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Journal of Financial Economics 86 (2007) 513–542
www.elsevier.com/locate/jfec
Affirmative obligations and market making
with inventory$
Marios A. Panayides
David Eccles School of Business, University of Utah, 1645 E. Campus Center, Salt Lake City, UT 84112, USA
Received 13 April 2006; received in revised form 24 October 2006; accepted 28 November 2006
Available online 1 July 2007
Abstract
Existing empirical studies provide little support for the theoretical prediction that market makers
rebalance their inventory through revisions of quoted prices. This study provides evidence that the
NYSE’s specialist does engage in significant inventory rebalancing, but only when not constrained by
the affirmative obligation to provide liquidity imposed by the Price Continuity rule. The evidence
also suggests that such obligations are associated with better market quality, but impose significant
costs on the specialist. The specialist mitigates these costs through discretionary trading when the rule
is not binding. These findings shed light on how exchange rules affect market makers’ behavior and
market quality.
r 2007 Elsevier B.V. All rights reserved.
JEL classification: G14; G14; G19
Keywords: Specialist inventory; Affirmative obligations; Price continuity
$
The paper is based on the author’s dissertation at Yale University. The author would like to thank Paul
Bennett, Hank Bessembinder, Daniela Donno, William Goetzmann, John Hartigan, Joel Hasbrouck, Mike
Lemmon, Pamela Moulton, Elizabeth Odders-White, Matthew Spiegel and seminar participants of the NBER
market microstructure meeting in New York, University of Oxford, University of Utah, Wharton Business School,
and Yale School of Management for excellent comments and suggestions. An anonymous referee provided
valuable comments that significantly improved the manuscript. All errors are the author’s alone. Earlier drafts of
the paper were titled ‘‘The Specialist’s Participation in Quoted Prices and the NYSE’s Price Continuity Rule.’’
Corresponding author.
E-mail address: [email protected]
0304-405X/$ - see front matter r 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.jfineco.2006.11.002
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1. Introduction
Market makers face the risk of acquiring excessive inventory positions when providing
liquidity. Garman (1976) argues that market makers should adjust their posted quotes to
reduce this risk. Amihud and Mendelson (1980) and Ho and Stoll (1981) extend this
reasoning, predicting that when market makers’ inventory increases, both the bid and the
ask quotes should decline, and vice versa. These theoretical papers imply that quote
adjustments should rapidly follow the accumulation of inventory, and should therefore
depend on immediately preceding trades.
The empirical literature, however, has found little evidence of market maker inventory
rebalancing through quoted prices as predicted by theory. Focusing on the NYSE,
Hasbrouck (1991) and Hasbrouck and Sofianos (1993) find that specialists do quote prices
that induce reversion towards their target inventory value. However, at any point in time
the movement towards the target inventory is small, and imbalances have a half-life of a
few weeks. Madhavan and Smidt (1993) report similar results, indicating slow inventory
adjustment. More recently, Kavajecz and Odders-White (2001) study the factors that affect
the NYSE’s specialist quoted prices focusing on the limit order book. They find that the
specialist inventory position has no effect on the quoted prices. Bessembinder (2003a)
relates market order imbalance—i.e., an excess of investors’ buy orders—to the
competitiveness of the NYSE quotes with other markets. While his evidence is consistent
with inventory control, the documented effects are, as he notes, economically small. Thus,
to date the evidence in the empirical literature shows inventory adjustment to be slow and
small, in contrast to theoretical predictions of rapid first-order effects.
This paper resolves the apparent inconsistency between theory and empirical evidence
by focusing on the effect of an important constraint on the NYSE’s specialist quotation
behavior: the Price Continuity rule.1 The rule requires the specialist to smooth transaction
prices by providing extra liquidity as necessary to keep transaction price changes small.
Using data drawn from two distinct time periods, including the pre-decimalization TORQ
data set and a post-decimalization System Order Database (SOD) data set, I find
compelling evidence that the specialist rebalances his inventory through quoted prices. By
partitioning the specialist contribution to liquidity in the quoted prices into discretionary
participation (actions taken when the Price Continuity rule is not binding) and mandatory
participation (actions taken when the rule is binding), I test and verify the paper’s main
hypothesis that the specialist loses money and accumulates inventory imbalances in periods
of mandatory participation, but makes money and rebalances his inventory in periods of
discretionary participation. In addition, I show that the two periods’ effects on inventory
offset each other, resulting in the inability to detect inventory rebalancing through the
quoted prices in the full data set. Thus, this paper identifies, and corrects for, the reason
that extant empirical studies relying on pre-decimalization data have not identified
specialist inventory control.
Overall, the specialist mitigates the losses incurred when the rule is binding to emerge
with net positive gains. Using the SOD sample I find, in accordance with Coughenour and
1
This paper focuses on the Price Continuity rule rather than the Quotation rule (Maximum Spread rule) because
I find that any violation of the Quotation rule also constitutes a violation the Price Continuity rule. Moreover,
there are cases in which the Price Continuity rule is binding but the Quotation rule is not. This issue is discussed in
more detail in footnote 11.
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Harris (2006), that the specialist daily-average profits are $13,930 per stock. These positive
net profits are due to the specialist discretionary participation, which garners a mean dailyaverage profit of $14,878, compared with a loss of $938 produced by mandatory
participation when he is constrained by the Price Continuity rule. These results are
consistent with Dutta and Madhavan’s (1995) theoretical prediction that the Price
Continuity rule helps redistribute profits from the specialist to both informed and liquidity
investors. In addition, I show that the specialist losses during mandatory participation
result from price depreciation of his inventory (positioning losses) that are much more
significant than gains related to spreads. Thus, I provide evidence of a cross-subsidization
of the profits when the Price Continuity rule is not binding to periods when the rule
is binding.
While the key conclusions of this paper are consistent across the pre- and postdecimalization samples, some differences across these two samples emerge. Postdecimalization, with a more competitive limit order book, the Price Continuity rule is
binding less frequently. However, the specialist percentage participation in the quoted
prices does not change pre- and post-decimalization. This leads to more instances when the
specialist trades without constraints, and a stronger inventory effect on quoted prices.
These results imply that decimalization has lowered specialists’ inventory risk.
Finally, while the main focus of the paper is on specialist inventory management, I also
explore the effect of the Price Continuity rule on market quality. I find evidence of a
decrease in both intraday price volatility and price reversals when the rule is in effect. This
is consistent with the reasoning that the Price Continuity rule prevents transaction prices
from overshooting beyond their equilibrium levels. This finding is relevant to the debate
over NYSE restructuring, indicating that price smoothing obligations may indeed be an
optimal market design feature. While this study focuses only on the NYSE in order to
facilitate comparison with existing empirical studies on inventory management, the
findings contribute to the growing literature assessing the optimal set of affirmative
obligations.2 There is good reason to believe that rules in other exchanges, such as those
dictating the maximum spread and minimum depth that market makers must provide, may
also have important effects on market quality.3
The findings of this paper contribute to the understanding of price formation and
financial market design in three ways. First, I show that market makers’ inventory risks are
reflected in quoted prices, as has long been implied by theoretical work. Second, I highlight
the importance of including exchange rules in models of market-making decisions.
Without accounting for exchange rules, the behavior of market makers cannot be fully
understood. And lastly, I show that market rules can affect market quality, thereby
focusing attention on the importance of affirmative obligations for financial markets.
2
Many capital markets rely on designated market makers, who are bound by affirmative obligations requiring
them to provide liquidity to facilitate the trading process (Venkataraman and Waisburd, 2006; Charitou and
Panayides, 2006; Nimalendran and Petrella, 2003). The economic basis for and the effects of such affirmative
obligations are not yet well understood. The paper sheds light on this issue by looking at the effects of the Price
Continuity rule on specialist behavior and market quality.
3
In this paper I show that the Price Continuity rule has the effect of lowering the book spreads in accordance
with the maximum spread rule, the most frequently observed affirmative obligation in electronic markets
(Charitou and Panayides, 2006). A recent theoretical paper by Bessembinder, Hao and Lemmon (2006) implies
that the maximum spread rule found in electronic markets improves social welfare.
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The remainder of the article is organized as follows. Section 2 presents the empirical
model, describes the data, and establishes the puzzle. Section 3 describes my possible
explanation for the puzzle and introduces the hypothesis. Section 4 looks at the NYSE
rules focusing on Price Continuity. Section 5 empirically examines how the Price
Continuity rule affects specialist inventory management and quote revision. Section 6
investigates how specialist price smoothing behavior affects market quality. Section 7
looks at specialist profits, and Section 8 concludes. The Appendix contains a detailed
description of the algorithm created to accurately estimate the specialist inventory position
by accounting for overnight trades.
2. Empirical model
Harris and Panchapagesan (2005) and Kavajecz and Odders-White (2001) have
previously studied the factors that affect the NYSE’s specialists quoted prices, focusing
on the limit order book (LOB). They find that order imbalances (Harris and
Panchapagesan, 2005) and the changes in the best buy and sell prices in the LOB
(Kavajecz and Odders-White, 2001) are significant factors in predicting specialist quote
revisions. This is in consistent with theoretical work by Rock (1990) and Seppi (1997)
implying that the limit order book has a substantial impact on the specialist quoted prices.
In contrast to theory, however, both Harris and Panchapagesan (2005) and Kavajecz and
Odders-White (2001) find that the specialist’s inventory position has no effect on quoted
prices. I reexamine the effects of inventory and the LOB using data from both 1991
(TORQ data set) and 2001 (SOD data set)—i.e., before and after decimalization. I also add
variables for floor participation, and specialist’s information signal of future price changes.
These variables are not included in previous studies investigating revisions in quoted prices
even though the variables are expected to influence the specialist’s quote revision.4
My goals are to investigate (1) whether the absence of an inventory effect in the current
empirical literature is a result of an omitted variable bias, and (2) whether decimalization
has any effect on inventory adjustment of quoted prices. To investigate these issues, I
estimate a linear regression model predicting the change in the specialist quoted prices
(midpoint revision) between transaction times t and t1 (DMidquotet,t1) using a number
of variables that could potentially cause the specialist to change the quoted prices.
Throughout the paper, the unit of analysis in the time series is transaction time, t.
The quoted prices at time t represent what the specialist quotes just before the transaction
at time t.
