Market Making Obligations and Firm Value*
Hendrik Bessembinder
University of Utah
Jia Hao
Wayne State University
Kuncheng Zheng
University of Michigan
This Draft: September 2013
Abstract:
We examine the effect of secondary market liquidity on firm value and on the decision to conduct an
Initial Public Offering (IPO). Illiquidity can lead to complete market failure, as the IPO does not occur,
or partial market failure where the IPO occurs at a price that is discounted because some welfareenhancing secondary market trades do not occur. Competitive liquidity provision can lead to inefficient
outcomes, in particular when both uncertainty regarding fundamental value and asymmetric information
are substantial. 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.
*This paper supersedes an earlier working paper titled “Why Designate Market Makers? Affirmative Obligations
and Market Quality.” The authors thank Robert Battalio, Thierry Foucault, David Hirshleifer, Michael Lemmon,
Marios Panayides, Uday Rajan, 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, University of Utah, 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, and York
University for useful comments. Special thanks are due to Bruno Biais for his modeling suggestions and insights.
1 Market Making Obligations and Firm Value
1. Introduction
Recent market turmoil, including the financial crisis of 2008-2009 and the “flash crash” of May
6, 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), limit order traders are
typically not obligated to supply liquidity or otherwise facilitate trading.
The desirability of such endogenous liquidity provision has recently been questioned,
particularly in the wake of the sharp, albeit brief, decline in U.S. equity prices during the flash crash.
Mary L. Shapiro, chairman of the United States Securities and Exchange Commission (SEC),
highlighted the issue as follows:
“May 6 was clearly a market failure, and it brought to the fore concerns about our equity market
structure…. Where were the high frequency trading firms that typically dominate liquidity
provision in those stocks? …. 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
Further, a joint SEC-CFTC advisory committee comprised of prominent academic and industry
representatives recently issued a report in response to the flash crash that include the observation that
“incentives to display liquidity may be deficient in normal market, and are seriously deficient in turbulent
markets.”2 The committee recommends that U.S. regulators consider affirmative liquidity provision
obligations.
Interestingly, several stock markets, including the leading markets in Germany, France, Italy, the
Netherlands, Sweden, and Norway, make use of “Designated Market Makers” (DMMs) who are
1
From a speech to the Economic Club of New York, September 7, 2010. Available at
http://www.sec.gov/news/speech/2010/spch090710mls.htm.
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.
http://www.cftc.gov/ucm/groups/public/@aboutcftc/documents/file/jacreport_021811.pdf.
2 obligated to improve liquidity supply at certain times, for at least some stocks.3 These DMM agreements
are voluntary contracts between the listed firms and one or more financial firms who provide stock
market liquidity. 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.4
The DMM is
typically compensated by the listed firm in the form of a flat fee.
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.”5 The NYSE and Nasdaq
markets have both recently requested partial exemptions from rule 5250, to allow DMM contracts for
certain Exchange Traded Funds.6 Some commentators have criticized these proposals on the grounds
that DMM contracts “distort market forces.”7
In this paper, we introduce a simple three-date model to evaluate the economics of DMM
contract that require the narrowing of bid-ask spreads. At t=0, the firm potentially sells the rights to the
risky cash flows from its existing assets to investors in an IPO. At t=1 secondary trading can occur,
potentially motivated by either information or liquidity needs. At t=2 the asset is liquidated.
We show that illiquidity in the secondary market can lead to market failure. Complete market
failure occurs when the firm chooses to not conduct the IPO, even though social welfare would be
enhanced by doing so. Partial market failure occurs when the IPO is completed, but only at a discounted
3
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).
4
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.
5
FINRA Regulatory Notice 09-60.
6
See SEC Release No. 34-67411, available at http://www.sec.gov/rules/sro/nasdaq/2012/34-67411.pdf. The
proposals only call for DMM’s to match the best existing quotes at certain times, and thus are less aggressive than
the “maximum spread” obligations considered here.
7
SEC Release No. 34-67411, page 58.
3 price that reflects that some welfare enhancing secondary market trades will not occur. Market failure
can arise if secondary market liquidity suppliers possess monopoly power. Perhaps more surprisingly,
market failure can occur even when secondary market liquidity provision is competitive.
Our analysis shows 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 has two
effects. First, it reduces market maker trading profits and/or imposes expected trading losses on them.
Second, it increases the equilibrium IPO price, as investors take into account the benefits of the being
able to subsequently trade at lower cost. Notably, the increase in the IPO price can exceed the requisite
payment to the market makers, thereby increasing the firm’s net proceeds. Further, as long as the IPO
market is competitive, in the sense that the firm captures in a higher IPO price all of the expected
benefits from improved secondary market liquidity, the value-maximizing firm will always choose the
DMM contract that maximizes social welfare. 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), the bid-ask spread arises
due 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 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 can enhance 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 regarding the fundamental value of the firm’s assets and
asymmetric information regarding firm value.
In the absence of asymmetric information, competitive
liquidity provision is optimal, regardless of the degree of uncertainty regarding underlying value.
Similarly, if the probability of information asymmetry is high but uncertainty regarding asset value is
low, competitive liquidity provision is optimal.
It is the combination of a high probability of
4 information asymmetry and high uncertainty regarding fundamental value that leads to potential market
failure, and to improved firm value and social welfare from a DMM agreement.
Our model’s implications differ in an important but subtle way from the simple insight that
DMMs are most useful in illiquid stocks. If stocks have wide bid-ask spreads because of high real costs
of competing trades, e.g. due to the inventory costs that Demsetz (1968) predicts will be high for thinlytraded assets, then the marginal social cost of providing liquidity is high, and it is efficient for spreads to
be wide. In contrast, our analysis implies that DMM contracts will enhance value for firms where
competitive spreads are wide due to the combination of fundamental uncertainty and information
asymmetry.
These are likely to be smaller, younger, and growth-oriented firms. Further, the model
implies that reductions in liquidity that are attributable to real or perceived increases in information
asymmetry are economically inefficient, providing justification for the requirement to enhance liquidity
at times of high perceived information asymmetries.
Our model also has regulatory implications. We show that contracts by which a firm compensates
a DMM for enhancing liquidity provision in its own shares can enhance trader welfare and firm value.
As there are no meaningful barriers to entry, essentially any investor can supply liquidity in electronic
limit order markets. If the market for liquidity provision is competitive, then contracts that call for
further narrowing of bid-ask spreads will impose expected trading losses on and require side payments to
the DMM. A regulatory requirement that certain DMMs provide liquidity beyond competitive levels
without such compensation would lead to exit from the industry and would ultimately be
counterproductive to the goal of enhancing liquidity.
II. The Related Literature and Alternative Models
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
5 DMM in their model is essentially an additional trader who is present in every round of trading, thereby
improving risk sharing. Sabourin (2006) presents a model where a designated market maker is imposed
in an imperfectly competitive limit order market.
In her model, the presence of a designated market
maker will cause some limit order traders to substitute to market orders, which reduces competition in
liquidity supply and allows the possibility of wider spreads with a designated market maker.
A small group of empirical researchers have studied the effects of DMMs on market quality.
Anand and Weaver (2006) examine the Chicago Board Options Exchange (CBOE), documenting
decreased bid-ask spreads and increased CBOE market share following the introduction of DMMs.
Petrella and Nimalendran (2003) study the Italian Stock Exchange, documenting improved market
quality on a hybrid market that includes a designated market maker, as compared to stocks traded on a
pure limit order market. 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. Each study reports improvements in liquidity associated with DMM introduction, and
positive stock valuation effects on announcement of DMM introduction.
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 a reduction in firms’ cost of capital due to improved liquidity.
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 shows that value can be enhanced by such contracts for some, but
not for all, firms.
III.
