Do Individual NYSE Specialists Cross-Subsidize Illiquid ...finance/020601/news/Huang paper.pdf ·...
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Do Individual NYSE Specialists Cross-Subsidize Illiquid Stocks?
Roger D. Huang
Mendoza College of Business University of Notre Dame
Notre Dame, IN 46556 Phone: 574-631-6370 Fax: 574-631-5544
Email: [email protected]
Jerry W. Liu Krannert School of Management
Purdue University 425 West State Street
West Lafayette, IN 47907 Phone: 765-496-7674 Fax: 765-494-0818
Email: [email protected]
First Draft: November 2003
Do Individual NYSE Specialists Cross-Subsidize Illiquid Stocks?
Abstract
Do individual New York Stock Exchange (NYSE) specialists fulfill their affirmative
obligation by cross-subsidizing trading on illiquid stocks with their profits from trading
liquid stocks? A simple model of cross-subsidization is constructed and is used to
develop testable implications of this hypothesis. In a departure from the existing
literature, the empirical analysis is conducted at the individual specialist portfolio level
rather than at the specialist firm level. We find that specialist portfolios are characterized
by one or two frequently traded stocks and several illiquid stocks. The existence of cross-
subsidization is confirmed by tests from the perspectives of both donor and beneficiary
stocks within the same portfolio. Our results document support for illiquid stocks in a
specialist market and suggest the need to examine jointly all of the stocks in specialist
portfolios when examining NYSE stocks.
Do Individual NYSE Specialists Cross-Subsidize Illiquid Stocks?
1. Introduction
A central feature of the New York Stock Exchange (NYSE) structure is the role of
specialists in the trading process. Every specialist makes a market in a portfolio of stocks
and each stock is assigned exclusively to a specific specialist. In return for their exclusive
rights, specialists have an affirmative obligation to be the liquidity supplier of the last
resort and to maintain “fair and orderly markets.” Although this obligation applies to all
stocks in their portfolios, the level of intervention needed differs among stocks; less
intervention is required for frequently traded stocks and more is required for infrequently
traded ones. This difference in need suggests the possibility that specialists cross-
subsidize low volume stocks with profits from high volume stocks to fulfill their
affirmative obligation.
Whether or not NYSE specialists engage in cross-subsidization speaks directly to
the efficacy of the NYSE trading system. The controversy over the relative benefits of the
NYSE system with its human intervention, as opposed to those of the computerized
systems used by Nasdaq market makers and electronic communication networks (ECNs)
is an ongoing public debate. Opponents of the specialist system often emphasize the
possibility of opportunistic trading that exists with human intermediation. On the other
hand, advocates of the NYSE system highlight the benefits provided by specialists in
fulfilling their affirmative obligation, especially for thinly traded stocks.1 They argue that
the NYSE system may provide significantly more support for inactive stocks than do
computerized systems. Therefore, our analysis provides insights into how the NYSE
structure promotes illiquid stocks.
Our paper makes two important contributions to the literature. First, while cross-
stock subsidization is generally acknowledged in the context of affirmative obligation,
there is little empirical analysis of it.2 In contrast to cross-stock subsidization, there is a
long and rich history of non-stock subsidization studies in numerous regulated
industries.3 A notable exception is the informal examination of cross subsidization
1 See, for example, Grossman and Miller (1988). 2 See Glosten (1989) and Stoll (1998) for competing views of the role of affirmative obligation. 3 See, for example, Wattles (1973), Palmer (1992), and Troyer (2002).
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provided by Cao, Choe, and Hatheway (1997). Our analysis differs in our approach,
which includes the identification and analyses of donor and beneficiary stocks.
Second, we provide the first study of NYSE specialist behavior at the level of
individual specialist portfolios. Our study contrasts with a growing literature that
examines NYSE specialists at the firm level: for example, Cao, Choe, and Hatheway
(1997), Corwin (1999, 2002), Coughenour and Deli (2002), and Hatch and Johnson
(2002). In addition, there are a few studies at the level of individual stock portfolios, but
these are studies of exchanges other than the NYSE. For example, Naik and Yadav
(2002) study the role of individual dealer portfolios on the London Stock Exchange, and
Anand (2002) examine their counterparts on the Chicago Board of Exchange and the
Pacific Stock Exchange.
We develop a general conceptual framework for examining cross-stock
subsidization. The basic intuition of our approach is to compare subsidized profits with
stand-alone profits. A set of sufficient conditions for cross-subsidization are used to
develop testable hypotheses. These implications test for cross-stock subsidization in both
subsidizing and subsidized stocks.
More specifically, our approach is to differentiate stocks in specialist portfolios by
trading volume and then to examine the specialist profits that they generate. The sample
covers a period from October to December 1998 and includes 2771 stocks and 334
individual specialists’ portfolios. The analysis proceeds in five steps. First, we document
the pattern of stock trading volumes in specialist portfolios. We show that specialist
portfolios consist primarily of infrequently traded stocks with just one or two high
volume stocks.
Second, we estimate the fixed costs of making a market in each stock in the
portfolio using the Huang and Stoll (1997) model. This estimation procedure is
compatible with a large number of bid-ask spread component models and it yields a fixed
costs consisting of order processing costs and specialist profits.4 The results show that
fixed costs and specialist profits increase with trading volume. These findings at the
4 Other recent examples that use a similar approach include Weston (2000) and Gibson, Singh, and Yerramilli (2003). An alternative approach that uses non-public data to estimate specialist profits is to use NYSE proprietary data on specialist revenues. Examples of the latter are Sofianos (1995), Hasbrouck and Sofianos (1993), and Madhavan and Sofianos (1998).
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portfolio level are consistent with those of Cao, Choe, and Hatheway (1997) at the firm
level.
Third, we test whether there is more stock volume variation at the firm level or at
the specialist portfolio level. The results reveal that there is more volume variation across
stocks within specialist portfolios than across specialists within a specialist firm. This
evidence suggests that cross-stock subsidization decisions are more likely to be made at
the portfolio level than at the firm level.
Steps four and five are our two tests for cross-subsidization. The tests differ in
their methods for controlling order processing costs, which must be isolated in order to
infer profits. The fourth step examines hypotheses that cannot be explained in terms of
order processing costs after we control for differences in portfolio and stock
characteristics. Overall, the results indicate that specialists need to earn more from donor
stocks when there are more mouths to feed in the family. Our results reveal that the
profits of beneficiary stocks are lower when donor stocks are more frequently traded.
This negative association is stronger when the beneficiary stocks are less actively traded.
Less frequently traded stocks are more heavily subsidized when donor stocks have higher
trading volumes. Our results also show that profits of donor stocks are higher when there
are more stocks in the specialist portfolios. These results are consistent with cross-stock
subsidization.
In the fifth step, we pair stocks from different specialist portfolios within the same
firm. The pairing controls for differences in stock characteristics as well as in trading
characteristics, so that we can interpret differences in fixed costs as reflecting differences
in profits. The hypotheses correspond to those in the previous tests they are applied to
paired stocks. Our results show that specialists extract less profit from beneficiary stocks
if their donor stocks in their portfolios are more frequently traded than when they are less
actively traded. Our results also show that the profit of the most active stock in a portfolio
with many stocks exceeds that of the most active stock in a portfolio with fewer stocks.
Again, this evidence is consistent with cross-stock subsidization.
Proponents argue that a key advantage of the NYSE system is the support that
specialists provide for inactive stocks. Cross-subsidization is a mechanism that specialists
can use to enhance the liquidity of inactive stocks. Thus, our evidence is consistent with
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individual specialists acting to fulfill their affirmative obligation, and consequently, it
also provides evidence supporting the argument that the NYSE provides extra liquidity
for thinly traded stocks. Another implication of cross-subsidization is the importance of
conducting analyses at the portfolio level. In particular, the evidence calls for NYSE
stocks to be examined in conjunction with other stocks in the same specialist portfolio.
The remainder of the paper is organized as follows. In Section 2, we provide a
description of the NYSE auction-dealer market structure and review the related literature.
In Section 3, we construct our conceptual framework and develop testable hypotheses
from it. The five sections that follow present the empirical analyses. Section 4 describes
the construction of the data samples. Section 5 examines the pattern of trading volume in
specialist portfolios. Section 6 estimates the fixed component of the bid-ask spreads.
Section 7 investigates variation in stock volume across specialists within a firm as
opposed to variation within specialist portfolios. Section 8 presents the cross-stock
subsidization tests. The paper ends with a summary of our results and a discussion of the
implications of our research in Section 9.
2. NYSE Market Structure and Related Literature
The specialist plays a central role in the NYSE auction-dealer market structure.
Every stock is assigned to a specific specialist on the NYSE. In return, specialists have an
affirmative obligation to maintain both a market presence and a fair and orderly market,
as specified in SEC Rule 11b-1. This obligation requires specialists to act as residual
liquidity suppliers by posting bid and ask quotes, even when no one else is willing to do
so. To ensure compliance with their affirmative obligation, the Exchange evaluates
specialists’ performance based on numerous criteria that reflect liquidity provision. These
include their ability to maintain narrow spreads and continuous prices, and their
involvement in price stabilization. The latter criterion requires buying on downticks and
selling on upticks. Poor performance may result in ineligibility for new stock allocations,
loss of assigned stocks, and fines. Glosten (1989) provides a rationalization for the
monopolist specialist system. He contends that in an adverse information environment, a
monopolist system is more resilient to market failure than is a competitive market
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structure. On the other hand, Stoll (1998) argues that the rationale for affirmative
obligation is no longer valid in light of increased competition across markets.
An affirmative obligation applies to all the stocks in the specialists’ portfolios.
Since it is also not the practice on the NYSE for specialists to exit from assigned stocks,
and since some stocks are more profitable than others, affirmative obligation makes
cross-subsidization a potentially useful strategy for specialists. We provide the first
formal empirical study of whether specialists subsidize across stocks in their portfolios.
Cross-stock subsidization is similar to cross-subsidization in regulated industries.
The U.S. Postal Service may charge artificially low rates to bulk-rate customers and
artificially high rates to first-class customers (Wattles (1973)). Local telephone
companies may use revenues from business service to subsidize residential service
(Palmer (1992)). Nursing home industry claims that Medicaid does not provide enough
reimbursement for their services. To offset this deficit, private-pay patients probably pay
more (Troyer (2002)). Surprisingly, this literature has not been extended to the case of
whether NYSE specialists engage in cross-stock subsidization.
Obviously, NYSE affirmative obligation is less important for liquid stocks, for
which large numbers of buyers and sellers are able to cross with one another. Grossman
and Miller (1988) also note that the specialist role is most valued for infrequently traded
stocks because of the specialists’ ability to initiate order-imbalance trading halts or to
send larger orders to the “upstairs” market in search of counterparties. Therefore, the
critical factor in the success of the specialist system may be whether specialists exercise
their affirmative obligation to support illiquid stocks.
Numerous studies have examined specialists’ liquidity provision for active and
inactive stocks. For example, Easley, Kiefer, O’Hara, and Paperman (1996) report that
bid-ask spreads decrease with trading volume. As in studies that document liquidity
measures by trading activity, we also rank stocks by trading volume, but we differ in our
search for cross-subsidization. Our objective is more demanding of the data in that the
evidence we seek lies not in how affirmative obligation may have impacted liquid or
illiquid stocks’ trading characteristics but in the indirect effects of how these
characteristics are related to one another.
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While there is no systematic study of cross-stock subsidization in the literature,
Cao, Choe, and Hatheway (1997) conducted an informal study. They find that the sum of
order processing costs and specialist profits, which we define as fixed costs, increases
with the trading volume of the stocks handled by a specialist firm. Since their prior is that
the relation should be negative for a monopolist specialist, they interpret their results as
evidence of subsidization. However, a direct comparison of active and inactive stocks
may merely reflect volume differences. Higher trading activity may mitigate inventory
and adverse selection costs, thereby generating higher profits and order processing costs
than illiquid stocks. We propose that evidence of cross-subsidization may be found by
comparing a donor (beneficiary) stock with its stand-alone counterpart, after controlling
for trading activity.
Our work is a contribution to the large literature on NYSE specialist behavior.
