Market Making Obligations and Firm Value* Hendrik Bessembinder University of Utah. Jia Hao Wayne State University

Transcription

1 Market Making Obligations and Firm Value* Hendrik Bessembinder University of Utah Jia Hao Wayne State University Kuncheng Zheng University of Michigan This Draft: November 2013 Abstract: We examine the effects of secondary market liquidity on firm value and the decision to conduct an Initial Public Offering (IPO). Illiquidity can lead to complete market failure, where the IPO does not occur, or partial market failure where the IPO price is discounted to reflect that some efficient secondary trades may not occur. Competitive liquidity provision leads to market failure when uncertainty regarding fundamental value and asymmetric information are large in combination. In these cases, firm value and social welfare are enhanced by a contract where the firm engages a Designated Market Maker (DMM) to enhance liquidity. Our model implies that such contracts, which are currently prohibited in the U.S., can represent a market solution to a market imperfection, particularly for small growth firms. In contrast, proposals to encourage IPOs by use of a larger tick size are likely to be counterproductive. *The authors thank Robert Battalio, Thierry Foucault, David Hirshleifer, Michael Lemmon, Marios Panayides, Hans Stoll, Avanidhar Subrahmanyam, an anonymous Associate Editor, two anonymous referees, as well as seminar participants at Northwestern University, University of Washington, University of Pittsburgh, Case Western Reserve University, Southern Methodist University, University of Texas at Austin, the New Economic School, University of Auckland, University of Sydney, University of California at Irvine, Pontifica Universidade Catolica, Fundacao Getulio Vargas, Arizona State University, Cheung Kong Graduate School, Tsinghua University, the Asian Bureau of Finance and Economic Research Conference, the 2013 Financial Management Association Conference, and York University for useful comments. Special thanks are due to Bruno Biais and Uday Rajan for their modeling suggestions and insights.

2 Market Making Obligations and Firm Value 1. Introduction Recent market turmoil, including the financial crisis of and the flash crash of May 2010, highlight the importance of liquidity in financial markets. Modern stock markets mainly rely on limit order submissions to provide liquidity. In contrast to the designated specialists who in past decades coordinated trading on the flagship New York Stock Exchange (NYSE), most limit order traders are not obligated to supply liquidity or otherwise facilitate trading. The desirability of endogenous liquidity provision has been questioned, particularly in the wake of the sharp, albeit brief, decline in U.S. equity prices during the flash crash. In response, Mary L. Shapiro, chair of the United States Securities and Exchange Commission (SEC) stated The issue is whether the firms that effectively act as market makers during normal times should have any obligation to support the market in reasonable ways in tough times. 1 Also in response to the flash crash, a joint SEC-CFTC advisory committee observed that incentives to display liquidity may be deficient in normal market, and are seriously deficient in turbulent markets. 2 Related, a SEC advisory committee on small and emerging companies recently recommended an increase the minimum price increment or tick size for smaller exchange-listed companies to increase their liquidity and facilitate IPOs and capital formation. 3 Although there are no obvious barriers to entry to liquidity provision, each of these policy initiatives is predicated on the notion that limit order traders do not supply sufficient liquidity. In this 1 From a speech to the Economic Club of New York, September 7, Available at 2 Recommendations Regarding Regulatory Responses to the Market Events of May 6, 2010, Summary Report of the joint CFTC-SEC Advisory Committee on Emerging Regulatory Issues. 3 Recommendations Regarding Trading Spreads for Smaller Exchange-Listed Companies, US Securities and Exchange Commission Advisory Committee on Small and Emerging Companies. Available at 1

3 paper, we introduce a simple model of secondary market illiquidity and its effect on stock prices and incentives to conduct IPOs. Our model shows that competitive liquidity provision in the secondary market can indeed lead to market failure. Failure occurs in particular for those firms or at those times when the combination of uncertainty regarding asset value and the likelihood of information asymmetry is high. As a potential cure, we focus on contracts by which the firm hires a Designated Market Maker (DMM) to enhance liquidity. Such contracts are observed on several stock markets, including the leading markets in Germany, France, Italy, the Netherlands, Sweden, and Norway. 4 The most frequently observed obligation is a maximum spread rule, which requires the DMM to keep the bid-ask spread (the difference between the lowest price for an unexecuted sell order and the highest price for an unexecuted buy order) within a specified width, in exchange for a periodic payment from the firm. 5 DMM contracts of this type are currently prohibited in the U.S. by FINRA rule 5250, which prohibits any payments by an issuer or an issuer s affiliates and promoters for publishing a quotation, acting as a market maker or submitting an application in connection therewith. 6 The NYSE and Nasdaq markets have both recently requested partial exemptions from rule 5250, to allow DMM contracts for certain Exchange Traded Funds. 7 Some commentators have criticized these proposals on the grounds that DMM contracts distort market forces. 8 Our model shows that illiquid secondary markets can lead to complete market failure, where the firm chooses to not conduct the IPO even though social welfare would be enhanced by doing so, or 4 See, for example, Venkataraman and Waisburd (2007), Anand, Tanggaard, and Weaver (2009), Menkveld and Wang (2013), Skjeltorp and Odegaard (2011) and Petrella and Nimalendran (2003). 5 Such obligations typically bind. For example, Anand, Tanggaard, and Weaver (2009) study DMM agreements on the Stockholm Stock Exchange and document that the contracted maximum spreads are typically narrower than the average spread that prevailed prior to the introduction of DMMs. In contrast, the Supplemental Liquidity Suppliers and Designated Market Makers currently employed on the NYSE are only obligated to enter orders that match the best existing prices a certain percentage of the time, and are not required to improve on the best prices from public limit orders. 6 FINRA Regulatory Notice See SEC Release No , available at The proposals only call for DMM s to match the best existing quotes at certain times, and thus are less aggressive than the obligations considered here. 8 SEC Release No , page 58. 2

