Time Variation in Liquidity: The Role of Market Maker Inventories and Revenues

Transcription

1 Time Variation in Liquidity: The Role of Market Maker Inventories and Revenues Carole Comerton-Forde Terrence Hendershott Charles M. Jones Pamela C. Moulton Mark S. Seasholes * January 8, 2008 * Comerton-Forde is at University of Sydney (C.Comerton-Forde@econ.usyd.edu.au); Hendershott is at Haas School of Business, University of California, Berkeley (hender@haas.berkeley.edu); Jones is at Columbia Business School (cj88@columbia.edu); Moulton is at Fordham Graduate School of Business (pmoulton@fordham.edu); and Seasholes is at Santa Clara University (Mark.S.Seasholes@ ias.com). We thank the NYSE for providing data. We thank Yakov Amihud, Ekkehart Boehmer, Robin Greenwood, Joel Hasbrouck, Jerry Liu, Marios Panayides, Lubos Pastor, Avanidhar Subrahmanyam, Dimitri Vayanos, Vish Viswanathan, Masahiro Watanabe, Pierre-Olivier Weill, and participants at the NBER Market Microstructure meeting, Barclays Global Investors, Columbia, the Federal Reserve Bank of New York, Maryland, Michigan, Office of Economic Analysis of the U.S. Securities and Exchange Commission, University of Amsterdam, University of California Santa Barbara, University of Toronto, University of Utah, and University of Washington for helpful comments. Hendershott gratefully acknowledges support from the National Science Foundation. Part of this research was conducted while Moulton was an economist and Comerton-Forde and Hendershott were visiting economists at the New York Stock Exchange. This paper combines two working papers by subsets of the authors: Market Maker Inventories and Liquidity and Market Maker Revenues and Stock Market Liquidity. Preliminary Results Please Contact Authors Before Citing Results

2 Time Variation in Liquidity: The Role of Market Maker Inventories and Revenues Abstract We study time variation in stock market liquidity using an 11-year panel of daily NYSE specialist inventory positions and revenues. When specialists in aggregate have large positions or when they lose money, market-wide effective spreads widen. Results hold after controlling for recent stock returns and conditional volatility. Inventories and revenues for a given specialist firm explain changes in the liquidity of stocks assigned to that firm. The relationship between spreads, inventories, and revenues is stronger for stocks handled by specialist-owned firms than corporate-owned specialist firms. Mergers of specialist-owned firms with corporate-owned firms provide evidence consistent with deeper pockets easing financing constraints. The liquidity of high-volatility stocks is more sensitive to larger inventories and losses than is the liquidity of low-volatility stocks. Finally, we show that the liquidity effects of inventories and revenues are nonlinear and most prominent when inventories are high and revenues are low or negative. In total, our results suggest an important role for market makers financial positions in explaining the time variation of liquidity.

3 1. Introduction Asset market liquidity varies considerably over time. This matters to market participants, who typically worry about the cost of trading into or out of a desired position in a short period of time. Liquidity can affect asset prices, too. When markets are illiquid, for example, investors may demand higher rates of return to compensate. Despite the interest in aggregate liquidity from both of these angles, we know relatively little about exactly why market liquidity varies over time. Recent theoretical work by Gromb and Vayanos (2002, 2007) and Brunnermeier and Pedersen (2006), among others, postulates that limited market-maker capital can explain some of these empirical features of asset market liquidity. Data limitations have hampered empirical work in this area, making it difficult to demonstrate direct links between liquidity supplier behavior and capital constraints. In this paper, we provide direct evidence that shocks to market-maker balance sheets and income statements impact daily stock market liquidity. Using 11 years ( ) of New York Stock Exchange (NYSE) specialist inventory position and trading revenue data, we show for the first time that if specialists find themselves with large positions or lose money on their inventories, effective spreads widen, even after controlling for stock returns and volatility. This relationship holds at both the aggregate market level and the specialist-firm level. How are our findings consistent with the presence of market-maker financing constraints? In the short run at least, specialists and other market makers have limited capital. Lenders typically impose limits on leverage ratios (or equivalently fix required margins), and information problems can make it hard to raise equity quickly or cheaply. This means that market makers face short-term limits on their risk-bearing capacity. As their inventory positions grow larger (in either direction, long or short) and approach the constraint, market makers should reduce the amount of liquidity they are willing to provide. Similarly, losses from trading directly reduce the market maker s equity capital, and if leverage ratios remain fixed, then the market maker s position limits decrease proportionately. 1 Again, market makers should reduce the amount of liquidity they are willing to provide as they approach these limits. Specialist inventories and trading revenues vary considerably over time, so there is ample scope for shocks in these variables to force contractions in liquidity provision. Aggregate 1 Adrian and Shin (2007) show that there is relatively little variation in leverage ratios at investment banks and money-center commercial banks. 1

