implemented with the following price schedule: p(n) = vn , ∀n < N , 1−π N p(N ) = v N − k (v1 − p(0)). π The proposition has a simple intuition. The mechanism designer must ensure that investors with a good signal announce their information truthfully rather than pretending they have a bad signal. To makes misrepresentation unattractive, the optimal mechanism minimizes the amount allocated to investors who announce bad information. This implies setting this amount equal to 0, except when it is not possible, because all informed investors announce bad signals. In that situation it is not possible to exclude all the informed agents, because the retail investors cannot absorb the whole issue. Hence underpricing must be used, in addition to quantity discrimination, to induce truthful revelation. This gives rise to informational rents for the large investors. The corresponding wedge between the expected proceeds and the expected value of the shares is proportional to the amount which the uninformed retail investors cannot buy (k S). Indeed, if the uninformed retail investors could buy all the shares, allocating them the whole issue would be a simple way to avoid adverse selection and sell all the shares at their a priori expected value, thus eliminating underpricing. Note that, as in Rock (1986), a winner’s curse problem, arises for the uninformed investors in the optimal mechanism, as the amount they are allocated is maximı́zed when the the value of the stock is lowest. Yet, they are still willing to participate to the auction, because the mechanism is designed to satisfy their individual rationality constraint. Next we discuss the extent to which our results are robust to the informational requirements of our approach: • In contrast with Allen and Faulhaber (1989), Welch (1989) or Chemmanur (1993), we do not assume that corporate insiders selling their shares in the IPO have private information about the market value of the stock. While clearly important and interesting, the case where there is two-way information asymmetry, i.e., both the sellers and the buyers have private signals, is beyond the scope of the present paper. Note that Chemmanur (1993) analyzes two-way information asymmetry, in the context of fixed-price offers. • In our framework, it is possible to exclude investors who report bad signals, except when all of them do so. This directly reflects our assumption that each large IPO AUCTIONS 17 investor has the potential to absorb the whole issue. If instead we assumed, like Benveniste and Spindt (1989) that the bidding capacity of the informed investors was below S, the threat to be excluded from the allocation would be less strong. Correspondingly, quantity discrimination would be a less powerful tool, and it would be necessary to rely on underpricing to a larger extent. In that context, the optimal price schedule would entail underpricing in several states, as in Benveniste and Spindt (1989). • In our model, underpricing is decreasing in the number of bidders, and the outcome of the mechanism goes to the competitive outcome (no underpricing) as the number of bidders goes to infinity. Note, however, that it would not be very reasonable to assume infinitely many bidders in our framework. In practice, there is only a limited number of professional investors who, like the large traders we consider in the model, have private information about the value of the shares and have the capacity to absorb the whole issue. With the pricing schedule presented in Proposition 1, underpricing arises when the IPO price is high. This suggests that underpricing and IPO prices are likely to be positively correlated. Now, with this pricing schedule, the covariance between underpricing and IPO prices cov(v − p, p) simplifies to π N (1 − π N )(v N − p(N ))( p(N ) − E(v | b)). This is positive if E(v) − E(v | b)) > kπ (1 − π ) N (v1 − v0 ), which is likely to hold, especially when k is relatively low. This positive covariance can be interpreted in terms of underreaction of prices to demand. Note that, if no large investor could absorb the whole issue, and correspondingly there was underpricing in more states of the world, as in Benveniste and Spindt (1989), underreaction would also arise. Benveniste and Spindt (1989) and Benveniste and Wilhelm (1990) provide an interpretation of the Book Building method along the lines of this type of optimal mechanism. The indications of interest transmitted by investors to the investment bank are similar to messages about signals, and their reflection in the price adustment and discretionary allocation set by the intermediary are similar to the direct mechanism. Consistent with this theory, Hanley (1993) found positive correlation between price adjustment and underpricing in Book Building data. 3. THEORETICAL ANALYSIS OF FIXED PRICE