4 partial market failure, where the IPO is completed at a discounted price that reflects the possibility that some welfare-enhancing secondary market trades will not occur. We show that a DMM contract by which the firm pays a market maker a fixed fee in exchange for narrowing the bid-ask spread can cure these market failures. Such a contract reduces market maker trading profits and/or imposes expected trading losses, but also increases the equilibrium IPO price, as investors take into account the benefits of being able to subsequently trade at lower cost. Notably, the increase in the IPO price can exceed the requisite payment to compensate market makers, thereby increasing the firm s net proceeds. That is, the DMM contract comprises a market solution to a potential market failure. In our model, as in the classic analysis of Glosten and Milgrom (1985), illiquidity is attributable to information asymmetry. A key point of perspective is that, while informational losses comprise a private cost to liquidity suppliers, these are zero-sum transfers rather than a cost when aggregated across all agents. Competitive bid-ask spreads compensate liquidity suppliers for their private losses to better informed traders, and are therefore wider than the net social cost of completing trades. A maximum spread rule can improve social welfare and firm value because more investors will choose to trade when the spread is narrower. This increased trading enhances allocative efficiency and firm value. Our model generates cross-sectional predictions. It implies that the efficacy of DMM contracts depends on the interaction of uncertainty and asymmetric information regarding the fundamental value of the firm s assets. In the absence of asymmetric information, competitive liquidity provision is optimal, regardless of the degree of uncertainty regarding underlying value. In contrast, the combination of a high probability of information asymmetry and high uncertainty regarding fundamental value leads to potential market failure, and to improved firm value and social welfare from a DMM agreement. This combination is likely to arise for smaller, younger, and growth-oriented firms in particular. Further, the model implies that reductions in liquidity that are attributable to real or perceived increases in information asymmetry are economically inefficient, providing economic justification for a contractual requirement to enhance liquidity at times of high perceived information asymmetries. 3

5 Our model also has regulatory implications. If the market for liquidity provision is competitive, then contracts that required further narrowing of bid-ask spreads will impose expected trading losses on and require side payments to the DMM. A regulatory requirement that certain liquidity suppliers provide liquidity beyond competitive levels without compensation could lead to exit from the industry and ultimately be counterproductive to the goal of enhancing liquidity. Our analysis is also relevant to regulatory initiatives related to the minimum price increment or tick size. The U.S. Congress recently directed the SEC to reassess the effects the 2001 decimalization of the U.S. equity markets, which reduced the minimum price increment to one cent. 9 The SEC s advisory committee has recommended larger tick sizes for smaller exchange-listed companies, to increase market making profits, attract additional liquidity supply, and encourage IPOs. 10 Our model indicates that this approach is also likely to be counterproductive. Monopoly profits in liquidity provision reduce IPO prices as rational investors take into account increased secondary market trading costs. Lower IPO prices, in turn, can lead to market failure as firms elect to forgo the IPO entirely. In contrast, our model implies that the DMM contracts considered here lead to higher IPO prices and facilitate efficient IPOs. II. The Related Literature The literature on market making is vast. However, in most models the emphasis is on endogenous liquidity provision, i.e. on dealer and trader behavior in the absence of any specific obligation to supply liquidity. Among the few exceptions, Venkataraman and Waisburd (2007) consider the effect of a DMM in a periodic auction market characterized by a finite number of investors. The DMM in their model is an additional trader present in every round of trading, thereby improving risk sharing. Sabourin (2006) presents a model where a non-compensated market maker is introduced to an imperfectly competitive limit order market. In her model, the continuous presence of a market maker 9 The directive is contained in Section 106(b) of the 2012 Jumpstart Our Business Startups Act

6 causes some limit order traders to substitute to market orders, allowing the possibility of wider spreads with a market maker, for some parameters. Among the empirical studies of DMMs, Venkataraman and Waisburd (2007), Anand, Tanggaard, and Weaver (2009), Skjeltorp and Odegaard (2011), and Menkveld and Wang (2013) study the introduction of DMMs on Euronext-Paris, the Stockholm Stock Exchange, the Olso Stock Exchange, and Euronext-Amsterdam, respectively. In contrast to the implications of Sabourin (2006), each study reports improvements in liquidity associated with DMM introduction, and positive stock valuation effects on announcement of DMM introduction. Anand and Venkataraman (2013) and Petrella and Nimalendran (2003) study markets (the Toronto and Milan Stock Exchanges, respectively) where DMMs operate in parallel with endogenous liquidity providers, each documenting improved market quality associated with the hybrid structure. While the empirical evidence strongly supports the reasoning that DMMs enhance liquidity and firm value for at least some stocks, the evidence does not clarify the source of the value gain. Amihud and Mendelson s (1986) model implies that improved liquidity will reduce firms cost of capital. However, providing enhanced liquidity is costly, and the DMMs must be compensated for these costs. Our analysis clarifies the economic mechanism by which firm value can be enhanced by more than the cost of compensating the DMM, and provides cross-sectional implications regarding the firms for which such an agreement will be value-enhancing. III. Overview of The Model We consider a three-date model to assess relations between market liquidity and firm value in a simple manner. At t=0 the firm considers selling its existing asset to an investor in an IPO. The firm can elect to forgo the IPO, complete the IPO without entering a DMM contract, or complete the IPO while also making fixed payment C to market makers in exchange for a commitment to enhance secondary market liquidity. If the firm conducts the IPO, the investor potentially trades again in a t=1 secondary market. At t=2 the asset is liquidated. All agents are risk-neutral. The asset s expected liquidation value 5

