Affirmative obligations and market making with inventory $

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1 Journal of Financial Economics 86 (2007) 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. address: marios.panayides@business.utah.edu X/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi: /j.jfineco

2 514 M.A. Panayides / Journal of Financial Economics 86 (2007) 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.

3 M.A. Panayides / Journal of Financial Economics 86 (2007) 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.

4 516 M.A. Panayides / Journal of Financial Economics 86 (2007) 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 t 1 (DMidquote t,t 1 ) 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 Odders- White (2001), I use the changes in the LOB s best buy and sell prices (DBestBuy t,t 1 and DBestSell t,t 1 ) 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 (FloorVolume t ). 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.

5 M.A. Panayides / Journal of Financial Economics 86 (2007) Table 1 Variable definitions This table describes each individual variable used in a linear regression model predicting changes in the quoted prices: DMidquote t;t 1 ¼ b 0 þ b 1 DBestBuy t;t 1 þ b 2 DBestSell t;t 1 The variables are as follows. þ b 3 DMidquote t 1;t 2 þ b 4 DMidquote t 2;t 3 þ b 4 DMidquote t 3;t 4 þ b 6 SignofTrade t 1 þ b 7 DInventory t 1;t 2 þ b 8 Forecast tþ1;t þ b 9 FloorVolume t þ t. Variable Description DMidquote t,t 1 Change in the Quote midpoint (midquote) between transaction time t and t 1. DBestBuy t,t 1 Change in the Limit Order Book best buy price between transaction time t and t 1. DBestSell t,t 1 Change in the Limit Order Book best sell price between transaction time t and t 1. FloorVolume t Signed transaction volume of floor brokers on opposite side to specialist s trades at time t. DInventory t 1,t 2 The change in specialist inventory positions between transactions t 1 and t 2, i.e., specialist s signed transaction volume at time t 1. SignofTrade t 1 Sign of a lagged trade. Takes the value +1 for a buy trade and 1 for a sell trade. Forecast t+1,t First nonzero change in transaction prices after transaction at time 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 (DMidquote t 1,t 2, DMidquote t 2,t 3, and DMidquote t 3,t 4 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 (SignofTrade t 1 ) 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 (Forecast t+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 (DInventory t 1,t 2 ). 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).

6 518 M.A. Panayides / Journal of Financial Economics 86 (2007) Based on the above, I run time-series regressions for each stock in my sample as follows: b 0 þ b 1 DBestBuy t;t 1 þ b 2 DBestSell t;t 1 þb 3 DMidquote t 1;t 2 þ b 4 DMidquote t 2;t 3 þ b 4 DMidquote t 3;t 4 : DMidquote t;t 1 ¼ b 6 SignofTrade t 1 þ b 7 DInventory t 1;t 2 þb 8 Forecast tþ1;t þ b 9 FloorVolume t 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 jb i i:i:d:nðb i ; s 2 i Þ, and each b i i:i:d:nðb; s 2 Þ, where N is the Gaussian distribution. I estimate b and s 2 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 P N i¼1 ^b ¼ ^b i =ðs 2 i þ ^s 2 m:l:e P Þ N i¼1 1=ðs2 i þ ^s 2 m:l:e Þ (2) and, similarly, its variance is Varð^bÞ ¼ 1 P N i¼1 1=ðs2 i þ ^s 2 m:l:e Þ, (3) where ^s 2 m: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 b i. Using the Bayesian aggregation method, I capture the variation among stocks in the predictive contribution of each individual ^b i estimate 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).

7 M.A. Panayides / Journal of Financial Economics 86 (2007) 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, P t ¼ I t21 ðp t 2p t21 Þ, where p t denotes the transaction price at time t and I t is the specialist inventory at time t. For any given period the total profit is the sum of P t 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 (5) and (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.