OFFERS, MARKET CLEARING AUCTIONS, AND MISES EN VENTE 3.1. Fixed Price Auction Our analysis in this section is similar to Rock (1986). The differences are the following. First, unlike Rock (1986), we do not impose the condition that informed 18 BIAIS AND FAUGERON-CROUZET investors do not have enough funds to buy the whole IPO. This is more realistic, given the relatively small size of IPO issues, compared to the large bidding power of institutional investors. Second, we consider N informed investors, with different and imperfect signals, rather than a single, perfectly informed investor. In the case of fixed price offers, the only choice of the seller is to set the price, p. Since the uninformed agents cannot absorb the whole issue, and since the seller must sell the S shares, he must ensure that the informed agents are willing to bid for the shares, even when they have observed bad signals. Hence, the price must be set to satisfy the individual rationality constraint of the informed agent with a bad signal. We assume that informed investors can costlessly bid for up to S shares. If they want to bid for a larger amount, up to Q̄ > S, they incur cost c. As only S shares are for sale, such very large bids are expected not to be fully executed. They can be optimal, however, to the extent that they enable the investor to obtain a larger share of underpriced and overbid issues. The cost c can be thought of as the cost of immobilizing funds during the period of the IPO (Keloharju (1993) notes that in Finland this period can be quite long). Consider the candidate equilibrium where investors with good signals bid for a large amount ( Q̄), while investors with a bad signal bid for a lower amount (S) and retail investors also participate to the IPO. In this context, the execution rate when there are n good signals is τn = S . S(1 − k + N − n) + n Q̄ Setting the expected gain of the informed with a bad signal bidding for S shares to 0 E(Sτ (v − p) | b) = 0, pins down the IPO price. Correspondingly, we obtain the following proposition: PROPOSITION 2. If K 1 ≤ c ≤ K 2 (where K 1 and K 2 are constants defined in the proof ), then in the fixed price offer the highest possible IPO price is p= N −1 λl v(l), l=0 where, πl τl λl = N −1 , l=0 πl τl and the informed agent with a good signal bids for Q̄, while the informed agent with a bad signal bids for S, and the uninformed agent bids for S(1 − k). IPO AUCTIONS 19 First note that consistent with empirical evidence (Koh and Walter (1989), Levis (1990), Keloharju (1993)) in the equilibrium described in Proposition 2, demand is positively correlated with underpricing. Indeed the latter is equal to vn − p, while the former is equal to: S(1 − k + N − n) + n Q, so that both are increasing in n. Second, manipulating the 0 profit condition of the informed investors with a bad signal, the IPO price can be expressed as p = E(v | b) + cov(τ, v − p | b) . E(τ | b) As the execution rate is decreasing in the number of good signals (n), the covariance is negative. Hence, the IPO price is lower than the expectation of the value of the asset conditional on a bad signal (E(v | b)). Underpricing pricing is necessary to convince the investors with bad signals to participate to the offer, in spite of the winner’s curse problem they face (in the same spirit as in Rock (1986)). Indeed they obtain worse execution when the share is worth a lot, and many investors with good signals place large bids, resulting in low execution rates. Further note that the expected profit of the uninformed agent is greater than that of the investors with bad signals: E(τ (v − p)) > E(τ (v − p) | b) = 0. Hence retail investors earn positive expected profits in the fixed price offer. These results emphasize that the lack of adjustment of prices to demand leads to large rents, left both to the informed and the uninformed agents, and consequently large underpricing. 3.2. Uniform Price Walrasian Auction In this mechanism, the seller sets a reservation price p, the investors submit ¯ and demand. In this demand functions, and the IPO price is set to equate supply market clearing uniform price auction, as in the analyses of Wilson (1979) and Back and Zender (1993), there is scope for tacit collusion between investors, as stated in the next proposition: PROPOSITION 3. For any reservation price p ≥ E(v | b), there exists a ¯ are constant whatever the Bayesian Nash equilibrium where investors’ demands realization of the signals, and the resulting IPO price is equal to the reservation price. The equilibrium demand of each investor is, at price p, N S+ 1 − σ ( p − p) ¯ S 1 with σ ≤ . N (N + 1) E(v | g) − p ¯ The intuition for this result is the following. The demand functions have a relativelly small slope (σ ). Hence the residual supply function faced by each investor 20 BIAIS