Overview of The Model
We consider a three-date model to assess relations between market liquidity and firm value in a
simple manner. The firm considers selling its existing asset to an investor in a t=0 IPO. The investor
6 potentially trades again in a t=1 secondary market, and the asset is liquidated at t=2. The asset’s
liquidation value can take two, equally probable, outcomes,
unconditional expectation . 0
1
1
or
, with
1, 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 V = 1
, where 0 <
1. This discount can reflect that the firm’s owners wish to
diversify their holdings, or that the firm needs new capital to invest in additional projects. The potential
investor is risk-neutral, but will with probability λ be subject to a liquidity shock that reduce her
subjective valuation of the asset by the amount
, where 0
1.8 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, the ex ante expected cost of the possible liquidity shock is
the value of the asset to the investor is VNT = 1
and
.
Should the investor acquire 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. As in the classic analysis of
Glosten and Milgrom (1985), we consider a secondary market with risk-neutral market makers, who are
not subject to liquidity shocks.9 The market maker sets quotations in the knowledge that the investor
may be motivated to trade either by liquidity needs or by private information regarding asset value. Let
M denote the investor’s expected monetary gain, or equivalently, the market maker’s expected monetary
loss, from t=1 secondary market trading.
In addition, let π(B) denote the probability that the investor will choose to not sell her asset,
conditional on a t=1 liquidity shock, where B is the t=1 bid quote. Let U(B) =
1
denote the
8 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).
9
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
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. Similarly, 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 investor’s expected non-monetary utility gain from trading in response to a t=1 liquidity shock.
Note
that while M and U 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 is the value
in the absence of trading plus the expected utility and monetary gains due to secondary market trade.
That is,
.
(1)
Finally, let C denote the cash payment from the firm to the market maker, if any. The total gain
in the time 0 value of the asset due to trading opportunities is G ≡ VT – V. It is useful to further
decompose the gain from trade into G0 ≡ VNT – V =
which reflects the gain from transferring
the asset from the firm to the investor in the time 0 IPO, even if no further trading is possible, and G1 ≡
VT – VNT = U+M, which reflects the investor’s expected gain due to the ability to trade in the secondary
market at t=1.
We assess relations between secondary market making, social welfare, and firm value. To do so,
we consider outcomes when (i) there is no secondary market, (ii) a monopolist market maker selects the
bid price to maximize expected profits, (iii) secondary liquidity provision is competitive, leading to the
highest bid price consistent with zero expected market-making profit, and (iv) the firm contracts with the
market maker to set the bid price to maximize firm value, net of any required payment to the maker. The
market maker’s expected loss (trader’s expected gain) from trading with the investor in the secondary
market, M, is zero if market making is competitive, is negative if market makers have monopoly power,
or can be positive if the firm contracts with the market maker to narrow the spread beyond competitive
levels.
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. In our
main analysis we set
1, so that the firm captures all of the expected gains from trade. We also
8 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.
Given these definitions, we can define the net t=0 gain to each party, relative to the status quo, as
Firm Net Gain (FNG) = Q – V – C, Market Maker Net Gain (MMNG) = C – M, and Investor Net Gain
(ING) = VT – Q. Aggregating across all three agents, we can define Social Net Gain (SNG) = FNG +
MMNG + ING = G – M = G0 + U. The Firm’s Net Gain can be restated as:
FNG = βG – C = β(SNG + M) – C = β(δµ - πλ µ + M) – C.
(3).
Note that, if β = 1 and C = M then FNG = SNG. 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
offsets 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 exactly offset by a payment from
the firm, then welfare maximization and firm value maximization need not coincide.
IV. Model Outcomes when Market Making is Competitive and the Firm Has Full Bargaining
Power.
We first assess model outcomes when the IPO market and the market for secondary trading are both
competitive.
The competitive IPO market implies 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, ING = 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 conditional on a liquidity shock is µ-δµ,
9 implying π = 0. The expected gain from secondary market trading is
, the t=0 value of the asset
to the investor and the IPO price are VT = Q = , and the Firm Net Gain, which equals the Social Net
Gain, is FNG =SNG = G =
. Under these assumptions the FNG 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, the completely liquid secondary market leads to an IPO at
full value, maximum firm value, and maximum social welfare.
IV.B The No-Secondary-Market Benchmark.
As a second benchmark, consider the case where there is no opportunity for secondary market
trading. The investor values the shares at VNT = 1
Gain are G0 = VNT – V =
. The net gain from trading and the Firm Net
. The firm will conduct the IPO only if , i.e. if the firm’s
need for cash is large relative to the product of the probability and magnitude of the investor liquidity
shock. These insights lead to the following:
PROPOSITION 1: The absence of secondary market trading causes the IPO to occur for a narrower
range of parameters, and leads to a decrease in welfare for all parameters, relative to the fully liquid
secondary market.
In particular, the IPO fails to occur, and welfare improvement is zero, if
The IPO occurs at the discounted price Q = VNT = 1
if
, but welfare is reduced by
.
as
compared to the case of a completely liquid secondary market.
Proposition 1 shows that the absence of secondary markets reduces economic efficiency and
welfare compared to fully liquid secondary markets.
We next assess economic efficiency with
competitive secondary markets that are not perfectly liquid.
IV.C. Competitive Market Making with Information Asymmetry.
We now turn to the scenario, similar to that considered in the classic analysis of Glosten and
Milgrom (1985), where there is a competitive secondary market, but the market is not completely liquid
10 due to information asymmetry. When the probability that the investor becomes privately informed prior
to t=1, p, is greater than zero the market maker potentially suffers trading losses, and reduces the bid price
to compensate. Let V1 denote the trader’s subjective time 1 value of the asset. The trader will sell in the
t=1 secondary market if V1 is less than the market maker bid quote, B.
There are six possible outcomes for V1, 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 liquidity shock, 1
1
if she is uninformed and does incur the liquidity shock,
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
( A ) 0
,
, and
.
( B ) Figure 1: The Investor’s Private t=1 Valuation, V1, for possible ranges of private valuation is stated in the square brackets.
11 ( C ) . The probability of each
As in Glosten and Milgrom (1985), the zero profit bid quote is the expected asset value
conditional on a sale by the investor.10 The expressions for 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 profit bid quote, B, is:
B= 1
,
given intermediate relative fundamental uncertainty, defined as
∗
∗∗
,
B = (1 – ϵ)μ given high relative fundamental uncertainty, defined as Where
∗
given low relative fundamental uncertainty, defined as B= 1
∗
≡
and
∗∗
≡
∗∗
,
.
Note that the bid quote is always discounted relative to the expected value of the asset, μ, as long
as p > 0. The discount is the expected informational content of the sale, which depends on uncertainty
regarding fundamental value, , and the probability that the trader is privately informed, p, relative to the
likelihood and magnitude of liquidity shocks.
We use the label relative fundamental uncertainty because the breakpoints
∗
and
∗∗
depend not
only on ε, which determines the differential between the two possible asset values, H – L, but also on
liquidity shocks and the probability of information asymmetry. Each breakpoint increases (implying
lower relative fundamental uncertainty) with increases in , the magnitude of the investor’s potential
liquidity shock and in λ, the probability of the liquidity shock. Conversely, each breakpoint decreases
(implying higher relative fundamental uncertainty) with increases in p, the probability that the investor
become privately informed.
10
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.
12 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 possible outcomes on
fundamental uncertainty ϵ and the probability that the trader becomes informed, p. Figure 2B displays
outcomes for possible outcomes on ϵ and λ. Most notably, 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
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
13 IV.D Firm Choice and Social Welfare with Competitive Market Making
We next assess the firm’s decision to conduct the IPO and social welfare when market making is
competitive. Setting M=0 and β=1, we have from expressions (1) and (2) that the IPO price is
1
. The firm net gain and social net gain are FNG = SNG = VT – V = μ(δ - πλρ). The firm
will complete the IPO only if Q > V, which requires πλρ < δ. That is, the IPO occurs only if the
anticipated utility losses from not being able to trade in the secondary market are 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 never dissuades the investor from selling in response
to a liquidity shock. That is, π = 0 when relative fundamental uncertainty is low and the bid price is
competitive. In this case the IPO price is Q = VT = µ, the IPO occurs for all δ >0, i.e. if the firm has any
need for cash.