4 specialist inventories have a standard deviation of roughly $100 million. Specialists in aggregate lose money on about 10% of the trading days during our sample, the average loss is about $4 million on these days, and these losses tend to cluster together in time. Because of their structural advantages, specialists usually earn positive trading revenue on short-term roundtrip transactions, but are exposed to the possibility of losses on inventories held for longer periods. This suggests that the revenues associated with longer-term inventories could be better indicators of whether financial constraints are easing or tightening. When we decompose revenues into intraday vs. longer-term components, we find that revenues associated with inventories held overnight are indeed the ones that are associated with future liquidity. This overnight breakpoint dovetails nicely with our story, because anecdotal evidence indicates that lenders and risk managers are most likely to evaluate financing terms and position limits based on daily P&L and end-of-day balance sheets. Interestingly, we find a long bias among specialists. Aggregate NYSE specialist positions are net long over 94 percent of the time, and individual specialist firms are net long over 83 percent of the time. Specialists also have an affirmative obligation to buffer order flow, buying when others want to sell and vice versa. This means that specialists tend to increase their inventory positions and lose money when the aggregate market declines. These losses may reduce the firm s available capital and thus its risk-bearing capacity; liquidity should be worse immediately thereafter. Thus, market-maker positions and losses might be able to account for the well-known fact that when the market declines, aggregate liquidity worsens (see, for example, Chordia, Roll, and Subrahmanyam (2001), Chordia, Sarkar, and Subrahmanyam (2005), and Hameed, Kang, and Viswanathan (2006)). Fortunately, specialist inventories and trading revenues are not perfectly correlated with contemporaneous stock returns, so it is possible to find times when specialists have large positions or lose money without a corresponding price decline, or when specialists have relatively small inventories and earn positive trading revenue in a declining market. When all these variables appear in a predictive regression, larger specialist inventories and losses are still associated with wider spreads in the following period. Also, as predicted by financing constraints, the effects of inventories and revenues exhibit nonlinearity: The marginal effects are greater when inventories are highest and revenues lowest. 2

5 While the effects are strong at the aggregate level, the financing constraints relationship should actually operate at the specialist firm level. There should be a common component in liquidity for all stocks assigned to a particular specialist firm, and that firm s inventories and revenues should affect liquidity in those stocks. Coughenour and Saad (2004) demonstrate the former; here we show that a specialist firm s inventories and trading revenues predict future liquidity in that firm s assigned stocks. As with the aggregate results, the inventory and trading revenue effects are greatest when inventories are highest and revenues lowest. Next we identify cases where a specialist firm may be closer to a funding constraint a priori. To do so we examine specialist firms in which the specialists themselves supply the capital; such specialist-owned firms may face tighter financing constraints than corporate-owned specialist firms (Coughenour and Deli (2002)). We show that for stocks assigned to specialist-owned firms, liquidity is more sensitive to inventories and specialist-firm losses. During our sample period, these specialist-owned firms all merged with larger corporateowned specialist firms. These mergers provide a potentially exogenous positive shock to capital. When we follow the stocks assigned to the specialist-owned firm before the merger, we find that liquidity in these stocks becomes somewhat less sensitive to specialist inventories and revenues after the merger, consistent with deep pockets easing these financing constraints. Brunnermeier and Pedersen (2006) show that limited risk-bearing capacity can have a differential impact on high- and low-fundamental-volatility stocks. They use the term flight to quality to refer to the result that the liquidity differential between high- and low-volatility securities is bigger when market makers have taken on larger positions or when their wealth decreases. 2 We test these predictions by examining the relation between inventories and revenues and the liquidity of high- and low-volatility stocks. Supporting the theoretical prediction, the liquidity of high-volatility stocks is more sensitive to larger inventories and losses than is the liquidity of low-volatility stocks. We also show that when a specialist firm loses money on its overnight inventory, it is more likely to reduce its inventory position. This provides a mechanism for the illiquidity we observe in the data following a decline in trading revenues. 2 Flight to quality is also present in Pastor and Stambaugh (2003). 3

6 Our data cover only one market maker per stock the specialist assigned by the NYSE to that stock but that liquidity provider is probably the most important one, given the structural advantages that accrued to the specialist over our sample period. In addition, specialist inventories and revenues may be good proxies for the inventories and trading revenues of other competing liquidity suppliers, such as market makers on regional exchanges, proprietary trading desks at various Wall Street firms, hedge funds following a market-making strategy, and so on. 3 While we have no direct evidence, it may be appropriate to think of our specialist inventory and revenue numbers as reflective of broader market-maker inventory and revenues. The remainder of the paper is organized as follows. Section 2 reviews related literature. Section 3 provides a general description of our data and sample. Section 4 shows the basic relations between aggregate market-maker revenues, inventories, and market liquidity. Section 5 looks at the specialist-firm level. Sections 6 and 7 study the set of specialist-owned firms where we a priori expect financing constraints to bind. Section 6 makes the cross-sectional comparison; Section 7 studies the mergers of these firms. Section 8 investigates whether market makers demonstrate a flight to quality in their liquidity provision. Section 9 looks briefly at the behavior of inventories following declines in trading revenue, and Section 10 concludes. 2. Related Literature Most models of market liquidity focus on three types of trading costs: fixed, inventory, and information. 4 These classic models can themselves generate time variation in liquidity, as liquidity is typically driven by the volatility of fundamental values, which could presumably change over time. Thus we control for volatility changes in our empirical work. Theory focusing on funding costs and financing constraints is more recent. Kyle and Xiong (2001) show how convergence traders (arbitrageurs ) having decreasing risk aversion leads to correlated liquidations and higher volatility. Gromb and Vayanos (2002) study a model in which arbitrageurs face margin constraints and show how these arbitrageurs' liquidity provision 3 4 See Boehmer and Wu (2006) for evidence on relations among signed trading activity by different market participants at the NYSE. Kyle (1985) and Gloston and Milgrom (1985) examine the impact of private information. Stoll (1978), Amihud and Mendelson (1980), Ho and Stoll (1981, 1983), Mildenstein and Schleef (1983), and Grossman and Miller (1988) examine the impact of inventories. Inventory models without capital constraints predict that liquidity (the width of the bid-ask spread) is not affected by the market maker s inventory position. 4