AND FAUGERON-CROUZET is rather inelastic: It takes a big price increase to increase the residual supply. This large price impact makes it unattractive for each investor to attempt to increase her purchases. Our theoretical model provides an alternative interpretation for the thought-provoking empirical findings of Kandel et al. (1997) on the uniform price, market clearing IPO mechanism used in Israel. In particular, Kandel et al. (1997) find that (i) there is significant underpricing, and (ii) the (absolute value of the) slope of the demand schedules is low, i.e., there is a flat, around the IPO price. This is consistent with our theoretical result that the slope of the demand curve σ must be low in the tacit-collusion Bayes-Nash equilibrium. Because of the strategic complementarities between the actions of the bidders in this auction, there exist multiple equilibria, some of which do not involve tacit collusion. Yet, it is likely that the bidders will focus on the tacit collusion Nash equilibrium presented in the proposition, since it is the most advantageous for them. To cope with tacit collusion within this mechanism while satisfying the individual rationality condition of the informed investor with a bad signal, it is best for the seller to set p to E(v | b). ¯ subsection, note that although underpricing is less severe in this To conclude this auction than in the fixed price offer, it is still quite significant, due the possibility of tacit collusion it offers to the bidders. 3.3. The Mise en Vente The Mise en Vente is an auction-like IPO procedure commonly used in France. It operates as follows. Five days prior to the IPO the quantity offered and the reservation price are set jointly by the bank, the broker, and the firm. On the day of the IPO, investors submit limit orders to their brokers. The latter transmit these orders to the stock exchange. The total demand function is computed and graphically plotted by the auctioneer, who is a Bourse official. As a function of this demand, the auctioneer sets the IPO price. As in the Book Building method, there is no formal explicit algorithm mapping demand into prices. But price adjustment in the Mise en Vente exhibits strong empirical regularities, as shown in the next section. Eligible orders, above the IPO price, obtain prorata execution. To illustrate this description, consider the Mise en Vente of Partouche. On March 29, 1995, 500,000 shares were offered. The reservation price was 185. The total demand, expressed at all prices, amounted to 8.4 million shares, i.e., 16.29 times the supply. Figure 1 plots the demand expressed at each price. The IPO price was set to 200, which corresponds to a percentage price adjustment of 8.1%. (Note that the price at which supply would have been equal to demand was 220, i.e., the IPO price was deliberately set below market clearing). Eligible orders, placed above 200, obtained prorata execution. The first secondary market price, set after a tâtonnement process which lasted two days, was equal to 215, which corresponds to 7.5% underpricing. FIG. 1. Buy orders placed at the different prices for the Mise en Vente of Partouche, March 29, 1995. IPO AUCTIONS 21 22 BIAIS AND FAUGERON-CROUZET Denote D( p) the cumulated demand stemming from limit orders placed at prices equal to or higher than p. The optimal Mise en Vente arising in our framework is described in the next proposition: PROPOSITION 4. If c < k(1 − π ) N −1 N −1 Q̄ − S S N (N − 1) Q̄ + S the optimal mechanism can be implemented with a Mise en Vente where (i) the reservation price is v0 , (ii) investors place limit orders at prices p ∈ {v0 , v1 , . . . , v N −1 , p N }, (iii) the price schedule is if D( p N ) < S, then p = v0 , while if D( p N ) ≥ S, then p = max p[ D( p) ]+ , min{ p, s.t., D( p) = D( p N )} , N (where [.]+ means that if the number within brackets is not an integer it is rounded up to the next integer), (iv) the equilibrium strategies of the investors are to demand Q shares at price pn for investors with good signals, to demand S shares at price v0 for investors with bad signals, and to demand S(1 − k) shares at price v0 for retail investors. In the optimal Mise en Vente, consistent with the workings of the actual mechanism, prices increase with total demand, as the latter is equal to n Q̄ + (N − n + 1 − k)S. In equilibrium, in the optimal Mise en Vente, investors with good signals place more aggressive demands, as they are more eager to purchase the shares. Consequently, the higher the value of the asset, the better the private signals, the higher the demand, and the higher the IPO price. This theoretical result is consistent with the empirical findings by Derrien and Womack (1999) that this auction-like IPO method efficiently incorporates market information into IPO prices. Yet, the price set in