Two subsets of this literature are particularly relevant to our analysis. The first is the
empirical literature focusing on the specialist firm. We differ from this literature not only
in formally studying the cross-subsidization issue, as discussed above, but also in
conducting our analysis at the level of the NYSE specialist portfolio. Cao, Choe, and
Hatheway (1997) find that effective spreads and order processing costs differ
significantly among specialist firms. Corwin (1999) similarly document differences
across specialist firms in execution costs but also reports material differences in transitory
volatility and non-regulatory trading halts. Coughenour and Deli (2002) relate the
differences in liquidity provision to the organizational form of the specialist firm. Their
results suggest that while owner-specialist firms are better able to reduce adverse
selection costs, employee-specialist firms are able to realize lower capital costs. Hatch
and Johnson (2002) examine the effects on market quality of the consolidation of
specialist firms which has greatly reduces the number of specialist firms. They find
market quality improvements, such as reduced execution costs, after acquisitions, but
they do not appear to be abnormal when compared to the control sample. Corwin (2003)
investigates the new listing allocation process on the NYSE. He finds that preference is
given to large specialist firms and that firm performance plays a minor role in
assignment. While the analysis is at the specialist firm level, some of these studies
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acknowledge the potential importance of conducting the analyses at the specialist
portfolio level.
In addition to many previous studies of NYSE specialists at the firm level, there
also are studies of individual market makers in other markets. Naik and Yadav (2003)
examine whether dealer firms on the London Stock Exchange manage inventories on a
stock-by-stock, or on a portfolio basis. They find that individual dealers focus solely on
their own inventories, while ignoring correlated stocks managed by other dealers in the
same firm. They conjecture that this may be due either to organizational design, with its
attendant incentive and compensation structures, and/or to the practical difficulties of
sharing information between dealers in real time. Anand (2002) investigates the
individual options specialists on the Chicago Board Options Exchange and the Pacific
Stock Exchange. He finds that while there are significant differences among specialist
firms, individual specialists within a firm differ in their quoting behavior but not in their
execution quality.
The second relevant literature uses proprietary datasets to investigate specialist
revenue and specialist participation rate. The data are either the NYSE specialist trade file
or the specialist trade summary file or both. These data are reported by the specialist to
the Exchange as part of the surveillance process. We differ from these studies in our
reliance on market data and in our focus on specialist cross-subsidization. Hasbrouck and
Sofianos (1993) compute gross trading profits that ignore operational expenses. They find
that these profits come entirely from the bid-ask spread and that most of the profits are
from short- and medium-term trading. We also rely on the bid-ask spread to infer
specialist profits. Madhavan and Sofianos (1998) examine the relation between share
volume and specialist participation rate.5 The latter is the ratio of specialist share volume
to total share volume. They find that the NYSE functions more as an auction (dealer)
market with low (high) specialist participation rate for actively (inactively) traded stocks.
The higher participation rate for inactive stocks may be due to lower competition from
public limit orders. This may occur as a result of low trading activity increasing the value
of the free trading options inherent in limit orders. As modeled by Seppi (1997), this
5 Bacidore and Sofianos (2002) use the same data source to study specialist participation rate for NYSE-listed non-U.S. stocks.
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finding may also be because the large bid-ask spreads of illiquid stocks entice specialists
to participate more. They may do so because small orders are more profitable and in
order to fulfill their affirmative obligation. In our analysis, we rely on Madhavan’s and
Sofianos’ results and control for specialist participation rate differences by controlling for
volume differences. Sofianos (1995) defines gross trading revenues as the sum of daily
change in dollar inventory position and in trading-related cash position. He further
decomposes gross trading revenues into spread and positioning revenues. Of the two
components, spread revenues are the most reliable and they increase with share volume.
We infer specialist profits from the fixed component of the spread using publicly
available data, and we obtain results that are consistent with Sofianos’ association
between spreads and revenue-volume. Sofianos also finds that specialists make a zero
contribution margin on over 70% of the stocks in his sample. Although subsidization was
not the focus of his study, this result suggests that cross-subsidization across stocks must
exist. As shown in the following section, any stand-alone stock must make a positive
contribution margin, and therefore, the zero contribution margin of these stocks implies
that they are being subsidized.
3. Theory
In this section, we develop a simple general model of cross-subsidization and its
testable implications. We begin with some definitions. According to Oxford English
Dictionary, to subsidize is “to support by grants of money.” Therefore, subsidization
involves a donor and a beneficiary. If the donor comes from the same community as the
beneficiary, then we say that cross-subsidization occurs. Otherwise, it is subsidization
with outside money. Our paper is concerned with the cross-subsidization of stocks within
a specialist portfolio.
To determine if cross-subsidization occurs, we apply the stand-alone principle
from the non-stock subsidization literature. This principle involves a comparison of what
one group of customers pay with what they would have paid if they were stand-alone
customers. This leads us the following definition.
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Definition I: Cross-subsidization exists when two conditions are satisfied
simultaneously:
(i) One group pays less than if it stood alone; and
(ii) Another group pays more than if it stood alone.
Suppose a firm has two lines of business, one that is profitable (good) and one
that is not profitable (bad). For our application, a firm corresponds to an NYSE specialist
portfolio, lines of business correspond to stocks, and good and bad correspond to
classification of stocks on the basis of trading volume.
The firm also pays overhead expenses such as rent for office space, electricity,
and employee salaries. We designate these costs as common costs C . The firm also
requires a profit net of all operating expenses. For simplicity, we include profit as part of
common costs.
Definition II: Common costs are the sum of a firm’s overhead expenses and profits.
For NYSE specialists, common costs include fees paid to the exchange, specialist clerk
salaries, imputed specialist compensation, and specialist firm profits. Obviously, common
costs are always positive.
Assume that for each production unit, the firm charges a price of . For NYSE
specialists, can be thought of as the bid-ask spread. Also let unit costs be represented
by . For the NYSE specialists, unit costs include the inventory costs and asymmetric
information costs that are associated with each trade. Each production unit provides a
contribution margin of
s
s
k
ks −=π .
For NYSE specialists, π is the difference between the spread and the sum of inventory
and asymmetric information costs.
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To control for scale effects, we assume that the firm produces units of product
in total.
Q6 Additionally, assume that the total contribution margin offsets the firm’s
common costs, which include overhead expenses and profits.
1
i Q
ki
Cπ=
=
=∑ . (1)
Now, consider three firm structures. In the first, the firm is only involved in a good
business and the following budget equation is satisfied: A AGQ Cπ = G , (2)
where subscript denotes the good business type and the superscript indicates that
the firm is concentrating on one good business alone.
G A
In the second firm structure, the firm is involved in a bad business only and its
budget equation is A ABQ Cπ = B , (3)
where the subscript B indicates the bad business type.
In the third, more realistic structure, the firm has both good and bad businesses.
There are units of good products and units of bad products, with Gq Bq
Qqq BG =+ .
The budget equation is then
&M M
G G B B G Bq q Cπ π+ = M , (4)
where the superscript M indicates that the firm includes both good and bad business
types and and are the unit contribution margins of the good and bad businesses, MGπ
MBπ
6 Our definition of cross-subsidization is distinct from the concept of economies of scale. Although the two concepts are often entangled in the economics subsidization literature, it is important to distinguish them. An example best illustrates the relation between the two concepts. Suppose that at an airport, a couple is about to take a taxi. The cab driver is capable of taking up to three passengers and he charges $20 for two and $25 for three. A third person is going the same direction and the couple requests $7 from him for sharing the cab. The third person would have to pay a fare of $15 if he takes the taxi alone but saves $8 by sharing it with the couple. With $7 from the third person, the couple pays only $18 for the ride. If the couple takes the taxi by themselves, they would have to pay $20 out-of-pocket. This is a case of economies of scale since everyone pays less and no one pays more than they would if the third person rode alone. Cross-subsidization occurs if the couple gives the third person a free ride. In this case, two conditions are satisfied: (i) The third person pays less. By declining the couple’s offer, the cost is at least $5 to go home. (ii) The couple pays more. Giving the third person a ride costs them an additional $5.
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M MG G Gs kπ = − M and M M
B Bs kπ = − MB . The sum of the contribution margins from good and
bad types pay for the firm’s common costs . MBGC &
Lemma 1. In the stand-alone state, the unit contribution margins of both good and bad
businesses must be positive: and . 0>ABπ 0>A
Gπ
Proof. Rearrange (3) as Q
C ABA
B =π . Then since common cost, , is positive.
Using (2), can be proved in the same way.
0>ABπ
ABC
0>AGπ
Lemma 1 states that, on a per unit basis, both good and bad types must make positive
contribution margins in stand-alone states. If NYSE specialists have only inactive stocks
in their portfolios, they must make money on them.
Lemma 2. If A AGC C> B in the stand-alone state, then A A
G Bπ π> .
Proof. Subtract (3) from (2) to get A A
A A GG B
C CQ
π π −− = B . The result follows since
A AG BC C> .
Lemma 2 compares per unit contribution margins of good and bad types in the stand-
alone state. The firm is profitable if all of its businesses are good. If it has only a bad
business, the firm’s profit level should be lower than that of a firm with a good business.
Lemma 2 states an obvious but important fact: the contribution margins for good and bad
types cannot be the same in the stand-alone state.
Proposition 1. The necessary and sufficient conditions for cross-subsidization are
and . AB
MB ππ < A
GMG ππ >
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Proposition 1 is just a mathematical definition of cross-subsidization. Cross-subsidization
is said to exist when the bad (good) types are making a smaller (larger) contribution
margin than they would in the stand-alone state.
Proposition 2. If , then ABB
AGG
MBG qqC ππ +=&
)()( MB
ABB
AG
MGG qq ππππ −×=−× . (5)
Proof. This result is obvious if one subtracts from both side of (4) to obtain ABB
AGG qq ππ +
])[()()( &M
BGABB
AGG
AG
MGG
MB
ABB Cqqqq −++−×=−× ππππππ . (6)
Proposition 2 states that, if the firm receives no subsidy from outside, the total subsidy
received by the bad business is equal to the total subsidy provided by the good business.
If the bad types are subsidized in the mixed state, then they must make less contribution
than if they stood alone, . This subsidy could come either from the good types
or from outside, as represented by the two terms on the right side of (6).
MB
AB ππ >
The amount is the total contribution made by units of good
product and units of bad product in the stand-alone state. If , this
firm has a lower profit due to combining good and bad products, and therefore receives
outside aid. The second and even less likely scenario is . In this
case, the firm generates more profit by combining bad products and good products. The
most likely scenario is one in which the total profit for the firm remains the same. In this
case, there is no money from outside and the good types make an extra contribution to
support the bad types.
ABB
AGG qq ππ + Gq
Bq ABB
AGG
MBG qqC ππ +<&
ABB
AGG
MBG qqC ππ +>&
The case of has an implication for the public investor’s
benefit from cross-subsidization. Denote the total amount of the subsidy as
ABB
AGG
MBG qqC ππ +=&
)()( MB
ABB
AG
MGG qqM ππππ −×=−×= .
Let m be the value of the subsidization on each product unit or
G
AG
MGG q
Mm =−= ππ
and
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B
MB
ABB q
Mm =−= ππ .
Therefore,
G
B
B
G
mm
= . (7)
Equation (7) states that the relative size of the per unit subsidy depends on the relative
production numbers of the good and bad businesses within the firm. For example, if a
NYSE specialist makes a market in a high volume stock and a low volume stock,
then and . In this case, the per-unit subsidy provided by active stocks is
smaller than the unit subsidy received by inactive stocks, which suggests a net liquidity
benefit from cross-subsidization.
BG qq > BG mm <
Our two-product model, with one good and one bad product ( ) is easily
generalized to the multiple-product firm ( ) which has at least one good (bad)
product and more than one bad (good) products. The left side of Figure 1 shows the
subsidization structure of the two-product firm. To generalize to the multiple-product
case, group the good and bad products into two separate pools. The right side of Figure 1
illustrates an example in which there are two good products and three bad products
( ). For this multiple-product case, (5) can be generalized as
2N =
3N ≥
5N =
∑∑==
−×=−×BG n
j
MBj
ABjBj
n
i
AGi
MGiGi qq
11)()( ππππ , { }Gn ..., 1,i∈ , and { Bn ..., 1,j }∈ , (8)
where is the number of good products, is the number of bad products, and
.
Gn Bn
Nnn BG =+
3.1. Testable Implications
The following proposition states a direct testable implication of our model.
Proposition 3. If , then is a sufficient condition for the
existence of cross-subsidization.
ABB
AGG
MBG qqC ππ +=& 0≤M
Bπ
13
Proof. From Lemma 1, , and when 0>ABπ 0M
Bπ ≤ , then . Therefore, by
Proposition 2, so that
AB
MB ππ <
)()( MB
ABB
AG
MGG qq ππππ −×=−× M A
G Gπ π> , satisfying both
conditions for cross-subsidization.