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 conditional on a
liquidity shock is π = p/2. As a consequence the IPO price is reduced to Q = VT = 1
IPO occurs only if
and the
.
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 (probability1
) and subject to a liquidity shock (probability
Given high relative fundamental uncertainty and competitive market making the probability that the
14 .
investor does not sell, conditional on a liquidity shock, is reduced to Q = VT = 1
1
1
1
1
. The IPO fails to occur if
. The IPO price is
.
This discussion gives rise to the following:
PROPOSITION 2: Given β =1 and competitive market making in the presence of information
asymmetries,
(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 is social welfare is SNG = δµ, the maximum
attainable.
(ii)
If relative fundamental uncertainty is intermediate, i.e.
occur when
15 , the IPO does not
and the
.
. If the IPO occurs, the price is Q = 1
improvement is social welfare is SNG =
If relative fundamental uncertainty is high, i.e. if
1
∗∗
. If the IPO occurs the price is Q = 1
improvement is social welfare is SNG =
(iii)
∗
1
∗∗
, the IPO does not occur when
1
.
, and the
Figure 3: Firm Net Gains with Low, Intermediate, and High Relative Fundamental Uncertainty when
Market Making is Competitive
Proposition 2 demonstrates that, with low relative fundamental uncertainty, the competitive
equilibrium also maximizes social welfare. The IPO occurs in all cases where the firm has a liquidity
need, and the improvement in social welfare is the maximum attainable. There is no market failure and
no need for a DMM agreement when relative fundamental uncertainty is low.
However, Proposition 2 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, even for those parameters where 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 Firm Net Gain (FNG), (which in this case also equals the Social Net Gain),
that results from completing the IPO in competitive markets, for the same parameters used in Figure 2. In
those regions where the FNG is positive, the IPO occurs, while regions where FNG is zero are those
where the firm does not complete the IPO. Given these parameters, the FNG is δμ = 5 when relative
fundamental uncertainty is low. FNG is reduced when relative fundamental uncertainty is intermediate
or high, and more so when the probability of informed trading, p, is high. The IPO fails to occur when p
is sufficiently high, whether relative fundamental uncertainty is high or intermediate.
16 Why the Competitive Market Can Fail.
The potential market failures that arise in this model with competitive market making are
attributable to an information-based externality. Note that the market does not fail if the probability of
informed trading, p, equals zero. Setting p = 0, ϵ** is infinite, so that relative fundamental uncertainty
cannot be high. Further, with intermediate fundamental uncertainty π = p/2. So, with p = 0 the IPO
occurs for all ρ > 0, the IPO price is Q = μ, and the increase in social welfare is the maximum attainable.
Efficiency gains occur in this model for two reasons. First, the firm, which needs cash, can sell
the assets to the investor. Second, the investor can sell the assets to the market maker in the wake of a
possible personal liquidity shock. Social welfare is reduced by the possibility that an efficiencyimproving transaction may not occur. If the 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.
When p = 0 the competitive bid price is µ and the investor will always sell at t= 1 if she suffers a
liquidity shock. With p > 0, in contrast, the market can fail. The failure occurs because the competitive
bid price is reduced to offset expected market maker losses should the trader turn out to be informed
regarding the asset’s final value. Importantly, however, while trading losses due to asymmetric
information are indeed a private cost from the viewpoint of a market maker, such trading losses do not
comprise a social cost. 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 (relative to expected
asset value) by an amount greater than the net social cost of completing the trade. Social welfare is
damaged if this discounting of the bid price dissuades the trader from completing a secondary market
trade that would have enhanced welfare.
17 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
following central proposition, proofs for which are provided in the Appendix.
PROPOSITION 3: Given β =1 and competitive market making in the presence of information
asymmetries,
(i)
∗
If relative fundamental uncertainty is low, i.e. when
, the firm maximizes its value
and also social welfare by completing the IPO, without any subsidy to market makers.
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, the maximum attainable.
(ii)
If relative fundamental uncertainty is intermediate or high, i.e.
∗
the firm
maximizes its value and social welfare by completing the IPO and contracting with the
market maker to maintain a bid price equal to
∗
1
. 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, the
maximum attainable.
(iii)
Within the range where subsidization of the market maker is optimal, i.e.
magnitude of the optimal payment from the firm to the market maker is.
C =M=
C =M=
1
∗
1
1
∗
> 0 when
18 > 0 when
.
and
∗
, the
Figure 4: Optimal Payment from the Firm to the Market Makers with Low, Intermediate, and High
relative fundamental Uncertainty
Note that the optimal contracted bid price,
∗
, is the highest possible subjective valuation
conditional on the investor suffering a liquidity shock. As such, it ensures that the investor will always
sell in the wake of a liquidity shock. Given the contracted bid price, the time zero value of the asset to the
investor is VT = µ + M, where M = C enters because the investor has positive expected monetary gains
when the bid price in 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 VT by
more than the required payment to the market maker, because it increases U, the expected non-monetary
utility gain from trading in response to liquidity shocks, which enhances welfare.
Testable Implications Regarding DMM Contracts
Several aspects of Proposition 3 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
previously noted, the boundary point
∗
. As
increases with the probability, λ and magnitude, ρ, of investor
19 ∗
liquidity shocks, implying that larger and more frequent liquidity shocks reduce the need for DMMs.
However, these liquidity shock parameters are investor characteristics than do not differ across firms, if
investors hold diversified portfolios.
The breakpoint
∗
decreases with p, the probability that the investor will become informed. 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
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.
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. The model presented here suggests that a
DMM contract that binds only during times of increased asymmetric information can also be welfare and
value enhancing.
Proposition 3 also implies testable implications regarding the magnitude of the efficient payment
from firms to market makers. Figure 4 displays the efficient payment, 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 uncertainly 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. In practice, investors with cash inflows may experience subjective
20 increases in asset value that induce a desire to buy. Our model implies that a contract calling for the
market maker to increase the bid price can enhance firm value and social welfare. The direct extension
to a model with 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.
DMM contracts that focus on a narrowing of the bid-ask spread are in fact observed on a number
of markets, including the main stock markets in France, the Netherlands, Italy, Sweden, Norway, and
Italy.
On these markets, DMM contracts are typically employed for less liquid stocks. Note, though,
that our model implies that DMM contracts will enhance value and efficiency only when 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 information asymmetry.
Value is not enhanced
by constraining bid-ask spreads to offset order processing or inventory-carrying costs, which may also be
greater for thinly traded securities.
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 (the IPO occurs but some efficient secondary market trades do
not) or fully (the IPO does not occur) 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 a valuemaximizing firm will always cure any market failure by contracting with a market maker to enhance
secondary market liquidity.
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
21 market value of the shares issued, reflecting that some of the gains from trade are captured by
intermediaries in the form of commissions or by investors in the form of the “underpricing” of shares [See,
for example, Ibbotson (1975), and Ibbotson, Sindelar, and Ritter (1994)]. A full game theoretic model of
the IPO process is beyond the scope of this paper 11 . 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 β VT–V .
As noted earlier, the social net gain, which is the sum of trading gains to the firm, the investor,
and the market maker, can be written as SNG G0 U. Assuming that the firm will make a payment to
the market maker to offset any trading loss, i.e. C M, the firm’s net gain from trading can be written as
FNG β*SNG C β–1 . Let K denote a contracted secondary market bid price. The sensitivity of
SNG with respect to K is dU/dK. In contrast, the sensitivity of FNG with respect to K can be written as
β dU/dK β–1 dC/dK). If β =1 the sensitivities are equal, implying that a contracted bid price that
maximizes firm value (IPO price less payment to market maker) will also cure any market failures and
maximize the social gain from trade.