this mechanism does not clear market in order to satisfy the incentive compatibility constraint. Correspondingly, there is oversubscription at the IPO price. Our analysis suggests that the Mise en Vente and the Book Building methods have similar incentive properties and can reach similar outcomes. This contrasts with the discussion in Benveniste and Wilhelm (1990) that, with uniform prices and even-handed allocations, information revelation should be impossible. The point is that, in the Mise en Vente, while the pro-rata allocation rule is indeed even-handed, it leads to investors with different signals being treated differently because they have placed different bids. IPO AUCTIONS 23 Consistent with our theoretical result, a recent empirical study of the Book Building method in the United Kingdom, by Cornelli and Goldreich (1998), shows that in this IPO institution: (i) the IPO price is deliberately set below market clearing, so that there is oversubscription at the IPO price, (ii) good deals are underpriced, and (iii) rationally anticipating this, investors inflate their demand and apply for more shares than they actually desire to buy. All these features are exhibited in our theoretical model of the Mise en Vente. This highlights that, in spite of institutional differences, Book Building and Mise en Vente can have similar properties. In the uniform price market clearing auction, there exists a tacit collusion Nash equilibrium whereby the bidders place demands such that the IPO price is always equal to the reservation price. The issue arises, therefore, if such tacit collusion equilibria exist in the Mise en Vente. The following proposition states that it is not the case. PROPOSITION 5. If E(v | g) − v1 > 1 (E(v | g) − v0 ), N +1−k then tacit collusion (such that the IPO price is equal to the reservation price irrespective of the signal) is not a Bayesian Nash equilibrium in the optimal Mise en Vente. In contrast with the case of the market clearing uniform price auction, tacit collusion can be unravelled in the case of the Mise en Vente. This is because in the Mise en Vente prices respond less strongly to demand than in the market clearing case. This is conducive to outbidding, since the investors can increase their market share, by raising their demand, without affecting the price too much. The condition stated in Proposition 5 is not very demanding. For example, in the linear parametrization assumed in Benveniste and Spindt (1989), where vn = αn, the condition holds. 4. EMPIRICAL ANALYSIS OF THE MISE EN VENTE To assess the empirical relevance of our theoretical analysis we confront it to a sample of 92 Mises en Vente which took place between 1983 and 1996. Our data corresponds to firms listed on the “Second Marché” an intermediary tier of the stock market created in France in 1983 for growth companies and for which the listing requirements are less stringent than for the first tier (the “Cote Officielle” or Official List). Practically all IPOs between 1983 and 1996 have taken place on the “Second Marché” (only a few exceptions, including privatizations, are on the Official List). This contrasts with the United Kingdom where IPOs are more frequently on the Official List than on the Unlisted Securities Market (see Levis (1990)). In Finland, there are IPOs on the Helsinki Stock Exchange or on the 24 BIAIS AND FAUGERON-CROUZET TABLE 2 Summary Statistics on 92 Mises en Ventes, 1983–1996 Variable Average Standard deviation Underpricing = ln(stock market clearing price/IPO price) demand ) ln( Total Supply Supply (number of shares) Price adjustment = ln(IPO price/ reservation price) Sales year before IPO∗ Age at time of IPO∗ 13% 16.52% 55 159262 17.36% 74 141401 10.66% FF 635, 805, 979 28.32 1, 377, 289, 794 21.7 ∗ Statistics based on 68 observations between 1983 and 1994. OTC market (see Keloharju (1993)). In 1996, an additional tier of the French equity market, the “Nouveau Marché,” was created. It aims at attracting younger companies to the Bourse. Because the companies listing on this market are quite different from those listing on the “Second Marché” they are not included in the present analysis. For the IPOs in our sample we observe: • the IPO price, the reservation price, and the secondary market clearing price, • the number of shares sold, • the total number of shares demanded, • the age of the firm at the time of IPO, and the sales during the year prior to IPO (these variables were available only for the period up to 1994). Table 2 reports summary statistics on these variables. In particular, note that the firms going public in France are relatively older than their U.S. counterparts (a feature shared with firms going public in other European countries). Note also that underpricing is on average equal to 13%, a figure very similar to those observed