7 is, while the ex post liquidation value can take two outcomes, 1 or 1, with equal probability. We assume 01, to ensure that asset values remain positive. Table 1 contains a complete listing of the notation used in the model. To motivate the potential IPO, we assume that the firm needs cash. The t=0 value of the asset to the firm is 1, where 0 < 1. This discount can reflect that the firm s owners wish to diversify their holdings or need capital to invest in additional projects. The discount gives rise to a potential welfare enhancement of if the asset can be transferred to an investor who values it at the expected liquidation value,. The potential investor is risk-neutral, but will with probability λ be subject to a liquidity shock that reduces her subjective valuation of the asset by, where This liquidity shock captures any non-informational motive for selling the asset, such as an unexpected personal funding need. In the absence of secondary market trading opportunities, the investor s t=0 valuation of the asset is reduced by the expected cost of the liquidity shock to 1. In this case the IPO enhances social welfare only if > 0, i.e. if the firm s need for cash is large relative to the expected investor liquidity shock. We consider a secondary market characterized by illiquidity that arises endogenously due to information asymmetry. If the investor acquires the asset in the IPO, she may, with probability p, become privately informed as to whether the t=2 liquidation value of the asset will be H or L. We assume that each random outcome (whether the investor becomes informed or suffers a liquidity shock, and whether firm value is high or low) is statistically independent of the others. As in the classic analysis of Glosten and Milgrom (1985), we assume the presence of risk-neutral market makers who are not subject to liquidity shocks. 12 The market maker sets the bid quote in the knowledge that the investor may be motivated to trade either by liquidity needs or by private information. 11 The two point distribution for liquidity shocks or intrinsic preference is for simplicity, and follows Duffie Garleanu, and Pedersen (RFS, 2007), as well as Holmstrom and Tirole (AER, 1996). 12 Since the investor is subject to liquidity shocks while the market maker is not, it would be efficient in our simple model for the firm to sell the asset directly to the market maker rather than the investor. In general, IPOs are used 6

8 Let M denote the investor s expected monetary gain, or equivalently, the market maker s expected monetary loss, from t=1 secondary market trading. M is zero if market making is competitive. In addition, let q(b) denote the endogenous probability that the investor will choose to not sell her asset, conditional on a t=1 liquidity shock and the t=1 bid quote, B. Let U 1 (B) = 1 denote the investor s expected non-monetary utility gain from trading in the secondary market in response to a t=1 liquidity shock. Note that while M and U 1 both comprise sources of trading gains to the investor, only M is a loss to the market maker. The t=0 value of the asset to the investor when secondary market trading is possible, V T, is the value in the absence of trading plus the expected gains due to secondary market trade. That is,. (1) The total gain in the t=0 value of the asset due to both IPO and secondary market trading opportunities is G V T V. We also assess the potential role of bargaining power in the IPO market. We posit that the IPO price is determined as: Q = V + G, (2) so that the firm captures in the IPO price the proportion β of the gain in asset value due to trading. While in our main analysis we set 1, we also consider outcomes when 1, implying that some of the anticipated gains from trade are captured by the investor or by an intermediary such as an investment bank, rather than the firm. The net t=0 welfare improvement to each party, relative to the status quo, can be specified as: Gain to the firm, π F = Q V C, Gain to the market maker, π M = C M, and to raise cash while transferring ownership to a broad base of long term investors. We assume that the IPO must be sold to investors, to incorporate in the simplest way possible the distinction between long term investors and market makers who typically tie up capital for only short periods of time. Incorporating in the model multiple time periods before asset liquidation would help to clarify the distinction between long term investing and short term market making, but at the cost of additional complexity. Related, we assume that the firm cannot repurchase the asset from the investor at t=1, to capture the notion that the firm s initial need for cash is long lived. 7

9 Gain to the Investor π I = V T Q. Aggregating across all three agents we have: Gain to society π S = π F + π M + π I =. (3) Expression (3) shows that the gain in social welfare in this model comes from both transferring the asset from the firm to the investor in the t=0 IPO and from transferring the asset from the investor to the market maker, should the investor incur a liquidity shock. While the maximum welfare gain is, the actual gain is reduced proportionate to the probability, q, that the investor will not sell in the secondary market after suffering a liquidity shock. The firm s net gain can also be stated as: π F = βg C = β( ) C= β(π S + M) C. (4) Note that, if β = 1 and C = M then π F = π S. That is, if the firm extracts in the IPO price all of the increase in asset value due to trading, and the payment from the firm to the market maker exactly offset the market maker s expected monetary losses from secondary market trading, then any action taken to maximize the firm s net gain will simultaneously maximize social welfare. However, if β < 1 or the market maker has expected trading gains or losses that are not offset by a payment from the firm, then welfare maximization and firm value maximization need not coincide. We assess relations between secondary market making, social welfare, and firm value. To do so, we consider outcomes when (i) secondary liquidity provision is competitive, leading to the highest bid price consistent with zero expected market-making profit, and (ii) secondary liquidity is provided by a monopolist market maker who selects the bid price to maximize expected profits. In each case, the firm can elect to enter a contract with the market maker to set the bid price so as to maximize firm value, net of any required payment to the market maker. The market maker s expected monetary loss M is zero if market making is competitive, negative if market makers have monopoly power, or positive if the firm contracts with the market maker to narrow the spread beyond competitive levels. 8