Proposition 3 states that if the bad products are not making a positive unit contribution,
then they must be subsidized. This provides a feasible way to verify the presence of
cross-subsidization. In the empirical analysis, a stock with a non-positive contribution
margin would be sufficient to indicate the presence of cross-subsidization.
Aside from the situation in Proposition 3, testing for the existence of cross-
security subsidization is difficult due to the absence of stand-alone stocks on the NYSE.
Our approach is to extend our model to comparisons of firms with varying degrees of
mixed states. This is justified by the following proposition.
Proposition 4. Sufficient conditions for the existence of cross-subsidization are
GB M
1∝π and G Bnπ ∝ .
Proof. When the total subsidy from good stocks , the subsidy for bad stocks
disappears, and the stand-alone state for bad stocks emerges. At the same time,
0→GM
Bπ increases from the initial , and . MBπ
AB
MB ππ <
When there are both good and bad stocks, the number of bad stocks in the firm
. When good stocks are in the stand-alone state 0Bn > 0ABn = . Since M A
Bn n> B
B
and
G nπ ∝ , we have . AG
MG ππ >
When both conditions hold, and , and cross-subsidization
exists by Proposition I.
AB
MB ππ < A
GMG ππ >
Proposition 4 states that once we establish the two monotonic trends G
B M1
∝π and
G nBπ ∝ , then the bad product profit margin is lower in the mixed state than in the stand-
alone state and the good product profit margin is higher in the mixed state than in the
14
stand-alone state. The proposition enables us to confirm the existence of cross-
subsidization even without stand-alone data.
We provide two stylized examples of our application to NYSE specialists as
illustrations of the two conditions in Proposition 4. The first example takes the
perspective of beneficiary stocks. The size of the subsidy received depends on the funds
available from donor stocks in the specialist portfolio. We designate the most (least)
frequently traded stock in a portfolio as T1 (R1) stock, the next most (least) frequently
trade stock as T2 (R2) stock, and so on. Figure 2 shows two portfolios with very different
T1 share volumes ( ) but with a similar number of stocks in the portfolios
( ). Therefore, the first specialist has more funds with which to subsidize illiquid
stocks, or . Assuming that the total subsidy is evenly divided among inactive
stocks, we obtain
21 GG qq >>
1B Bn n= 2
21 MM >>
11
1B B
B
M q mn
= 1 and 22
2B B
B
M q mn
= 2 . (9)
If , then 21 BB qq =
2
1
2
1
MM
mm
B
B = , (10)
or the value of subsidies received by beneficiary stocks is positively related to the
volumes of T1 stocks in their portfolio.
The second example takes the perspective of donor stocks. Figure 3 presents two
portfolios which have T1 stocks that have similar share volumes but which have very
different number of stocks in the portfolios.
The total subsidy needed by the beneficiary stocks is: 1
11
( )Bi n
Bi Bii
M q m=
=
= ∑ and 2
22
( )Bj n
Bj Bjj
M q m=
=
= ∑ ,
where and are number of dependent stocks in those two portfolios. We simplify
the last two equations and assume
1Bn 2Bn
1 1 1( )B B B1M n q m= × and 2 2 2(B B BM n q m 2 )= × (11).
15
The two terms represent the average subsidy received by each beneficiary stock.
Predictably, the more (less) liquid the stock, the lower (more) the subsidy needed for each
share of stock. Therefore, and should be negatively correlated. Assume that
BBmq
Bq Bm
2211 BBBB mqmq = ,
or the amount of subsidy required by beneficiary stocks is the same for these two
portfolios on average.
The available subsidy is
111 GG mqM ×= and 222 GG mqM ×= , (12)
where is the subsidization impact on the profit margin of donor stocks. Gm
Setting supply in (12) equal to demand in (11), we have
11
1
B BG
G
n m qmq
B×= and 2
22
B BG
G
n m qmq
B×= .
If , then 21 GG qq =
1 1
2 2
G B
G B
m nm n
= . (13)
That is, the subsidization impact on each donor stock is positively related to the number
of beneficiary stocks in the portfolio.
We apply these implication of Proposition 4 to build testable hypotheses for the
two monotonic trend conditions: (a) The marginal contribution of inactive stocks is
negatively related to the subsidies available from active stocks; (b) the marginal
contribution of frequently traded stocks is positively related to number of beneficiary
stocks in the portfolio. These two conditions consider the quantity of funds available for
subsidization by the donors and the size of the subsidy needed by the beneficiaries.
Specifically, we examine the following four hypotheses:
P1: Specialist profits from beneficiary stocks are negatively associated with trading
volume of donor stocks. The association is stronger for beneficiary stocks with
lower trading volumes.
P2: Specialist profits from donor stocks are positively associated with the number of
stocks in the specialist portfolio.
16
M1: Specialist profits from beneficiary stocks that have actively traded donors are less
than those of beneficiary stocks with less actively traded donors.
M2: Specialist profits from donor stocks in portfolios that have few stocks are less
than those of donor stocks in portfolios with more stocks.
Hypotheses P1 and P2 are related to M1 and M2 respectively. Tests of P1 and P2 differ
from tests of M1 and M2 in that data on matched specialist portfolios are not needed for
P1 and P2, but are required for M1 and M2. The intuition underlying P1 and M1 is that
the richer the donor, the more subsidy the beneficiaries will receive. For P2 and M2, the
intuition is that donors need to make more when there are more beneficiaries to subsidize.
Our tests are based on a set of sufficient conditions. Therefore, cross-
subsidization may exist in their absence. For example, we would fail to detect cross-
subsidization, even if it occurred in every specialist portfolio, if all of the portfolios were
identical. Our findings supporting the presence of cross-subsidization shows that this is
not the case.
4. Sample Construction
Our empirical analysis examines specialist portfolios over 64 trading days in the
last three months of 1998. We settle on three months in order to have adequate number of
trades and quotes to estimate bid-ask spread components. The tradeoff is that a longer
sample period entails more changes within specialist portfolios.
The analysis employs several data sources. We begin with the basic specialist data
in the monthly NYSE specialist directories. For each specialist unit, the directories list
the firm code, panel, and post of every security traded on October 15, November 16, and
December 17. There are 18 posts (Post 1-17 and Post 30) on the NYSE and there are
different panels on each post, which are labeled alphabetically. Individual specialists are
identified by a unique post and panel. From this data set, we construct the portfolio
sample and the matching sample.
In the portfolio sample, our objective is to include all stocks that contribute to
each specialist’s common costs. The TAQ database provides the trade and quote data
17
needed to estimate the fixed component of bid-ask spreads. In the smaller matching
sample, we use CRSP and Compustat data to identify pairs of comparable stocks. The
CRSP data set is used to identify ordinary common stocks. The Compustat data are used
to obtain SIC code, long-term debt, shares outstanding and book value of equity.
We start with a sample of 3847 securities that are in the December specialist
directory. We use the December directory because the number of securities in December
exceeds those in October and November. Three securities were excluded due to missing
specialist firm identity. We construct the portfolio and the samples from the remaining
3844 securities. To obtain the portfolio pool we first exclude 274 securities with
incomplete and inconsistent trading positions. The former are securities that are not listed
for all three months and the latter are securities that do not reside with the same specialist
unit for all three months.7 Second, we exclude 802 securities that fail to yield the fixed
component of bid-ask spreads. Many of these securities are preferred stocks, warrants,
and stocks with suffix identifiers that do not have the necessary quote and trade data to
estimate bid-ask spread components. Finally, we exclude entire portfolios that are traded
in panels designated by two letter alphabets such as AZ. These portfolios appear to be
different from portfolios traded in panels designated by one letter.8 This produces a
portfolio sample of 2566 stocks.
To construct the matching pool, we further exclude stocks without CRSP data,
stocks with CRSP share code other than 10 and 11, stocks with a last trading date before
12/31/1998, delisted stocks, stocks that split, stocks with prices below $1 or above $500,
stocks without Compustat Data, stocks without two-digit SIC code, and stocks with
negative Compustat data. This results in a matching sample of 1397 stocks. Most of the
deletions are due to CRSP share codes other than 10 or 11, which ensures that we exclude
ADRs, closed-end funds, Units, and REITs, and that we retain only ordinary stocks.
5. Trading Volume Characteristics of Specialist Portfolios
In this section, we consider trading volume characteristics of the stocks in
specialist portfolios. Table 1A shows the number of stocks and specialists for each
7 We also corrected several obvious typos. 8 They seem to be mostly debentures and preferred stocks.
18
specialist firm and for all firms. The specialist firms are identified by firm code and the
associated firm name is given in Appendix A. The statistics are provided for the directory
sample, the portfolio sample, and the matching sample. Specialist firms range in size
from one specialist with one stock to 430 stocks in 50 specialist portfolios.9
In Table 1B, we examine the trading activity of stocks in specialist portfolios. The
table presents the number and trading volume of stocks from each specialist firm and for
all firms in the portfolio sample. It shows that the average specialist portfolio has nine
stocks and Figure 4 presents the distribution of the number of stocks across specialist
portfolios. Table 1B further shows that the average portfolio has a total volume of 96
million shares traded during the last three months of 1998, or 1.5 million shares per
trading day. A comparison of the most active stock (T1) in the average portfolio with the
least active stock (R1) reveals a dramatic difference in volume. It is clear that inactive
stocks can be very inactive. The additional information from the volume-ranked median
stock in the portfolio suggests that the volume in specialist portfolios is dominated by one
or two very actively traded stocks. This characterization is also suggested by Figure 5
that plots the distribution of stock trading volume by stock. It shows that only a handful
of stocks have very high trading volume. Indeed, out of the total of 2566 stocks in the
portfolio sample, over 97% have trading volume of less than 100 million shares, over
71% have trading volume of less than 10 million shares, and over 62% have trading
volume of less than 1 million shares. To corroborate our inferences from Table 1B and
Figure 5, we include Figure 6, which plots the stock trading volume of specialist
portfolios traded in Panel A of all trading posts on the NYSE. The figure confirms that
most specialist portfolios consist of only one or two very active stocks and several
inactive ones.
Table 1C, in which portfolios are sorted into quartiles based on the number of
stocks and trading volume provides additional information about the characteristics of
stocks in specialist portfolios. When ranked by number of stocks, trading volume tends to
decline with increasing numbers of stocks in the portfolios. It is also worth noting that the
number of specialists differs substantially across quartiles due to clustering in the number
9 Firm 1026 is not listed in this table because the sole specialist in the firm trades only preferred stocks and preferred stocks are excluded from both the portfolio and matching samples.
19
of stocks in portfolios. When ranked by volume, the quartiles have similar numbers of
stocks. Therefore, our analysis below focuses on trading volume. More importantly, the
mean volumes for T1, median, and R1 stocks indicate that specialist portfolios contain
many inactive stocks and very few active stocks. Table 1C suggests that volume
characteristics are robust across number-of-stocks and volume quartiles. In summary,
Table 1 and Figures 4, 5, and 6 indicate that individual specialist portfolio volumes are
driven by either T1and T2 stocks together or by T1 alone.
6. Specialist Fixed Costs
This section is concerned with the estimation of common costs and the association
of common costs with trading volume. Following the literature on the composnents of the
bid-ask spread, our estimate of common cost is the fixed component of the bid-ask
spread, which we refer to as fixed costs. The bid-ask spread consists of four components.
The inventory and asymmetric information components of the spread vary over time,
whereas order processing costs and market maker rents are fixed.
Recent examples that use the same approach to infer order processing costs and
specialist rents are Weston (2000) and Gibson, Singh, and Yerramili (2003). An
alternative approach is to use NYSE proprietary data on specialist revenue, as in Sofianos
(1995), Hasbrouck and Sofianos (1993), and Madhavan and Sofianos (1998). Our
approach uses publicly available market data.
The empirical literature on the bid-ask spread components has focused on the
variable components. A complicating issue is the differentiation of inventory and adverse
selection components. Since we are interested only in the fixed costs and are unconcerned
with identification of variable costs, our procedure can be considerable simpler.
Specifically, we employ the Huang and Stoll (1997) basic model, which is consistent
with numerous models of bid-ask spreads:
1 1( )2 2t t t tS SP Q Q Qλ− −∆ = − + + te ,
where Pt is the transaction price at time t, Qt is the buy/sell trade indicator variable at
time t, which is +1 if the transaction is buyer initiated and -1 if it is seller initiated, S is
the traded spread estimated from the data, and λ is the sum of the percentage of the half-
20
spread attributable to adverse selection and inventory holding costs. Huang and Stoll
show that this model generalizes many existing spread models. The specialist fixed cost
is estimated as 1-λ.