7 benefits all investors. 5 However, because the arbitrageurs cannot capture all of the benefits, they fail to take the socially optimal level of risk. Weill (2006) examines dynamic liquidity provision by market makers and shows that if they have access to sufficient capital, the market makers provide the socially optimal amount of liquidity, but if capital is insufficient or too costly then market makers will undersupply liquidity. Brunnermeier and Pedersen (2006) construct a model along the lines of Grossman and Miller (1988) that also links market makers funding and market liquidity. 6 Chordia, Roll, and Subrahmanyam (2000), Hasbrouck and Seppi (2001), and Huberman and Halka (2001) examine the common component in liquidity changes across stocks. Coughenour and Saad (2004) show that the co-movement in liquidity is stronger among stocks traded by the same NYSE specialist firm. Both liquidity supplier wealth (revenues) and the amount of capital committed by liquidity suppliers (inventories) play significant roles in the theoretical work on capital constraints and liquidity. 7 Prior data on market-maker inventories and trading typically cover relatively short periods of time and/or a limited number of securities. 8 While these limitations precluded testing for the relation between aggregate liquidity and limited market maker risk-bearing capacity at interday horizons, the microstructure literature has been successful in showing that inventories play an important role in intraday trading and price formation. For example, Madhavan and Smidt (1993), Hansch, Naik, and Viswanathan (1998), Reiss and Werner (1998), and Naik and Yadav (2003a) all find support for market makers controlling risk by mean reverting their inventory positions towards target levels. Hansch, Naik, and Viswanathan (1998) and Reiss and Werner (1998) show that differences in inventory positions across dealers determine which dealers offer the best prices and when dealers trade Yuan (2005) provides a model which shows a link between information asymmetry and liquidity when informed investors are constrained. This effect is more severe if market makers face market-liquidity-reducing predation (Attari, Mello, and Ruckes (2005) and Brunnermeier and Pedersen (2005)). Naik and Yadav (2003b) show that the contemporaneous relationship between government bond price changes and changes in market-maker inventories differs when market-maker inventories are very long or very short, but they do not directly examine liquidity. For examples using NYSE specialist data see Hasbrouck and Sofianos (1993), Madhavan and Smidt (1993), and Madhavan and Sofianos (1998). For examples using London Stock Exchange market-maker data see Hansch, Naik, and Viswanathan (1998), Reiss and Werner (1998), and Naik and Yadav (2003a). For futures markets data see Mann and Manaster (1996). For options market data see Garleanu, Pedersen, and Poteshman (2005). For foreign exchange data see Lyons (2001) and Cao, Evans, and Lyons (2006). 5

8 A number of papers examine the profitability of specialists. 9 Hasbrouck and Sofianos (1993) decompose specialist profits by trading horizon and find that most profits are due to their high frequency (short-term) trading strategies. Coughenour and Harris (2004) extend this econometrically and examine how the tick size change from 1/16 to $0.01 impacts specialist profits. Panayides (2007) analyzes how specialists trading, inventory, and profitability depend on their obligations under NYSE rules. 3. Data and Descriptive Statistics We use three data sources CRSP, NYSE s Specialist Equity Trade Summary (SPETS), 10 and Trades and Quotes (TAQ) to construct a daily sample of liquidity, specialist trading revenues, inventories, returns, and volatility. We measure each of these quantities and conduct empirical work at two different levels of aggregation: market-wide and at the specialist-firm level. Market-level daily time series extend from 1994 to 2004 (2,770 days) and are denoted with subscript m. The specialist-firm level analysis is conducted using an unbalanced panel denoted with subscript f. The panel is unbalanced because there is substantial consolidation among specialist firms over our 11-year sample period. There were 41 specialist firms in 1994, declining to seven by 2004, and over the sample period a total of 55 distinct specialist firms operated at the NYSE. 11 The specialist-firm level analysis includes the 37 specialist firms that have at least 750 days of trading data (about three years), and every day we update the set of common stocks assigned to each specialist firm. The resulting panel incorporates 96.7% of the stock-day observations used in the market-wide time-series analysis. Liquidity: To measure liquidity at both the market level and specialist-firm level, we construct a daily effective spread measure. The effective spread is the difference between an estimate of the true value of the security (the midpoint of the bid and ask quotes) and the actual transaction Market-maker profits have also been examined in other markets. For example, Hansch, Naik, and Viswanathan (1999) examine how London Stock Exchange market-maker trading profits vary depending on whether the trade is preferenced or internalized. As its name suggests, SPETS provides a daily summary of specialist activity. The file records, on a stock-bystock basis, daily specialist purchases in dollars and shares, daily specialist sales in dollars and shares, and opening and closing specialist inventory positions. SPETS data is also employed by Madhavan and Sofianos (1998) and Hendershott and Seasholes (2007). See Hatch and Johnson (2002) for a discussion of specialist firm consolidation. See Corwin (2004) for a discussion of the allocation of stocks to specialist firms. 6