In contrast, if β 1, the sensitivities are not equal, and actions taken to improve firm value need
not lead to socially efficient outcomes. 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 trading
gains from the higher bid price.
The firm will conduct the IPO only if FNG is positive, and given that
the IPO occurs, the firm will contract to increase the bid price only if FNG 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.
11
Asymmetric information models of IPO underpricing are presented by Rock (1986) and Aggarwal, Krigman, and Womack (2002), among others. 22 PROPOSITION 4: Given β <1 and competitive market making in the presence of information
asymmetries,
(i)
∗
If relative fundamental uncertainty is low, i.e. when
, the firm will choose to
complete the IPO and will not choose to subsidize market makers, regardless of the
bargaining parameter, β. The net gain in social welfare is δμ, the maximum attainable.
(ii)
If relative fundamental uncertainty is intermediate, i.e.
∗
∗∗
there exists a range
of parameters for which the firm will choose to not compete the IPO, a range of
parameters for which the firm will complete the IPO but will not contract to increase the
bid price beyond competitive levels, and a range of parameters for which the firm will
∗
complete the IPO and will contract to increase the bid price to
1
.
Only the last of these leads to the maximum gain in social welfare, δμ.
(iii)
If relative fundamental uncertainty is high, i.e.
∗
, there exists a range of
parameters for which the firm will choose to not compete the IPO, a range of parameters
for which the firm will complete the IPO but will not contract to increase the bid price
beyond competitive levels, a range of parameters for which the firm will complete the
IPO and will contract to increase the bid price to B = (1-ρ)μ, and a range of parameters
for which the firm will complete the IPO and will contract to increase the bid price to
price to
∗
1
. Only the last of these leads to the maximum gain in social
welfare, δμ.
(iv)
Decreasing the firm’s bargaining power never improves social welfare, but can decrease
social welfare. In particular, if relative fundamental uncertainty is moderate or high,
decreasing β can cause the firm to switch from conducting the IPO and paying the
market maker to maintain a the socially optimal bid quote of
∗
1
to
contracting for a lower bid quote, not contracting for improved liquidity, or for some
parameters, not conducting the IPO.
23 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. When relative fundamental uncertainty is medium or high and β = 1 the value-maximizing firm
contracts to maintain a bid price
∗
1
, and the social net gain is still maximized.
However, decreasing the firm’s bargaining power when relative fundamental uncertainty is medium or
high 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 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 Table 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 are now bimodal, with the welfare gain either equal to the
maximum of 5 or equal to zero.
24 To summarize, frictions such as investment bank commissions or market underpricing that
prevent the firm from capturing in a higher IPO price the full market value of the asset it considers selling
in the IPO can only impede efficiency. That underpricing and other costs of conducting an IPO could
dissuade a firm from issuing public shares is to some extent obvious and intuitive.
Our model also
produces the more subtle result that these frictions may lead to a partial market failure, where the firm
conducts the IPO, but does not enter the efficient DMM contract. In situations where efficiency and firm
value would otherwise be maximized by a DMM agreement calling for the bid price to be increased to
∗
a reduction in the firms bargaining power will, for some parameters, induce the firm to contract for a
lower bid price or to decline to enter a DMM agreement at all. 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.
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
, 3 = IPO with subsidy to quote at ∗
1 .
to quote at B 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, it is
25 ,
possible that 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, it is
possible that a trading exchange may be able to extract monopoly rents in the form of trading fees, even if
competition prevails among potential market makers on the exchange. 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 insights obtained apply as well to cases where market makers have more modest
degree of monopoly power.
The key intuition of this analysis is the following. Monopolist rents are similar to asymmetric
information costs in the sense that they cause the secondary market bid price to be decreased (relative to μ,
the 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 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 first assess the effects of monopoly power in the secondary market, without considering a
possible DMM agreement. 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 for the following:
PROPOSITION 5: Given monopolist market making in the presence of information asymmetries,
26 (i)
The range of parameters over which there is total market failure, in the sense that the
firm declines to conduct the IPO, is narrower than if there is no secondary market
trading, but is wider than if market making is competitive.
(ii)
There is a range of parameters over which the IPO occurs and the social net gain is
equal to δµ, the maximum attainable. However, the range of parameters is narrower
than when market making is competitive.
Proposition 5 is intuitive, and reflects the fact that the investor bears higher expected liquidity
costs when the market maker has monopoly power. Consider expression (3) for the Firms Net Gain,
when the payment to the market maker, C, is zero. The IPO will occur only if the FNG is positive, which
requires that the social net gain (SNG) exceed the market making rent, -M*, However, the social net gain
is reduced by the lower bid price associated with market maker rents, leading to more frequent market
failure.
Figure 6 displays firm choices for a set of parameters, when market making is competitive and
when the market maker chooses the bid price to maximize market making profits. The range of
parameters for which the market fails completely in that the firm declines to engage in the IPO is strictly
increased by monopoly power in the secondary market, while the range of parameters for which the IPO
occurs and social net gains are maximized is strictly reduced by market making monopoly power. Further,
comparing Panel C of Table 6 to Panel A, an increased probability of informed trading, p, worsens the
effect of monopoly power, as the market fails completely over a larger range of parameters.
27 Figure 6: Social Net Gains with Competitive vs. Monopoly Market Making. The vertical axis is Social
Net Gain. In those regions where the SNG is positive, the IPO occurs, while those regions where SNG is
zero reflect that the firm does not complete the IPO.
We next assess the effect of a potential DMM contract between the firm and the monopolist
market maker. In the appendix we provide proof of the following:
PROPOSITION 6: Given monopolist market making in the presence of information asymmetries,
28 (i)
If δµ < -M* there is complete market failure, as the firm does not conduct the IPO.
(ii)
If δµ > -M* and β = 1 then the firm will conduct the IPO and social welfare will be
maximized. If is sufficiently small this outcome is achieved with monopoly market making,
otherwise it is achieved by the firm choosing to contract with the market maker for the
secondary market bid price
(iii)
∗
1
.
If δµ > -M*, β < 1 and is sufficiently small the firm will complete the IPO. However, the
range of parameters with partial market failure because the firm does not contract for the
socially optimal bid price, B*, expands.
(iv)
If δµ > -M*, β < 1 and is not sufficiently small then the range of parameters with market
failure due to the firm not contracting for B* expands. Further, the market failure in this
case is full, as the firm does not conduct the IPO. Decreasing β expands the range of
parameters with total market failure.
Proposition 6 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
preclude the firm from conducting the IPO. Further, the range of parameters where efficient outcomes
are reached even without a DMM agreement is reduced by monopoly power. Proposition 6 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 7 displays outcomes 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
29 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.
Figure 7: 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
, 3 = IPO with subsidy to quote at ∗
1 subsidy, 2 = IPO with subsidy to quote at B 1
.
30 VI. Conclusions and Implications
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. Such a contract can potentially 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
market provides less liquidity than the socially-efficient level.
DMM contracts comprise a potential
market solution to this market imperfection.
Our model shows that illiquidity in the secondary market can lead to a complete market failure, in
the sense that the firm never completes an initial public offering (IPO) of its shares, or a partial market
failure where the IPO occurs, but at a price that is discounted to reflect the possibility that efficient
secondary market trades will not occur.
However, we show that, if the firm is able to capture in a higher
IPO price all of the benefits from improved liquidity and the market for liquidity provision is otherwise
competitive, then the firm will choose to enter a contract where a DMM improves secondary market
liquidity such that socially efficient outcomes will be obtained. In contrast, if either liquidity is supplied
by a monopolist or the firm lacks full bargaining power, such that some of the benefits from improved
liquidity are captured by investors or intermediaries, the market may still fail.