in the United States in the context of the Book Building procedure, while on average the price adjustment is 17.36%. Our theoretical analysis implies that the adjustment of the IPO price over the reservation price should increase with total demand. To test this hypothesis, we regressed price adjustment on the strength of demand and estimated the following regression ln(P j /R j ) = a + b ln(D j /S j ) + e j , where P j is the price of IPO j, R j is the initial reservation price for this IPO, D j is the total demand (i.e., sum of the quantities of all the orders placed at all prices in this IPO) and S j is the number of shares sold. The results are in Table 3. The first column in Table 3 presents the simple OLS results, for which the slope is significantly positive. The second and third columns present estimates 25 IPO AUCTIONS TABLE 3 IPO price Regression of Price Adjustment (ln( reservation price )) on Demand and Control Variables (t Statistics Are in Parentheses) Sample period Number of observations Estimation method Constant demand ) ln ( Total Supply ln (sales year before IPO) ln (age at time of IPO) ∗ 1983–1996 1983–1996 1983–1994∗ 92 OLS 92 White correction for heteroschedasticity −0.03 (−1.88) 0.053 (72.8) — 68 OLS −0.027 (−1.47) 0.061 (11.79) — — — −0.1 (−0.79) 0.06 (12.1) 0.0008 (0.13) 0.01 (1.77) Statistics based on 68 observations between 1983 and 1994. obtained after correcting for heteroskedasticity, using the White adjustment, and after controlling for exogenous variables such as the age of the firm and the level of its sales. The estimates obtained in these regressions are similar to those obtained in the simplest version of the test, and the coefficient of total sales is significantly positive in the three specifications. Figure 2 illustrates this analysis by plotting price adjustment (measured as the logarithm of the ratio of the IPO price to the initial reservation price) against total demand (measured as the logarithm of the ratio of total demand to supply). Our maintained hypothesis is that the Mise en Vente implements the optimal mechanism, like the Book Building method. Under this hypothesis, it should exhibit empirical regularities which are characteristic of this mechanism, and which are also observed in the Book Building method. One such empirical regularity is the underadjustment of prices to demand, which manifests itself in positive covariance between price adjustment and underpricing, and which was documented empirically in the case of the Book Building method by Hanley (1993). To test this hypothesis, we regressed underpricing on price adjustment, as ln(v j /P j ) = a + b ln(P j /R j ) + e j , where v j is the first market clearing price after the IPO, P j is the price of IPO j, and R j is the initial reservation price for this IPO. The results are in Table 4. As in the previous regression we estimated a simple OLS specification, as well as two other specifications, one correcting for heteroskedasticity and the other controlling for age and sales. Consistent with the underadjustment hypothesis, the slope is significantly positive, in all three specifications. Figure 3 illustrates this analysis by plotting underpricing (measured as the logarithm of the ratio of the first market clearing price to the IPO price) against price adjustment. FIG. 2. OLS regression of price adjustment on strength of demand, 92 Mises en Vente, 1983–1996. 26 BIAIS AND FAUGERON-CROUZET FIG. 3. OLS regression of underpricing on price adjustment, 92 Mises en Vente, 1983–1996. IPO AUCTIONS 27 28 BIAIS AND FAUGERON-CROUZET TABLE 4 clearing price Regression of Underpricing (ln ( stock market )) on Price Adjustment and IPO price Control Variables (t Statistics Are in Parentheses) Sample period 1983–1996 1983–1996 1983–1994∗ Number of observations Estimation method 92 OLS 68 OLS −0.03 (−1.15) 0.91 (6.92) — 92 White correction for heteroschedasticity −0.5 (−3.28) 0.77 (80.3) — ln (age at time of IPO) — — demand ) ln ( Total Supply — — Constant IPO price ln ( reservation price ) ln (sales year before IPO) ∗ 0.32 (1.04) 0.97 (3.2) −0.01 (−0.87) −0.03 (−1.7) −0.00024 (−0.009) Statistics based on 68 observations between 1983 and 1994. 