The data used to estimate the Huang and Stoll basic model comes from TAQ. We
apply a series of filters to the TAQ data to ensure data set integrity. The data set is
restricted to NYSE trades and quotes. Overnight quote and price changes are ignored, as
are quotes and trades placed outside of market hours (9:30 am to 4:00 pm ET). Only
transactions coded as regular trades and BBO eligible quotes are used. All prices and
quotes must be positive and divisible by 16, and asks must exceed bids. Each trade is
paired with the last quote posted at least 5 seconds earlier, but within the same trading
day. This pairing excludes all call-auction opening trades. Bid (ask) quotes or trades that
are more than 100% away from the previous bid (ask) quote or trade are eliminated.
Using the remaining data, all stocks that yield estimates from the HS basic model make
up the portfolio sample.
Table 2 reports the fixed cost estimates. Table 2A presents the summary statistics
for all the stocks and for each firm in the portfolio sample. The summary statistics show
that the average stock has a price of $25 and trades 105 times each day, yielding a total
three month trading volume of 14.67 million shares.10 The average specialist fixed cost
accounts for 52.6% of the estimated bid-ask spread of $0.098. This amounts to five cents.
Stocks with negative fixed costs are of particular interest, as they correspond to the case
in Proposition 3. Since order processing costs must be positive, negative fixed costs
suggest that the specialists lose money on these stocks. According to the proposition,
these stocks are being subsidized by the specialists. We find 13 stocks with non-positive
profits. All of these stocks are low-volume stocks, and 11 of them are the smallest one in
their respective individual specialist portfolios. These results can be interpreted as
providing some direct evidence of cross-stock subsidization.11
Table 2B presents the fixed cost percent by trading volume deciles. It shows that
the fixed cost percent increases with trading volume. To the extent the order processing
component of fixed costs does not increase with increasing volume, the results suggest
10 The three-month trading volume translates into about 330,000 shares per trading day. 11 There are also seven securities with unrealistic fixed costs estimates that exceed 100%.
21
that the specialist profits are higher for more active stocks. These results are consistent
with those of Cao, Choe, and Hatheway (1997).
Additionally, Table 2B shows the well-known result that (estimated) spreads
decrease with increasing volume. The fixed cost percentage can be combined with the
estimated spread to obtain the dollar fixed cost. The Table reports that dollar fixed costs
decline with volume for the least liquid five deciles, and are relatively constant for the
more liquid deciles. In the analysis that follows, we do not use the dollar fixed costs since
it is contaminated by the inventory and adverse selection costs in the estimated spread,
and we refer to the fixed cost percentage as fixed costs.
7. Stock Assignment Across Specialists and Within Specialist Portfolios
Cross-stock subsidization is more likely to occur between stocks that differ
markedly in their contribution to market making rents. In this section, we examine
whether there is more variation in stock trading volume across specialists within a firm
than within specialist portfolios. This issue is related to how stocks are allocated across
specialists. We consider two possibilities. Specialist firms may assign frequently traded
stocks to one group of specialists and infrequently traded stocks to another group. Profits
from the first group are then used to support the second group. Alternatively, firms may
assign both active and inactive stocks to individual specialist portfolios, so that cross-
subsidization occurs at the portfolio level.
Given the link between stock trading volume and market making rents noted in
the previous section, we focus only on trading volume here. Specifically, we examine
differences in stock trading volume across specialists within a firm and across stocks
within specialist portfolios as specified by the following two hypotheses.
H1: The mean share volume across specialists within a firm is equal.
H2: The mean share volume of stocks within a portfolio is equal for all portfolios
within a firm.
We use unbalanced ANOVA to test these hypotheses. Table 3 presents the p-
values from F tests of the hypotheses. At the five percent level, tests of H1 fail to reject
22
the null that mean stock volumes are the same across specialists within a firm for 20 out
of 30 firms.12 In contrast to H1, the null of H2 that mean stock volumes of ranked stocks
in a portfolio across specialists within a firm are the same is rejected for 24 of 30 firms at
the same significance level. In summary, the results suggest that liquid and illiquid stocks
are assigned in a balanced manner to individual specialists within a firm.
Cross-subsidization may occur at the individual specialist level rather than at the
firm level for various reasons. The cross-subsidization choice may be a result of how the
compensation contracts are structured. The incentive structure may be geared toward
evaluating specialists only on the basis of stocks assigned to them; this approach avoids
the agency costs associated with evaluating individuals on the basis of group
performance. It may also be a result of the difficulty with which information can be
shared in real time across specialists within a firm.
There is yet another specialist firm stock allocation strategy not examined in
Table 3. This is the hypothesis that the specialist firms cross-subsidize between active
and inactive stocks across all specialists in the entire firm. If so, we would expect active
(inactive) stocks to exhibit uniform profitability. In the following section, we test this
hypothesis using a method which controls for volume and other characteristics.
8. Cross-Stock Subsidization Tests
We test for cross-stock subsidization using both the portfolio sample and the
matching sample. Fixed costs may vary across stocks due either to changes in order
processing costs or to specialist profits. For the portfolio sample, we use regressions to
control for factors that may affect the order processing component across stocks. These
portfolio results provide evidence on cross-stock subsidization of profits. With the
matching sample, we attribute differences in fixed costs to differences in specialist
profits, under the assumption that order processing costs are similar across comparable
stocks within the same specialist firm. As such, therefore, the matching sample analyses
also focus on cross-stock subsidization of profits.
8.1. Portfolio Sample Results
12 We drop three specialist firms which have two or fewer specialists.
23
The portfolio sample tests are based on the cross-stock subsidization hypotheses,
P1 and P2. Hypothesis P1 considers cross-stock subsidization from the beneficiaries’
perspective, and says that profits of subsidized stocks are negatively associated with the
trading volume of donor stocks. In other words, the more actively traded the donor
stocks, the more they are able to cross-subsidize the beneficiary stocks. We also expect
the P1 relation to be stronger for beneficiary stocks with lower volume rankings in the
portfolio. Hypothesis P2 says that presence of cross-stock subsidization suggests that the
profits of T1 or of T1 and T2 stocks together are positively associated with the number of
stocks in the portfolio. That is to say, when there are more stocks to subsidize, the
specialists need to extract more rent from donor stocks in their portfolio.
To test P1 and P2, we regress fixed cost variables on the trading volume of donor
stocks or the number of stocks in the portfolio, and on two groups of control variables
that may affect specialist fixed costs. The first group contains additional portfolio
characteristics to supplement the hypothesized variables. For P1, these variables are mean
portfolio volume, rank of stock in the portfolio, number of stocks in the portfolio, and
mean of stock return variances in the portfolio. Any finding of significant effects in the
portfolio variables is inconsistent with the notion that specialists manage each of their
stocks in isolation from other stocks. In general, these effects have been ignored in the
literature. The second supplemental group controls for stock trading characteristics. For
P1, these are price, volume, return variance, and number of trades. The control variables
for P2 plus the number of stocks in the portfolio are the same as the corresponding list for
P1, with the notable exception of stock rank in the portfolio, which is no longer relevant.
It is worth emphasizing that we control for both portfolio and individual volume
effects. This is especially important because Madhavan and Sofianos (1998) find that
specialist participation rate varies negatively with stock trading volume. Therefore, by
controlling for trading volume, we also control for differences in specialist participation
rate across stocks. This ensures that the hypothesized relations are not being driven by
differences in trading volume or specialist participation rate.
To test P1, the beneficiary stocks’ fixed costs are regressed on the trading volume
of possible donor stocks and on the control variables. We restrict the inactive stocks to T3
to Tn stocks in the portfolio since the role of T2 stock varies by portfolio. For donor
24
stocks, we use T1 or T1 and T2 stocks. Table 4A reports P1 test results. In addition to a
regression with all T3 to Tn stocks, we also examine subsets of beneficiary stocks. We
sort the beneficiary stocks by trading volume and examine subsets of lower 70%, lower
50%, lower 30%, and lower 10% of T3 to Tn stocks. Each subset is regressed on T1
volume and combined T1 and T2 volumes separately. According to P1, we expect donor
share volumes to have more negative impact on beneficiary fixed costs for beneficiaries
with lower trading volumes.
The coefficients on donor volume are negative in all cases as predicted by P1. The
coefficients are highly significant in almost all cases. The donor volume coefficients also
increase in magnitude as we move towards lower volume subsets of T3 to Tn stocks.
These results cannot be explained in terms of order processing costs. Therefore, the
results are strongly consistent with cross-subsidization.
The additional portfolio variables are generally significant, highlighting the need
to account for portfolio effects. The results also yield plausible interpretations in terms of
their effects on specialist profits. The coefficients on mean portfolio volume are positive,
significant, and inversely related to the coefficients for active stock (donor) volume. The
need for subsidy decreases when, on average, stocks in the portfolio are more liquid. This
result suggests that beneficiary stocks have higher profits or need less subsidization when
they are relatively liquid. The coefficients for the reverse ranking variable are positive
and significant. Since the reverse ranking variable (R) is coded as 1 for the least active
stock in the portfolio, 2 for the second least active, and so on, this result indicates that
more actively traded stocks in the portfolio need less subsidization. The coefficients on
the number of trades are negative but are significant at the standard levels for only for the
largest subset of beneficiary stocks. The negative association suggests the need for more
subsidization when there are more mouths to feed in the family. The mean portfolio
return volatility is insignificant in all cases.
The remaining variables in the regressions control for differences in stock trading
features. They tend to be more significant for lower subsets of volume-sorted beneficiary
stocks. Negative price coefficients suggest that stocks with higher prices have lower
profits. This outcome is consistent with dollar profits that are similar, so that larger dollar
spreads associated with higher prices yield lower percent profits. The stock volume
25
coefficients are positive as expected. The stock return volatility coefficients are
insignificant. Finally, the coefficient on number of trades is negative, which suggests that,
holding volume constant, an increase in the number of trades is associated with more
specialist subsidization, which implies lower profits for beneficiary stocks.
To test P2, T1 fixed costs and T1 and T2 fixed costs are regressed on the number
of stocks in the portfolio and the other supplemental variables. Table 4B presents the test
results of the first two regressions. In both cases, the coefficients on the number of stocks
in the portfolio are positive and significant, as predicted in P2. This is a very different
result compared to the same variable in Table 4A when the dependent variables are
beneficiary stocks. The two other portfolio variables are insignificant. Almost all of the
trading control variables are significant. The mean price and volume variable have the
same signs as those for the beneficiary stocks in Table 4A. However, the stock return
volatility has a significantly positive association with donor fixed costs in this set of
regressions. Additionally, the coefficients for the number of trades are positive, which is
the opposite of those for beneficiary stocks.
Again it is difficult to explain the P2 test results in Table 4B in terms of order
processing costs. It is even more problematic since P2 only applies to donor stocks. The
last three regressions in Table 4B show that the P2 prediction does not extend to
beneficiary stocks T3 to Tn, to the combined R1 and R2 stocks, and to R1 stocks.
Therefore, the evidence in Table 4B can be interpreted as relating specialist profits from
donor stocks to the number of stocks in the portfolio.
In summary, evidence based on the portfolio sample is consistent with cross-
subsidization of inactive stocks by profits from active stocks within specialist portfolios.
In addition, the results document the importance of portfolio effects on specialist fixed
costs and profits. The evidence suggests that specialists make markets from the
perspective of their entire portfolios, and not by evaluating individual stocks in isolation.
Importantly, their profits from individual stocks are affected by the profits of other stocks
in their portfolios. This dependence reflects the effects of cross-stock subsidization by
specialists.
8.2. Matched Sample Results
26
We use the matched sample to test cross-stock subsidization hypotheses M1 and
M2. Hypothesis M1 states that specialist profits are lower for beneficiary stocks in
portfolios with more actively traded donors. In effect, specialists can afford to make less
on inactive stocks when they have very active stocks to subsidize them in their portfolios.
Hypothesis M2 states that in portfolios with many inactive stocks, specialist profits from
active stocks are higher than those in portfolios with fewer inactive stocks. In effect,
specialists need to make more from donor stocks to support more beneficiaries in the
family.