9 price. 12 We use effective spreads because specialists and floor brokers are sometimes willing to trade at prices within quoted bid and ask prices. The wider the effective spread, the less liquid is the stock. [ Insert Figure 1 Here] To get a market-level or specialist firm-level liquidity measure, effective spreads for each stock are averaged each day using share volume weights and then averaged across stocks using market capitalization weights. Chordia, Roll, and Subrahmanyam (2001), Jones (2006), and Hameed, Kang, and Viswanathan (2006) document a downward trend in average effective spreads over much of our sample period. Figure 1 highlights the narrowing trend along with two sharp declines due to reductions in the minimum tick size. The first reduction was from eighths to sixteenths on June 24, 1997 and the second was from sixteenths to pennies on January 29, To account for these trends, we define the dollar effective spread measure Spr($) t as the effective spread on day t relative to its average value in the recent past (subscripts m and f suppressed): Spr($) t = ES($) t j= 6 ES ($), (1) where ES($) t refers to the market-wide effective spread (subscript m) or the average effective spread on the set of stocks assigned to the specialist firm (subscript f) on day t. Proportional effective spreads (Spr(%) t ) are defined analogously; please see Appendix A for full details. Lags 6 through 10 are used because many of our specifications predict future effective spreads using specialist revenues, inventories, and returns at lags 1 through 5 as explanatory variables. We want to ensure that our effective spread measure is not affected by contemporaneous correlation among these right-hand side variables. t j Specialist Trading Revenues: For each stock i on each day t, we decompose specialist gross trading revenues into two parts. The first part reflects revenues related to inventories held overnight and equals the mark-to-market profits on day t-1 inventory (the starting position on day t) plus mark-to-market profits on the net change in inventory from day t-1 to day t. The 12 Other liquidity measures such as quoted spreads yield very similar results. 7

10 second part corresponds to intraday trading and equals the revenues earned on all round-trip transactions on day t. Please see Appendix B for details related to specialist profit decomposition. Specialist revenues are aggregated each day at the market level or for each specialist firm and then demeaned. There are four regimes for demeaning, since specialist participation rates and the nature of specialist trading change markedly when the minimum tick size changes and at the beginning of We also envisage sustained losses affecting liquidity more than a oneday temporary loss. Therefore, our analysis sums revenues over five-day periods, and we define the gross trading revenue measure RevGr t-1, the revenue from inventories measure RevInv t-1, and the intraday round-trip revenue measure RevTr t-1 as the sum of the relevant daily revenue over the interval [t-5, t-1], with the following decomposition (subscripts m or f suppressed): RevGr t-1 = RevInv t-1 + RevTr t-1 (2) Inventories: We obtain the specialist dollar inventory I for each stock i at the end of day t. Inventories are summed cross-sectionally each day at the market level or for each specialist firm, as appropriate. Figure 2 graphs market-level specialist inventories between 1994 and [ Insert Figure 2 Here ] The average aggregate inventory position over the 11 years is $196 million, with a range of - $331 million to $988 million and a daily standard deviation of $137 million. Inventory is negative on only 163 of the 2,770 days in our sample, so that specialists in aggregate are net long 94% of the time. Similar calculations at the specialist-firm level indicate that a specialist firm is on average net long 83% of the time. To measure the amount of risk assumed by market makers, we aggregate (signed) dollar inventories up to the specialist-firm level or the market level and then take the absolute value to get the magnitude of the overall position (subscripts m or f suppressed): 13 In early 2003, the NYSE and SEC begin to investigate the trading behavior of specialists, leading to criminal indictments of individual specialists and fines for specialist firms see Ip and Craig (2003). In addition to the two dates related to tick-size changes, we also use January 1, 2003 to mark a regime change. 8

