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: roger.huang.31@nd.edu

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: wliu1@mgmt.purdue.edu

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).

1

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).

2

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

3

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

4

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.

5

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

6

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.

7

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.

8

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.

9

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.

10

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 >

11

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

12

B

MB

ABB q

Mm =−= ππ .

Therefore,

G

B

B

G

qq

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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NYSE Working paper.

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Analysts Journal 54 (September/October), 72-82.

Troyer, J., 2002. Cross-Subsidization in Nursing Homes: Explaining Rate Differentials

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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