Our analysis shows that the potential benefits of contracts that require enhanced liquidity supply
are related to information, rather than illiquidity, per se. A simple insight is that contracts for additional
liquidity supply are needed for those firms or at those times when liquidity is scarce. Our analysis does
not support this view, to the extent that illiquidity is attributable to high real costs, e.g. the high inventory
costs associated with large volatility and/or infrequent trading. Value will not be enhanced by contracts
31 that reduce spreads below the real social costs of market making.
Instead, our analysis implies that
efficiency and firm value can be enhanced for those firms or at those times when liquidity due to a
combination of high fundamental uncertainty and information asymmetries. Our analysis indicates that
competitive market making leads to efficient outcomes when relative fundamental uncertainty is low,
while DMM contracts can enhance firm value when relative fundamental uncertainty is high. In the cross
section, our analysis implies that DMM contracts are likely to be useful for smaller and younger firms, as
opposed to larger firms with a high proportion of assets-in-place. In the time series, our analysis implies
that DMM contracts may be useful if the require additional liquidity provision at times when perceived
fundamental uncertainty and information asymmetries are temporarily elevated.
The model presented here has a number of implications for researchers and policy makers. First,
and most important, our analysis shows that economic efficiency and firm value can be enhanced by
contracts that require liquidity providers to provide more liquidity than they would otherwise choose. In
light of the absence of barriers to entry in providing liquidity in electronic limit order markets, it seems
reasonable to assume the business of liquidity provision is competitive. If so, side payments will be
required to induce one or more designated market makers to take on such affirmative obligations, and our
model implies that affirmative obligations to provide liquidity should not be imposed in the absence of
compensation to the DMMs. Contracts of the type studied here, calling for a contract between the listed
firm and the DMM, are observed on some international markets, but are currently prohibited in U.S.
markets by FINRA Rule 5250. Our model shows that the competitive bid-ask spread fails to maximize
trader welfare or firm value, due to externalities associated with information asymmetries.
DMM
contracts of the type considered here comprise a potential market solution to a market imperfection.
Some limitations of our analysis should be noted. In particular, our model focuses for simplicity
on a single trader, a single round of trading, and trades of unit size. As such, we have not considered
potential effects of market maker affirmative obligations on trade timing, trade sizes, repeat trading, or
trading aggressiveness, each of which provides useful possibilities for future research.
32 Further, we have not considered the full range of potential DMM agreements. We focus only on
a contract by which a listed firm pays a flat fee to a DMM to increase the market bid price, or by
extension, to narrow the bid-ask spread. While this contract is indeed of interest because of its simplicity,
because it is representative of contracts observed on a number of markets, and because it is currently
prohibited in the U.S., numerous other contracts could be evaluated.
A number of stock exchanges have in recent years implemented differential fees for orders that
“take” (marketable orders, which execute against standing limit orders) liquidity as compared to orders
that “make” (limit orders that do not execute immediately, thereby providing trading options to others)
liquidity. In some cases the make fees are negative, implying a subsidy for liquidity provision. 12
Further, it is noteworthy that U.S. exchanges have been at the forefront of efforts to allow for DMM
contracts, suggesting that exchanges may also benefit from DMM contracts, due to their effect on trading
volume. While we defer a complete analysis of potential DMM contracts between exchanges and
liquidity providers for future research, we make the following observations.
An exchange may choose to enhance liquidity through a smaller total (make plus take) fee. 13 If
the exchange previously earned monopoly rents from its fees then the effect is similar to that of monopoly
market making, as discussed in Section V.
Alternatively, if the reduction in trading fees implies
economic losses to the exchange then a transfer payment would be required. If the exchange recovers the
lost trading fee revenue through a higher listing fee, the final outcome parallels that of our model, but may
bypass explicit prohibitions against market making payments by issuers.
A phenomenon that we have not considered is the possibility of a liquidity externality of the type
considered by Foucault, Kadan and Kandel (2013).
In their model an exogenous shock that increases
trading frequencies reduces the marginal cost of monitoring, and induces market makers to invest in
12
See, for example, Foucault, Kadan, and Kandel (2013), Malinova and Park (2011) and Cardella, Hao, and
Kalcheva (2013.)
13
Angel, Harris and Spatt (2011) argue that given (i) a fixed total exchange fee and (ii) the absence of any friction,
any subsidization of liquidity provision through reduced or negative “make” fees will be neutralized in competitive
equilibrium by offsetting changes in bid and ask quotes. However, Foucault, Kadan, and Kandel (2013) show that
the make-take fee breakdown is indeed relevant in markets with a non-trivial tick size, even with a fixed total fee. 33 technology to monitor markets more closely. A DMM contract of the type considered here induces
higher trading frequencies and could trigger such liquidity externalities, both within and across stocks. A
model that is extended to incorporate such effects may well lead to the implication that the most efficient
contract involves a combination of liquidity rebates by the exchange and direct market making payments
by the listed firm.
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35 Table 1: Definition of Notation
Symbol
Description
Algebraic
Definition
The unconditional expected value of the asset.
The amount of uncertainty regarding asset value.
The high ex post outcome on asset liquidation value.
∗
∗
G
∗
∗
relative fundamental uncertainty.
High relative fundamental uncertainty.
A contracted secondary market bid price.
36 1
1
The low ex post outcome on asset liquidation value.
1
The discount factor that determines the t=0 value of the asset to the firm. 0
1
The t=0 value of the asset to the firm.
1
The probability that the investor incurs a liquidity shock.
The fraction by which the investor’s subjective valuation of the asset is 0
1
reduced when she incurs a liquidity shock.
The t=0 value of the asset to the investor without secondary market
1
trading.
The probability that the investor will become privately informed as to
whether the liquidation value of the asset will be H or L.
The investor’s expected monetary gain, or equivalently, the market
maker’s expected monetary loss, from t=1 secondary market trading.
The outcome on M if the market maker chooses the bid quote to
minimize M (maximize –M).
The t=1 bid quote.
∗
The bid quote that maximizes social net gain.
1
The probability that the investor will choose not to sell her asset,
conditional on a t=1 liquidity shock.
The investor’s expected non-monetary utility gain from trading in
1
response to a t=1 liquidity shock.
The t=0 value of the asset to the investor with secondary market trading.
The cash payment from the firm to the market maker, if any.
The increase in the time 0 value of the asset due to trading opportunities. ≡ –
The gain in the t=0 value from transferring the asset from the firm to the
≡
–
investor in the time 0 IPO, when no further trading is possible.
The gain in the t=0 value due to the investor’s ability to trade in the
≡ –
secondary market at t=1.
The firm’s bargaining power in the IPO market.
The IPO price.
The Firm Net Gain, relative to the status quo.
– –
The Market Maker Net Gain.
–
The investor Net Gain relative to the status quo.
–
The Social Net Gain.
SNG = FNG +
MMNG + ING
The trader’s subjective time 1 value of the asset
2λ
1 λ p
Low relative fundamental uncertainty.
ϵ∗ ≡ ∗∗ Intermediate
∗∗
0
ϵ∗∗
2 p λ
p 2 1
≡
p
pλ
p λ
ρ
Appendix:
Proof of Lemma 1:
With competitive market making and information asymmetry, as Glosten and Milgrom (1985),
the market maker in equilibrium sets the bid price equal to the expected asset value conditional on a sell,
which is less than the unconditional expected asset value μ and greater than the lowest possible realized
value of the asset 1
ϵ μ. We use prefix M and P with number suffix to denote the ranges of ϵ relative
to ρ with which the different equilibrium bids hold. Prefix M refers to market equilibria in cases where
the competitive market leads to efficient outcomes, and prefix P refers to partial market equilibria in cases
where the competitive market leads to partial market failure, as discussed in the main text.