The explanatory variables (summarized in Table 1) are drawn from previous empirical
and theoretical studies. Following Rock (1990), Seppi (1997), and Kavajecz and OddersWhite (2001), I use the changes in the LOB’s best buy and sell prices (DBestBuyt,t1 and
DBestSellt,t1) to capture the information that comes from changes in the demand
and supply sides of the limit order book. In addition, in my model I use a proxy for the
floor brokers’ intentions at transaction time t (FloorVolumet). The floor brokers may
participate passively in the transaction process by leaving their orders (either percentage
or limit orders) at the specialist post. These orders are typically included in the display
book as if they were coming from the LOB. Most frequently though, the floor brokers
4
As Sofianos and Werner (2000, p. 142) write, ‘‘it is misleading to make inferences concerning liquidity based
solely on the limit order book as represented in the TORQ data set without considering floor participation.’’
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Table 1
Variable definitions
This table describes each individual variable used in a linear regression model predicting changes in the quoted
prices:
DMidquotet;t1 ¼ b0 þ b1 DBestBuyt;t1 þ b2 DBestSell t;t1
þ b3 DMidquotet1;t2 þ b4 DMidquotet2;t3 þ b4 DMidquotet3;t4
þ b6 SignofTradet1 þ b7 DInventoryt1;t2
þ b8 Forecasttþ1;t þ b9 FloorVolumet þ t .
The variables are as follows.
Variable
Description
DMidquotet,t1
DBestBuyt,t1
DBestSellt,t1
FloorVolumet
DInventoryt1,t2
Change in the Quote midpoint (midquote) between transaction time t and t1.
Change in the Limit Order Book best buy price between transaction time t and t1.
Change in the Limit Order Book best sell price between transaction time t and t1.
Signed transaction volume of floor brokers on opposite side to specialist’s trades at time t.
The change in specialist inventory positions between transactions t1 and t2,
i.e., specialist’s signed transaction volume at time t1.
Sign of a lagged trade. Takes the value +1 for a buy trade and 1 for a sell trade.
First nonzero change in transaction prices after transaction at time t.
SignofTradet1
Forecastt+1,t
stand at the specialist post and request information from him about the LOB. They also
reveal to the specialist their intentions to buy or sell at particular prices that the
specialist can only display as part of his quotes. Therefore, the specialist has the
knowledge of the floor brokers’ pending orders. I use the floor brokers’ participation
against specialist transactions as a proxy for the floor brokers’ overall participation. This
approximation assumes that the specialist knows the intentions of the floor broker
(that are realized in the subsequent transaction against him) when he announces the
quoted prices.
Moreover, I include lag variables of the midquote revisions (DMidquotet1,t2,
DMidquotet2,t3, and DMidquotet3,t4 denote the three lag variables) to address the
autoregressive nature of the midquote time series. To account for the Hasbrouck (1991)
finding that the sign of a trade is informative in the simultaneous quote and trade revision
processes (VAR model), I include in my model the sign of a lag trade (SignofTradet1) that
takes the value +1 for a buy and –1 for a sell trade as a proxy for order flow.5 I also
include a forecasting price variable (Forecastt+1,t) to investigate the effect on quoted prices
of any possible private information signal that the specialist has. For this variable I take
the first nonzero change between the present and future transaction price as a proxy for the
forecasting signal. This approach follows Kavajecz’s (1999) analysis on specialist signals of
future prices. Lastly, I include the change in the specialist inventory (DInventoryt1,t2). I
use the standardized change in inventory instead of inventory levels. Inventory models
such as Huang and Stoll (1997) show that the change in inventory should be related to the
change in the midquote. I standardize the variable to adjust for large specialist changes in
inventory (large specialist transactions).
5
I use the Lee and Ready (1991) algorithm to assign a trade as a buy or sell only when the trade direction is not
clearly defined from the electronic order data (crowd buy and/or sell side of the trade).
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Based on the above, I run time-series regressions for each stock in my sample as follows:
DMidquotet;t1 ¼
b0 þ b1 DBestBuyt;t1 þ b2 DBestSell t;t1
þb3 DMidquotet1;t2 þ b4 DMidquotet2;t3 þ b4 DMidquotet3;t4 :
b6 SignofTradet1 þ b7 DInventoryt1;t2
þb8 Forecasttþ1;t þ b9 FloorVolumet þ t :
(1)
In order to aggregate the individual time-series regressions I follow the Bayesian
framework of DuMouchel (1994). In particular, I use the following model for each
individual time-series’ estimated coefficient b^ i (i is the ith time-series),
b^ i jbi i:i:d:Nðbi ; s2i Þ,
and each
bi i:i:d:Nðb; s2 Þ,
where N is the Gaussian distribution. I estimate b and s2 by maximum likelihood. Thus,
the estimate of the aggregate effect of each explanatory variable based on all the time-series
regressions (1–N) is calculated to be
PN ^
2
2
^b ¼ Pi¼1 bi =ðsi þ s^ m:l:e Þ
(2)
N
2
^ 2m:l:e Þ
i¼1 1=ðsi þ s
and, similarly, its variance is
^ ¼P
VarðbÞ
N
1
2
i¼1 1=ðsi
þ s^ 2m:l:e Þ
,
(3)
where s^ 2m:l:e is the maximum likelihood estimator of s2.
Previous studies use different methods to aggregate individual time-series regressions
using crude measures to estimate the significance of the mean effect of each explanatory
variable. For example, methods using either aggregated t-statistics or p-values do not take
into account the variability across stocks of bi. Using the Bayesian aggregation method,
I capture the variation among stocks in the predictive contribution of each individual b^ i
estimate.
2.1. The SOD and TORQ data sets
I use a proprietary data set of recent (post-decimalization) high-frequency trading data
provided by the NYSE. I also use the TORQ data set (pre-decimalization) to compare the
effects of the NYSE rules before and after decimalization. The NYSE proprietary data set
is the SOD daily file, which covers intraday activity for 148 NYSE listed stocks from April
1 to June 31, 2001 (post-decimalization).6 The sample of stocks is stratified by volume and
price taken from the complete set of all NYSE-listed securities. The SOD data set contains
6
This data set was selected with the help of Professor Robert Jennings, Indiana University. Specific details of the
selection process plus summary statistics of the stocks included in the SOD sample can be found in Ellul, Holden,
Jain, and Jennings (2006). Regarding the TORQ data set, more details can be found in Hasbrouck (1992) and
Hasbrouck, Sofianos, and Sosebee (1993).
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all electronic orders (SuperDot orders) as they are shown in the specialist display book.
Using the SOD data, I can reconstruct all pending orders, both buy and sell electronic
ones, at any point in time, and obtain an accurate picture of the LOB. This allows me to
disaggregate the specialist participation in quoted prices, as I use the residual of the quoted
prices and the LOB best prices to measure specialist additions to liquidity, similar to
Kavajecz and Odders-White (2001) and Chung, Van Ness, and Van Ness (1999).
Furthermore, the SOD data set contains full information on specialist participation by
providing a unique identifier of specialist trades as a contra side of a system order. When
the specialist participates as a contra side of a crowd (floor brokers’) order, the displayed
book generates a unique system report. Thus, I can identify specialist trades against both
electronic orders and floor brokers’ orders, and hence have an accurate estimate of the
change in the specialist’s inventory position, which is necessary to gauge whether there are
inventory effects on quoted prices. Consequently, in my analysis of quoted prices, I include
the floor brokers’ trades contra the specialist as a proxy for floor participation. Therefore,
I account in part for the large volume of floor broker participation in the transaction
process that also influences the quoted prices (Sofianos and Werner, 2000).
For my final sample, I exclude from the SOD data those stocks that provide insufficient
data for the analysis. This includes stocks that have less than 10 trades per day executed at
the NYSE during the sample period (10 stocks), non-common stocks (15 stocks), and
stocks for which the specialist did not provide sufficient liquidity by improving on the
book’s best prices adequately for at least four days in the sample (6 stocks). Thus, the final
analysis in the paper uses 117 stocks. Also, due to the large number of trades, I confine my
analysis of the SOD data to the month of April. Results are reported both in the aggregate
and in quartiles with respect to frequency of trading. Previous papers have found different
specialist behavior on active and less active stocks by either percentage participation in
trades (Madhavan and Sofianos, 1998) or subsidization of trading for the less active stocks
(Cao, Chloe, and Hatheway, 1997). I also investigate possible differences in specialist
behavior with respect to trading volume.
In Section 7, I relate specialist participation in quoted prices to the specialist’s profits. To
calculate specialist profits, I follow Hasbrouck and Sofianos (1993) and measure trading
profits on a mark-to-market basis for each transaction—specifically, the change in the
market value of the specialist inventory, Pt ¼ I t21 ðpt 2pt21 Þ, where pt denotes the
transaction price at time t and It is the specialist inventory at time t. For any given period
the total profit is the sum of Pt for that period. I therefore need to know the specialist
inventory position at any point in time. Past research uses either the change in specialist
inventory or the accumulated inventory over a period of time. This can be misleading,
however, not only because the specialist’s inventory at the beginning of a sample is
unknown, but also because inventory positions can change significantly due to various
adjustments at the end of the day (odd lots) or during after-hours trading.7 I create an
estimate of the actual inventory levels in the SOD data by using an algorithm based on the
NYSE exchange rules 104.10(5) and 104.10(6). These rules prohibit the specialist from
buying stock on a direct plus tick or selling on a direct minus tick based on his inventory
7
Both Sofianos (1995) and Hasbrouck and Sofianos (1993) identify inventory corrections from the closing to the
following opening specialist position. Therefore, the total number of shares that the specialist bought and sold
during a trading period, even knowing the specialist position at the beginning of the sample, can be a false
estimate of his total inventory over the sample period.
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position. Thus, following his transactions under the assumption that the rules of the
exchange are not violated, I am able to approximate the specialist’s inventory position at
the beginning of each day. A more detailed description of the algorithm can be found in
the Appendix, along with validation statistics between my inventory position estimates and
true inventory values. My estimate of the specialist inventory position allows me to
calculate the specialist’s mark-to-market profits and directly relate them to the effect of
inventory in the quote revision model.
It is well documented in the finance literature that the NYSE decimalization had a
significant impact on liquidity and price efficiency. However, its effect on specialist
behavior and profits is still an open question. To investigate whether specialist behavior
has changed after decimalization, I also estimate the same models using the 1991 TORQ
data set. The key difference between the TORQ and SOD data is that the TORQ data set
does not include the unique specialist identifier found in the SOD data set. I therefore rely
on the Panchapagesan (2000) algorithm to identify specialist participation in trades for the
1991 TORQ data. The TORQ data set contains 144 randomly chosen companies from
NYSE stratified with respect to their market capitalization. Therefore, the TORQ data set,
albeit in an earlier period, resembles the SOD sample in that it provides a representative
sample of the whole market. And similarly to the SOD sample, I exclude from the TORQ
data stocks that provide insufficient data for the analysis. In particular, this includes stocks
that have less than 10 trades per day during the sample period (25 stocks), stocks that were
listed at the exchange for less than the whole sample period (1 stock), and stocks that the
specialist did not provide sufficient liquidity (2 stocks). Thus, the analysis uses 116 stocks
in the TORQ data set.