8 520 M.A. Panayides / Journal of Financial Economics 86 (2007) 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 Specialist inventory management and quote revisions Aggregated results of the linear regression model predicting quotation midpoint changes (DMidquote t,t 1 ) 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 (DBestBuy t,t 1 and DBestSell t,t 1 ). 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 (DMidquote t 1,t 2, DMidquote t 2,t 3, and DMidquote t 3,t 4 ). 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 (FloorVolume t ) 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.

9 M.A. Panayides / Journal of Financial Economics 86 (2007) Table 2 Linear regression model predicting quotation midpoint changes (DMidquote t,t 1 ) The table reports coefficients estimates from regressions predicting the quotation midpoint change (DMidquote t,t 1 ). The independent variables include measures of the limit order book best buy and sell price changes (DBestBuy t,t 1 and DBestSell t,t 1 ), lag values of the quote midpoint change to adjust for possible autocorrelation (DMidquote t 1, t 2 DMidquote t 2, t 3, DMidquote t 3, t 4 ), floor participation (FloorVolume t ), the sign of lagged trade to account for order flow (SignofTrade t 1 ), the specialist s change of inventory levels (DInventory t 1,t 2 ), and the following period s price change (Forecast t+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 SOD Overall Overall High Quartile 2nd Quartile 3rd Quartile Low Quartile Number of stocks Intercept ** ** ** ** ** (3.1) ( 8.6) ( 6.2) ( 6.1) ( 7.1) (1.2) DBestBuy t,t ** ** ** ** ** ** (11.3) (17.9) (33.0) (16.5) (7.8) (5.8) DBestSell t,t ** ** ** ** ** ** (16.3) (17.0) (46.2) (17.7) (6.1) (5.2) DMidquote t,t 1,t ** ** ** ** ( 9.2) ( 4.2) ( 0.2) ( 1.4) ( 4.5) ( 2.5) DMidquote t,t 2,t ** ** ( 1.5) (3.7) (2.5) (5.2) (-0.7) (0.9) DMidquote t,t 3,t ** ** ** (0.7) (7.2) (4.0) (7.5) (1.1) (0.6) FloorVolume t 8.2e-7** 3.7e-8** 2.9e-8** 3.1e-8** 5.4e-7* 4.8e-7 (3.1) (3.9) (2.5) (2.2) (2.1) (1.8) SignofTrade t ** ** ** ** ** ** (4.7) (9.9) (7.0) (5.3) (11.9) (7.7) DInventory t 1,t ** ** ** ** ** (1.2) ( 8.3) ( 6.8) ( 7.8) ( 9.4) ( 3.9) Forecast t+1,t ** ** ** 0.000* (0.7) ( 2.5) ( 7.1) ( 4.1) (2.1) (0.4) 1991) the sign of a lag trade (SignofTrade t 1 ) is positively correlated with quote price changes. By including the SignofTrade t 1 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 (Forecast t+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 SignofTrade t 1 as a proxy for order flow and Forecast t+1,t as the realization of private information.

10 522 M.A. Panayides / Journal of Financial Economics 86 (2007) 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 (DInventory t 1,t 2 ) 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 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 (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 (3)), which requires the specialist to achieve small consecutive price changes; the Quotation rule (NYSE 1999, Rule (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 (5)) and liquidating or decreasing a position (NYSE 1999, Rule (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.

11 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 M.A. Panayides / Journal of Financial Economics 86 (2007) 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 t 1) 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: BuyGap pre ¼fp Transaction;t 1 p BestBookBuy;t gfp BestBookSell;t p BestBookBuy;t g BuyGap post ¼fp Transaction;t 1 p BestBookBuy;t 40:12gfp BestBookSell;t p BestBookBuy;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): SellGap pre ¼fp BestBookSell;t p Transaction;t gfp BestBookSell;t p BestBookBuy;t g SellGap post ¼fp BestBookSell;t p Transaction;t 1 40:12gfp BestBookSell;t p BestBookBuy;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.