Specifically, when 0
1
1
, the relative ordering of the investor’s six private valuations is
1
1
1
. In this case, there is one
possible equilibrium (M1) with a competitive bid price BidM1, as illustrated in figure 1 (A). When
, the relative ordering of the investor’s six private valuations is 1
1
1
1
1
. In this case, there are two possible equilibria (M2, P1),
1, the relative
corresponding to bid prices BidM2 and BidP1 illustrated in figure 1 (B). When
ordering of the investor’s six private valuations is 1
1
1
1
1
. As in the previous case, there are two possible equilibria (P2, P3), corresponding
to bid prices BidP2 and BidP3, as illustrated in figure 1 (C).
For the candidate Market Equilibria (M1 and M2), as shown in figure 1 (A) and (B) with BidM1
and BidM2, the investor sells at time l if and only if she is i) informed with good news and incurs the
liquidity shock, or ii) uninformed and incurs the liquidity shock, or iii) informed with bad news.
Conditional on a sale, the expectation of the asset value and bid price is 1
for both M1
and M2. For the candidate M1 to be an equilibrium, it must be that the investor is willing to follow the
37 conjectured strategy, given the bid price. This is the case if and only if the asset valuation by the investor
with bad news and absent a liquidity shock is below the bid price, and the asset valuation by the investor
who is uninformed and absent a liquidity shock is above the bid price , i.e., if 1
. That is 0
1
. Similarly, the condition for M2 to be an equilibrium is 1
. That is
∗
when 0
, where
.
∗
Thus, the competitive bid price is 1
.
For the candidate Partial Market Equilibria (P1 and P2), as shown in figure 1 (B) and (C) with
BidP1 and BidP2, the investor sells at time l if and only if she is i) uninformed and incurs the liquidity
shock, or ii) informed with bad news. This arises when, after good news, the investor prefers keeping the
share to selling it, even if she incurs a liquidity shock. Conditional on a sale, the expectation of the asset
value and correspondingly the bid price is 1
candidates to be equilibria are 1
in both P1 and P2. The conditions for these
1
for P1 and 1
for P2,
respectively. That is, the ranges of the parameters with which the equilibria hold are
1,
for P114 and
when
∗
∗∗
, where
∗∗
for P2. Thus, the competitive bid price is 1
.
For the candidate Partial Market Equilibrium (P3), as shown in figure 1(C) with BidP3, the
investor sells at time l if and only if she is informed with bad news. In another word, the investor prefers
14
When
either 1
, both M2 and P1 are possible. The marker makers can set the bid price to
or to 1
, and break-even in either case. Competition between market
makers should lead to equilibrium with the higher bid price, 1
. In case the market makers collude
to quote the lower one, the firm can request the market makers to quote the higher bid price 1
without subsidy. Hence, M2 is achieved. The parameter range with which the equilibrium holds are
for P1.
38 to keep the shares when she is informed with good news or uninformed, even if she incurs a liquidity
shock. Conditional on a sale, the expectation of asset value and correspondingly the bid price is 1
The condition for P3 to be an equilibrium is 1
parameters, with which P315 holds, is
when
∗∗
1
.
. That is, the range of the
1 . Thus, the competitive bid price is 1
1.
1
1
2λ
1
λ p
ϵ λ p
1
1
2 1
Figure A1: Range of the Relative Fundamental Uncertainty with which Each Equilibrium Bid Holds
Proof of Proposition 3:
We assume β =1 and the presence of information asymmetries. When ϵ
∗
the market maker to quote at
1
∗
, the firm can require
and reduces π to zero. However, this leads to an
expected monetary loss M to the market maker, which need to be subsidized by the firm with payment
15
When (or
bid price to either
λ
, both P2 and P3 are possible. The marker makers can set the
λ
or
, and break even in either case. The competition between the market
makers should lead them to set the bid price to the higher one 1
λ
ϵ μ. If the market makers collude to
quote the lower one, the firm can request the market makers to quote the higher bid price 1
λ
subsidy. Hence, P2 is achieved. And the range of the parameters, with which P3 holds, is
Since
1, it is possible that
ρ
1. If
ρ
1,
ρ
ϵ μ without
ρ
1.
can never be satisfied
because ϵ is no larger than 1. In this case, this P3 equilibrium cannot be reached. In this rest of the paper, we always
include P3 equilibrium in our discussion. Whether P3 can be reached does not have any influence on other
equilibria. 39 C=M >0. From expression (1) and (2), the IPO price is
gain are
. The firm net gain and social net
, the maximum attainable. The subsidy to the market maker that
needs to be paid by the firm to offset the loss is the product of the probability of sell conditional on the
contracted bid and the difference between the market maker’s expectation of the asset value conditional
on a sale and the contracted bid price.
Specifically, given the contracted bid price
∗
1
∗
, when
, as shown in
figure 1(B), the investor sells at time l if she is (i) informed with good news and incurs the liquidity shock
(which occurs with probability
probability 1
), or (iii) informed with bad news (which occurs with probability ). The probability
1
of sell is
1
), (ii) uninformed and incurs the liquidity shock (which occurs with
, and the market maker’s expected asset value conditional on a sale at
is 1
1
. Hence, the expected subsidy to the market maker is
∗
1
1
1
∗
1
∗
∗
. Since
Similarly, when
∗
1
∗
where
, as shown in figure 1(C), the investor sells at time l if she is (i) informed
occurs with probability 1
), (ii) uninformed (which
), or (iii) informed with bad news (which occurs with probability ). The
1
probability of sell is
, and the market maker’s expectation of the value of the asset
conditional on a sale at 1
∗
is 1
1
. Hence, the subsidy to the market maker is
1
1
. Because
40 ,
0.
,
with good news and incurs a liquidity shock (which occurs with probability
1
1
1
,
1
∗
λ
0.
Proof of Proposition 4:
Given β <1 and competitive market making in the presence of information asymmetries, when
∗
relative fundamental uncertainty is low, i.e.,
(in equilibrium M1 and M2), the competitive bids
BidM1 and BidM2 as shown in figure 1 are higher than 1
. The investor will always transfer the
asset to the market maker after a liquidity shock. Hence π= 0 and there is no subsidy M=C=0. Let
and
denote the firm net gain and the social net gain with competitive market making
with no subsidy, respectively. From expression (3), we have
and
, the
maximum attainable, when relative fundamental uncertainty is low.
When relative fundamental uncertainty is intermediate, i.e.,
∗
∗∗
(in equilibrium P1 and
P2), with competitive bids BidP1 and BidP2 as shown in figure 1, the informed trader with good news will
not sell when after incurring a liquidity shock, which is
social net gains are reduced to
. With no subsidy (M=C 0), firm and
and
. A DMM
contract by which the firm induces the market maker to quote a higher bid price can potentially cure the
market failure.
More specifically, in equilibrium P1, requiring the market maker to quote at ∗
1
reduces π to zero , while imposing a monetary cost
, to the
market maker, which needs to be subsidized by the firm with payment C M .
1
value of the shares to the investor becomes
and
. Let
denote the firm net gain and the social net gain respectively when the firm subsidizes
the market maker to quote at B ∗
1
ϵ
ρ μ.
and
the full cost C and recovering only a portion
In P1, we have
1
∗
, the maximum attainable. However, bearing
from the higher IPO price, the firm may not choose to
41 With this subsidy, the
fully subsidize the market maker, implying that the firm’s optimal choice may be different from the social
optimal choice.
Specifically, in equilibrium P1, we have the following:
It is optimal for the firm to choose to conduct the IPO and to also subsidize the market maker to
quote at B* = 1
and
(i.e. first best, maximizing social welfare), if and only if:
0. That is
,
.
It is optimal for the firm to choose to forgo the IPO, (i.e., the IPO market breaks down), if and
only if:
0 and
0. That is
and
.
It is optimal for the firm to choose to conduct the IPO and to rely on competitive market making
without subsidy (i.e. the secondary market partially breaks down), if and only if:
0. That is
and
and
.