To infer the profit component from the fixed costs with the matching sample, we
compute differences in fixed costs between matched stocks. The implicit assumption is
that the order processing components of matched pairs are the same. We match stocks on
size, price, book to market (BME), assets to market (AME), and share volume (Vol)
based on the following score measure: 2 2
1 2 1 2 1 2
1 2 1 2 1 2
2 2
1 2 1 2
1 2 1 2
Pr Pr( ) / 2 (Pr Pr ) / 2 ( ) / 2
.( ) / 2 ( ) / 2
Size Size ice ice BME BMEScoreSize Size ice ice BME BME
AME AME Vol VolAME AME Vol Vol
⎛ ⎞ ⎛ ⎞ ⎛− − −= + +⎜ ⎟ ⎜ ⎟ ⎜− − −⎝ ⎠ ⎝ ⎠ ⎝
⎛ ⎞ ⎛ ⎞− −+⎜ ⎟ ⎜ ⎟− −⎝ ⎠ ⎝ ⎠
2⎞+⎟
⎠
The five matching variables include the four used in Huang and Stoll (1996) and volume.
Volume is added because Cao, Choe, and Hatheway (1997) document that fixed cost is
positively correlated with volume. The list also includes three of the four matching
variables used by Hatch and Johnson (2002): Size, Price, and Volume. They also include
volatility, which we exclude, because it can be construed as an alternative variable to
trading volume for measuring the effects of affirmative obligation.
To test M1, we match the T3 to Tn beneficiary stocks using the following
procedure.
1. Sort every T3 to Tn stocks by the volume of T1 stock in their portfolios.
2. Divide the sample in two. Group the bottom 50% of the sorted T3 to Tn stocks
into the “small” T1 pool and group the top 50% of the sorted T1 stocks into the
“big” T1 pool.
3. For each inactive stock in the big T1 pool, calculate the matching score with all
other inactive stocks in the small T1 pool belonging to the same specialist firm
27
and having a T1 volume ratio (of big T1 pool to small T1 pool) of greater than or
equal to 10. The matched paired is one with the minimum score.
4. To further ensure that price and volume are comparable, we require that prices
and trading volumes be within a specified percentage of each other.
5. Remove the pair with the minimum score from the small and big T1 pools.
6. Repeat steps 4 and 5 until all the inactive stocks in the big T1 pool have a match.
Pairs are grouped into three subsamples based on percent difference between them
computed in step 4. The three subsamples have 50%, 100%, and 200% differences. We
obtain 23 pairs for 50%, 38 pairs for 100%, and 45 pairs for 200%.13
Appendix B identifies the three beneficiary matched samples. In addition to the
ticker, the appendix lists each stock’s post and panel, which shows that the matched pairs
belong to different specialist portfolios in the same specialist firm. Table 5A shows the
outcome of our matching procedure. It compares the outcome for the five matching
variables, for return volatility and for number of trades. All of the variables appear to be
well matched.
Table 5B presents the M1 test results. The table shows results of the regressions
of the differences in fixed costs between inactive stocks in the big and the small T1 pools
on a constant and on the differences in the matching variables. The matching variables
are included to soak up any imperfections in the matching procedure. Hypothesis M1
predicts that the constant term will be negative for all three matched samples. The
coefficients are negative as predicted but only the coefficient for the smallest paired
sample is significant at the usual level.
To test M2, we match T1 donor stocks using the following procedure.
1. Sort all T1 stocks in the matching sample by the number of stocks in the portfolio
to which they belong.
2. Group sorted T1 stocks into the “small portfolio pool” if their specialist portfolios
contain five or fewer stocks and into the “big portfolio pool” if they contain 10 or
more stocks.
13 Twenty four of the 38 pairs are not in the 23-pair sample and 13 of the 45 pairs are not in the two smaller matched samples.
28
3. For each T1 stock in the small portfolio pool, calculate the matching scores with
all T1 stocks in the same specialist firm in the big portfolio pool. The matched
paired is one with the minimum score.
4. Among the matched pairs, group those with prices and trading volumes that are
within a certain percentage of each other. We add this requirement in case price
and volume are not well matched.
5. Remove the pair with the minimum score from the small and big portfolio pools.
6. Repeat steps 4 and 5 until all the T1 stocks in the small portfolio pool have a
match.
Although a lower percentage in step 4 is more desirable, the procedure fails to yield a
reasonable number of pairs. Therefore, the smallest percentage we use is 100%, which
gives us 17 pairs. With 200%, we obtain 23 pairs. The sample of 23 pairs contains 12
pairs that are not in the smaller sample. We do not include T2 stocks in our matching, as
their role as donor stocks is less obvious.
Appendix C identifies the two donor matched samples. Table 6A shows the
outcome of our matching procedure for the two matched samples. All the variables are
closely matched with, perhaps, the exception of market value. For market value, the
median sizes are much more similar than the means due to the presence of outliers.
Table 6B presents the M2 test results. The table shows regressions of differences
between the fixed costs of small and big T1 pools on a constant and the differences in the
matching variables. The pairs appear to be properly matched since most of the matching
variable coefficients are insignificant. The constant terms are negative for the two
matched samples as predicted by M2. The smaller sample is significant at the 10% level
but the bigger sample slightly exceeds that level.
To check the robustness of our results, we conduct additional tests on pairs
selected using different matching procedures. First, we experiment with different
matching variables. We conduct matching without assets to market (AME) and without
both assets to market and book to market (AME and BME). Second, for tests of M1, we
conduct tests on samples with many different T1 volume ratios. Third, for tests of M2,
small portfolio pools are defined for four or fewer stocks and big portfolio pools are
defined for 11 or more stocks. These tests confirm the results in Tables 5 and 6
29
respectively. We also match without the requirement that they come from the same firm.
Overall, with more stringent matching criteria, the sample sizes are smaller and the
evidence is more supportive of the cross-stock subsidization hypotheses M1 and M2.
With less stringent matching criteria, we obtain larger sample sizes, and the results
supporting the cross-stock subsidization hypotheses are similar but have lower
significance levels.
9. Conclusion and Implications
We have used both theoretical and empirical tools to investigate the issue of
cross-subsidization. We construct a general theoretical model of cross-subsidization. The
model is then used to develop testable hypotheses based on a set of sufficient conditions
for cross-subsidization. Our sample comprises of stocks in specialist portfolios during
October to December of 1998. For these stocks, we examine trading volume patterns,
compute fixed costs from bid-ask spreads, compare variability in trading volume across
stocks both within each portfolio and across portfolios within each firm, and we test the
cross-stock subsidization hypotheses. Our basic results are:
1. Theory. Our model indicates that we must identify donor stocks, which
subsidize others, and beneficiary stocks, which benefit from subsidies, for our cross-
subsidization tests. Additionally, our tests should compare profits between portfolio
stocks and stand-alone stocks, or alternatively between portfolios with different mixtures
of donor and beneficiary stocks. The model also shows that per share subsidization
impact is expected to be small for liquid stocks and large for illiquid stocks.
2. Portfolio Volume Pattern. Specialist portfolios include a mixture of liquid and
illiquid stocks. They are generally characterized by one or two frequently traded stocks
with several low volume stocks. This provides specialists with an opportunity to cross-
subsidize low volume stocks.
3. Fixed Costs. Fixed costs estimated from bid-ask spreads are greater for higher
volume stocks. This suggests the possibility of cross-subsidizing low volume stocks with
profits from high volume stocks.
4. Non-positive Fixed Costs. Some stocks have non-positive fixed costs. They
satisfy the sufficient condition for the existence of cross-subsidization.
30
5. Portfolio or Firm Level. The variation in trading volume across stocks within
the same portfolio vastly exceeds that of variation in volume across portfolios within the
same firm. The result suggests that cross-stock subsidization is more likely to occur at the
portfolio level rather than at the firm level.
6. Cross-subsidization I. The profits of beneficiary stocks are negatively
associated with donor trading volume. The association is stronger for beneficiary stocks
that have lower volume rankings in the portfolio. Additionally, the profits of beneficiary
stocks in portfolios with more actively traded donor stocks are less than those with less
actively traded donor stocks. These results are consistent with cross-stock subsidization
hypotheses predicted by our model.
7. Cross-subsidization II. Profits of donor stocks are positively associated with the
number of stocks in the portfolio. Additionally, profits of donor stocks in small portfolios
are less than those in portfolios with more stocks. These results are supportive of the
cross-subsidization hypotheses predicted by our model.
Our analysis of cross-subsidization depends on an indirect effect because it
measures the impact of affirmative obligation on the interaction between donors and
beneficiaries. Therefore, since indirect effects are more difficult to detect than direct
effects, our finding is particularly notable. It is also important to emphasize that our
results are obtained after controlling for volume and other portfolio and stock
characteristics.
Our analysis contributes to the vast market microstructure literature. The literature
often alludes to NYSE specialists’ affirmative obligation and to the possibility of cross-
stock subsidization. However, ours is the first systematic analysis of cross-stock
subsidization. In addition, we provide the first empirical analysis conducted at the level
of NYSE individual specialist portfolios. Previous studies focus is at a more macro
specialist firm level. Our evidence reveals that cross-stock subsidization occurs at the
portfolio level. This may be due to organizational structures that evaluate specialists on
the basis of stocks assigned to them or to the practical difficulties of sharing information
in real time across many specialists in a firm.
Our results provide insight into NYSE specialist behavior. They suggest that
specialists cross-subsidize low volume stocks with profits from high volume stocks in
31
their portfolios. These results provide evidence of the implementation of affirmative
obligation, since they are consistent with specialists maintaining liquid and efficient
markets in less frequently traded stocks. However, our study does not say anything about
whether cross-subsidization is adequate. Nonetheless, the existence of cross-subsidization
on the NYSE is important when comparing it to exchange venues that lack an explicit
mechanism for promoting inactive stocks. Most importantly, in pure dealer markets such
as Nasdaq, market makers have no affirmative obligation to provide liquidity, and in
purely electronic markets, such as electronic communication networks (ECNs), investors
trade stocks without the intervention of a market maker.
Our results also have implication for the overall liquidity of the market. For the
specialist, cross-stock subsidization is a zero sum game and there is no welfare
improvement for them. However, it is compatible with the exchange’s motive to provide
liquidity for all stocks, including inactive stocks. Our theoretical results show that the per
share subsidy provided to less frequently traded stocks is smaller than the per share
subsidy taken from frequently traded stocks. This increases the number of stocks for
which NYSE listing is feasible, thereby enhancing their liquidity at a minimal cost to
traders of actively traded stocks. Therefore, the net effect of specialist cross-stock
subsidization is to increase overall market liquidity.
Further, our results have implications for how specialists should be evaluated. Our
finding of cross-stock subsidization means that specialists take a portfolio perspective in
making markets in their stocks. Therefore, their performance should be evaluated on the
basis of all the stocks in their portfolio and not on the basis of individual stocks. A
specialist might have an unusually wide quoted spread for a liquid stock and an unusually
narrow spread on an illiquid stock. In this case, analysis of the stocks individually does
not reflect the specialists’ decisions and performance. Our results also highlight the
possibility of within-firm differences in specialist affirmative obligation performance.
Intra-firm analysis is appropriate because decisions are not centralized at the firm level.
Finally, our results have implications for future analyses of NYSE stocks.
Previous studies of NYSE stocks have not been conditioned on the specialist portfolios to
which they belong. For example, a focus only on individual stocks may be misleading in
research on trading costs. A stock’s high execution cost may benefit another stock, or one
32
stock’s low execution cost may be at the expense of another stock. In other words,
individual stock characteristics may not be independent, but may depend on other stocks
in a specialist portfolio.
Our study opens up numerous avenues for future research. Among other
possibilities, studies of NYSE stocks could be performed from a portfolio perspective,
with stocks categorized by specialist portfolio and firm. For example, comparisons of the
NYSE and Nasdaq trading costs may be affected by specialist cross-subsidization. Our
analysis could also be replicated for alternative ways of classifying stock within specialist
portfolios. For example, stocks could be differentiated by their volatility instead of
trading volume. We plan to investigate some of these issues in future studies.