11 Inv t-1 = Ii, t 1 (3) Dynamic models with market-maker inventories, e.g., Amihud and Mendelson (1980) and Madhavan and Smidt (1993), predict that market makers mean revert their inventory levels to a target level. Madhavan and Smidt (1993) find empirically that the target level is greater than zero, which we also find. We have also calculated inventories as the deviation from the average inventory level (a proxy for the target inventory level). When we do this, positive demeaned inventories predict higher future spreads, while negative demeaned inventories have no predictive power for future spreads. This suggests that simply taking the absolute value is the right way to proceed, consistent with the idea that lenders are concerned with the absolute risk that an inventory position entails, rather than the risk associated with a deviation from a target position. i Returns: We measure the daily return on the value-weighted portfolio of NYSE common stocks, as well as the return on the value-weighted portfolio of common stocks assigned to each specialist firm. Lagged returns r are logged and summed over five days (t-1 to t-5) and used as a predictor variable in our analysis (subscript m or f suppressed): 5 1 Ret t-1 = ln( 1+ t j ) 5 j= 1 r (4) Volatility: To measure changes in volatility we estimate the asymmetric GARCH(1,1) model of Glosten, Jagannathan, and Runkle (1993) on daily log stock returns on the market or on the specialist firm portfolio (subscript m or f suppressed): h t 2 2 = + δ ht 1 + α ut 1 + φ ut 1I t 1 κ, (5) where u t = r t μ is distributed N(0, h t ), and I t-1 = 1 if u t-1 0 and I t-1 = 0 otherwise. In order to match the treatment of effective spreads, we define the conditional return variance measure as: 9

12 VarRet t = h t j= 6 h (6) t j Many of the variables in the regressions are calculated relative to recent means over the interval [t-10, t-6]. This is a kind of hybrid approach, as it is somewhere between working with levels and working with first differences. First differences are not appropriate, since there is no theoretical reason to believe that any of the variables here contain a unit root. Levels are not appropriate in the presence of apparent non-stationarity. While we are not aware of any econometric theory that directly addresses our approach, subtracting off recent means is a common approach in other areas of finance (cf. the relative T-bill yield, introduced by Campbell (1991) and now common in the return predictability literature). The hybrid approach induces a modest amount of moving average behavior, which requires the use of autocorrelation-consistent standard errors throughout Descriptive statistics Table 1 contains correlations and standard deviations for the market-wide variables used in this paper. Aggregate specialist revenues (RevGr m,t-1 ) are fairly volatile, with a standard deviation of $16.1 million around the regime means. Note that all revenue variables are aggregated over five trading days in the regressions, so the standard deviations essentially refer to weekly trading revenues. Revenues from intraday round-trips (RevTr m,t-1 ) are more volatile than revenues from overnight inventory (RevInv m,t-1 ), with a daily standard deviation of $13.9 million vs. $7.7 million. As a result, the 0.88 contemporaneous correlation between RevTr m,t-1 and gross trading revenues is much higher than the 0.50 correlation between RevInv m,t-1 and RevGr m,t-1. Interestingly, the two components of specialist revenue are virtually uncorrelated with each other (ρ = 0.03), while revenues from overnight inventory are strongly correlated with contemporaneous stock market returns (ρ = 0.61). The latter correlation makes sense given our earlier observation that aggregate specialist inventories are almost always net long. Given that we are using absolute values of inventories and specialist trading revenues as proxies for financing constraints, we expect the two measures to be negatively related. This is indeed the case, especially for revenues from overnight inventory positions. While the correlation between inventories and RevGr m,t-1 or RevTr m,t-1 are a modest 0.15 or 0.08, 10

13 respectively, the correlation with RevInv m,t-1 is a much stronger This correlation is a function of the average long specialist position combined with the specialist s liquidity provision role. Specialists tend to find themselves with even bigger long positions when the market declines, and they lose money in the process (the correlation between ending inventories on day t and the 5-day market return ending on day t is 0.52). [ Insert Table 1 Here ] 4. Market Liquidity and Market Maker Inventories and Revenues The main empirical goal of the paper is to see if economic state variables related to financing constraints can account for the observed time-series variation in stock market liquidity. Our main innovation is the use of specialist revenues and specialist inventories as a proxy for financial constraints faced by intermediaries, but we also benchmark the findings by examining other possible mechanisms, such as the standard theoretical link between conditional volatility and market liquidity that is present in most microstructure models. We start by simply regressing market-wide effective spreads on day t on aggregate gross trading revenues summed over the interval [t 5, t 1]. The results are in the first column of each panel of Table 2. Panel A examines proportional effective spreads; Panel B examines dollar effective spreads. In both cases, the coefficients are only marginally different from zero. At first glance, this would seem to provide little support for a financing constraints story, because it is aggregate losses that would impair a market-maker s capital position and make it more difficult for an intermediary to finance its trading positions. However, specification (2) in the same table reveals that when gross trading revenues are partitioned into revenues associated with overnight inventory (RevInv m,t-1 ) and revenues associated with intraday round-trips (RevTr m,t-1 ), inventory revenues have a large negative effect on spreads, while the coefficient on round-trip revenues is indistinguishable from zero. [ Insert Table 2 Here ] Throughout the paper, we focus on inventory revenues because there are confounding effects between intraday trading revenues and future spreads. RevTr is essentially the total dollar 11