2.2. Specialist inventory management and quote revisions
Aggregated results of the linear regression model predicting quotation midpoint changes
(DMidquotet,t1) as described in Eq. (1) are shown in Table 2. I report regression results for both
the 1991 (TORQ data) and 2001 stocks (SOD data), along with aggregated results divided into
volume quartiles based on the daily-average number of trades (SOD data). Each column in
Table 2 shows the Bayesian aggregated coefficient estimates (t values are in parentheses).
As expected, the two most important variables in explaining midquote revision are the
changes in the LOB best buy and sell prices (DBestBuyt,t1 and DBestSellt,t1). The
significant explanatory power of these variables is indicated by their large t values, which
appear not only in the overall aggregated regression before and after decimalization
(columns 2 and 3 of Table 2), but also in all of the subsample quartiles. There is also a clear
autoregressive time-series effect that is captured by the significant lag variables of the
midquote change (DMidquotet1,t2, DMidquotet2,t3, and DMidquotet3,t4). The mean
reversion (negative correlation of lag 1) is also found in Hasbrouck (1991) and Dufour and
Engle (2000).8 The floor brokers’ effect is statistically significantly captured by the floor
volume variable (FloorVolumet) as a proxy for the floor brokers’ intentions. Its positive
sign indicates that the specialist moves the quotes in the direction of floor brokers trades
(i.e., lower if they are selling and higher if they are buying). As anticipated (Hasbrouck,
8
Hasbrouck (1991) attributes the negative autocorrelation in the quote revisions to quote reporting errors. The
slight reduction in the negative autocorrelation in the post-decimalization period results (faster quote reporting,
improved automation mechanisms for quote reporting) provides such evidence.
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Table 2
Linear regression model predicting quotation midpoint changes (DMidquotet,t1)
The table reports coefficients estimates from regressions predicting the quotation midpoint change
(DMidquotet,t1). The independent variables include measures of the limit order book best buy and sell price
changes (DBestBuyt,t1 and DBestSellt,t1), lag values of the quote midpoint change to adjust for possible
autocorrelation (DMidquotet1,t2 DMidquotet2,t3, DMidquotet3,t4), floor participation (FloorVolumet), the
sign of lagged trade to account for order flow (SignofTradet1), the specialist’s change of inventory levels
(DInventoryt1,t2), and the following period’s price change (Forecastt+1,t). The table shows aggregated regression
results for all 116 companies in the TORQ data set (November 1990–January 1991), the more recent SOD data set
(April 2001, 117 companies), and regression results from the SOD sample divided into volume quartiles based on
the daily average number of trades. The symbols ** and * indicate statistical significance at the 1% and 5% levels,
respectively (t-values are reported in parentheses).
TORQ
Number of stocks
Intercept
DBestBuyt,t1
DBestSellt,t1
DMidquotet,t1,t2
DMidquotet,t2,t3
DMidquotet,t3,t4
FloorVolumet
SignofTradet1
DInventoryt1,t2
Forecastt+1,t
SOD
Overall
Overall
High Quartile
2nd Quartile
3rd Quartile
Low Quartile
116
117
30
29
29
29
0.0009**
(3.1)
0.0005**
(8.6)
0.0005**
(6.2)
0.0005**
(6.1)
0.0011**
(7.1)
0.0005
(1.2)
0.2915**
(11.3)
0.3326**
(16.3)
0.0454**
(9.2)
0.0034
(1.5)
0.0015
(0.7)
8.2e-7**
(3.1)
0.0055**
(4.7)
0.0003
(1.2)
0.0001
(0.7)
0.2595**
(17.9)
0.2612**
(17.0)
0.0081**
(4.2)
0.0005**
(3.7)
0.0068**
(7.2)
3.7e-8**
(3.9)
0.0058**
(9.9)
0.0008**
(8.3)
0.0002**
(2.5)
0.4160**
(33.0)
0.4224**
(46.2)
0.0002
(0.2)
0.0036**
(2.5)
0.0043**
(4.0)
2.9e-8**
(2.5)
0.0011**
(7.0)
0.0003**
(6.8)
0.0004**
(7.1)
0.3007**
(16.5)
0.3006**
(17.7)
0.0028
(1.4)
0.0095
(5.2)
0.0103**
(7.5)
3.1e-8**
(2.2)
0.0026**
(5.3)
0.0004**
(7.8)
0.0003**
(4.1)
0.1307**
(7.8)
0.1221**
(6.1)
0.0271**
(4.5)
0.0045
(-0.7)
0.0042
(1.1)
5.4e-7*
(2.1)
0.0086**
(11.9)
0.0018**
(9.4)
0.000*
(2.1)
0.1767**
(5.8)
0.1566**
(5.2)
0.0243**
(2.5)
0.0093
(0.9)
0.0064
(0.6)
4.8e-7
(1.8)
0.0136**
(7.7)
0.0046**
(3.9)
0.0002
(0.4)
1991) the sign of a lag trade (SignofTradet1) is positively correlated with quote price
changes. By including the SignofTradet1 variable in my model, I control for any private
information in the last trade reflected in the quote change. I thus expect any specialist
inventory effects that appear in the model to be related only to inventory control, and not
to be a proxy for order flow.9
The forecast variable (Forecastt+1,t), though not significant in the 1991 data, seems to
have negative and significant explanatory power predicting changes in quoted prices after
9
Hasbrouck and Sofianos (1993) state that inventory changes can be a proxy for the specialist’s informational
advantage. In the model on quote revision, such an effect should be directionally opposite to an inventory control
effect. I attempt to account for such a limitation of the change in inventory effect on quote revision by including
both SignofTradet1 as a proxy for order flow and Forecastt+1,t as the realization of private information.
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decimalization (SOD data). This future price reversal relates to the inventory argument,
which dictates that more sellers are attracted after the specialist increases quoted prices,
while buyers are attracted after decreases in prices. Alternatively, as Kavajecz (1999)
shows, this could indicate that the specialist does not have a private information signal, as
he moves prices away from the new future price levels.
Lastly, but most importantly, the specialist inventory variable (DInventoryt1,t2)
variable is found to have no effect on quoted prices in the TORQ data set, consistent with
the findings of Hasbrouck and Sofianos (1993) and Kavajecz and Odders-White (2001),
among others. However, post-decimalization (SOD data), both the overall regression and
all individual quartiles show a negative and significant inventory effect on the quoted
prices, in agreement with theoretical models. The specialist decreases (increases) the quoted
prices after inventory buys (sells) to elicit orders of the desired sign and rebalance his
position. In addition, this effect is stronger (with a larger magnitude coefficient) as we
move from the highest quartile to the lowest quartile of trading frequency. This finding is
consistent with the reasoning that inventory risks are higher in less actively traded stocks,
and as a result, any rebalancing by the specialist will be more aggressive.10
3. Explanation for the puzzle
The evidence in Table 2 that inventory is a significant factor in predicting the change in
quoted prices post-decimalization but not pre-decimalization is striking. While the theoretical
models of Garman (1976), Amihud and Mendelson (1980), and Ho and Stoll (1981) suggest
that the specialist should alter posted quotes to avoid excessive inventory, previous empirical
work using pre–decimalization data, has failed to support the theoretical prediction.
I investigate the causes for the discrepancy between the pre-decimalization and postdecimalization data by incorporating the effect of exchange rules on specialist behavior.
A number of rules constrain the specialist in assigning quotes and transacting for his
personal account. I focus on the Price Continuity rule (NYSE 1999, Rule 104.10(3)), which
requires the specialist to keep transaction price changes small by providing extra liquidity
when necessary.11 Dutta and Madhavan (1995), in their theoretical paper predict that the
Price Continuity rule affects specialist profits by causing a redistribution of wealth from
10
All regressions are tested for possible collinearity effects that might account for the insignificant inventory
effect in the TORQ results. There is no evidence of possible collinearity among the explanatory variables.
11
I reviewed all NYSE Hearing panel decisions from 1976 onward on specialist disciplinary proceedings. I also
conducted interviews with both specialists on the floor and senior officials of the NYSE (Market Surveillance)
confirming that specialists are primarily evaluated based on the extent to which they adhere to the following three
rules: the Price Continuity rule (NYSE 1999, Rule 104.10(3)), which requires the specialist to achieve small
consecutive price changes; the Quotation rule (NYSE 1999, Rule 104.10(4)), which requires the specialist to keep
small quoted spreads; and the Price Stabilization rule, in connection with destabilizing transactions by establishing
or increasing a position (NYSE 1999, Rule 104.10(5)) and liquidating or decreasing a position (NYSE 1999, Rule
104.10(6)), which require the specialist to transact against the market trend. Of these three rules, I expect the Price
Continuity rule to have the largest effect on the quote revision process, in part because any violation of the
Quotation rule also constitutes a violation of the Price Continuity rule. While in theory the specialist can satisfy
the Price Continuity rule without using the quotes, empirically I find that the specialist almost always improves the
buy or sell side of the book especially when the book spreads are larger than $2/8. To avoid sell-gaps, the
specialist’s quoted ask price does not exceed the last transaction price by more than $1/8. Similarly, to avoid buygaps, the quoted bid price is not more than $1/8 below the last transaction price. Together these conditions imply
a maximum quoted spread of $2/8, consistent with the Quotation rule. In addition, there are cases when the Price
Continuity rule is binding and the book spread is $2/8.
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523
him to both informed and liquidity investors. Following this logic I hypothesize that the
specialist can rebalance his inventory by use of quoted prices only when the Price Continuity
rule is not constraining. If my hypothesis is true and showing that the Price Continuity rule
is binding less frequently post-decimalization than pre-decimalization, this would provide
a possible explanation for the findings in Table 2, i.e. that inventory is a significant factor
in predicting the change in quoted prices post-decimalization but not pre-decimalization
In addition, I relate inventory rebalancing to specialist profits following Sofianos (1995).
I predict that the specialist profits are affected by the Price Continuity rule, and expect
greater profits when the rule is not binding. In the next sections I examine empirically the
impact of the rule on the specialist’s quoted prices, profits, and inventory management.