12 524 M.A. Panayides / Journal of Financial Economics 86 (2007) Consequently, I can also define the NoGap scenario as occurring when neither a buy nor a sell gap exists. NoGap pre ¼fSellGap pre a1gfbuygap pre a1gfp BestBookSell;t p BestBookBuy;t g NoGap post ¼fSellGap post a1gfbuygap post a1gfp BestBookSell;t p BestBookBuy;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 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.

13 M.A. Panayides / Journal of Financial Economics 86 (2007) 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 (BuyGap post, SellGap post, BothGaps post and NoGap post ) and the TORQ data (BuyGap pre, SellGap pre, BothGaps pre, and NoGap pre ). 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 BuyGap post SellGap post Both Gaps post No Gap post Greater than 12 cents Specialist Improvement LOB Buy Side LOB Sell Side No Improvement Panel B: Mean % for 116 Companies in TORQ Gaps BuyGap post SellGap post Both Gaps post No Gap post Greater than $ 1 8 : Specialist Improvement LOB Buy Side LOB Sell Side No Improvement Panel C: % Change between SOD and TORQ Gap Change: Gap post Gap post 9** ( 6.1) 8** ( 5.2) 7** ( 5.1) 50** (20.2) Specialist Improvement LOB Buy Side 0 ( 0.2) 2 ( 1.8) 6 (1.9) 5** (6.0) LOB Sell Side 0 (0.2) 0 (0.1) 1 ( 0.4) 9** (8.1) No Improvement 0 (0.1) 2 (0.6) 5 ( 1.9) 14** ( 9.5) 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

14 526 M.A. Panayides / Journal of Financial Economics 86 (2007) 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). Total specialist participation (%) Discretionary participation (%) Mandatory participation (%) Price discontinuity (%) SOD data set Torq data set Change 3 (1.3) 44** (13.3) 40** ( 12.2) 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.

15 M.A. Panayides / Journal of Financial Economics 86 (2007) 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 (DInventory t 1,t 2 :BuyGap, DInventory t 1,t 2 :SellGap, DInventory t 1,t 2 :NoGap) and Forecasting:Gap (Forecast t+1,t :BuyGap, Forecast t+1,t :SellGap, Forecast t+1,t NoGap) 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 DInventory t 1,t 2 :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

16 528 M.A. Panayides / Journal of Financial Economics 86 (2007) Table 5 Linear regression model predicting quotation midpoint changes (DMidquote t,t 1 ). Adjustments for the Price Continuity rule The table shows aggregated results of the linear model regressions predicting the specialist quote revision (DMidquote t,t 1 ) 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 (DBestBuy t,t 1, DBestSell t 1,t 1 ), the specialist inventory effect and its interaction with each one of the gap subsamples (DInventory t 1, t 2, DInventory t 1, t 2 : NoGap, DInventory t 1, t 2 : SellGap, DInventory t 1, t 2 : BuyGap), and similarly a forecasting variable and its interaction with each subsample (Forecast t+1,t, Forecast t+1,t : NoGap, Forecast t+1,t : SellGap, Forecast t+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 SOD Overall Overall High Quartile 2nd Quartile 3rd Quartile Low Quartile Number of stocks BuyGap ** ** 0.007** ** (4.1) (4.6) (5.5) (5.4) (0.8) (1.0) SellGap ** ** ** 0.014** ( 3.3) ( 4.2) ( 5.9) ( 7.1) ( 0.3) ( 0.7) NoGap ** ** ** * (1.7) ( 10.1) ( 6.3) ( 9.4) ( 2.6) (0.2) DBestBuy t,t ** ** ** ** ** ** (11.7) (17.9) (38.5) (16.9) (7.2) (5.8) DBestSell t 1,t ** ** ** ** ** ** (16.0) (17.0) (48.3) (18.7) (5.7) (5.2) DInventory t 1, t ** ** ** ** ** ( 1.9) ( 7.6) ( 6.0) ( 9.5) ( 7.1) ( 3.9) DInventory t 1, t 2 : NoGap ** ** ** ** ** ( 3.6) ( 6.3) ( 4.3) ( 3.2) ( 0.4) ( 0.7) DInventory t 1, t 2 : BuyGap * ( 0.9) (1.5) (1.5) (1.2) ( 1.7) (2.0) DInventory t 1, t 2 : SellGap ** ( 0.3) (0.9) (0.3) (2.9) ( 1.8) (1.2) Forecast t+1,t ** ** ** (0.8) ( 4.3) ( 7.3) ( 4.6) (1.4) ( 0.6) Forecast t+1,t : NoGap ** ** ** (2.7) ( 13.6) ( 10.7) ( 8.3) (0.1) ( 1.1) Forecast t+1,t : BuyGap * ** ** ** (-2.2) ( 6.5) ( 6.2) ( 4.0) ( 1.8) (2.5) Forecast t+1,t : SellGap ** ** ** ( 1.1) ( 4.8) ( 4.7) ( 3.1) ( 1.5) (1.2) 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.