14 amount of effective spread earned on intraday round-trips by specialists less the associated losses to informed traders. Thus, it is a realized or net spread for specialists. If these realized spread changes are persistent for whatever reason (say, for example, that the specialist has market power or the amount of intraday specialist trading is persistent), then the relationship between today s RevTr and tomorrow s spread could be fairly mechanical. If RevTr and spreads both increase today, they are likely to both remain high tomorrow, and a higher RevTr today ends up predicting a higher effective spread tomorrow. In contrast, inventory-related revenues are not tied up with spreads in this way and are much easier to interpret. When specialists make money on their inventories, market-wide spreads tend to narrow the next period. The statistical evidence is compelling, as revenues alone explain about 23% of the daily variance in the proportional effective spread measure. In terms of economic magnitude, Panel A of Table 2 shows that a one standard deviation increase in inventory-related revenues (equal to $7.7 million from Table 1) narrows our aggregate proportional effective spread measure by 7.7 * / 1000 = 0.3 basis points on average the next day, about half of the daily standard deviation of basis points from Table 1 for the spread measure itself. Financial constraints are generally non-linear, so we look next at whether these sensitivities are greater following extreme specialist losses. In specification (3) we add a kink to both RevInv m,t-1 and RevTr m,t-1 at the lowest quartile (25 th percentile). Consistent with theory, the biggest losses are associated with bigger spread widenings, and the non-linearity is fairly pronounced. Based on the numbers in Panel A, the slope coefficient on RevInv m,t-1 is about 22 for 75% of days and 50 in the left tail of the inventory revenues distribution. We also obtain similar results when the kink is located at zero or one standard deviation below zero. To differentiate between traditional inventory models and models in which liquidity providers have limited risk-bearing capacity, we next test the spread-inventory relationship. Specification (4) includes a constant and the absolute value of aggregate specialist inventories (in hundreds of millions of dollars) on the right-hand side. We find that larger inventories yesterday lead to higher spreads today. Panel A shows that an additional $100 million in inventory, which is slightly less than a one-standard deviation change, corresponds to an increase of 0.17 basis points in our proportional effective spread measure; results are of similar magnitude when we examine dollar spreads. In specification (5), we add a kink to the linear 12

15 relationship between inventories and future liquidity, located at the upper quartile (75 th percentile) of the absolute inventory distribution. The idea is that when inventories are particularly large in either direction, market makers may be more constrained and require more compensation to provide liquidity. The data reveal strong evidence of this kind of non-linearity. On typical days, a $100 million increase in aggregate inventories increases the market-wide effective spread by basis points. But when inventories are beyond the 75 th percentile, the sensitivity of spreads to inventories more than doubles. In addition to our market-maker state variables, there are other variables that have been associated with changes in liquidity, both theoretically and empirically. For example, classic microstructure models, such as Kyle (1985) and Glosten and Milgrom (1985), say that liquidity should be decreasing in the variance of fundamental value. On the empirical side, Chordia, Roll, and Subrahmanyam (2000, 2001) show that when markets fall, liquidity dries up. Perhaps our revenue and inventory variables are simply co-linear with these other, previously identified effects. For example, since specialists are net long over 94% of the time, we know that profits on overnight inventory positions will be quite correlated with market returns (Table 1 shows that the correlation between the two is 0.61). Similarly, the specialist s obligation to buffer order flow suggests that inventories are likely to grow large following a sharp market decline (the Table 1 correlation between absolute inventories and returns is -0.52). While financing constraints plus average net long intermediary positions together imply a correlation between market returns and next period s average liquidity, a financing constraint explanation is even more plausible if markets become illiquid when specialists lose money or take on large positions without a big market move. To investigate this, we estimate specification (6) of Table 2, which combines specialist revenue variables, absolute inventories, market returns, and the conditional return variance: Spr m, t = t α + β1revinvm, t 1 + β2revtrm, t 1 + β3invm, t 1 + β4retm, t 1 + β5varretm, t + ε m,. (7) As noted above, there is a fair bit of collinearity between the various explanatory variables, so not all of the right-hand side variables remain significant. Regardless of whether we use proportional effective spreads in Panel A or dollar effective spreads in Panel B, we find that the 13