5. CONCLUSION Our analysis suggests that it is important to organize IPO auctions so that the IPO price reflects the information held by investors. If this is not the case, as in fixed price offers, underpricing is bound to be large and very little information can be generated about the value of the stock during the IPO process. Yet, our analysis suggests that the optimal auction may not be the (a priori natural) Walrasian uniform price auction. In such an auction, the strong reaction of prices to demand can lead to tacit collusion between bidders, as in Wilson (1979), which leads to large underpricing. For optimal information elicitation to be immune to tacit collusion, some form of underadjustment of prices to the informational content of demand is required. Such information elicitation can be achieved in similar ways by apparently very different institutions: the Book Building method used in the United States and the Mise en Vente used in France. While our analysis suggests that the Dutch auction used by Open IPO may not be optimal, it raises—but does not resolve—the issue how to translate into explicit computerizable rules the mapping of demand into prices that occurs in the Mise en Vente or the Book Building. While the present paper emphasizes the similarities between the Book Building method and the Mise en Vente auction, there are some important potential differences between the two systems. In the Mise en Vente, bids are anonymous, while in the Book Building the investment banker observes (and has entire discretion to condition on) the identity of the investors sending indications of interest. Lack of IPO AUCTIONS 29 investor’s anonymity and discretionary allocation in the Book Building can have positive consequences, as they can be used to enhance the ability to extract information from the bidders. Indeed, Benveniste and Spindt (1989) analyze how long term nonanonymous relationship can be used efficiently in the IPO process, while Sherman (1999) analyzes the superiority of the book building over auction mechanisms (see also Sherman (2000)). On the other hand, if the investment banker is not acting in the best interest of the seller, discretionary allocations can have negative consequences. In particular, they can worsen winner’s curse problems for retail investors and consequently reduce their participation in auctions. In this context, the anonymity and nondiscretionary rules used in auctions can be attractive. This may well be why Open IPO insists that its Dutch auction mecanism “levels the playing field” and “ensures that all bidders are on equal footing.” Mechanisms other than the Dutch auction could potentially be used to “level the playing field.” Biais et al. (2002) analyzed the case where the investment bank and the institutional investors can collude (so that the investment bankers are tempted to treat large institutional investors more favorably than retail investors). They showed theoretically and econometrically that the Mise en Vente can be an efficient mechanism in this context. Wilhelm (1999) discussed that, while traditional investment banking was based on relationships with a small number of large investors, Internet technology could potentially allow one to sell unseasoned shares to a large number of relatively small investors, with no or litttle relationship with the investment bank. An interesting avenue of further research could be to investigate the consequences of this evolution for the optimal pricing and allocation of IPOs. In particular, it would be interesting to analyze price discovery, information elicitation, and strategic issues in the context of Internet–based sales to a large diffuse investor base. APPENDIX: PROOFS Proof of Proposition 1. As is typical in such two-type mechanism design problems, the incentive compatibility condition of the informed investor with bad news is redundant, and only the incentive compatibility condition of the informed agent with a good signal is binding. The constraint that all shares be sold is ∀l = 0, . . . N − 1, (l + 1)q(g; l) + (N − l − 1)q(b; l + 1) + qu (l + 1) = S, which can be rewritten as ∀l, q(g; l) = S − qu (l + 1) − (N − (l + 1))q(b; l + 1) . l +1 30 BIAIS AND FAUGERON-CROUZET Substituting this value of q(g; l) in the incentive compatibility condition becomes N −1 πl l=0 ≥ S − qu (l + 1) − (N − (l + 1))q(b; l + 1) (vl+1 − p(l + 1)) l +1 N −1 πl q(b; l)(vl+1 − p(l)). l=0 To relax this condition, minimize qu (l + 1), for l = 0, . . . N − 1, by setting it equal to 0, and minimize q(b; l), l = 0, . . . N , by setting: q(b; l) = 0, for l > 0, and q(b; 0) = Sk . Thus the incentive compatibility condition simplifies to N N −1 πl l=0 S Sk (vl+1 − p(l + 1) ≥ π0 (v1 − p(0)). l +1 N Treating this constraint as an equality, p(N ) can be written as a function of the other prices π N −1 p(N ) = π N −1 v N + N −2 l=0 N πl (vl+1 − p(l + 1)) l +1 − π0 k(v1 − p(0)). Now, the objective of the mechanism designer is to maximize (under the incentive compatibility and individual rationality conditions) the expected proceeds, which can be written as N −1 µn p(n) = µ N p(N ) + n=0 N −2 µn p(n), n=0 where µn denotes the probability that n signals out of N are good. Noting that µ N = ππ N , and substituting the incentive compatibility condition into the objective, the latter becomes π π N −1 v N + N −2 l=0 + N −1 N −2 πl πl N N vl+1 − p(l + 1) − π0 k(v1 − p(0)) l +1 l +1 l=0 µn p(n) + µ0 p(0). n=1 N Noting that µn+1 = ππn