10 IV. Model Outcomes when Market Making and the IPO Market are Competitive We first assess model outcomes when the IPO market and the market for secondary trading are both competitive. We interpret the competitive IPO market to imply that the firm is able to extract all of the investor s gains from trade in the form of a higher IPO price, while the competitive secondary market implies zero expected profits to market making. In particular, π I = 0, M = 0, and β = 1. IV.A. The Completely Liquid Benchmark Consider, as a benchmark, the case where the probability that the trader becomes privately informed regarding asset value, p, equals zero, implying that the market maker suffers no losses due to information asymmetry. In the absence of any other market making costs, the competitive bid quote in the secondary market is. The investor s private valuation if she suffers a liquidity shock is µ(1-. Since this is less than the bid quote the investor will always sell following a liquidity shock. Setting q = 0, we have V T = Q =, and the net gain to the firm and the net social gain are π F = π S =. In the absence of illiquidity due to asymmetric information the gain to the firm is positive, implying that the IPO will occur, for any positive δ, i.e. if the firm has any need for cash. The social net gain of is the maximum that can be obtained in this model. That is, in the absence of information asymmetry the competitive secondary market leads to an IPO at full value and maximum social welfare. IV.B. Outcomes when the Secondary Market is Illiquid. As in the classic analysis of Glosten and Milgrom (1985), we consider a competitive secondary market in the presence of an information asymmetry. Given a non-zero probability that the investor becomes privately informed prior to t=1 the market maker potentially suffers trading losses, and reduces the bid price to compensate. Let V 1 denote the trader s subjective t=1 value of the asset, for which there are six possible outcomes, as illustrated on Figure 1. The investor s subjective value is 1 if she is privately informed with good news and does not incur the liquidity shock, 1 if she is privately informed with good news and does incur the liquidity shock, if she is uninformed and does not incur the 9

11 liquidity shock, 1 if she is uninformed and does incur the liquidity shock, 1 if she is privately informed with bad news and does not incur the liquidity shock, and 1 if she is privately informed with bad news and also incurs the liquidity shock. The relative ordering of these six private valuations differs depending on the magnitudes of the uncertainty regarding fundamental value,, and the potential liquidity shock, ρ. Figure 1 displays the ordering for three parameter ranges, 0,, and. Figure 1: The Investor s Private t=1 Valuation, V 1, for possible ranges of. The probability of each private valuation is stated in the square brackets. As in Glosten and Milgrom (1985), the zero-profit bid quote is the expected asset value conditional on a sale by the investor, which occurs if V 1 is less than the market maker bid quote, B. 13 The competitive bid quote depend on a quantity that we refer to as relative fundamental uncertainty. In particular, we provide in the appendix the proof for the following: Lemma 1: The zero-expected-profit bid quote, B, is: B = 1 given low relative fundamental uncertainty, defined as, B = 1 given intermediate relative fundamental uncertainty, 13 In the present model the zero profit bid quote is not unique for some parameters. We assume that competition pushes the bid quote to the higher of the two zero-profit bids in these cases. 10

12 defined as, B = (1 ϵ)μ given high relative fundamental uncertainty, defined as, Where and. We use the label relative fundamental uncertainty because the ranges of the equilibria depend not only on, which determines the differential between the two possible asset values, H L, and is therefore a measure of fundamental uncertainty, but also on liquidity shocks and the probability of information asymmetry. Both breakpoints, and, increase (implying lower relative fundamental uncertainty) with increases in both the probability, λ, and magnitude, ρ, of liquidity shocks. Conversely, both breakpoints decrease (implying higher relative fundamental uncertainty) with increases in the probability that the investor become privately informed. Note that the bid quote is always discounted relative to the expected value of the asset, μ, as long as the probability of informed trading, p, is positive. The discount is the expected informational content of the sale. Figure 2 displays the competitive bid quote for a set of parameter values that include μ = 100, δ=.05, ρ =.3, λ =.5, p =.5, and β = 1. Figure 2A displays the bid quote for various possible outcomes on fundamental uncertainty ϵ and the probability that the trader becomes informed, p, while Figure 2B displays the bid quote for possible outcomes on ϵ and λ. The bid quote always decreases with increases in fundamental uncertainty, ϵ. The bid quote also decreases with the probability that the trader is privately informed, p, except when relative fundamental uncertainty is high (in which case the bid quote is already equal to the lowest possible asset value). The bid quote also increases with the probability of a liquidity shock, λ, except within the range where fundamental uncertainty is high. The discrete changes in the equilibrium bid quote at and can be attributed to shifts in investor behavior at these points. With high fundamental uncertainty, the investor sells in equilibrium only if she is informed with bad news. The zero profit bid therefore equals asset value conditional on bad news. With intermediate fundamental uncertainty the investor also sells in equilibrium if she is 11

13 uninformed but incurs a liquidity shock. The possibility that the sale is uninformed supports a higher equilibrium bid price. With low fundamental uncertainty the investor will sell in equilibrium even if privately informed with good news when incurring a liquidity shock, which supports a yet higher bid price. Figure 2: The Zero Profit Bid Quote with Low, Intermediate, and High Relative Fundamental Uncertainty IV.C. Firm Choice and Social Welfare with Competitive Market Making We next assess the firm s decision to conduct the IPO and the resulting social welfare. Setting M=0 and β=1, we have from expression (2) that the IPO price is 1. The firm net gain and social net gain are π F = π S = μ(δ - qλρ). The firm will complete the IPO only if π F > 0, which requires qλρ < δ. That is, the IPO occurs only if the anticipated utility losses from the endogenous choice to not trade in the secondary market are sufficiently small relative to the firm s need for cash. As noted, when relative fundamental uncertainty is low the bid price is reduced only modestly, and the discount in the secondary market bid price is never large enough to dissuade the investor from selling in response to a liquidity shock. That is, q = 0 when relative fundamental uncertainty is low and the bid price is competitive. When relative fundamental uncertainty is intermediate the competitive bid price is reduced further. An investor who is subject to a liquidity shock and is also informed that the asset value is high would not sell given the competitive bid price in this case. The probability of no sale 12