4. Price Continuity rule
The Price Continuity rule requires the specialist to smooth transaction prices by
providing extra liquidity as necessary to keep transaction price changes small. Thus, the
specialist is expected to intervene when there is a large price gap between the previous
transaction price (at time t1) and the current LOB best buy or sell prices (at time t). In
such situations, the specialist is expected to improve the current liquidity by providing
more competitive prices than those in the LOB. In this way, the specialist can announce
quoted spreads that are small and avoid large price changes. I investigate whether the
regression results in Table 2, which show a lack of inventory effect in quotes predecimalization and a strong inventory effect post-decimalization, are due to changes in
how the specialist improves book prices. I expect these improvements to be a function of
whether the Price Continuity rule is binding.
I define a ‘‘one-sided-gap’’ for the two sample periods (TORQ data 1991 and SOD data
2001) as follows:
BuyGap: For the pre-decimalization period, the best book buy price is more than $1/8
lower than the last transaction price, and the spread between the book’s best buy and sell
prices is greater than one tick. For the post-decimalization period, the best book buy price
is more than $0.12 lower than the last transaction price, and the spread between the book’s
best buy and sell prices is greater than one tick.12
Thus, I define the BuyGap for the two periods as follows:
BuyGappre ¼ fpTransaction;t1 pBestBookBuy;t 418gfpBestBookSell;t pBestBookBuy;t 418g
BuyGappost ¼ fpTransaction;t1 pBestBookBuy;t 40:12gfpBestBookSell;t pBestBookBuy;t 40:01g:
Note that BuyGap is defined so that the specialist can improve the current LOB best prices
(i.e., the book spread is greater than the minimum price increment).
SellGap: The book best sell is more than $1/8 (or $0.12 post-decimalization) higher
than the last transaction price and the spread between the book’s best buy and sell prices is
greater than one tick (either $1/8 or one cent, respectively):
SellGappre ¼ fpBestBookSell;t pTransaction;t1 418gfpBestBookSell;t pBestBookBuy;t 418g
SellGappost ¼ fpBestBookSell;t pTransaction;t1 40:12gfpBestBookSell;t pBestBookBuy;t 40:01g:
12
For the pre-decimalization data sample (1991), the tick size is $1/8, whereas post-decimalization the tick size is
one cent.
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Consequently, I can also define the NoGap scenario as occurring when neither a buy nor a
sell gap exists.
NoGappre ¼ fSellGappre a1gfBuyGappre a1gfpBestBookSell;t pBestBookBuy;t 418g
NoGappost ¼ fSellGappost a1gfBuyGappost a1gfpBestBookSell;t pBestBookBuy;t 40:01g:
In the above definitions, the choice of $1/8 and $0.12 as a threshold for the pre- and
post-decimal periods, respectively, is based on NYSE-published reports on market quality.
In these reports, the exchange defines price continuity as a change between consecutive
prices of less than or equal to $1/8 pre-decimalization and 12 cents post-decimalization.13
The Buy and Sell Gap variables identify those cases in which the LOB best prices have a
spread of more than 12 cents which would imply a price discontinuity in the absence of
specialist participation. Under these circumstances, the rule requires the specialist to use
his own capital to improve the book prices and avoid the possibility of transaction price
jumps of more than 12 cents. Table 3 reports mean percentages of the frequency of the
three gap scenarios for my two samples. Table 3 also identifies the specialist improvement
of the LOB best prices for the different gap scenarios. I report mean percentages for the
whole sample of 117 stocks in the SOD sample (Panel A), 116 stocks in the TORQ sample
(Panel B), and their differences (Panel C).
For the SOD sample (Panel A), 26% of the time there are instances of gaps (11% buy
gaps, 11% sell gaps, and 4% both buy and sell gaps). These represent possible price jumps.
In addition, 67% of the SOD sample shows a No Gap scenario, as defined above. The rest
of the time, the LOB spread is one tick. The table shows that for the scenarios of a gap
(possible price discontinuity), the specialist is stepping in to smooth prices when
announcing quotes. That is, he is reducing the gap created by the best prices of the
LOB. Specifically, 60% of the time the specialist improves on the LOB buy side when there
is a buy gap, and 60% of the time the specialist is improving the LOB sell side when there is
a sell gap, on average. The high rate of specialist inactivity that is shown in the summary
statistics (35% on the occurrence of a buy gap and 36% on the occurrence of a sell gap)
suggests that the specialist does not always reveal his intentions through the quoted prices.
However, he is expected to step in and transact within the spread to smooth prices in those
instances.14 For the instances when there is both a buy and a sell gap (4%), the specialist is
improving either side almost equally (46% buy improvements and 41% sell improvements)
in accordance with the Price Continuity rule. Lastly, the specialist does not improve the
opposite side of the LOB as much as the side that creates the gap (5% improvement of the
LOB sell side on a buy gap and 4% LOB buy side on a sell gap).
The pre-decimalization period (TORQ data) is shown in Panel B. It shows that the
instances of possible price discontinuities (gap scenarios) are significantly more frequent
than they are post-decimalization. For the sample period, 50% of the time there are gaps
(20% buy gaps, 19% sell gaps, and 11% both buy and sell gaps) representing instances of
possible price discontinuity. This highly significant decrease in the frequency of gaps postdecimalization is shown in Panel C. The result is in accordance with empirical evidence
showing that spreads are lower after decimalization because limit order traders are more
13
Information on NYSE market quality can be found at the NYSE’s official data dissemination page at http://
www.nysedata.com/factbook.
14
The specialist can either transact within the quotes, or stop market orders from ‘‘hitting’’ the quotes. Ready
(1999) investigates thoroughly the specialist’s actions when a market order arrives.
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Table 3
Summary statistics of Price Continuity rule instances (possible price discontinuities-gaps) and specialist’s price
smoothing behavior
Table 3 reports the frequency of the three gap scenarios of possible price discontinuities (Price Continuity rule is
binding) and the No Gap scenario for both samples: for the SOD data (BuyGappost, SellGappost, BothGapspost and
NoGappost) and the TORQ data (BuyGappre, SellGappre, BothGapspre, and NoGappre). Table 3 also reports the
specialist improvement of the limit order book best prices for the different gap occurrences. I report mean
percentages for companies in both the SOD (Panel A) and TORQ (Panel B) data sets. For the differences between
the SOD and TORQ Gap frequencies (Panel C), the symbols ** and * indicate statistical significance at the 1%
and 5% percent levels, respectively (t-values are reported in parentheses).
Panel A: Mean % for 117 Companies in SOD
Gaps
Greater than 12 cents
Specialist Improvement
LOB Buy Side
LOB Sell Side
No Improvement
BuyGappost
11
SellGappost
11
Both Gapspost
4
No Gappost
67
60
5
35
4
60
36
46
41
13
16
20
64
BuyGappost
20
SellGappost
19
Both Gapspost
11
No Gappost
17
60
5
35
6
60
34
40
42
18
11
11
78
9** (6.1)
8** (5.2)
7** (5.1)
50** (20.2)
0 (0.2)
0 (0.2)
0 (0.1)
2 (1.8)
0 (0.1)
2 (0.6)
6 (1.9)
1 (0.4)
5 (1.9)
5** (6.0)
9** (8.1)
14** (9.5)
Panel B: Mean % for 116 Companies in TORQ
Gaps
Greater than $18:
Specialist Improvement
LOB Buy Side
LOB Sell Side
No Improvement
Panel C: % Change between SOD and TORQ
Gap Change: Gappost–Gappost
Specialist Improvement
LOB Buy Side
LOB Sell Side
No Improvement
competitive (Chakravarty, Wood and VanNess 2004 and Bessembinder, 2003b). This
increase in competition causes the LOB best bid and ask prices at time t to be closer to the
realized price where supply meets demand, as represented by the transaction price at time t
– 1. Thus, the LOB appears to have smoother price changes after decimalization.
Importantly, however, Table 3 Panel C also shows that although there was a decrease in
the frequency of possible price jumps (from pre- to post-decimalization), the specialist
price smoothing behavior is almost unchanged, in that specialist improvement differences
in the two samples are almost all not significant. This signifies that specialist behavior with
respect to the Price Continuity obligation has not changed with decimalization. What has
changed is the frequency of instances in which this affirmative obligation is binding.
The results in Table 3 suggest that specialists often improve upon limit order prices in
order to smooth price changes in accordance with the Price Continuity rule. Existing
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Table 4
The partition of specialist actions based on the Price Continuity rule
The table reports the frequency in percentages of the specialist overall price improvements of the book best
prices when the specialist announces the quotes (column labeled Total Specialist Participation). The table also
depicts percentages for the three partition categories of the total specialist participation based on the Price
Continuity rule, namely, Discretionary Participation, when the Price Continuity rule is not binding, Mandatory
Partici-pation, when the Price Continuity rule is binding, and Price Discontinuity, when the rule is binding but the
specialist does not smooth the book best prices according to the rule. The data are reported here for both the
TORQ (November 1990–January 1991) and SOD (April 2001) databases. For the change between the SOD and
TORQ spe-cialist participation (last row), the symbols ** and * indicate statistical significance at the 1% and 5%
levels, respectively (t-values are reported in parentheses).
SOD data set
Torq data set
Change
Total specialist
participation (%)
Discretionary
participation (%)
Mandatory
participation (%)
Price discontinuity
(%)
45
42
3 (1.3)
65
21
44** (13.3)
32
72
40** (12.2)
3
7
4** (6.6)
theoretical work indicates that the specialist may actively participate in the quotes to
manage inventory. To better understand the relative importance of these two motives, I
partition the specialist improvement of the LOB best prices into three categories: (1) the
Price Continuity rule is binding and the specialist reduces the buy or sell gaps; (2) the Price
Continuity rule is binding but the specialist does not act according to the rule; rather, he
improves the other side of the book from the gap;15 and (3) the Price Continuity rule is not
binding. I refer to these categories as mandatory participation, price discontinuity, and
discretionary participation, respectively. Table 4 gives a summary of the frequency of the
three categories in the two samples (TORQ and SOD data). It shows that the overall rate
of specialist behavior to improve the best prices in the LOB does not change between the
two periods. The specialist posts quotes that improve on either the LOB best buy or sell
price 45% of the time post-decimalization (SOD sample) and 42% of the time predecimalization (TORQ sample). Therefore, I conclude that the specialist has a significant
presence in the quote process both before and after decimalization. The clear difference
between the two samples, as seen in the table, is in the percentage of discretionary,
mandatory, and price discontinuity specialist participation. In particular, for the SOD
sample, the majority of LOB price improvements are due to discretionary specialist
participation, i.e., when the Price Continuity rule is not binding (65% discretionary
participation versus 32% mandatory participation, i.e., when the rule is binding). This is
not the case for the TORQ data set, in which the vast majority of specialist participation is
constrained by the rule (21% discretionary participation versus 72% mandatory
participation). Price discontinuity actions take place less than 8% of the time in both
data sets, as specialist actions rarely stray from the responsibility to follow the Price
Continuity rule.