In equilibrium P2, subsidizing market maker to quote at B ∗ reduces π to zero, but involves a
1
market making cost
C=M. The value to the investor becomes
to the market maker which must be subsidized with
1
1
. If the firm chooses to
subsidize the market maker to quote at B* the firm and social net gains are
1
1
and
. However, as in P1, the firm’s optimal choice may
deviate from the social optimal choice. In equilibrium P2, we have the following:
It is optimal for the firm to engage in the IPO and subsidize the market maker to quote at
and
0. That is, if
42 ,
.
∗
, if
0 and
It is optimal for the firm to forego the IPO if
and
0. That is, if
.
It is optimal for the firm to complete the IPO and rely on competitive market making (i.e. the
and
0 . That is, if
and
secondary market partially breaks down), if
.
When relative fundamental uncertainty is high, i.e.,
∗∗
(in equilibrium P3), with
competitive bid BidP3 as shown in figure 1, the investor will not sell despite incurring a liquidity shock if
1
she is informed with good news or is uninformed, which is
1
the investor to
1
1
. This reduces the value to
. With competitive market making (M=C=0),
and
1
, respectively.
Similar to P1 and P2, in equilibrium P3, the firm can choose to fully subsidize the market maker
to quote at
1
∗
1
. In this case,
to the market maker, which needs to be subsidized with C=M. The value to the investor
with this full subsidy becomes
1
0 while the market making cost is
1
1
1
. The firm net gain is
, while the social net gain is
. Alternately, in equilibrium
P3, the firm can choose to subsidize the market maker to quote at
1
In this case,
and the market making cost is
, which is less than
. Let
and
and
43 1
denote the firm net gain and the social net gain
respectively, when the firm partially subsidizes the market maker to quote at 1
1
.
which is also the amount
to be subsidized C M. With this smaller subsidy, the value of the asset to the investor is
∗
.
.
In equilibrium P3, we have the following:
It is optimal for the firm to complete the IPO and to contract with the market maker to quote at
∗
1
(i.e., the first best, maximizing social welfare), if
,
0. This requires
, and
,
,
.
It is optimal for the firm to choose forego the IPO (i.e., the IPO market breaks down), if
0,
0, and
0. This requires
,
1
and
.
It is optimal for the firm to choose to conduct the IPO and to rely on competitive market making
without subsidy (i.e. the secondary market partially breaks down), if:
0. This requires
, and
,
1
,
and
.
It is optimal for the firm to conduct the IPO and partially subsidize the market maker to quote at
B=
,
(i.e., the secondary market partially breaks down), if
0. This requires
, and
,
.
The preceding analysis implies that, when relative fundamental uncertainty is moderate or high,
the firm is more likely to enter a DMM agreement that maximizes social welfare the higher its bargaining
power in the IPO market, β.
44 Proof of Proposition 5:
To prove Proposition 5, we focus on three cases defined by the relation between
0
,
and
,
1. We then identify the equilibrium monopoly bids that maximize
, and
the market maker’s expected profit (–M), and the corresponding ranges of the parameters where each
equilibrium monopoly bid holds. The maximum monopoly rent in each equilibrium is denoted as –M*>0.
The monopoly case is denoted with a prime symbol as illustrated in figure A2.
Bid’M2’
Bid’P3’
Bid’P2’
Bid’M1’ Bid’P1’ Bid’P5’
Bid’P4’
( B ) ( A ) 0
( C ) Figure A2: Investor’s Private t=1 Valuation and Equilibrium Monopoly Bid for possible ranges of
. The probability of each private valuation is in the square bracket.
In Market Equilibria (M1’ and M2’), the monopoly bid is 1
, which is the investor’s
highest possible private valuation of the asset given that she incurs a liquidity shock. With this bid, the
investor can always sell when incurs a liquidity shock. Therefore,
∗
0. In M1’, the monopoly rent is
and the range of the parameters with which M1’ holds is 0
M2’, the monopoly rent is
which M2’ hold is
∗
1
,
and the range of the parameters with
,
.
In Partial Market Equilibria (P1’, P2’ and P3’), the monopoly bids are 1
. The investor
will not sell when she is informed with good new after incurring a liquidity shock, which means
45 . In
. In
∗
P1’, the monopoly rent is
2
,
holds is
and the range of the parameters with which P1’
of the parameters with which P2’ holds is
when 10
∗
is
4
6
0, or
1
min 1,
∗
. In P2’, the monopoly rent is
2
. The range
,
0 when 10
4
,
6
and either
0. In P3’, the monopoly rent
and the range of the parameters with which P3’ holds is
.
In Partial Market Equilibria (P4’ and P5’), the monopoly bid is 1
. The investor will
not sell when she is informed with good news or uninformed after a liquidity shock, which means
1
. In both P4’ and P5’, the monopoly rent is
∗
,
with which the equilibria hold are
and the ranges of the parameters
in P4’ and
in P5’.
Given monopoly market making and no subsidy (C=0), the market maker’s monetary gain from
trading with the investor (
net gain is
∗
μ
μ
∗
. The investor’s net gain is
∗
. From expression (3), firm
1
μ
μ
. Combining firm net gain, investor net gain, and the monopoly market maker’s rent, we have the
social net gain
rent
) equals to the maximum possible profit (
∗
μ
μ. This implies that, just as information asymmetry cost, the monopoly
is a zero-sum monetary transfer rather than a cost from the viewpoint of society as a whole,
with fraction
transferred from the firm to the monopoly market maker and fraction 1
transferred
from the investor to the monopoly market maker.
In equilibrium M1’ and M2’, the monopoly bid is 1
conditional on a liquidity shock is
is non-negative, i.e.,
∗
. The probability of no sell
0 and the firm net gain is
. If the firm net gain
, the firm will engage in the IPO and will rely on monopoly market
making. Despite the extraction of monopoly rents, the social net gain is
46 ∗
, the maximum
if 0
attainable. This outcome obtains with
1
if
,
,
, or with
. Compared to competitive
market making (where the IPO occurs and the social net gain is maximized without a DMM contract
when
∗
for any ), the range of parameters over which IPO occurs and the social net gain is
maximized is narrower with monopoly market making.
In the partial market equilibria P1’ to P5’, the monopoly bid is less than 1
, implying
π > 0, i.e that the investor who incurs a liquidity shock is not always willing to sell. As in the competitive
market, when the discounting of the bid price dissuades the investor to sell after a liquidity shock, the
secondary market will partially break down, leading either to a failure of the IPO market or a lower IPO
price. Furthermore, the selection by the monopoly market maker of a bid quote lower than the competitive
bid implies the possibility of outcomes where the investor would decline to sell in response to a liquidity
shock at the monopoly bid, but would have sold at the competitive bid. Specifically, as illustrated in
figure A2, in P1’ (defined as
,
), the monopoly bid Bid’P1’ is less than both the
competitive bid BidM1 in the same parameter range and 1
. In this range the investor when
informed with good news and incurring a liquidity shock would sell at the competitive bid but not at the
and max
monopoly bid. In P2’ (defined by
,
min
,
), the
competitive bid in this parameter range can be either BidM2 or BidP1. If
,
,
and
, the competitive bid is BidM2.
For these
parameters the investor when informed with good news and incurring a shock would sell at the
competitive bid, but not at the monopoly bid. If
and
min
,
,
the competitive bid is BidP1, and the investor when incurring a shock would make the same trading
decisions in either a competitive or monopoly market. In P3’(defined by
47 min 1,
),
the investor’s trading behavior is the same in both competitive and monopoly market. In P4’ (defined by
,
,
, if
, the competitive
bid is BidM2, which means the investor will always sell after a liquidity shock. With the monopoly bid
BidP4’ the investor when incurring a liquidity shock will sell only if observing bad news. Also within P4’,
, the competitive bid is BidP1, and the uninformed investor when incurring a
if
liquidity shock will sell in the competitive market but not in the monopoly market. In P5’ (defined by
), when
, the competitive bid is BidP2. The uninformed
investor with a liquidity shock would sell in the competitive market, but not in monopoly market. Also in
, the competitive bid is BidP3. When incurring a shock, the investor’s trading
P5’, when
behavior given these parameters is the same with competitive or monopoly market making.