17 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 DInventory t 1,t 2 :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 (DInventory t 1,t 2 :BuyGap and DInventory t 1,t 2 :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) Sensitivity tests M.A. Panayides / Journal of Financial Economics 86 (2007) 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 (DInventory t 1,t 2 ) as a dummy variable (+1,0 or 1) and include the variable SignVolume t 1 instead of the variable SignofTrade t 1. 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.

18 530 M.A. Panayides / Journal of Financial Economics 86 (2007) 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 Specialist Improvement: LOB Buy Side LOB Sell Side No Improvement Panel B: Mean percentages for periods of low volatility Gaps: Specialist Improvement: LOB Buy Side LOB Sell Side No Improvement Panel C: Percentage change between periods of high and low volatility Gaps: 2 (0.9) 3 (1.1) 4 ( 1.0) Specialist Improvement: LOB Buy Side 2 ( 0.5) 1 (1.5) 1 ( 0.8) LOB Sell Side 1 ( 0.9) 3 ( 0.9) 1 (1.4) No Improvement 3 (0.6) 1 (0.5) 2 (1.6)

19 M.A. Panayides / Journal of Financial Economics 86 (2007) Table 7 Linear regression model results predicting quotation midpoint changes (DMidquote t,t 1 ). 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 ** ** (7.4) (6.2) SellGap ** ** ( 7.8) ( 6.5) NoGap ** ** (8.9) ( 10.5) DBestBuy t,t ** ** (19.0) (20.0) DBestSell t 1,t ** ** (18.6) &(18.8) DInventory t 1, t ** ** ( 9.6) ( 9.6) DInventory t 1, t 2 : NoGap ** ** (5.6) (-4.2) DInventory t 1, t 2 : BuyGap * (0.8) (2.1) DInventory t 1, t 2 : SellGap * (0.4) (2.4) Forecast t+1,t ** ** ( 9.1) ( 12.0) Forecast t+1,t : NoGap ** ** ( 11.2) ( 15.4) Forecast t+1,t : BuyGap ** ** 6.5 ( 4.0) Forecast t+1,t : SellGap ** ** ( 4.8) ( 4.7) 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 DInventory t 1,t 2 :NoGap explanatory variable in Table 7 show that the specialist still

20 532 M.A. Panayides / Journal of Financial Economics 86 (2007) 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 DInventory t 1,t 2 :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 Simultaneous equation models I run the following two-equation model to predict the changes in the bid and ask prices simultaneously: DBidprice t;t 1 ¼ g 1 DAskprice t;t 1 þ b 0 1 X 1 þ 1 ; DAskprice t;t 1 ¼ g 2 DBidprice t;t 1 þ b 0 1X 2 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 X 1 and X 2 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 DInventory t 1,t 2 :NoGap is a negative and strongly significant predictor of changes in the bid and ask prices (DBidprice t,t 1 and DAskprice t,t 1 ). 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 DBidprice t,t 1 and DAskprice t,t 1 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.