In sum, as both Tables 3 and 4 show, the specialist’s affirmative obligation to provide
price continuity is still in effect post-decimalization. The specialist complies with the rule in
a similar manner as pre-decimalization by smoothing prices as needed. In addition, and as
15
The specialist in these instances does not support Price Continuity, even though his moves do lower the book
spread.
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527
expected, the intraday instances in which the rule is binding are less frequent postdecimalization. Nevertheless, specialist overall percentage participation in improving LOB
best prices is the same in both the TORQ and SOD samples. This suggests that postdecimalization, the specialist participates at his discretion in the quoted prices for reasons
that might relate to inventory adjustment and profits. I investigate this further in the next
sections.
5. Inventory management, Price Continuity rule, and Quote revisions
The specialist decision to improve the buy or sell side of the book is partly driven by the
Price Continuity rule, as seen above in Tables 3 and 4. The impact of this constraint is of
great interest to scholars and practitioners, particularly if it can resolve the disagreement
between empirical and theoretical results regarding inventory adjustments and quoted
prices. If the specialist can rebalance his inventory by use of quoted prices only when the
Price Continuity rule is not constraining, then that would explain why previous empirical
literature has had problems identifying inventory rebalancing.
I address this issue allowing for instances when the Price Continuity rule is binding and
non-binding in the linear model of equation 1 predicting the change in quoted prices. I run
linear time-series regressions predicting quote revisions for each of the 117 stocks in the
SOD data set and 116 stocks in the TORQ data set, using the specialist inventory, his
inferred forecasting ability, and occurrences of pricing gaps as the key explanatory
variables. The inclusion of the gap scenarios in the model allows me to determine the
significance of the Price Continuity rule. All of the other variables appearing in Tables 1
and 2 and Eq. (1)—the floor brokers’ proxy variable, the sign of trades as proxy for order
flow, and book prices change—are also included in the new regression equation as
controls. For the inventory and forecasting variables, I include interaction terms with the
gap indicators to identify any difference in the specialist behavior when he is obliged to
follow the Price Continuity rule (BuyGap, SellGap scenarios) versus when the rule is not
binding (a NoGap scenario).
I cluster the explanatory variables of interest into four groups that describe the gap
effect, the book effect, and the Inventory:Gap (DInventoryt1,t2:BuyGap, DInventoryt1,t2:SellGap, DInventoryt1,t2:NoGap) and Forecasting:Gap (Forecastt+1,t:BuyGap,
Forecastt+1,t:SellGap, Forecastt+1,tNoGap) interactions. In particular, I incorporate the
Price Continuity rule using the gap indicators (BuyGap, SellGap, and NoGap) as defined
in Section 4 above, and test whether each one affects the change in quoted prices. I expect
the Buy Gap (Sell Gap) variable to have a significant positive (negative) coefficient as
quoted prices are updated upward (downward) to adjust for the gap. I also test for a
difference in specialist behavior when the Price Continuity rule is binding versus when it is
not. I expect to see the specialist adjust his inventory through quoted prices when the rule
is not binding. This is shown by a significant negative coefficient in the DInventoryt1,t2:NoGap interaction, and not in the other interactions.
Table 5 reports regression results in the aggregate for both samples (TORQ and SOD
data) and for stocks divided into quartiles with respect to frequency of trading (SOD data
only). The gap group of variables (BuyGap, SellGap, NoGap) shows clear evidence of a
significant difference between the impact of buy and sell gaps on specialist decisions to
change quoted prices. As expected according to the Price Continuity rule, the existence of a
buy gap causes an upward quote change, which reflects specialist adjustment of the
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Table 5
Linear regression model predicting quotation midpoint changes (DMidquotet,t1). Adjustments for the Price
Continuity rule
The table shows aggregated results of the linear model regressions predicting the specialist quote revision
(DMidquotet,t1) in both TORQ and SOD companies, adjusting for the Price Continuity rule. It also reports
aggregated results by volume quartiles based on the daily average number of trades for the SOD sample. The
reportedexplanatory variables are: the gap indicators (BuyGap, SellGap) identifying when the Price Continuity
rule is binding and NoGap when is not, (i.e., when the specialist is obliged to improve either the best book buy or
sell price in order to achieve Price Continuity), the change in the book best prices (DBestBuyt,t1, DBestSellt1,t1),
the specialist inventory effect and its interaction with each one of the gap subsamples (DInventoryt1,t2,
DInventoryt1,t2 : NoGap, DInventoryt1,t2 : SellGap, DInventoryt1,t2 : BuyGap), and similarly a forecasting
variable and its interaction with each subsample (Forecastt+1,t, Forecastt+1,t : NoGap, Forecastt+1,t : SellGap,
Forecastt+1,t : BuyGap ). These regression results are compared with the results of Table 2, where there is no
adjustments for the Price Continuity rule. The symbols ** and * indicate statistical significance at the 1% and 5%
levels, respectively (t-values are reported in parentheses).
TORQ
Number of stocks
117
29
0.007**
(5.5)
0.0078**
(5.9)
0.0005**
(6.3)
0.0093**
(5.4)
0.014**
(7.1)
0.0005**
(9.4)
0.0019
(0.8)
0.0008
(0.3)
0.0007*
(2.6)
0.004
(1.0)
0.0036
(0.7)
0.0001
(0.2)
0.2707**
(17.9)
0.2716**
(17.0)
0.4257**
(38.5)
0.4320**
(48.3)
0.3192**
(16.9)
0.3496**
(18.7)
0.3166**
(7.2)
0.1299**
(5.7)
0.1883**
(5.8)
0.1614**
(5.2)
0.0002 0.0008**
(1.9)
(7.6)
: NoGap 0.0006** 0.0001**
(3.6)
(6.3)
: BuyGap 0.0006
0.0002
(0.9)
(1.5)
: SellGap
0.0004
0.0002
(0.3)
(0.9)
0.0002**
(6.0)
0.0002**
(4.3)
0.0002
(1.5)
0.0001
(0.3)
0.0002**
(9.5)
0.0001**
(3.2)
0.0004
(1.2)
0.0008**
(2.9)
0.0002**
(7.1)
0.0001**
(0.4)
0.0015
(1.7)
0.0018
(1.8)
0.0047**
(3.9)
0.0002
(0.7)
0.0051*
(2.0)
0.0047
(1.2)
0.0001
(0.8)
0.0005
(2.7)
0.0011*
(-2.2)
0.0009
(1.1)
0.0004**
(7.3)
0.0004**
(10.7)
0.0014**
(6.2)
0.0012**
(4.7)
0.0003**
(4.6)
0.0004**
(8.3)
0.0018**
(4.0)
0.0019**
(3.1)
0.0003
(1.4)
0.0000
(0.1)
0.0011
(1.8)
0.0013
(1.5)
0.0002
(0.6)
0.0003
(1.1)
0.0055
(2.5)
0.0039
(1.2)
0.0089**
0.0050**
(4.1)
(4.6)
0.0058** 0.0053**
(3.3)
(4.2)
0.0008
0.0005**
(1.7)
(10.1)
0.3102**
(11.7)
0.3439**
(16.0)
DBestBuyt,t1
DBestSellt1,t1
DInventoryt1,t2
116
High Quartile 2nd Quartile 3rd Quartile Low Quartile
29
NoGap
DInventoryt1,t2
Overall
29
SellGap
DInventoryt1,t2
Overall
30
BuyGap
DInventoryt1,t2
SOD
Forecastt+1,t
Forecastt+1,t : NoGap
Forecastt+1,t : BuyGap
Forecastt+1,t : SellGap
0.0002**
(4.3)
0.0004**
(13.6)
0.0015**
(6.5)
0.0014**
(4.8)
possible discontinuity driven by the buy side of the book. The opposite holds for a sell gap,
which causes a downward quote change. This indicates that the Price Continuity rule has a
significant effect on quoted prices, a result not previously accounted for in the literature.
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This effect is present both pre-decimalization (TORQ data, second column) and postdecimalization (SOD data, third column).
By controlling for the effects of the price continuity rule, results in Table 5 uncover the
specialist inventory effect on quoted prices. For both samples (TORQ and SOD data), the
aggregated regression results show an inventory rebalancing effect (significant negative
sign) on the DInventoryt1,t2:NoGap interaction, which reflects discretionary specialist
participation, when the Price Continuity rule is not binding. No such effect is present
whenever the specialist has to follow the rule in the Gap interaction variables
(DInventoryt1,t2:BuyGap and DInventoryt1,t2:SellGap). This evidence shows that the
specialist adjusts quotes based on inventory imbalance when he is not obliged to follow
the Price Continuity rule of the exchange. On the other hand, the Price Continuity rule,
and not inventory imbalance, mainly determines specialist quotes when a buy or sell gap
is present. These results shed light on why the empirical literature has failed to identify a
strong inventory effect in the past (pre-decimalization). By dividing the specialist
actions into discretionary and mandatory participation, I uncover the source of the
inventory rebalancing in the quote revision process that has repeatedly been predicted in
theoretical work. The inventory effect is obscured if no allowance is made for the Price
Continuity rule.
In addition, the rule constrains the majority of specialist actions on quotes predecimalization—as seen in Section 4, Table 3—and forces inventory not to be an
important variable in predicting quote changes. Post-decimalization, the majority of the
specialist actions are not constrained by the Price Continuity rule. For these actions,
inventory is an important variable in predicting quote changes. This majority of specialist
actions that are unconstrained by the rule can lead to a significant inventory effect in the
aggregate without any partitioning of specialist actions. And, this can explain why I find
inventory effects post-decimalization but not pre-decimalization (Table 2).
5.1. Sensitivity tests
I perform two robustness checks of my results. First, I investigate whether specialist
inventory rebalancing is present in the quote revision process in two different sub-samples:
periods of high and low volatility. My goal is to verify that results for price smoothing and
inventory adjustments when the Price Continuity rule is not binding are not being driven
by stable periods with low volatility only. That is, if I find that it is the rule and not the
market conditions that drive inventory rebalancing, then the results will be stronger.
Second I look at a different specification for the model predicting changes in the quoted
prices.16 Instead of estimating a single-equation regression using the quoted midpoint as
the dependent variable, I estimate a system of equations with the quoted bid and ask price
changes as separate series. If the specialist selectively updates the bid or ask prices in
response to his inventory (in the no gap scenario) then a model of simultaneous equations
can uncover such an effect even better than a single regression specification. Kavajecz and
Odders-White (2001) and Hasbrouck (1991) use a system of simultaneous equations in
similar scenarios where they investigate differential effects on endogenous variables.