14 conditional on a liquidity shock is q = p/2. When relative fundamental uncertainty is high the competitive bid price is 1. As was the case with intermediate relative fundamental uncertainty, the bid price is less than the investors private valuation should she be subject to a liquidity shock (probability and informed that the asset value is high (probability p/2). In addition, the bid price is now lower than the investors private valuation of 1 should she be uninformed (probability 1 ) and subject to a liquidity shock (probability. The probability that the investor does not sell, conditional on a liquidity shock, is 1 1. This discussion gives rise to the following: asymmetries, PROPOSITION 1: Given β =1 and competitive market making in the presence of information (i) If relative fundamental uncertainty is low, i.e. when, the IPO occurs for all δ > 0, the IPO price is Q = µ, and the improvement in social welfare is π S = δµ, the maximum attainable. (ii) If relative fundamental uncertainty is intermediate, i.e., the IPO does not occur when. If the IPO occurs the price is Q = 1 and the improvement in social welfare is π S =. (iii) If relative fundamental uncertainty is high, i.e. if, the IPO does not occur when 1. If the IPO occurs, the price is Q = 1 1, and the improvement in social welfare is π S = 1. 13

15 Figure 3: Social Net Gains with Low, Intermediate, and High Relative Fundamental Uncertainty when Market Making is Competitive Proposition 1 demonstrates that, with low relative fundamental uncertainty, the competitive equilibrium also maximizes social welfare and firm value, implying that there is no need for a DMM agreement. However, Proposition 1 also demonstrates that markets will fail, either partially or completely, when fundamental uncertainty exceeds certain thresholds, even with competitive secondary and IPO markets. For both intermediate and high fundamental uncertainty there is a range of parameters for which the market fails completely, as the IPO does not occur. Since 1 for all p < 1, the range of firm liquidity needs, δ, for which the market fails completely is larger when relative fundamental uncertainty is high. Further, when the firm chooses to conduct the IPO, the IPO price is reduced and social welfare is less than the maximum attainable. The reduction in the IPO price and in social welfare are greater when fundamental uncertainty is high as compared to intermediate, for all p < 1. Figure 3 displays the Social Net Gain, π S, which also equals the Firm net gain, π F, obtained in this case, for the same parameters used in Figure 2. In those regions where π S is positive, the IPO occurs, while regions where π S is zero are those where the firm does not complete the IPO. Given these parameters, π S = δμ =5 when relative fundamental uncertainty is low. The social net gain, π S, is reduced when relative fundamental uncertainty is intermediate, and more so when the probability of informed trading, p, is high. For a broad range of parameters π S is zero, reflecting that the IPO does not occur, when 14

16 relative fundamental uncertainty is high. 14 Very high outcomes on p lead to complete market failure with intermediate relative fundamental uncertainty as well. Why The Competitive Market Can Fail. The potential market failure with competitive market making is attributable to an informationbased externality. Efficiency gains occur in this model when the asset is sold to a party who values it more highly, i.e. by the firm to the investor at t=0 or by the investor, should she suffer a liquidity shock, to the market maker at t=1. If the secondary market bid price is low enough that the investor will, in some states, be dissuaded from selling in the secondary market after a liquidity shock, then she will reduce the amount she is willing to pay at the IPO. If the IPO price is reduced sufficiently the IPO does not occur. The inefficiency arises because the competitive secondary market bid price is reduced to offset expected market maker losses attributable to the possibility that the trader is privately informed regarding the asset s final value. A key point is that while trading losses due to asymmetric information are indeed a private cost from the viewpoint of a market maker, any loss to the market maker is a gain to the investor, and the net social cost of informed trading is zero when aggregated across all agents. Since the private cost to market makers exceeds the social cost of completing trades, the competitive bid price is discounted by an amount greater than the net social cost of providing liquidity. Social welfare is damaged if this discounting of the bid price potentially dissuades the trader from completing a secondary market trade that would have enhanced welfare. The result obtained here is the complement of that obtained in classic externality examples (e.g. pollution), where the social cost of the activity exceeds the private cost, leading to over production in 14 Interestingly, the net social gain actually increases with p when relative fundamental uncertainty is high. In this range π S = (δ-(1-p/2)λρ)). That reflects that in this case B = (1 ϵ)μ is fixed at the lowest possible level. However, unless δ is extremely large the net social gain and net firm gain remain negative and the market fails completely, as shown on Figure 3. 15

17 competitive equilibrium. Here, the private cost of providing liquidity exceeds the social cost, and competitive market making leads to less than the efficient supply of liquidity. IV.D. The Potential Role of a DMM Contract in a Competitive Market for Liquidity Provision The preceding discussion of how the competitive market can fail provides background for the role played by a DMM agreement. In particular, efficiency is enhanced by avoiding possible outcomes where the investor does not sell in the secondary market after suffering a liquidity shock. Lemma 2: To ensure that q=0, i.e. that the investor will always sell in the t=1 secondary market after suffering a liquidity shock, the bid quote should be set to 1 or higher. Conditional on suffering a liquidity shock, the investor s possible subjective valuations are, in increasing order, 1 if she is informed that the asset value is low, 1 if she is uninformed, and 1 if she is informed that the asset value is high. A bid quote equal to the largest of these, 1, or higher is sufficient to ensure that investor will sell after suffering a liquidity shock. Note that a bid quote of B* does not ensure that the investor always sells, as the investor s highest possible subjective valuation is 1, which is attained if she is privately informed that the asset value is high, and does not suffer a liquidity shock. However, in the absence of a liquidity shock a sale is not required to enhance welfare, as the investor gain is offset by an equivalent market maker loss. We now consider the effect of a potential DMM contract that calls for a flat t=0 payment, C, from the firm to the market maker in exchange for a commitment to maintain a minimum bid in the t=1 secondary market. The firm will enter a DMM contract if π F is larger with the contract than without, and is positive. The proof for the following central proposition is provided in the Appendix. 16