33
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35
Appendix A
Specialist Firms and NYSE Firm Codes
No. Specialist Firm NYSE Firm Code 1 M.J. MEEHAN & COMPANY 20 2 FAGENSON/FRANKEL/STREICHER 104 3 BENJAMIN JACOBSON & SONS LLC 137 4 LABRANCHE & COMPANY 210 5 HENDERSON BROTHERS, INC. 215 6 RSF PARTNERS 240 7 EINHORN & COMPANY, LLC 364 8 ROBB,PECK,MCCOOEY SPECIALIST 403 9 SPEAR, LEEDS & KELLOGG SPECIALISTS LLC 501/1206 10 STERN & KENNEDY 520 11 STUART, SCOTTO, CELLA/M.J. MEEHAN 1010 12 WALTER N. FRANK & CO., L.L.C. 1022 13 FREEDOM SPECIALISTS/R. ADRIAN/RPM SPEC. 1027 14 WAGNER, STOTT MERCATOR PARTNERS, L.L.C. 1032 15 SUSQUEHANNA BROKERAGE SERVICES, INC. 1034/1065 16 GAVIN, BENTON, PORPORA & CO. L.P. 1148 17 SCAVONE, MCKENNA, CLOUD LLC 1225 18 JJC SPEC. A DIV. OF FLEET SECURITIES 1227 19 SURNAMER, WEISSMAN & COMPANY LLC 1229 20 KV SPECIALIST LLC 1246 21 BOCKLET & COMPANY L.L.C. 1266 22 BUTTONWOOD SPECIALIST, LLC 1280 23 CORROON, LICHTENSTEIN & COMPANY LLC 1341 24 BEAR SPEC./HUNTER SPEC./R.M. EVANS LLC 1418 25 M. & J. COHEN & COMPANY 1424 26 LYDEN, DOLAN, NICK & CO., LLC 1687 27 LAWRENCE, O'DONNELL, MARCUS LLC 1726 28 WEISKOPF SILVER SPECIALISTS L.L.C. 1746 29 MERRILL LYNCH SPECIALIST, INC. 1903 30 PHOENIX PARTNERS, L.L.C. 1910 31 CMJ PARTNERS, L.L.C. 1941 32 WEBCO SECURITIES, INC. 2090 33 EQUITRADE PARTNERS, L.L.C. 3174
36
Appendix B Matched Beneficiary Pairs
The appendix lists two samples of matched pairs used to test the hypothesis that beneficiary stocks with more actively traded donors earn lower specialist profits.
Sample 1 Sample 2 Sample 3 n
Stock1
Post1 Panel1 Stock2 Post2 Panel2 Firm Code Stock1 Post1 Panel1 Stock2 Post2 Panel2 Firm
Code Stock1 Post1 Panel1 Stock2 Post2 Panel2 Firm Code
1 AVY 12 M PPG 12 C 210 ASV 7 C DM 7 H 3174 AVY 12 M DJ 12 C 2102
AYD 7 B DM 7 H 3174 AVY 12 M DJ 12 C 210 BXS 3 F RMY 4 C 10323 CFR 12 D SMI 14 H 210 BBR 12 D WTR 12 A 210 CFR 12 D SMI 14 H 210
4 CLN 14 A GTY 14 H 210 BXS 3 F RMY 4 C 1032 CNB 4 P IMP 4 O 12295 CNB 4 P IMP 4 O 1229 CFR 12 D SMI 14 H 210 CSU 12 Q HPS 14 H 2106 CSU 12 Q HPS 14 H 210 CNB 4 P IMP 4 O 1229 CVH 12 D PSG 14 H 210
7 DFS 12 S WHC 12 B 210 CSU 12 Q HPS 14 H 210 DDC 7 E WSO 7 H 31748 FAM 12 D NNS 12 A 210 CVH 12 D PSG 14 H 210 DEL 12 Q GTY 14 H 2109 FLE 12 U FTS 14 B 210 DDC 7 E WSO 7 H 3174 DFS 12 S WHC 12 B 21010 GVA 12 U FSS 12 B 210 DEL 12 Q GTY 14 H 210 FLE 12 U FTS 14 B 21011 IS 7 E TCB 7 G 3174 DFS 12 S WHC 12 B 210 GBX 9 K ALG 9 C 13712 IXX 7 N WSO 7 H 3174 FLE 12 U FTS 14 B 210 GLE 15 Q OCQ 15 J 403
13 KWR 4 P TEC 4 Q 1229 GBX 9 K ALG 9 C 137 GPO 5 H OSU 8 P 501
14 MLR 15 I OMM 15 J 403 GLE 15 Q OCQ 15 J 403 GVA 12 U FSS 12 B 21015 NDB 11 P BTN 11 U 104 GVA 12 U FSS 12 B 210 HSB 7 C VLY 7 H 317416 OSG 5 G UWR 8 C 501 ION 10 R FOM 10 V 520 ION 10 R FOM 10 V 52017 PXR 8 I MPP 8 P 501 IS 7 E TCB 7 G 3174 IS 7 E TCB 7 G 317418 SCT 12 I DVI 14 H 210 IXX 7 N VCD 7 H 3174 IXX 7 N VCD 7 H 317419 SMG 9 J PGL 9 C 137 KWR 4 P TEC 4 Q 1229 KNT 15 Q SKO 15 N 40320 TNL 17 N PXT 17 M 1424 MLR 15 I OMM 15 J 403 KWR 4 P TEC 4 Q 122921 VAL 7 B VLY 7 H 3174 MUR 12 Q NNS 12 A 210 MLR 15 I OMM 15 J 40322 VOL 1 P ABP 1 H 1418 NDB 11 P PGA 11 U 104 MUR 12 Q NNS 12 A 21023 WST 12 M WAK 12 B 210 OSG 5 G UWR 8 C 501 NDB 11 P PGA 11 U 104
24 PHB 8 V LZ 5 J 501 NJR 17 N CBH 17 M 142425
PVA 15 Q APR 15 N 403 NYT 16 L WIN 16 J 122726 PXR 8 I BW 5 O 501 OSG 5 G UWR 8 C 50127 RRC 12 E GIX 12 B 210 PHB 8 V LZ 5 J 50128 SCT 12 I DVI 14 H 210 PVA 15 Q APR 15 N 40329 SDP 5 H OSU 8 P 501 PXR 8 I BW 5 O 50130 SMG 9 J PGL 9 C 137 RGA 5 G MDU 8 C 50131 SVE 3 J TR 4 C 1032 RGC 17 N NSV 17 M 1424
37
Sample 1 Sample 2 Sample 3 n
Stock1
Post1 Panel1 Stock2 Post2 Panel2 Firm Code Stock1 Post1 Panel1 Stock2 Post2 Panel2 Firm
Code Stock1 Post1 Panel1 Stock2 Post2 Panel2 Firm Code
32 SY 10 R CPK 10 S 520 RLT 3 T TR 4 C 103233
TNL 17 N PXT 17 M 1424 RRC 12 E GIX 12 B 21034 TTN 5 G MPP 8 P 501 SAJ 14 J WTR 12 A 21035 VAL 7 B VLY 7 H 3174 SCT 12 I DVI 14 H 21036 VOL 1 P ABP 1 H 1418 SMG 9 J PGL 9 C 13737 WFR 1 D SGR 1 H 1418 SMS 9 J TEX 9 F 13738 WST 12 M LAP 12 T 210 ST 15 T AIF 15 E 403
39 SW 7 N DM 7 H 317440
SY 10 R CPK 10 S 52041 TNL 17 N PXT 17 M 142442 TTN 5 G MPP 8 P 50143 VOL 1 P ABP 1 H 141844 WFR 1 D SGR 1 H 141845 WST
12 M LAP 12 T 210
38
Appendix C Matched Donor Pairs
The appendix lists two samples of matched pairs used to test the hypothesis that specialist profits from
active stocks in portfolios with many inactive stocks are higher than those in portfolios with fewer inactive stocks.
Sample 1 Sample 2
N Stock1 Post1 Panel1 Stock2 Post2 Panel2 Firm Code Stock1 Post1 Panel1 Stock
2 Post Panel Firm Code
1 ABT 1 C UIS 1 J 1418 ABT 1 C AZA 1 E 14182
AMR 8 Q UCL 5 L 501 AIG 8 A CCE 5 U 5013 APD 7 M SRV 7 D 3174 AMR 8 Q UCL 5 L 5014 BAX 5 Q BDX 8 O 501 APD 7 M SRV 7 D 31745 BBY 7 J BKB 7 L 240 BAX 5 Q BDX 8 O 5016 BJS 5 D TDW 8 H 501 BBY 7 J BKB 7 L 2407 BK 1 N AZA 1 E 1418 BEV 10 Q PXD 10 S 5208 CHV 14 G CVS 14 D 210 BJS 5 D TDW 8 H 5019 HP 16 N MCN 16 G 1227 BK 1 N UIS 1 J 1418
10 IRF 10 T PXD 10 S 520 CHV 14 G CVS 14 D 21011 KSS 2 Q MCK 2 V 1225 GDW 2 R COX 2 U 122512 MRL 8 T SFR 5 J 501 HP 16 N MCN 16 G 122713 OMX 14 L WDC 14 P 1341 KSS 2 Q MCK 2 V 122514 PNU 15 L ABS 15 P 1342 LLY 9 L GDT 9 N 36415 PWJ 4 G TLC 4 I 1726 MOT 2 I BNI 2 H 194116 SCI 15 L GT 15 G 403 MRL 8 T SFR 5 J 50117 SII 2 G NMK 2 K 1941 OMX 14 L WDC 14
P 1341
18 PNU 3 B ABS 3 N 103219
RDC 16 A PKD 16
U 122720 ROK 4 M TLC 4 I 172621 SCI
15 L GT 15 G 403
22 SII 2 G NMK 2 K 194123 Z 8 R VLO 8 K 501
39
Fig. 1. Cross Subsidization Structures
40
Fig. 2. Two portfolios with similar sizes but different trading volumes for their most active stocks. The most active stock traded on Post 3, Panel S has a share volume of 36 million but its neighbor’s (Panel T) most active stock has a share volume of 249 million. However, both portfolios have similar number of stocks.
41
Fig. 3. Two portfolios with similar trading volumes for their most active stocks but different portfolio sizes. 17 stocks are traded on Post 7, Panel L and 5 stocks on Post 17, Panel N. However, the most active stocks in two portfolios have similar three-month share volumes of 84 million and 85 million respectively.
42
1 2 3 4 5 6 7 8 9 10 11 12 13 4 5 6 8 9 0 11 1 1 17 1 1 2 2
50
40
30
20
10
0
Fig 4. Distribution of Number of Stocks in NYSE Specialist Portfolios. The horizontal axis shows the number of stocks in the specialist portfolios and the vertical axis shows the number of portfolios during the last three months of 1998.
43
Fig. 5. Distribution of Stock Trading Volume. The vertical axis shows the three-month total share trading volume of individual stocks ranked by volume from lowest to highest in millions. The horizontal axis shows the number of stocks. Each point on the graph represents one stock. The most active stock (CPQ) has a total trading volume of 651 million shares. The sample period is last three months of 1998.
44
45
Fig.6. Examples of Specialist Portfolios. The plots are for Panel A of all the trading posts on the NYSE in December 17, 1998. Position 11A was excluded because Merill Lynch sold its specialist unit that includes positions 11A to 11N to JJC Specialist Corporation. Post 30 only contains one panel, called Panel X, and was also excluded. The horizontal axis shows the number of stocks in the specialist position and the vertical axis label shows the total share trading volume in millions for each stock in the last three-month of 1998.