16
I thank the anonymous referee for this suggestion. I also run all of my regression specifications having the
change in inventory variable (DInventoryt1,t2) as a dummy variable (+1,0 or –1) and include the variable
SignVolumet1 instead of the variable SignofTradet1. The main results on specialist inventory management when
Price Continuity rule is not binding are very similar. Due to space constraints these results are not reported.
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5.1.1. Periods of high and low volatility
I define periods of high volatility for each stock as those trading days in which the
difference between the highest and lowest transaction price is greater than one standard
deviation of the median difference. The rest of the days in my sample are defined as periods
of low volatility.
Table 6 reports summary statistics of specialist behavior for the two volatility periods.
Results are shown for the SOD data only. The TORQ data provide very similar results,
which are not reported here due to space considerations. The specialist price smoothing
behavior is almost identical for periods of high and low volatility. As expected, there are
more instances of possible price discontinuity (gaps) for periods of high volatility
compared with low volatility. However, the specialist improves the relevant best price of
the LOB consistently with respect to price continuity for both periods. In addition, for
Table 6
Summary statistics of possible price discontinuities (BuyGap, SellGap) and the specialist’s price smoothing
behavior: periods of high and low volatility
Table 6 reports summary statistics of the three gap scenarios of possible price discontinuities (BuyGap, SellGap,
NoGap). It also shows the specialist’s improvement of the limit order book best prices for the different gap
occurrences. I report mean percentages for both high and low volatility periods. I identify high volatility periods
as the days when the difference between the intraday high and intraday low transaction prices are higher than one
standard deviation of the median difference for that company. The table reports results for the sample of 117
companies after decimalization (SOD data set). Panel C reports the percentage differences between the high and
low volatility periods (t-values are in parentheses).
Gaps
BuyGap
SellGap
No Gap
Panel A: Mean percentages for periods of high volatility
Gaps
14
14
64
Specialist Improvement:
LOB Buy Side
LOB Sell Side
No Improvement
58
5
37
6
58
35
16
20
64
Panel B: Mean percentages for periods of low volatility
Gaps:
12
11
68
Specialist Improvement:
LOB Buy Side
LOB Sell Side
No Improvement
60
6
34
5
61
34
17
21
62
2 (0.9)
3 (1.1)
4 (1.0)
2 (0.5)
1 (0.9)
3 (0.6)
1 (1.5)
3 (0.9)
1 (0.5)
1 (0.8)
1 (1.4)
2 (1.6)
Panel C: Percentage change between periods of high and low volatility
Gaps:
Specialist Improvement:
LOB Buy Side
LOB Sell Side
No Improvement
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Table 7
Linear regression model results predicting quotation midpoint changes (DMidquotet,t1). Adjustments for the
price continuity rule: periods of high and low volatility
The table shows aggregate results of linear regressions predicting the specialist quote revision process
(DMidquote) for both high and low volatility periods. I identify high volatility periods as the days when the
difference between the intraday high and intraday low transaction prices are higher than one standard deviation of
the median difference for that company. The rest of the days in our sample are considered the low volatility
period. The table reports results for the sample of 117 companies after decimalization (SOD data set). The
symbols ** and * indicate statistical significance at the 1% and 5% levels, respectively (t-values are reported in
parentheses).
Period:
High volatility
Low volatility
BuyGap
0.0070**
(7.4)
0.0079**
(7.8)
0.0006**
(8.9)
0.0077**
(6.2)
0.0089**
(6.5)
0.0005**
(10.5)
0.2776**
(19.0)
0.2899**
(18.6)
0.2971**
(20.0)
0.3101**
&(18.8)
0.0006**
(9.6)
0.0002**
(5.6)
0.0002
(0.8)
0.0001
(0.4)
0.0003**
(9.6)
0.0001**
(-4.2)
0.0006*
(2.1)
0.0007*
(2.4)
0.0004**
(9.1)
0.0004**
(11.2)
0.0017**
6.5
0.0014**
(4.8)
0.0003**
(12.0)
0.0004**
(15.4)
0.0012**
(4.0)
0.0019**
(4.7)
SellGap
NoGap
DBestBuyt,t1
DBestSellt1,t1
DInventoryt1,t2
DInventoryt1,t2 : NoGap
DInventoryt1,t2 : BuyGap
DInventoryt1,t2 : SellGap
Forecastt+1,t
Forecastt+1,t : NoGap
Forecastt+1,t : BuyGap
Forecastt+1,t : SellGap
both periods, the specialist also participates at his discretion in the quoted prices, i.e., when
the rule is not binding.
Table 7 presents aggregate results for the linear model predicting changes in the
midquote estimated separately on high and low volatility periods. I can reasonably
anticipate that the specialist will be required to intervene to keep prices continuous more
often during periods of greater volatility. The evidence reported in Table 7 (first column)
supports this reasoning, showing that for periods of high intra-day volatility, price
continuity affects quoted prices. The coefficients for both of the indicator variables,
BuyGap and SellGap, show that the specialist, in accordance with the Price Continuity
rule, adjusts the quotes for possible price discontinuity. The significant coefficients for the
DInventoryt1,t2:NoGap explanatory variable in Table 7 show that the specialist still
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rebalances his inventory during periods of high volatility. However, Table 7 (second
column) shows that price continuity effects are also present for periods of low volatility, as
the BuyGap and SellGap coefficients for this regression are also highly significant. This
suggests that the specialist is constrained by the rule during both periods with a similar
effect on the quote revision process. I can also identify an inventory rebalancing effect
when the rule is not binding, as seen by the negative and significant coefficient for
DInventoryt1,t2:NoGap. The similarity of this result in both regressions implies that
periods of high volatility do not solely explain the specialist inventory effects on quoted
prices. Thus, I can conclude that the specialist acts to both smooth prices and rebalance his
inventory, and that this dual role is not affected by price volatility.17
5.1.2. Simultaneous equation models
I run the following two-equation model to predict the changes in the bid and ask prices
simultaneously:
0
DBidpricet;t1 ¼ g1 DAskpricet;t1 þ b1 X1 þ 1 ;
DAskpricet;t1 ¼ g2 DBidpricet;t1 þ b0 1 X2 þ 2 :
The model treats the bid and ask price changes as endogenous variables. I use the twostage least squares methodology to estimate the simultaneous equations model, following
Kavajecz and Odders-White (2001). I fit the model for each individual stock in the sample
and aggregate the results using the Bayesian aggregation method of DuMouchel (1994) as
in the previous sections. The matrices X1 and X2 represent the independent variables. To
resolve the identification issue, some predictors that appear in one equation do not appear
in the other. In particular, I use all of the variables defined in Table 1 (and Eq. (1)) plus the
price continuity variables (the gap instances). I exclude the lagged midquote variables and
replace them with lagged dependent variables (up to the third lag) in each equation to
account for both autocorrelation and identification. To test for over-identification
restrictions on the model I use Basmann’s (1960) test.
Table 8 reports aggregated results of the simultaneous equation model predicting bid
and ask prices. The coefficient estimates verify the main results in Table 5. The BuyGap
and SellGap variables are both strongly significant. This indicates that the specialist
improves each quote price when there is a gap to provide the necessary price smoothing
required by the Price Continuity rule. In addition, the specialist rebalances his inventory
when the rule is not binding. The interaction variable DInventoryt1,t2:NoGap is a
negative and strongly significant predictor of changes in the bid and ask prices
(DBidpricet,t1 and DAskpricet,t1). Its coefficient estimate is of larger magnitude than
the single-equation estimate of Table 5 (predicting the change in midpoint), which
indicates that the simultaneous equation model may better capture the selective update of
the bid or ask prices in response to the specialist’s inventory. This preferential update of
the quoted prices might also be the reason the endogenous variables DBidpricet,t1 and
DAskpricet,t1 appear negatively correlated with each other after accounting for the
17
I repeat the analysis for days in which the market (S&P 500) is volatile versus days in which it is stable. I find
weaker results but still supporting evidence that price continuity is binding in both regimes without any specialist
inventory adjustment during those instances.
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Table 8
Simultaneous equation model results
The table shows aggregate results of simultaneous equations predicting the change in the quoted prices, i.e., the
simultaneous change in the bid (DBidpricet,t1) and ask (DAskPricet,t1) prices. The table reports results for the
sample of 117 companies after decimalization (SOD data set). The symbols ** and * indicate statistical
significance at the 1% and 5% levels, respectively (t-values are reported in parentheses).
DBidpricet,t1
DBidpricet,t1
DAskpricet,t1
DBidpricet1,t2
DBidpricet2,t3
DBidpricet3,t4
0.8231
(26.3)
0.9230**
(21.9)
0.0184**
(3.4)
0.0121
(0.9)
0.0032
(0.4)
DAskpricet1,t2
DAskpricet2,t3
DAskpricet3,t4
BuyGap
SellGap
NoGap
DBestBuyt,t1
DBestSellt,t1
DInventoryt1,t2
DInventoryt1,t2 : NoGap
DInventoryt1,t2 : BuyGap
DInventoryt1,t2 : SellGap
Forecastt+1,t
Forecastt+1,t : NoGap
Forecastt+1,t : BuyGap
Forecastt+1,t : SellGap
DAskPricet,t1
0.0113**
(4.7)
0.0128**
(5.5)
0.0009**
(9.6)
0.5518**
(17.3)
0.5601**
0.0014**
(7.8)
0.0003**
(5.9)
0.0007*
(2.1)
0.0004
(0.8)
0.0005**
(4.4)
0.0008**
(13.1)
0.0030**
(6.4)
0.0031**
(5.7)
0.0141**
(3.4)
0.0032
(1.2)
0.0088**
(5.2)
0.0121**
(6.4)
0.0085**
(3.4)
0.0009**
(7.2)
0.4898**
(14.3)
0.5295
0.0012
(17.7)
0.0003
(6.6)
0.0008**
(2.9)
0.0003
(0.7)
0.0005**
(4.8)
0.0008
(12.6)
0.0028**
(6.6)
10.0028**
(5.2)
changes in the LOB best prices (DBestBuyt,t1 and DBestSellt,t1). In sum, the specialist, in
the vast majority of his quote price improvements, provides better price liquidity on only
one side of the quotes, but not on both.
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6. Price Continuity rule and market quality
So far, I have seen that the NYSE Price Continuity rule affects the quotes disseminated
by the specialist. An important question is whether this impact has any material effect on
the quality of the market, and in particular on price efficiency.18 Does specialist price
smoothing behavior provide better prices?