18 asymmetries, PROPOSITION 2: Given β =1 and competitive market making in the presence of information (i) If relative fundamental uncertainty is low, i.e. when, the firm maximizes its value and also social welfare by completing the IPO, without a DMM agreement. The t=0 value of the asset to the investor and the IPO price are Q = µ, and the net gain in welfare is δμ. (ii) If relative fundamental uncertainty is intermediate or high, i.e. the firm maximizes its value and social welfare by completing the IPO and entering a DMM contract calling for a bid price 1. The t=0 value of the asset to the investor and the IPO price are Q = µ+m, and the net gain in welfare is δμ. (iii) Within the range where a DMM agreement is optimal, i.e., the magnitude of the optimal payment from the firm to the market maker is: C =M= 1 1 > 0 when and C =M= 1 > 0 when. Figure 4: Optimal DMM Payment from the Firm to the Market Makers with Low, Intermediate, and High relative fundamental Uncertainty 17

19 The contracted bid price is just high enough to ensure q = 0, i.e. that the investor will always sell in the wake of a liquidity shock. Given the contracted bid price, the t=0 value of the asset to the investor is V T = µ + M, where M = C enters because the investor has positive expected monetary gains when the bid price is increased relative to the competitive level. Setting the contracted bid price higher than would involve greater investor gains and market maker losses, a higher value of the asset to the investor, a higher IPO price, and a larger required payment from the firm, but these increases payments would be zero sum. In contrast, moving the bid quote from the zero-profit level to increases V T by more than the required payment to the market maker, because it increases the expected non-monetary utility gain from trading in response to liquidity shocks, which enhances welfare. Testable Implications And Discussion Several aspects of Proposition 2 deserve emphasis. Most importantly, it presents testable implications regarding the conditions where DMM agreements are likely to be observed. Competitive liquidity provision is efficient if relative fundamental uncertainty is low, i.e. if, while DMM agreements will be efficient if relative fundamental uncertainty is intermediate or high, i.e. if. As previously noted, the boundary point increases with the probability, λ and magnitude, ρ, of investor liquidity shocks, implying that larger and more frequent liquidity shocks reduce the need for DMMs, ceteris paribus However, these liquidity shock parameters are investor characteristics that do not differ across firms, if investors hold diversified portfolios. The breakpoint decreases with p, the probability that the investor will become informed. 15 This implies that DMM agreements will be value enhancing (i) for those firms and/or at those times when uncertainty regarding asset value,, is high, in combination with (ii) the probability of informed trading, p, is high. The former arises from the fact that our model implies that DMM contracts enhance value when, while the latter arises because the threshold is lower for firms or at times when p is 18

20 greater. The model therefore implies that DMM contracts are most likely to be value enhancing for smaller and younger firms, to the extent these are characterized by more fundamental uncertainty and greater information asymmetries. This implication is generally consistent with the empirical evidence, e.g. Venkataraman and Waisburd (2007), Anand, Tanggaard, and Weaver (2009), and Menkveld and Wang (2013), indicating that DMM agreements are most often used for smaller and younger firms. In addition to altering the breakpoint,, that delineates the range of parameters where a DMM contract is efficient, changes in the probability of informed trading, p, affect both the magnitude of the efficiency gain, π S, from a DMM contract and the size of the requisite payment to the market maker. Regarding the latter, Proposition 2 also implies testable implications. Figure 4 displays the efficient payment from the firm to the market maker, for the same parameter values considered on Figures 2 and 3. The efficient payment is zero if relative fundamental uncertainty is low. When relative fundamental uncertainty is intermediate or high, the efficient payment is strictly increasing in uncertainty regarding fundamental value,, and in the probability that the trader is privately informed, p, and is strictly decreasing in the probability of an investor liquidity shock, λ. Our model considers explicitly only liquidity shocks that reduce the investor s subjective valuation and induce a desire to sell. Of course investors may also experience liquidity shocks (e.g. a sudden cash inflow) that induce a desire to buy. The direct extension to a model with both positive and negative liquidity shocks is a contract calling for the DMM to both decrease the ask price and increase the bid price, i.e. to narrow the bid-ask spread, relative to competitive levels. As noted, DMM contracts that require the bid-ask spread to be kept within a narrow range are in fact observed on a number of markets, and are typically employed for less liquid stocks. Note, though, that our model implies that DMM contracts will enhance value and efficiency only when used to offset market maker trading costs attributable to high relative fundamental uncertainty. That is, the model implies that it is efficient to narrow bid-ask spreads only to offset anticipated market making losses attributable to the information content of trades. Value is not enhanced by constraining bid-ask spreads to be narrower than the social 19