Table 1A Number of Securities and Specialists
The table contains the number of securities and specialists in each specialist firm, and for all specialist firms, in the last three months of 1998. The data are presented for securities in the specialist directories, the portfolio sample, and the matching sample. The portfolio sample consists of stocks for which we are able to estimate specialist fixed costs and the matching sample is used for our paired analysis. Firm Code Directory Portfolio Matched
Stock Spec. Stock Spec. Stock Spec. All Firms 3844 424 2566 330 1397 321
20 134 17 95 16 62 15 104 106 10 70 8 36 8 137 122 20 70 11 40 11 210 363 37 253 32 144 31 215 173 17 124 15 66 15 240 41 6 30 3 18 3 364 65 10 45 5 27 5 403 219 21 144 18 77 18 501 335 41 280 41 180 40 520 56 7 36 6 18 6 1010 34 4 16 3 12 3 1022 88 8 72 8 20 6 1027 35 7 22 5 13 4 1032 237 29 160 25 78 23 1034 38 4 20 1 7 1 1065 1 1 1 1 1 1 1148 54 6 42 5 23 5 1225 97 6 60 6 25 5 1227 430 50 222 30 123 30 1229 51 5 41 4 21 4 1246 29 2 21 1 9 1 1266 82 12 51 8 21 8 1280 41 4 23 2 14 2 1341 66 6 57 6 35 6 1418 148 19 113 15 64 15 1424 27 3 22 3 14 3 1687 92 8 70 6 36 6 1726 100 17 78 11 39 11 1746 63 6 39 3 14 3 1910 76 6 44 4 14 4 1941 130 14 96 11 56 11 2090 48 5 39 4 25 4 3174 161 15 110 13 65 13
46
Table 1B Number of Stocks and Trading Volume in Specialist Portfolios
The data presented is for the portfolio sample during the last three months of 1998. Volume is in millions of shares, T1 is the highest volume stock in the specialist portfolio, median stock is the median volume stock in the specialist portfolio, and R1 is the lowest volume stock in the specialist portfolio. Firm Code Number of Stocks Volume of All Stocks Volume of T1 Stock Volume of Median Stock Volume of R1 Stock
Mean Max Min Mean Max Min Mean Max Min Mean Max Min Mean Max Min All
Firms 8.9 21 1 96 720 1.0 56 651 1 8 254 0.1 1.98 223.61 0.03
20
5.9 12 2 114 221 42.9 74 196 28 16 91 0.6 2.11 9.72 0.06104 8.8 14 5 105 255 25.7 68 243 9 5 17 0.7 0.52 1.28 0.16137 6.4 12 2 108 242 33.7 58 123 12 16 40 1.3 2.73 10.03 0.14210 7.9 17 4 159 720 23.9 103 651 7 10 78 0.6 1.22 7.23 0.07215 8.3 11 4 160 278 89.4 94 179 21 5 14 0.5 0.70 5.92 0.09240 10.0 17 5 113 184 61.4 57 84 23 4 6 2.8 0.38 0.73 0.20364 9.0 21 1 96 132 43.5 63 130 12 30 130 1.6 27.24 130.30
0.44
403 8.0 15 1 124 371 1.5 68 310 1 7 31 0.1 1.32 6.44 0.04501 6.8 14 1 127 508 2.6 77 487 2 25 254 1.3 9.00 223.61 0.06520 6.0 11 4 102 250 12.8 87 244 9 2 3 1.4 0.26 0.50 0.07
1010 5.3 8 4 49 81 19.7 33 62 13 4 9 1.5 1.19 1.89 0.781022 9.0 13 6 80 146 13.4 38 100 6 6 16 1.0 0.69 2.43 0.111027 4.4 11 1 55 114 1.0 47 111 1 2 6 1.0 0.93 1.93 0.101032 6.4 12 4 100 283 8.2 63 249 5 6 22 1.0 0.78 5.46 0.031034 20.0 20 20 63 63 63.4 33 33 33 1 1 0.8 0.03 0.03 0.031065 1.0 1 1 4 4 4.5 4 4 4 4 4 4.5 4.49 4.49 4.491148 8.4 13 2 43 82 25.2 17 22 9 5 16 1.1 2.41 10.75 0.111225 10.0 14 4 92 193 32.2 32 58 9 5 9 1.7 1.05 3.50 0.271227 7.4 11 2 102 296 34.7 54 277 10 13 138 1.4 1.46 19.16 0.041229 10.3 14 4 170 359 58.8 135 325 21 4 6 2.3 0.45 0.73 0.211246 21.0 21 21 67 67 66.5 8 8 8 3 3 2.7 0.39 0.39 0.391266 6.4 9 4 83 196 22.8 41 79 11 7 15 1.2 0.48 1.41 0.041280 11.5 12 11 34 43 24.7 12 16 8 1 1 0.9 0.19 0.29 0.091341 9.5 12 5 133 222 57.0 58 98 17 5 10 1.0 0.37 0.70 0.181418 7.5 13 3 128 268 30.8 82 169 9 10 49 0.7 0.86 2.89 0.071424 7.3 9 5 57 96 27.4 38 85 9 2 3 1.8 0.40 0.80 0.181687 11.7 15 6 107 168 59.0 57 133 32 3 8 1.1 0.31 0.40 0.081726 7.1 13 2 87 174 38.1 48 174 12 16 87 1.6 0.87 4.26 0.051746 13.0 15 11 54 76 27.5 15 25 7 3 6 1.0 0.46 0.55 0.351910 11.0 20 2 95 173 40.9 68 173 22 24 87 0.8 0.29 0.49 0.121941 8.7 13 3 109 172 62.4 52 151 23 7 20 2.6 0.60 2.06 0.192090 9.8 13 8 104 161 34.2 68 129 24 4 6 1.3 0.39 0.82 0.053174 8.5 17 3 141 389 29.0 93 334 7 10 55 1.4 0.65 1.95 0.10
47
Table 1C Number of Stocks and Trading Volume in Ranked Specialist Portfolios
The data presented is for the portfolio sample in the last three months of 1998. Volume is in millions of shares, T1 is the highest volume stock in the specialist portfolio, median stock is the median volume stock in the specialist portfolio, and R1 is the lowest volume stock in the specialist portfolio.
Number of Stocks Volume of All Stocks Volume of T1 Stock Volume of Median Stock Volume of R1 Stock Rank
# of
Stocks # of
Spec. Mean Max Min Mean Max Min Mean Max
Min Mean Max Min Mean Max MinRanked by Number of Stocks
Q1 365 94 3.9 5 1 135 720 1 104 651 1 25 254 0.9 7.0 223.6 0.072Q2 446 69 6.5 7 6 130 436 14 72 249 4 9 78 0.5 1.0 6.4 0.033Q3 642 76 8.4 9 8 109 359 13 60 325 6 5 15 0.6 0.6 4.6 0.035Q4 1113 91 12.2 21 10 84 193 25 35 129 6 3 10 0.1 0.3 1.1 0.030
Ranked by Volume Q1 655 82 8.0 17 1 37 61 1 17 50 1 4 28 0.7 1.3 22.4 0.038Q2 711 83 8.6 21 4 78 96 62 37 94 8 6 18 0.1 0.7 4.3 0.030Q3 689 83 8.3 21 1 117 146 96 64 133 26 9 130 0.5 2.5 130.3 0.064Q4 511 82 6.2 17 1 224 720 146 153 651 40 26 254 0.7 5.2 223.6 0.051
48
49
Table 2A Fixed Component of the Bid-Ask Spread
The Huang and Stoll (1997) basic model is estimated for each stock in the portfolio sample over the last three months of 1998 to obtain the estimated spread (S) and the sum of the percentage of the spread attributable to adverse selection and inventory holding costs (λ). Fixed costs are fixed percentages of the bid-ask spread and are computed as 1-λ. $ fixed costs are estimated as S(1-λ). Daily Trades are daily mean number of trades. Volume is in millions of shares. Price is the average of daily ending trade prices.
All Stocks
Variable Mean Standard Deviation Maximum
Upper Quartile Median
Lower Quartile Minimum
Fixed Cost 52.6% 17.2% 123.9% 63.7% 53.4% 42.1% -51.8%
$ Fixed Cost 0.048 0.030 0.708 0.052 0.045 0.038 -0.118 $ Estimated Spread 0.098 0.057 0.929 0.103 0.086 0.074 -0.049
Daily Trades 105.2 204.2 2801.3 107.6 36.4 12.2 0.38 Volume (million) 14.67 34.75 650.87 12.33 3.48 1.09 0.03
Price ($) 24.91 23.94 520.88 31.73 18.80 10.93 0.27
Specialist Firm
Firm Code # of
Stocks Fixed Cost $
Fixed Cost
$
Estimated Spread
Daily Trades
Trading Volume (million)
Price ($)
20 95 48.0% 0.053 0.121 139.0 19.3 30.99
104 70 55.9% 0.050 0.092 88.8 12.0 19.29 137 70 50.7% 0.052 0.110 125.7 16.9 27.19 210 253 49.4% 0.042 0.096 134.2 20.1 26.62 215 124 50.0% 0.047 0.102 136.2 19.4 33.71 240 30 49.6% 0.043 0.089 98.3 11.3 25.95 364 45 49.4% 0.041 0.085 93.8 10.7 22.01 403 144 59.1% 0.060 0.104 113.3 15.5 32.17 501 280 50.8% 0.042 0.089 133.2 18.6 26.33 520 36 52.4% 0.048 0.108 93.4 16.9 22.63
1010 16 54.4% 0.047 0.091 62.5 9.2 19.29 1022 72 56.2% 0.055 0.112 58.4 8.8 19.78 1027 22 55.7% 0.053 0.100 75.6 12.6 20.54 1032 160 54.5% 0.050 0.094 122.4 15.7 27.50 1034 20 50.2% 0.043 0.125 29.0 3.2 16.78 1065 1 48.5% 0.049 0.101 37.5 4.5 13.74 1148 42 55.0% 0.040 0.077 49.0 5.2 16.06 1225 60 52.8% 0.046 0.094 70.9 9.2 21.93 1227 222 56.7% 0.050 0.094 110.6 13.7 25.90 1229 41 56.7% 0.051 0.093 106.6 16.6 18.24 1246 21 53.4% 0.048 0.096 29.5 3.2 18.10 1266 51 60.5% 0.068 0.113 90.6 13.1 25.94 1280 23 53.2% 0.052 0.103 37.7 2.9 19.08 1341 57 57.2% 0.052 0.095 85.9 14.0 19.71 1418 113 48.0% 0.040 0.094 118.7 17.0 22.58 1424 22 50.3% 0.052 0.107 74.5 7.7 21.75 1687 70 48.2% 0.043 0.098 62.0 9.2 19.54 1726 78 48.0% 0.047 0.110 98.3 12.3 24.73 1746 39 51.9% 0.041 0.085 32.5 4.2 14.65 1910 44 51.5% 0.051 0.108 51.8 8.6 19.89 1941 96 56.5% 0.049 0.092 89.8 12.5 23.71 2090 39 51.0% 0.045 0.093 72.8 10.7 19.12 3174 110 50.9% 0.049 0.094 103.2 16.7 24.76
Table 2B Fixed Component of the Bid-Ask Spread by Trading Volume Deciles
Huang and Stoll (1997) basic model is estimated for each stock in the portfolio sample over the last three months of 1998 to obtain the estimated spread (S) and the sum of the percentage of the spread attributable to adverse selection and inventory holding costs (λ). Fixed costs are fixed percentages of the bid-ask spread and are computed as 1-λ. $ fixed costs are estimated as S(1-λ). Daily Trades are daily mean number of trades. Volume is in millions of shares. Price is the average of daily ending trade prices.
Decile Number of Stocks Fixed
Cost $
Fixed Cost
$
Estimated Spread
Daily Trades
Trading Volume (million)
Price ($)
1 256 44.9% 0.062 0.150 3.8 2.4 22.05 2 257 47.3% 0.052 0.119 9.0 6.3 21.07 3 257 48.6% 0.047 0.102 14.5 11.2 17.46 4 256 49.5% 0.046 0.103 22.6 18.4 19.06 5 257 49.0% 0.045 0.096 33.1 28.1 20.41 6 257 53.2% 0.045 0.087 45.6 44.8 20.49 7 256 55.4% 0.045 0.084 67.3 73.6 22.40 8 257 56.0% 0.045 0.082 115.1 128.1 28.52 9 257 59.0% 0.045 0.078 192.9 253.5 33.00
10 256 63.2% 0.048 0.078 549.0 902.2 44.62
50
Table 3 Tests of Cross-Stock Subsidization Across Specialists and Within
Specialist Portfolios The results are obtained using unbalanced ANOVA. The table presents p-values for F tests of two hypotheses, using the portfolio sample during the last three months of 1998. The hypotheses are (H1) mean share volumes across specialists within a firm are equal and (H2) mean share volumes of stocks ranked by volume within a portfolio across all portfolios within a firm are equal.
Firm Code # of
Specialists H1
P-Value H2
P-Value 20 16 0.302 0.000 104 8 0.122 0.002 137 11 0.004 0.000 210 32 0.008 0.000 215 15 0.720 0.000 240 3 0.633 0.032 364 5 0.000 0.043 403 18 0.022 0.000 501 41 0.000 0.000 520 6 0.340 0.209
1010 3 0.267 0.209 1022 8 0.083 0.000 1027 5 0.674 0.631 1032 25 0.842 0.000 1148 5 0.041 0.000 1225 6 0.162 0.000 1227 30 0.000 0.000 1229 4 0.283 0.055 1266 8 0.394 0.000 1280 2 0.307 0.028 1341 6 0.569 0.000 1418 15 0.102 0.000 1424 3 0.263 0.253 1687 6 0.203 0.000 1726 11 0.001 0.000 1746 3 0.181 0.001 1910 4 0.000 0.290 1941 11 0.068 0.000 2090 4 0.729 0.000 3174 13 0.001 0.000
51
Table 4A Fixed Costs of Inactive Stocks and Trading Volumes of Active Stocks
The dependent variables are fixed costs of volume-sorted individual T3 to Tn stocks. The independent variables are share volumes of the most actively traded (T1) or second most actively traded (T2) stock in the specialist portfolio and control variables. Portfolio control variables are mean volume of stocks (Mean Volume), reverse volume rank of stocks (Reverse Rank), number of stocks (# of Stocks), and mean return variance of stocks (Mean Rvar) in the portfolio. Individual control variables are stock’s mean price (Mean Price), share volume (Volume), return volatility (Rvar), and number of trades (# of Trades). The number of observations (obs) is listed after the dependent variable. The regression is estimated for the last three months of 1998 using the portfolio sample.