I look at two measures of market quality: intraday volatility and the intraday variance
ratios also found in Bessembinder (2003b). To avoid the bid-ask bounce volatility bias,
I compute these measures by first calculating the returns from midpoints of the quoted
price. For each firm, volatility is measured with respect to continuously compounded
intraday (10:00 a.m. – 4:00 p.m.) returns. Similarly, variance ratios for each stock
are computed as six times the variance of the hourly quote midpoint return divided by
the variance of the six-hour (10:00 a.m. – 4:00 p.m.) quote midpoint return. Poterba
and Summers (1988) show that when quote midpoints follow random walks, meaning
that price changes are permanent on average, the return variance ratios will not
systematically deviate from one. If intraday price changes are systematically reversed,
indicating that prices overshoot in the short run, then variance ratios will tend to be greater
than one.
To test how the Price Continuity rule affects price quality, I compare volatility and
variance ratio measures in two different scenarios: (1) an actual scenario when the rule is
binding and the specialist smoothes prices—improves the LOB best prices to alleviate
either the buy or sell gap (2) a counterfactual (hypothetical) scenario absent any rule—the
specialist does not smooth prices when needed but instead announces the LOB best price as
the quoted prices.19 I thus compare volatility and variance ratio measures with and without
specialist price smoothing behavior.
Table 9 shows cross-sectional median (mean) measures of intraday volatility and
variance ratios, both with specialist price smoothing behavior (Volatility and Variance_
Ratio) and without (Volatility_Book and Variance_Ratio_Book). A clear pattern can be
observed. The median and mean intraday volatility in the sample is higher during the
hypothetical scenario when the specialist does not alleviate the price gap. The change,
however, is not statistically significant, with a z value (t value) for the median (mean)
change of 1.2 (1.4). More importantly, the variance ratio is much closer to the
random walk benchmark of 1.0 when the price continuity rule is binding and the specialist
alleviates the price gaps. The median variance ratio without specialist improvement
is 1.182, as compared to 0.98 with specialist improvement. Mean variance ratio
results appear very similar. In the absence of the Price Continuity rule, the significantly
higher than one variance ratios indicate price reversals. Thus, without specialist
improvement, order flow or other types of shocks push prices beyond their longer-term
equilibrium. In conclusion, specialist price smoothing behavior mitigates the noise in price
discovery.20
18
Market quality is multidimensional. In the current paper I look at one dimension, price efficiency.
The way I define the hypothetical scenario allows me to capture first-order effects of the absence of price
smoothing (next-period effects on transaction prices). A natural experiment of the absence of Price Continuity
rule is needed to capture the full effect of the rule on measures of price quality.
20
As a robustness test, I test for the effect of the Price Continuity rule on price volatility and price variance
ratios cross-sectionally, controlling for the volatility of the overall market. The results are very similar.
19
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Table 9
Price continuity and market quality: intraday volatility and variance ratios
The table reports summary statistics of intraday price volatility and variance ratios cross-sectionally for the 117
companies in the SOD data set. I calculate measures of intraday volatility and variance ratios, both with specialist
price smoothing behavior (Volatility and Variance_Ratio) and without (Volatility_Book and Variance_Ratio_Book). The latter is defined under the assumption that for instances of possible price discontinuities, the specialist
is not stepping ahead to smooth prices, but instead is reflecting the relevant best price of the limit order book as a
quoted price. Volatility is defined as the standard deviation of intraday returns that is based on quote midpoints
observed at 10:00 a.m. and 4:00 p.m. The variance ratio is the ratio of six times the variance of hourly quote
midpoint returns to the variance of six hour (10:00 a.m.–4:00 p.m.) returns. For the change between the with- and
without-specialist price smoothing behavior, the symbols ** and * indicate statistical significance at the 1% and
5% levels, respectively (t- and z-values for the relevant tests are in parentheses).
Mean
Median
Volatility
Volatility_Book
Change
0.024
0.028
0.004 (1.4)
0.019
0.021
0.002 (1.2)
Variance_Ratio
Variance_Ratio_Book
Change
1.204
1.985
0.781* (2.0)
0.998
1.182
0.184** (2.7)
7. Inventory management, Price Continuity rule, and specialist profits
To gauge the economic impact of the specialist’s inventory rebalancing and price
smoothing behavior I examine specialist profits. In order to calculate the intraday profits, I
follow Hasbrouck and Sofianos (1993) and Sofianos (1995). For each transaction at time t,
profit is defined as
Pt ¼ I t1 ðpt pt1 Þ,
where It–1 is the specialist’s inventory position before the transaction at time t, and p is the
transaction price taken both at times t and t–1.21 In other words, I calculate the specialist’s
mark-to-market profits per trade, which is the price appreciation of his inventory position.
I calculate daily specialist profits by summing Pt over all of the transactions made in a
given day. Unfortunately, since I lack data on operational expenses (floor clerk salaries,
interest costs, fees to the exchange, etc.) or other possible specialist revenue sources (e.g.,
floor brokerage commissions), I examine only trading revenues and not net specialist
profits. However, I do not expect this to substantially alter the difference in the profits
between periods when the Price Continuity rule is binding and when it is not. I proceed by
aggregating specialist transaction profits for the following subsamples:
1. Overall specialist profits: all transactions.
2. Passive specialist profits: transactions for which the Price Continuity rule is binding.
These are transactions that occur because of the specialist’s mandatory participation.
21
Inventory positions are adjusted using estimated values for overnight specialist trading. More details on the
estimation algorithm can be found in the Appendix. The results in this section appear similar in magnitude but less
statistically significant if I assume zero overnight trading.
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Table 10
Specialist profits and the Price Continuity rule
The table shows summary statistics of the total average daily specialist profits for all 117 companies in the SOD
sample along with mean results of the companies divided into volume quartiles based on the daily average number
of trades. In addition, the table reports summary statistics for the specialist profits as they are determined by either
Price Continuity rule actions, Passive Specialist Profits, or the specialist’s actions when the rule is not binding,
Active Specialist Profits. Companies with average profits that deviate more than three standard errors from the
mean are excluded from the study. The symbols ** and * indicate statistical significance at the 1% and 5% levels,
respectively (t-values are reported in parentheses).
Number of Stocks:
Overall
High Quartile
2nd Quartile
3rd Quartile
Low Quartile
117
30
29
29
29
13,930** (4.4)
938 (0.3)
14,870** (3.2)
44,160** (4.4)
759 (0.1)
44,920** (2.7)
10,940** (3.1)
2,315 (0.5)
13,260** (2.8)
651 (1.2)
635 (0.5)
1,286 (1.0)
38 (0.2)
137 (0.6)
100 (0.8)
33,660 (1.9)
8,762 (0.3)
42,420 (1.4)
4,226 (0.6)
11,540 (0.9)
15,760 (1.3)
1,277 (1.1)
3,727 (1.1)
2,450 (0.8)
128 (0.4)
295 (0.5)
167 (0.6)
38,530** (3.9)
14,370 (1.1)
24,210_ (2.0)
15,770** (3.6)
3,550 (0.8)
12,210_ (2.5)
1,696** (3.0)
1,010_ (2.1)
687 (1.7)
50 (0.6)
22.2 (0.3)
72.2 (1.5)
Panel A: SOD overall periods
Overall Specialist Profits($)
Passive Specialist Profits($)
Active Specialist Profits($)
Panel B: SOD high volatility periods
Overall Specialist Profits($)
Passive Specialist Profits($)
Active Specialist Profits($)
9,133 (1.9)
6,016 (0.7)
15,150 (1.8)
Panel C: SOD low volatility periods
Overall Specialist Profits($)
Passive Specialist Profits($)
Active Specialist Profits($)
13,990** (4.6)
4,851 (1.4)
9,140_ (2.6)
3. Active specialist profits: transactions for which the Price Continuity rule is not binding.
These are transactions that occur because of the specialist’s discretionary participation.
Table 10 reports the mean of the daily average profits overall and per quartile by the
number of trades for each stock. I report results from the more recent SOD data set. Panel
A shows that overall specialist average daily profits for all companies are $13,930 per
stock, while those produced from discretionary specialist participation are $14,878.22 At
the same time, the specialist incurs negative profits when he facilitates smooth price
changes. The aggregate average profits when the Price Continuity rule is binding (i.e.,
mandatory participation) are negative but statistically insignificant at –$938.23 Results are
very similar for the first quartile of highly traded stocks. For the second quartile, the
22
Coughenour and Harris (2006) find overall specialist daily profits for the NYSE after decimalization that
appear slightly smaller. I attribute the slightly higher result to the use of a different sample.
23
For the TORQ data (1991) I find that the active specialist profits are $2,165 on average. Interestingly, I find
passive specialist profits that are negative and significant: $1,714. The magnitude and significance of the negative
passive specialist profits for the TORQ data compared with the SOD data are in accordance with my findings of
larger inventory risks and higher frequency of the Price Continuity rule in the pre-decimalization period than in
the post-decimalization period.
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results are even more pronounced. The specialist incurs losses of $2,315 when his actions
are governed by the Price Continuity rule and he has to provide the necessary liquidity to
smooth prices. He recovers these losses, however, when the rule is not binding, incurring
positive profits of $13,260 for net profits of $10,940. These results support Dutta’s
and Madhavan’s (1995) theoretical predictions of the costs of following the Price
Continuity rule.
Panels B and C of Table 10 show how volatility can affect specialist profits. For high
volatility periods (Panel B), although profits are not statistically significant in all of the
subsamples, there are pronounced differences between active and passive specialist profits.
When the rule is binding, profits are always negative and large. These results hold for
almost all the quartiles of stocks (the first three quartiles of traded stocks). Panel C shows
that the overall specialist profits of Panel A are driven by his profits during periods of low
volatility. The overall specialist profits for Panel C are statistically and economically
significant, as are the active specialist profits. Interestingly, the profits from mandatory
specialist participation are also positive, but highly insignificant. This shows that the
specialist is better able to manage inventory positions using quotes for the periods of low
volatility, even in the presence of a gap.
In sum, Table 10 results depict that specialist profits are only statistically and
economically positive when the specialist participates in quotes when the Price Continuity
rule is not binding. When the rule is binding, the results show that the specialist loses
money by providing price smoothing. Even if these losses are not statistically significant,
they appear to be quite large in high volatility periods.
Sofianos (1995) shows that specialist profits can be divided into spread profits (those
related to the bid-ask spread of each of his transactions) and positioning profits (those
profits that are directly related to specialist inventory adjustments and forecasting ability).