16 coefficient on overnight inventory revenues RevInv m,t-1 remains negative and strongly statistically significant. When specialists lose money overall, both dollar and proportional spreads widen, even if the market is not falling at the same time. Inventory levels are also significant in Panel A. Note that the main reason we examine both dollar spreads and proportional spreads is that if spreads are limited by a discrete price grid, there will be a mechanical relationship between proportional spreads and the stock price level, and this may account for the relationship between market returns and future liquidity. Note that the R 2 measures for the dollar effective spread regressions in Panel B tend to be lower for the same reason. In fact, when we eliminate this denominator effect by using dollar spreads in Panel B, our revenue and inventory variables drive the effect of lagged market returns to virtually zero. In our final specification of Table 2, we allow a non-linear effect for both revenues and inventories. While this asks a lot of the data, given the collinearity between most of the explanatory variables, we continue to find evidence in specification (7) that the effects are biggest when specialists take on large positions and when they suffer the biggest losses on these overnight inventory positions. For robustness, we have also estimated (but do not report) a number of other variants of these specifications. The reported results are not driven by any particular subsample: the results are present during each of the tick-size periods in our sample, and the results are present in generally rising and generally falling markets. The results hold for quoted spreads as well as effective spreads. Including trading volume and the variance of trading volume has no effect on the coefficients of interest. 14 Finally, our quasi-differencing is not driving the results. When we estimate a vector autoregression on spreads, market returns, absolute market returns, intraday and overnight specialist revenues, and specialist inventories, taking a piecewise linear time trend out of the spreads for each tick regime, we get similar results on the importance of specialist inventories and revenues; these results are available from the authors upon request. The aggregate evidence strongly supports a role for financial constraints in shaping stock market liquidity. However, financial constraints should operate at the level of the financial intermediary, so we turn next to more disaggregated evidence to see if it too supports a capital constraint story. 14 See Lee, Mucklow, and Ready (1993) for intraday evidence that higher volume leads to higher subsequent spreads. 14

17 5. Liquidity and Market Maker Inventories and Revenues at the Specialist-firm Level If specialists are marginal liquidity suppliers, then a stock s liquidity should suffer if its specialist firm faces financing constraints. If financing constraints bind for all specialist firms at the same time, then we should indeed see all the effects at the aggregate level. However, if specialist firm revenues are imperfectly correlated, different specialist firms may face financing constraints at different times, and we might be able to find even better empirical support for the constraints hypothesis by identifying a relationship between specialist firm revenues and liquidity in that firm s assigned stocks. At the end of our sample, there are only seven specialist firms, each with a broadly diversified list of assigned stocks. Facing little idiosyncratic risk, these specialist firms are likely to generate revenues and take on inventories that are highly correlated with each other. However, at the beginning of the sample, there are 41 specialist firms, resulting in considerable cross-sectional dispersion in revenues and inventories, and thereby aiding identification. To proceed, we aggregate now only up to the specialist firm level and create an unbalanced panel with one observation for each specialist firm for each day. We quasi-difference and demean all variables as discussed in Section 3. In particular, we calculate gross trading revenues for each specialist firm f ending on day t (RevGr f,t ), which is then decomposed into overnight inventory-related revenues (RevInv f,t ) and intraday round-trip revenues (RevTr f,t ). We calculate the absolute dollar inventory position for each specialist firm based on its assigned stocks each day. A value-weighted effective spread measure is calculated each day for all the stocks assigned to a given specialist firm. We also calculate value-weighted returns (Ret f,t ) on this portfolio of assigned stocks in excess of the aggregate market return, along with the associated conditional volatility (VarRet f,t ) using an asymmetric GARCH model. Table 3 shows the correlations and standard deviations for the variables in the specialist-firm panel. The general patterns from the market-wide analysis carry over to the specialist-firm level, but magnitudes naturally are smaller. Specialist-firm gross trading revenues (RevGr f,t-1 ) have a standard deviation of $2.1 million around the regime means. Again, weekly revenues from intraday round-trips (RevTr f,t-1 ) are substantially more volatile (σ = $1.9 million) than revenues from overnight inventory (RevInv f,t-1 ), with a standard deviation of only $0.8 million. Compared to the market-wide correlations, the two components of specialist-firm revenue are somewhat 15

18 more positively correlated with each other (ρ = 0.012), while the correlation between RevInv f,t-1 and contemporaneous stock market returns Ret f,t-1 is more modest (ρ = 0.24). Note that these are pooled correlations, so cross-sectional differences in scale between the specialist firms may account for some of the differences from the market-wide correlations. For the specialist-firm panel, pooled regressions are estimated, and inference is conducted using double-clustered Thompson (2006) standard errors, which are robust to both crosssectional correlation and idiosyncratic time-series persistence. [ Insert Table 4 Here ] The results are in Table 4. Panel A examines proportional effective spreads, while Panel B displays results for dollar effective spreads. Specification (1) shows that, in contrast to earlier regressions at the aggregate level, specialist firm gross trading revenues are significant predictors of next day liquidity in that firm s assigned stocks, though the economic magnitude remains small. As discussed earlier, there could be confounding effects between intraday revenues (RevTr f,t-1 ) and future spreads, so we again decompose the specialist firm s daily revenues and focus on revenues that arise from overnight inventory (RevInv f,t-1 ). Specification (2) shows that these inventory-related revenues continue to predict liquidity at the specialist-firm level, with t- statistics in the neighborhood of 4 for both proportional and dollar effective spreads. In economic terms, if a specialist firm experiences a one standard deviation inventory revenue shortfall of $0.78 million, the spread on that firm s stocks the next day widens by an average of 0.16 basis points. We look next at non-linearities following extreme specialist losses. In specification (3) we add a kink to both RevInv and RevTr at the lower quartile point (25 th percentile). As in the market-level results, the biggest losses are associated with significantly bigger spread widenings. Based on the numbers in Panel B, the slope coefficient on RevInv is about 133 on a typical day and about 254 in the left tail of the inventory revenues distribution. Again, we find that larger inventories yesterday lead to higher spreads today. The kink in the spread-inventory relationship is particularly pronounced. Specification (5) shows that when specialist-firm absolute inventories are above their 75 th percentile value, market makers require more compensation to provide liquidity. For example, based on the results in Panel A, there is 16