21 cost (e.g. inventory-carrying costs or order processing costs) of completing trades, which may also be greater for thinly traded securities. Our model also helps to rationalize the empirical observation (e.g. Schultz and Zaman, 1994 and Ellis, Michaely, and O Hara, 2000) that underwriters often act to support or stabilize post-ipo market prices. Such aftermarket support potentially complements a DMM contract, focusing in particular on the period immediately after the IPO when information asymmetries are potentially large. However, such stabilization activities are typically temporary, and therefore do not comprise a complete substitute for longer-term DMM contracts. If the probability of informed trading varies (or is perceived by market participants to vary) across time, relative fundamental uncertainty is dynamic. A firm or market that is typically characterized by low relative fundamental uncertainty may not always be so. While the model presented here is static, the economic reasoning suggests that in addition to contracts that require DMMs to routinely narrow spreads for smaller and younger firms, DMM contracts that impose a binding obligation only during times of increased asymmetric information may be welfare and value enhancing for larger and better known firms. V. Model Outcomes with Partial Bargaining Power and Non-Competitive Market Making. The preceding section demonstrates that competitive market making need not lead to efficient outcomes, as the market may fail partially or fully when relative fundamental uncertainty exceeds a threshold. However, if the firm has complete bargaining power, in the sense that it captures in a higher IPO price any increase in the value of the asset attributable to better secondary market liquidity, then an unconstrained value-maximizing firm will always cure any market failure by contracting with a market maker to enhance secondary market liquidity. 20

22 V.A. Partial Bargaining Power In this section, we assess the effects of relaxing the assumption that the firm captures all of the benefits from enhanced liquidity. In practice, firms proceeds from IPOs are typically less than the open market value of the shares issued, reflecting that some of the gains from trade are captured by intermediaries in the form of commissions and by investors in the form of the widely-studied underpricing of shares [See, for example, Chen and Ritter (2000) for analysis of investment bank commissions and Ibbotson, Sindelar, and Ritter (1994) for evidence regarding underpricing]. A full model of the IPO process is beyond the scope of this paper. We instead presume that the bargaining game generates a parameter, β, which is the proportion of the gain in value captured by the firm. In particular, the IPO price is Q V βv T V. As noted in section III, decisions taken to maximize the firm net gain, π F, can differ from those that would maximize the social net gain π S, when β < 1. This reflects that the firm reimburses the market maker for all of the increased trading losses associated with a higher bid price, but captures only the fraction β of the investor s increased valuation of the asset due to the higher bid price. The firm will conduct the IPO only if π F is positive, and given that the IPO occurs, the firm will contract to increase the bid price only if π F is increased. The firm may choose to not conduct the IPO, or given that the IPO occurs, the firm may choose to contract for a bid price lower than 1. In the appendix, we provide proofs for the following proposition. PROPOSITION 3: Given β <1 and competitive market making, (i) If relative fundamental uncertainty is low, the firm will choose to complete the IPO and will not enter a DMM contract, regardless of the bargaining parameter, β. The net gain in social welfare is the maximum attainable. 21

23 (ii) If relative fundamental uncertainty is intermediate, there exists a range of parameters for which the firm will choose to not complete the IPO, a range of parameters for which the firm will complete the IPO but not enter a DMM contract, and a range of parameters for which the firm will complete the IPO and enter a DMM contract calling for a bid price of 1. Only the last of these leads to the maximum gain in social welfare. (iii) If relative fundamental uncertainty is high, there exists a range of parameters for which the firm will choose to not complete the IPO, a range of parameters for which the firm will complete the IPO but will not enter a DMM, a range of parameters for which the firm will complete the IPO and enter a DMM contract calling for a bid price of B = (1- ρ)μ, and a range of parameters for which the firm will complete the IPO and enter a DMM contract calling for a bid price of 1. Only the last of these leads to the maximum gain in social welfare. (iv) Decreasing the firm s bargaining power never improves social welfare, but can decrease social welfare. Figure 5 displays the outcomes of this analysis, for some specific parameter values. In Panel A, μ=100, δ=0.05, ρ=0.3, p=0.5, and λ=0.2. When relative fundamental uncertainty is low, social net gains are maximized at δμ 5, with no need for a DMM contract, regardless of the firm s bargaining power. The firm will proceed with the IPO for all β > 0, i.e. as long as it captures any of the increase in social welfare, since it incurs no cost in the absence of a DMM agreement. When relative fundamental uncertainty is medium or high and β = 1 the value-maximizing firm contracts to maintain a bid price 1, and efficiency gains are maximized. However, decreasing the firm s bargaining power leads to discrete changes in the firm decision, either to reduce the contracted bid price to 1, or to abandon the DMM agreement entirely. Social welfare is reduced when the firm alters its decision. However, the firm does complete the IPO, and there is some 22

24 improvement in social welfare relative to the status quo, for the full range of β and, given the other parameter values considered in Panel A of Figure 5. Panel B of Figure 5 displays outcomes when the probability of a liquidity shock, λ, is increased to 0.5, while other parameters are held constant. The key effect is that the figure now contains a range of parameters, in particular when β (the firm s bargaining power) is small and (fundamental uncertainty) is large, where the firm elects to not conduct the IPO. This reflects that the investor discounts the amount she is willing to pay for the IPO by a greater amount when λ is larger. While a DMM agreement can in principle offset this, the firm would not choose to enter a DMM contract when it captures only a small fraction of the benefit, while bearing the full cost. Panel C of Figure 5 is based on the same parameters as Panel B, except that the probability of informed trading, p, is increased from 0.5 to 0.7. Two effects are apparent. First, the range of parameters where the market fails completely as the firm elects to not conduct the IPO is increased, and now includes lower outcomes on fundamental uncertainty,, and higher outcomes on the firm s bargaining power, β. Second, outcomes on the welfare gain are now bimodal, either equal to the maximum of 5 or equal to zero. Chen and Ritter (2000) argue that investment bankers earn economic rents from conducting IPOs. Our analysis indicates that frictions such as investment bank commissions or market underpricing which prevent the firm from capturing the full market value of the assets it sells can cause complete market failure in the sense that firms decline to proceed with efficiency-enhancing IPOs. Our model also produces the more subtle result that such frictions can lead to a partial market failure, where the firm conducts the IPO, but does not enter the efficient DMM contract. The negative effects of decreased firm bargaining power are most pronounced when fundamental uncertainty,, the probability of informed trading, p, and the likelihood of liquidity shocks, λ, are high. 23