The proceeding discussion shows that the monopoly power will only increase, π, the probability
of not selling conditional on a liquidity shock. As noted, with monopoly market making and no subsidy,
μ
μ
∗
. If it is negative, the firm keeps the share and the IPO market breaks
∗
down. That is when the expected liquidity cost and the monopoly rent are large (
).
Comparing with the No-Secondary-Market Benchmark, where the IPO market breaks down if ,
the range of parameters over which the IPO market breaks down with monopoly market making is
narrower.16 However, comparing with competitive market making, where the IPO market breaks down if
, the range of parameters with monopoly market making is wider. It is wider by the amount of
the monopoly rent
∗
0 and the higher expected liquidity cost due to the increased π.
16
∗
In M1’ and M2’, ∗
1
∗
∗
. In P4’ and P5’, 48 ∗
. In P1’ and P2’,
. So, . In P3’ (
∗
. ), The increase in π due to monopoly power could also lead to lower social welfare. As noted, with
monopoly market making and no subsidy, social net gain is
μ
μ, which is never larger
than that in the competitive market, because monopoly power can only increase . Just as information
∗
asymmetry cost, the monopoly rent
0 is a also zero-sum monetary transfer rather than a social cost.
As such, monopoly rents in market making also potentially decreases allocative efficiency because the
lower bid prices associated with monopoly power also dissuade trading in response to liquidity shocks.
Proof of proposition 6:
Given monopolist market making in the presence of information asymmetries, if the firm
subsidizes the monopoly market maker to quote a bid price higher than the monopoly bid, the market
maker’s monetary gain from trading with the investor –M is less than the maximum possible rent,
∗
The payment a monopoly market maker requiring from the firm is
firm net gain is
gain is
–
∗
.
. From expression (3),
∗
–
and social net
.
When β=1, firm net gain becomes
and M2’), π is zero, which makes
∗
. If
∗
∗
. If is sufficiently small (in M1’
, the firm will conduct IPO with
monopoly market making, which leads to the maximum possible social net gain
(in P1’ to P5’), π is positive and firm net gain is reduced by
. If
is relatively large
due do the investor’s not trading after a
liquidity shock. Since β=1, the firm can contract with the market maker to quote at
∗
1
and capture in a higher IPO price any increase in the value of the asset attributable to better secondary
market liquidity. This reduces π to zero and improves the firm net gain to
implies that, when
market maker to bid at
∗
∗
∗
. This
and β=1, if is not sufficiently small, the firm should always subsidize the
1
and leads to the maximum possible social net gain
49 .
1, as was the case when β=1, if the maximum possible gain from secondary market
When
trading is less than the monopoly rent, i.e.,
1 and
breaks down. When
∗
,
∗
∗
, if
∗
, the firm will keep the share and the IPO market
is sufficiently small (in M1’ and M2’),
, and
∗
market maker to quote at the same
0,
. In this case, the firm will conduct IPO without subsidy
and
and leads to the maximum possible social net gain
∗
0,
. If
is relatively large (in P1’ to P5’),
0,
– . Compare to the case with β=1, requesting the
, the firm just captures fraction
of the gain from secondary market
trading while bearing the same full cost. This lower FNG due to the lower bargaining power leads to a
wider range of parameters with which the firm will switch from conducting the IPO and paying the
market maker to maintain a bid quote of
∗
1
to contracting for a lower bid quote, not
contracting for improved liquidity, or for some parameters, not conducting the IPO.
With both competitive and monopoly market making, the firm can choose no IPO, IPO with no
subsidy, IPO with full subsidy for the market maker to quote at B ∗
1
ϵ
parameter range, IPO with partial subsidy for the market maker to quote at B
ρ μ , and, in some
1
ρ μ. If the firm
chooses no IPO, FNG=0. The firm will choose the one that maximizes its net gain.
In a competitive market, the subsidy C paid by the firm equals to the market maker’s monetary
loss M. Let no subscript, subscript sub, and subscript subp denote the firm choice of IPO with no, full,
and partial subsidy respectively in the competitive market. From expression (3) we have:
FNG
FNG
FNG
β δμ
πλρμ
β δμ
β δμ
π
π
(1)
λρμ
λρμ
M
M
When the competitive bid is lower than
quote at
∗
if and only if FNG
M
(2)
M
∗
, the firm will choose to subsidize the market maker to
, FNG
50 (3)
, and FNG
0.
When β
, FNG
β
. When β
, FNG
0 . Let A
, FNG
. When
, B
, C
. It is optimal for the firm to subsidize the competitive market maker to quote
at
∗
if β
, ,
∗
In a monopoly market, if the firm conducts IPO without subsidy,
∗
IPO and subsidizes the market maker,
. If the firm conducts
. Let a prime symbol denote monopoly market making.
Notably, M and π only depend on the contracted bid price but not the type of market maker. From
expression (3) we have:
FNG
β δμ– π λρμ
FNG
FNG
β δμ
π
β δμ
π
M∗
(4)
λρμ
λρμ
M
M∗
M
M
(5)
M∗
M
(6)
The firm will choose to subsidize the market maker to quote at B* if and only if FNG
FNG
, FNG
FNG
. When β
Let A
FNG , and FNG
∗
, FNG
∗
∗
0 . When β
FNG . When β
∗
,B
, FNG
,C
∗
for the firm to subsidize the monopoly market maker to quote at
0,
and
. Also
∗
, FNG
0.
. It is optimal
∗
if β
A , B , C . Because
∗
.
Given the competitive and monopoly equilibrium bids in each range of ϵ, we compare the
condition with which the firm’s choice leads to maximum possible social net gain in competitive and
monopoly market respectively. Such firm choice is to conduct IPO if the range of ϵ is corresponding to
the market equilibrium which market making leads to efficient outcomes, i.e., the equilibrium with a “M”
prefix. And this firm choice is to conduct IPO and contract with the market maker to quote at
51 ∗
if the
range of ϵ is corresponding to the equilibrium which market making leads to partial market failure, i.e.,
the equilibrium with a “P” prefix. As shown in figure A3, for range 1 to 5, it is obvious that the range of
parameters (δ and/orβ) with which the firm choice leads to maximum possible social net gain is narrower
with monopoly than competitive market making. Since A
max A , B
max A, B for interval 6 and 8, max A , B , C
, B
max A , B
, and C
C , we have
,
for interval 7
max A, B, C for interval 10. This implies that the range of parameters (δ
and 9, and max A , B , C
and/orβ) with which the firm choice leads to maximum possible social net gain is narrower with in
monopoly market.
Table A1: The condition with which the firm’s choice leads to maximum possible social net gain in
competitive and monopoly market
Range of Competitive
Bid
1 1
,
2
0
1
,
2
2 3 2
2
2 2
4 ,
2
2
2
2
2
2
6 ,
2
2
10
2
2
2
min 1,
2
,
Any and 1′
max A , B 2
Any and 2′
µ
2
Any and 2′
max A , B 2
Any and 4′
1
max
,
2′
1
max
,
4′
2
max
,
3′
2
max
,
5′
max A , B , C
, ,
5′
max A , B , C
2
3
2
1
1
min
1
8
3
2
2
2
2
52 ∗
µ
∗
and
7
9
2
Condition 1′
,
and
,
5
3
Bid
Any and 1
2
2
Condition
1
2
Monopoly max
max A , B , C
max A , B max A , B , C
max A , B