n+1 , and that because of the participation constraint: 31 IPO AUCTIONS p(0) = v0 , this can be rewritten as µN vN + N −1 µn vn − n=1 + N −2 N −2 µn+1 p(n + 1) − π π0 k(v1 − v0 ) n=0 µn+1 p(n + 1) + µ0 v0 . n=0 Noting that π0 = (1 − π ) N −1 , the expected proceeds are equal to E(vn ) − kπ (1 − π ) N −1 (v1 − v0 ). Note that prices do not appear in this expression. Hence, prices are indeterminate, as long as the incentive compatibility condition is satisfied. One possible solution is to set p(l) = vl , ∀l = 1, . . . , N − 1, and p(N ) = v N − 1−π π N −1 k(v1 − v0 ). Note that, for this solution, the quantity allocated to the retail investors qu (n), n = 1, . . . N − 1, is no longer relevant since it is multiplied by 0 in the incentive compatibility condition. Thus, for the price solution above, the optimal mechanism does not require that the retail investors receive 0 shares for vn , n = 1, . . . N − 1. Proof of Proposition 2. This participation constraint of the informed investor with a bad signal, E(Sτ (v − p) | b) = 0, can be rewritten more explicitly as N −1 πl [v(l − p]τl = 0. l=0 Hence, the IPO price can be written as p= N −1 l=0 N −1 πl τl vl = λl vl . N −1 l=0 l=0 πl τl 32 BIAIS AND FAUGERON-CROUZET The investor with a bad signal is better off bidding for S shares than for Q̄ if c > Q̄ N −1 l=0 S πl [v(l) − p] S(1 − k + N − (l + 1)) + (l + 1) Q̄ . Denote K 1 the right-hand side of this inequality. Now consider the informed investor with a good signal. She is better off bidding for Q̄ than for S shares if N −1 S Q̄ πl [vl+1 − p] S(1 − k + N − (l + 1)) + (l + 1) Q̄ l=0 N −1 S >S πl [vl+1 − p] . S(1 − k + N − l) + (l) Q̄ l=0 −c That is, if N −1 πl [vl+1 − p]S l=0 × Q̄ S − S(1 − k + N − l) + l Q̄ + Q̄ S(1 − k + N − l) + l Q̄ + S > c. Denote K 2 the left-hand side of the inequality. Note that it is indeed positive, since Q̄ S > . S(1 − k + N − l) + l Q̄ + Q̄ S(1 − k + N − l) + l Q̄ + S Proof of Proposition 3. To establish that the strategies stated in the proposition form an equilibrium, we need to prove that the investor with a good signal, anticipating that the other investors follow the equilibrium strategy, prefers to purchase S/(N + 1) shares at price p, rather than bidding more aggressively, to increase her ¯ does not want to do so, then a fortiori, the uninformed market share. Indeed, if she investor or the informed investor with bad news do not want to undercut, while they are still willing to buy a constant amount at p. Anticipating that the other investors follow their¯ equilibrium strategies, she faces the residual supply curve: S−N S − σ ( p − p) . N +1 ¯ IPO AUCTIONS 33 Her task is to choose the price p which maximizes her expected profit, ( p), where S ( p) = + N σ ( p − p) (E(v | g) − p), N +1 which is equal to the product of the residual supply curve by the unit profit. To prove that she finds it optimal to purchase S/(N + 1) shares at price p, we need to ¯ show that this is decreasing for all prices above p. Now ¯ ∂( p) S = N σ (E(v | g) − p) − + N σ ( p − p) p N +1 is decreasing in p. Hence, to show that it is negative for all prices larger than or equal to p, we only need to show that it is negative for p, i.e., ¯ ¯ S N σ (E(v | g) − p) − < 0, N +1 ¯ that is 1 S . N (N + 1) E(v | g) − p ¯ Proof of Proposition 4. First, consider the case of the informed investor with a good signal. Her equilibrium expected gain is σ < π N −1 (vn − p) S − c. N Could she obtain more by deviating from her equilibrium strategy? First, suppose she demands a lower amount q, still at price pn . If q > S, her expected gain is strictly lower than in equilibrium, since she just obtains less shares. If q ≤ S, then her expected gain is π N −1 (vn − p)S S (N − 1) Q̄ + S which is lower than her equilibrium gain if π N −1 N −1 ( Q̄ − S) (vn − p)S > c. N (N − 1) Q̄ + S Second, suppose she places a bid at a lower price than pn , say P. If P < pn−1 , the IPO price is pn−1 , while if P ≥ pn−1 , then the IPO price is above P. In both cases she obtains 0 shares. 34 BIAIS AND FAUGERON-CROUZET The retail investors and the informed investor with a bad signal obtain 0-expected gains in equilibrium and it is straightforward to see that they cannot obtain positive profits by deviating. Proof of Proposition 5. Consider a candidate equilibrium, whereby tacit collusion would prevail, and in which the IPO price would always equal v0 . In such an equilibrium the investors would bid as much as possible while not pushing the price above v0 and still deterring the other investor from competing away market shares. To avoid pushing the price above v0 , they place bids for (slightly less than) S shares at p N and for S(1 − 1/N ) at v0 . The expected profit from such tacit N collusion after observing a good signal is S [E(v | g) − v0 ]. 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