25 Figure 5. Social Net Gains, Conditional on the Firm s Choice. The vertical axis is Social Net Gain. Firm Choices are denoted as 0 = No IPO, 1 = IPO with competitive market making, 2 = IPO with subsidy to quote at B 1, 3 = IPO with subsidy to quote at 1. V.B. The Effect of Possible Monopoly Power in Liquidity Provision To this point, we have assumed that secondary market liquidity provision is competitive, in the sense that expected market making profits are zero in the absence of a DMM contract. However, the business of liquidity provision may, in some cases, be imperfectly competitive. Glosten (1989) models the case of a monopolist liquidity provider, and the model presented by Bernhardt and Hughson (1997) allows for market makers earn positive expected profits in equilibrium. Further, depending on the degree of cross-market competition, a trading exchange may be able to extract monopoly rents in the form of trading fees, even if competition prevails among potential liquidity suppliers on the exchange. Monopoly profits from market making may also arise if the minimum price increment or tick size is large enough to constrain bid-ask spreads to be larger than the competitive level. To obtain insights into the potential role of market maker rents in the simplest possible manner we focus on the case of a monopolist market maker. The key intuition of this analysis is the following. Monopolist rents are similar to asymmetric information costs in that they cause the secondary market bid price to be decreased (relative to μ, the unconditional expected value of the asset) by more than the social cost of completing trades. A reduction in the bid price attributable to monopoly power, like a reduction 24

26 due to asymmetric information, is socially inefficient if it dissuades the trader from selling in the secondary market the in wake of a liquidity shock. Further, a reduction in secondary market bid price due to monopoly power reduces the equilibrium primary market IPO price. We next assess the effect of a potential DMM contract between the firm and the monopolist market maker. We assume that the monopolist selects the bid price to maximize the expected market making profit. Let M* denote the maximized profit, which is the product of the probability of an investor sell conditional on bid price, B, and the difference between the market makers expectation of asset value conditional on a sell (i.e. the competitive bid) and the bid price. In the appendix we provide proof of the following: PROPOSITION 4: Given monopolist market making in the presence of information asymmetries, and the ability to enter DMM contracts: (i) (ii) If δµ < -M* there is complete market failure, as the firm does not conduct the IPO. If δµ > -M* and is sufficiently small, the firm will conduct the IPO and social welfare will be maximized with monopoly market making regardless of β. (iii) If δµ > -M* and β=1 the firm will complete the IPO and social welfare will be maximized as the firm enters a DMM contract calling for the socially optimal secondary market bid price 1. (iv) If δµ > -M* and β < 1, there exists a range of parameters with partial or complete market failure. Decreasing β expands this range of parameters with market failures. (v) The range of parameters leading to full or partial market failure is larger with monopoly than with competitive market making. Proposition 4 shows that monopoly market making does not necessarily preclude the use of a private DMM contract to correct the inefficiencies that arise both from the existence of monopoly power and from the presence of information asymmetries. However, if the monopoly rents are too large they can 25

27 preclude the firm from conducting the IPO. Further, the range of parameters where efficient outcomes are reached without a DMM agreement is reduced by monopoly power. Proposition 4 also shows that the negative effects of monopoly power in the secondary market and those of reduced firm bargaining power in the primary market interact with and compound each other. Figure 6 displays outcomes, in terms of the social net gain π S and firm choices for selected parameters. Several points are noteworthy. First, comparing outcomes with competitive vs. monopolist market making in Panels A and B, we observe that monopoly market making is most likely to cause complete market failure when the probability of informed trading, p, and of investor liquidity shocks, λ are high. The former reflects that monopolist market makers will also decrease the bid quote to mitigate losses to informed traders, while the latter reflects that the decreased bid quotes are more damaging to economic efficiency when liquidity shocks are more prevalent. From Panel C we can observe that the negative effects attributable to a reduction in bargaining power (β < 1) are never mitigated, but are for some parameters exacerbated, by market making monopoly power. 26

28 Figure 6: Social Net Gains, Conditional on the Firm s Choice, in Competitive vs. Monopoly Market Making. The vertical axis is Social Net Gain. Firm Choices are denoted as 0 = No IPO, 1 = IPO without subsidy, 2 = IPO with subsidy to quote at B 1, 3 = IPO with subsidy to quote at 1. An advisory panel to the U.S. SEC has recently recommended increases in the tick size for smaller exchange-traded companies. The intent appears to be to increase bid-ask spreads beyond competitive levels in order to attract additional liquidity suppliers. However, our model indicates that such a proposal may be counterproductive. In particular the model implies that monopoly profits in secondary market liquidity provision damage efficiency and reduce IPO prices, as investors take into account the higher costs of secondary market trading. In particular, monopoly profits in secondary market liquidity provision can lead to total market failure, where the firm chooses to not complete the IPO. In contrast, DMM contracts of the type considered here improve efficiency and facilitate the IPO process. VI. Conclusions and Extensions We present a relatively simple model to assess the effects on firm value and social welfare of a contract by which a firm engages a Designated Market Maker (DMM) to improve secondary market liquidity. We show that a DMM contract can improve value and welfare because of an information-based externality. In particular, market maker losses from transactions with privately-informed traders are a private cost of providing liquidity, but comprise a zero-sum transfer rather than a cost when aggregated across all agents. Since the private costs of providing liquidity exceed the social costs, a competitive 27