Independent Variables Volume Mean Reverse # of Mean Mean # of Adj.
Dependent Variable
Active Stock (AS) Constant of AS Volume Rank Stocks Rvar Price Volume Rvar Trades R-sq
Coeff. 0.5197 -3.97E-10 1.75E-09 0.0111 -0.0055 -15.7 -0.0010 1.12E-08 29.254 -1.57E-05
T1 P-value 0.0001 0.0165 0.0253 0.0001 0.0004 0.8 0.0001 0.0001 0.099 0.0001
9.61%
Coeff. 0.5210 -4.95E-10 2.50E-09 0.0109 -0.0050 -19.4 -0.0010 1.15E-08 29.212 -1.59E-05
100% of T3~Tn Stocks
(1913 obs) T1 & T2
P-value 0.0001 0.0023 0.004 0.0001 0.0014 0.8 0.0001 0.0001 0.099 0.0001 9.78%
Coeff. 0.4938 -4.24E-10 1.95E-09 0.0089 -0.0036 -17.9 -0.0006 3.15E-08 12.555 -3.98E-05
T1
P-value 0.0001 0.0592 0.0791 0.0033 0.0759 0.8 0.0140 0.0004 0.554 0.0001 4.30%
Coeff. 0.4943 -5.95E-10 3.11E-09 0.0085 -0.0029 -22.6 -0.0005 3.23E-08 12.641 -4.03E-05
Lower 70% of T3~Tn Stocks
(1339 obs) T1 & T2
P-value 0.0001 0.007 0.0113 0.0047 0.1547 0.8 0.0171 0.0003 0.551 0.0001 4.57%
Coeff. 0.4808 -4.46E-10 2.15E-09 0.0120 -0.0042 21.0 -0.0002 6.32E-08 2.511 -7.23E-05
T1
P-value 0.0001 0.115 0.1155 0.0056 0.0702 0.8 0.4443 0.001 0.918 0.0001 3.76%
Coeff. 0.4832 -6.79E-10 3.60E-09 0.0117 -0.0035 10.6 -0.0002 6.38E-08 2.901 -7.34E-05
Lower 50% of T3~Tn Stocks
(956 obs) T1 & T2
P-value 0.0001 0.0132 0.0157 0.0066 0.1326 0.9 0.4964 0.0009 0.905 0.0001 4.13%
Coeff. 0.4649 -8.42E-10 4.11E-09 0.0240 -0.0059 25.2 0.0002 9.20E-08 -35.232 -1.03E-04
T1
P-value 0.0001 0.0435 0.0361 0.0011 0.0653 0.9 0.5040 0.0904 0.355 0.016 3.28%
Coeff. 0.4684 -1.09E-09 5.96E-09 0.0236 -0.0050 5.4 0.0002 9.33E-08 -33.704 -1.01E-04
Lower 30% of T3~Tn Stocks
(573 obs) T1 & T2
P-value 0.0001 0.0059 0.0056 0.0012 0.1217 1.0 0.4673 0.0844 0.374 0.017 3.88%
Coeff. 0.3194 -1.39E-09 8.49E-09 0.0567 -0.0049 291.1 -0.0007 4.93E-07 -122.254 -9.59E-05
T1
P-value 0.0011 0.0609 0.0107 0.0024 0.4614 0.4 0.5369 0.0799 0.248 0.5807 7.44%
Coeff. 0.3301 -1.54E-09 9.77E-09 0.0567 -0.0037 260.4 -0.0006 4.86E-07 -127.976 -9.70E-05
Lower 10% of T3~Tn Stocks
(191 obs) T1 & T2
P-value 0.0008 0.0286 0.0049 0.0022 0.5839 0.4 0.5897 0.0831 0.225 0.575 8.09%
52
Table 4B Fixed Costs of Active Stocks and Number of Stocks
The dependent variables are the fixed costs of T1 or of T1 and T2 stocks. The independent variables are number of stocks (# of Stocks), and specialist portfolio and control variables. Portfolio control variables are mean volume of stocks (Mean Volume) and mean return variance of stocks (Mean Rvar) in the portfolio. Individual control variables are stock’s mean price (Mean Price), share volume (Volume), return volatility (Rvar), and number of trades (# of Trades). The number of observations (obs) is listed after the dependent variable. The regression is estimated for the last three months of 1998 using the portfolio sample.
Independent VariablesDependent Variable Constant # of
Stocks Mean volume Mean
Rvar Mean Price Volume Rvar # of
Trades Adj R-sq
Coeff. 0.6540 0.0032 2.73E-10 -24.7436 -0.0032 4.36E-10 668.8822 1.16E-06 47.1% T1 Stocks (330 obs) P-value 0.0001 0.0421 0.4131 0.7257 0.0001 0.0138 0.0011 0.238
Coeff. 0.6363 0.0030 -3.29E-10 -5.1229 -0.0036 5.77E-10 210.1521 2.03E-06 43.1% T1 and T2
Stocks (653 obs) P-value 0.0001 0.0169 0.108 0.9283 0.0001 0.0009 0.0001 0.0001
Coeff. 0.5136 -0.0006 -1.75E-10 -8.2161 -0.0011 -1.31E-08 25.8970 -1.39E-05 7.8% T3~Tn Stocks
(1913 obs) P-value 0.0001 0.6267 0.6314 0.8969 0.0001 0.0001 0.1478 0.0001
Coeff. 0.5241 -0.0070 -1.09E-10 109.9508 -0.0003 -1.35E-10 25.1993 2.05E-06 1.7% R1 and R2 Stocks
(653 obs) P-value 0.0001 0.0078 0.8002 0.3809 0.2732 0.9153 0.5490 0.4993
Coeff. 0.5363 -0.0111 -2.97E-10 352.3427 -0.0007 -3.15E-09 -20.0585 9.88E-06 2.9% R1 Stocks (30 obs) P-value 0.0001 0.0061 0.6331 0.0836 0.0510 0.5597 0.7663 0.4233
53
Table 5A Characteristics of Matched Beneficiary Pairs
The characteristics are share volume in millions (Volume), price (Price), assets to market (AME), book to market (BME), size (Size), return volatility (Rvar), and number of trades (# of trades). Rvar and # of trades are not used in the matching process. The small (big) T1 pool comprises of stocks with below (above) median volume. The regression is estimated for the last three months of 1998 using the matching sample.
Sample of 23 Sample of 38 pairs Sample of 45 pairs Variable
T1 Pool mean Max median min mean max median min mean max median min
Small
4.7 21.6 3.2 .73 4.1 21.6 2.8 .41 5.0 31.9 2.7 .27Volume Large
4.3
19.6 2.5 .91 3.4
15.9 2.3 .45 3.6
15.9 2.4 .45
Small 23.25 52.32 19.73 4.76 21.29 52.32 19.25 4.76 23.78 61.71 19.73 4.76Price Large
21.29
57.96 20.25 3.25 19.62
46.78 16.72 3.25 20.78
46.78 18.29 3.25
Small 1.84 7.85 1.38 0.34 2.00 7.85 1.39 0.27 1.88 7.85 1.38 0.27AME Large
2.17
9.60 1.55 0.24 2.10
9.60 1.54 0.24 2.12
9.60 1.56 0.24
Small 0.50 1.20 0.47 0.05 0.56 1.20 0.53 0.05 0.56 1.39 0.51 0.05BME Large
0.58
1.81 0.52 0.16 0.64
1.81 0.58 0.12 0.61
1.81 0.55 0.12
Small 1014.2 5161.7 536.2 53.2 799.2 6368.7 455.5 74.6 948.5 6368.7 486.6 35.8Size Large
1049.7
10190.1 469.5 106.2 662.8
4426.0 335.5 71.3 812.0
6665.3 449.5 71.3
Small 2.08E-05 8.92E-05 1.69E-05 1.18E-06 2.36E-05 8.92E-05 1.92E-05 1.18E-06 2.27E-05 1.25E-04 1.58E-05 1.18E-06Rvar Large
2.38E-05
1.64E-04 1.52E-05 1.05E-06 3.19E-05
2.09E-04 1.99E-05 1.35E-06 3.03E-05
2.09E-04 1.95E-05 1.35E-06
Small 3395.4 16397.0 2526.0 310.0 3024.8 16397.0 1998.0 312.0 3623.8 16397.0 2108.0 237.0# of
Trades Large 3250.7 16762.0 2279.0 498.0 2529.2 10055.0 1794.5 286.0 2723.1 10708.0 2042.0 286.0
54
Table 5B Regression Tests of Matched Beneficiary Pairs
The dependent variable is the difference in fixed costs between inactive stocks with very active donors and inactive stocks with less active donors. The independent variables are differences in share volume (svolume), price (dprice), assets to market (dame), book to market (dbme), and size (dsize). The regression is estimated for the last three months of 1998 using the matching sample.
Independent Variables Number of Pairs
Constant Dsize Dprice DBME DAME Dvolume Adj. R-sq
Coeff. -6.77E-02 -1.01E-06 -1.58E-03 -7.77E-02 -1.85E-02 1.23E-08 23
P-value
0.0359 0.9662 0.8038 0.2906 0.3897 0.5384 -6.26%
Coeff. -2.07E-02 1.42E-05 -5.68E-03 -4.07E-02 -7.62E-03 5.99E-0938 P-value
0.472 0.7137 0.2238 0.5715 0.7151 0.6566 -4.79%
Coeff. -3.00E-02 -6.82E-06 -2.50E-03 -7.22E-02 -1.55E-02 1.23E-08
45 P-value
0.2474 0.8266 0.2676 0.3133 0.3828 0.0444 6.86%
55
Table 6A Characteristics of Matched Donor Pairs
The variables are share volume in millions (Volume), price (Price), assets to market (AME), book to market (BME), size (Size), return volatility (Rvar), and number of trades (# of trades). Rvar and # of trades are not used in the matching process. A small T1 pool contains specialist portfolios with five or fewer stocks and big T1 pool contains specialist portfolios with 10 or more stocks. The regression is estimated for the last three months of 1998 using the matching sample.
Sample of 17 pairs Sample of 23 pairs Variable
T1 Pool Mean max median min mean max median Min
Small 51.7 93.6 50.3 10.3 60.5 151.3 50.3 10.1Volume Large
45.8
84.1 45.1 14.2 44.9
84.1 45.1 14.2
Small 37.59 83.19 36.92 8.57 42.54 87.98 43.69 6.55Price Large
33.92
75.43 33.30 7.50 35.14
83.05 33.30 4.25
Small 1.54 9.64 1.14 0.18 1.48 7.38 1.14 0.13AME Large
1.64
6.40 1.08 0.31 1.68
6.40 1.13 0.09
Small 0.44 0.91 0.32 0.08 0.48 1.18 0.33 0.05BME Large
0.37
1.05 0.31 0.01 0.43
1.54 0.31 0.01
Small 15022 74287 6249 396 21813 101430 8459 396Size
Large
7682
22184 7045 735 8618
22184 7866 245
Small 3.97E-06 2.49E-05 1.54E-06 2.45E-07 3.81E-06 2.45E-05 1.54E-06 2.45E-07Rvar Large
3.79E-06
2.19E-05 1.35E-06 6.47E-07 4.09E-06
2.19E-05 1.44E-06 6.47E-07
Small 24637 52038 22410 4297 28041 66855 22410 5611# of Trades Large 19991 36998 21425 5597 19029 36998 21356 5597
56
Table 6B Regression Tests of Matched Donor Pairs
The dependent variable is the difference in fixed costs between the most active donor stock in a portfolio with five or fewer stocks and the most active donor stock in a portfolio with 10 or more stocks. The independent variables are differences in share volume (svolume), price (dprice), assets to market (dame), book to market (dbme), and size (dsize). The regression is estimated for the last three months of 1998 using the matching sample.
Independent VariablesNumber of Pairs constant dsize dprice dbme dame dvolume Adj. R-sq
Coeff. -6.54E-02
2.76E-06
-3.78E-03
1.97E-01
-9.92E-03
5.91E-10 17 P-value
0.0637
0.2183
0.0871
0.1399
0.4004
0.7613
10.61%
Coeff. -4.30E-02 2.38E-06 -2.49E-03 9.75E-02 7.09E-03 6.73E-10
23 P-value
0.1065
0.0402
0.0588
0.2986
0.5564
0.4968
37.24%
57