To test whether the passive and active specialist profits found in Table 10 are directly
related to specialist inventory rebalancing when the Price Continuity rule is not binding, I
calculate the specialist spread and positioning profits for each of the two profit categories.
Sofianos (1995) finds that specialist profits between transaction times 0 and N, P0,N, can be
decomposed into
P0;N ¼ PositioningRevenuesðPRÞ þ SpreadRevenuesðSRÞ,
where
PR ¼ ðmN I N m0 I 0 Þ t¼N
X
m t bt
t¼1
and
SR ¼
t¼N
X
xt bt ðxN I N x0 I 0 Þ.
t¼1
The variable mt is the midquote at transaction time t, IN is the specialist inventory position
at time N, bt is the number of shares the specialist bought (+) or sold (–) at transaction
time t, and xt ¼ mt 2pt is the effective half spread, i.e., the distance between the midquote
and the transaction price pt. I further subdivide the sample into active specialist profits,
A
A
RA
0;N ¼ PositioningRevenuesðPRÞ þ SpreadRevenuesðSRÞ ,
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Table 11
Specialist profits decomposition and the Price Continuity rule
The table reports the total, active, and passive average daily specialist profits for 117 companies in the SOD
data set. The profits are subdivided into spread and positioning profits following? The symbols ** and * indicate
statistical significance at the 1% and 5% levels, respectively (the table also reports the t-values).
Number of stocks: 117
Average daily specialist profits
Overall Specialist Profits ($)
Passive Specialist Profits ($)
Active Specialist Profits ($)
Spread profits
Positioning profits
Mean
t-value
Mean
t-value
17,290**
12,390**
4,900
5.4
3.4
1.1
3,357
13,370*
9,972
0.8
2.5
1.3
and passive specialist profits,
RP0;N ¼ PositioningRevenuesðPRÞP þ SpreadRevenuesðSRÞP .
This decomposition allows me to determine whether inventory rebalancing through quoted
prices directly affects specialist profits.
Table 11 reports average profits for the spread and positioning decomposition for all 117
stocks in the SOD data set. In particular, the table shows that active specialist profits, i.e.,
when the Price Continuity rule is not binding, are due to both spread and positioning
profits ($4,900 and $9,972, respectively). The picture appears to be different for passive
specialist profits in that the specialist is able to realize large spread profits ($12,390). This
can be explained by the large spreads when there is a need for price smoothing. Most
importantly though, the specialist is losing money on positioning when he is smoothing
prices because it forces him to go against the market and thus incur inventory imbalances.
In the sample, these losses appear to be statistically and economically significant ($13,390).
Thus, Table 11 verifies the main results of Table 10: the specialist incurs costs for providing
price continuity, and these losses stem from positioning costs. However, the specialist
adjustment of his inventory position, when the rule is not binding, allows him to recover
his losses and achieve net positive profits.
8. Summary and conclusions
This paper analyzes specialist participation in quoted prices at the NYSE, and identifies
the factors that drive him to update quoted prices and improve either the buy or sell side of
the LOB. This study was motivated by the disparity between theoretical predictions and
empirical findings with respect to specialist adjustment of inventory risk. Whereas
theoretical work has shown that specialist inventory rebalancing through quoted prices is
important to the functioning of the market, empirical studies have failed to identify
evidence of such rebalancing activity intradaily. Using data provided by the NYSE, this
study uncovers evidence of specialist inventory rebalancing through quoted prices both
pre- and post-decimalization.
In particular, I identify the mechanism by which inventory imbalances affect quoted
prices. Focusing on the principal rule of the exchange governing specialist actions—the
Price Continuity rule—I investigate the extent to which this rule affects specialist quotes.
Using two representative data sets of the NYSE market, the TORQ (pre-decimalization)
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and the SOD (post-decimalization) data sets, I find compelling evidence that the specialist
does rebalance his inventory through quoted prices. This effect of inventory on quotes
occurs when the Price Continuity rule is not binding. Specialist quote participation when
the rule is binding reflects the specialist’s obligations under the rule, rather than inventory
considerations. I also find evidence that decimalization has caused a reduction of the
instances in which the specialist is obliged by the exchange to smooth prices. However, his
percentage participation has remained the same, resulting in more instances of specialist
participation when the rule is not binding. This leads to stronger evidence of inventory
effects on quoted prices post-decimalization.
In economic terms, I find that the price smoothing required by the NYSE entails a cost
for the specialist. I also find that the specialist compensates for that loss when the Price
Continuity rule is not binding, and earns positive overall profits. My findings agree with
Dutta and Madhavan (1995), whose model predicts that the Price Continuity rule causes a
redistribution of specialist profits to both informed and liquidity investors.
My results also shed light on the ongoing debate over the specialist’s role in the market
and the question of whether the NYSE needs to be restructured. I show that the affirmative
obligation to provide price smoothing, the effects of which are clearly detected both preand post-decimalization, may improve market quality. Price smoothing reduces price
volatility and prevents prices from overshooting beyond their longer-term equilibrium (as
measured by the variance ratios). These results, which indicate the benefits of the Price
Continuity rule, should be taken into consideration in any market restructuring.
In recent years, more and more capital markets are turning toward electronic trading
and away from floor-based trading. However, intermediaries still play an important role in
the transaction process.24 Most electronic markets have introduced dealers to act as
designated market makers, providing the necessary liquidity and alleviating problems
created by asynchronous trading and large spreads. Investigating how exchange-mandated
affirmative obligations affect market makers’ inventory management and profits in these
markets can be a fruitful avenue for further research.
Appendix. : Inferring the specialist inventory using Rules 104.10(5) & 104.10(6)
Sofianos (1995) and Hasbrouck and Sofianos (1993) observe that specialists occasionally
make adjustments to their inventories by trading in other markets outside exchange hours.
Therefore, knowing the total number of shares that the specialist bought and sold during
the trading period can be a false estimate of the specialist’s inventory position. In this
section, using NYSE exchange rules, I construct an estimate of the specialist’s inventory
position that accounts for after-hours trading, thus creating a better picture of his current
status.
The exchange rules 104.10(5) and 104.10(6) (NYSE 1999, Rule 114.10)) relate the
destabilizing transactions of the specialist—buying on a plus or a zero plus tick (a positive
transaction price change) and selling on a minus or a zero minus tick (a negative
transaction price change)—to his inventory. In particular, in increasing or establishing an
inventory position (either long or short), the specialist is not allowed to buy stocks on a
24
For example, the new NYSE hybrid market structure and the NYSE Arca market have moved the NYSE
toward more reliance on electronic trading. At the same time both the NYSE and the NYSE Arca markets keep or
introduce market makers (i.e., specialists and designated/lead market makers).
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direct plus tick or sell on a direct minus tick (Rule 104.10(5)). However, he is allowed to do
so when he is decreasing or liquidating a position (Rule 104.10(6)). Therefore, assuming
that the specialist is following the rules of the exchange, I deduce that any direct plus tick
purchases of stock from the specialist can only happen when he has negative inventory
(decreasing a short position) and, similarly any sells on a minus tick by the specialist can
only happen when he has positive inventory (decreasing a long position).
Following the above rules, I construct an algorithm for estimating changes in inventory
that occur outside exchange hours as follows. I calculate the minimum after-hours change
in inventory so that I have the least number of non-agreements with rules 104.10(5 and 6)
in the following trading day. If the resulting change in inventory is greater than zero,
I assume that the change represents the specialist’s after-hours trades. I then recalculate the
specialist’s opening inventory position at the beginning of the day by adding the previous
day’s after-hours trades. I define adjusted inventory position as the total number of
shares traded by the specialist during the day adjusting for the change in inventory the
night before.
In order to investigate whether the adjusted intraday inventory position is a better
estimate for the true specialist inventory position than the estimate assuming zero afterhours specialist trades (total inventory) used in the literature, I proceed as follows.
Hasbrouck and Sofianos (1993) depict actual inventory position summary statistics for a
sample of 138 stocks from November 1988 to 1990. They report for the highest quartile
subsample (average daily number of transactions) two ratio measures involving true
inventory positions: the average absolute closing inventory over the average daily volume
and the average absolute change in inventory over the average daily volume. For the same
stocks (largest quartile based on trading frequency), I calculate for the period of November
Table 12
Evaluating the inventory estimated values
The table shows how the two estimated specialist inventory measurements using Adjusted Inventory and Total
Inventory relate to measurements using actual inventory positions (True Inventory) as depicted in Hasbrouck and
Sofianos (1993). The measurements used are the average absolute closing inventory over the average daily volume
Avg:jInventoryj
Avg:jDInventoryj
Avg:DailyVolume and the average absolute change in inventory over the average daily volume Avg:DailyVolume. Both ratio
measures are calculated using the the highest quartile subsample (average daily number of transactions) in the
TORQ data set. Standard deviations are in parentheses. Whereas Hasbrouck and Sofianos (1993) measurements
are based on 36 stocks, my estimates are based on 35 stocks as I exclude one company that had large values in
both ratio variables (outlier). However, even when I include that company, the matching of the Adjusted Inventory
and Total Inventory ratio estimates with the true values is also in favor of the adjusted measure. In particular, for
the absolute inventory ratio estimate, the value for the Adjusted Inventory is 0.19 (0.28) and the Total Inventory is
0.58 (0.43), and the absolute difference in the inventory ratio estimate for Adjusted Inventory is 0.08 (0.04) and
Total Inventory is 0.07 (0.03).
Hasbrouck and Sofianos (1993)
Variable
Number of securities
Avg:jInventoryj
Avg:DailyVolume
Avg:jDInventoryj
Avg:DailyVolume
True inventory
My sample
Adjusted inventory
36
Total inventory
35
0.13 (0.06)
0.15 (0.13)
0.55 (0.39)
0.06 (0.04)
0.08 (0.04)
0.07 (0.03)
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1990 to January 1991 the estimated ratio measures based on the two inventory position
estimates
andreport them in Table 12.25 Looking at the first ratio variable of Table 12
Avg:jInventoryj
Avg:DailyVolume
, I observe that the adjusted inventory measurements are much closer to the
true value than the total inventory estimate. By adding the overnight estimated adjustment
to the intraday inventory, I capture more closely the true inventory value than I do when I
assume
zero after-hours specialist trading. The changes in inventory estimates
Avg:jDInventoryj
Avg:DailyVolume
are both very close to the true values, showing that the overnight
estimated adjustments calculated for constructing the adjusted inventory estimate are not
large in magnitude compared with intraday specialist transaction volume.
I conclude that the adjusted specialist inventory position is an accurate estimate of the
true inventory position. Assuming that the specialist does not trade afterhours can lead to
a false estimate of the specialist’s inventory.
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