19 virtually no relationship between inventories and spreads for typical inventory levels. However, when inventories are beyond the 75 th percentile, the sensitivity of spreads to inventories of is strongly significant and means that a one-standard deviation inventory shock of about $19.8 million in the tail of the distribution predicts a spread narrowing of about * = 0.1 basis point. Specification (6) is the kitchen-sink version, which predicts tomorrow s effective spreads on the value-weighted portfolio of assigned stocks using specialist-firm level RevInv f,t-1 and RevTr f,t- 1, returns on the portfolio of assigned stocks, and conditional volatility on the assigned stocks: Spr f, t = t α + β1revinv f, t 1 + β 2RevTrf, t 1 + β 3Inv f, t 1 + β 4Ret f, t 1 + β5varret f, t + ε f,. (8) Recall that all of these explanatory variables exhibit considerable covariation, so we expect some of them to become insignificant when all are included together. Revenues related to overnight inventory survive in the Panel B dollar spread regressions, but inventory does not fare well in either Panel A or Panel B. When we add kinks to the revenue and inventory variables in specification (7), we find that the significant coefficient on RevInv is driven by the left tail of the distribution, again consistent with financial constraints binding more severely following relatively large revenue losses. Overall at the specialist firm level, there is evidence that specialist-firm trading revenues and inventories affect next period s spreads. We suspect that there is considerable heterogeneity across specialist firms and over time, and in the next section we identify and examine specialist firms that are a priori most likely to be constrained. 6. Evidence from Specialist Firm Ownership Early in our sample period, there is considerable variation in the size and ownership structure of specialist firms. If some specialist firms have less access to capital, we would expect to see cross-sectional differences in the sensitivity of spreads to inventories and trading losses. While we do not have access to specialist firm balance sheets or income statements per se, Coughenour and Deli (2002) have identified three specialist firms that are owned by the specialists themselves, along with three specialist firms in which the specialists are employees. The 17

20 difference in ownership structure suggests that specialist-owned firms may have less access to capital than corporate-owned specialist firms. In this section, we investigate whether there is a cross-sectional difference in how these two kinds of specialist firms react to trading losses and inventory shocks. To do this, we construct a daily panel for these six specialist firms, beginning on January 1, Each specialist firm remains in the sample until it is acquired or March 1, 2002, when the last specialist-owned firm is acquired, whichever is earlier. The format is similar to the pooled regressions in the previous section, aggregating to the specialist-firm level, except that we define a dummy variable Dum f,t which is equal to 1 for specialist-owned firms and zero otherwise, and we interact this dummy with all of the right-hand side variables. For example, the specification with inventories alone on the right-hand side becomes: Spr f, t = t α 1 + α 2Dum f, t 1 + β1 Inv f, t 1 + β 2 Inv f, t 1 Dum f, t 1 + ε f,. (9) In this case, we are interested in the null hypothesis that β 2 = 0; more generally, we look to all of the interaction terms for evidence that spreads in stocks assigned to specialist-owned firms are more sensitive to inventory and revenue shocks. Standard errors are based on Thompson (2006). Table 5 presents the results. In each specification, we reject the null in favor of the alternative that spreads are more sensitive for specialist-owned firms. For example, specification (1) reveals that a $1 million shock to inventory revenues causes a basis point change in spreads for corporate-owned specialist firms. The effect is more than quadrupled for specialistowned firms. Specification (2) in the table corresponds to equation (9) above, with inventories as explanatory variables, and the effect of firm type is similarly strong, with a t-statistic of 2.35 on the interacted inventory variable. When we throw revenues, inventories, past stock returns, and conditional return variances into the regression together, the specialist revenue variables become insignificant, but the coefficient on the interacted inventory variable remains at 10.29, with a t-statistic of This means that an additional $1 million of inventory is associated with an additional basis points of spread for the specialist-owned firm relative to other specialist firms. 18

21 Thus, we have strong evidence that access to capital can affect the sensitivity of spreads to market-maker revenue and inventory shocks. However, it is possible that the stocks assigned to specialist-owned firms are somehow different from the stocks assigned to corporate-owned specialist firms, and that this somehow accounts for our results. To address this possibility, we look next at a time-series analysis of the same stocks following a relaxation of financial constraints. 7. Evidence from Specialist-Firm Mergers What should happen if financing constraints are suddenly relaxed? Specialists should become less sensitive to losses and less constrained by large inventory positions. In this section, we investigate whether deep pockets help specialists provide liquidity by looking at the mergers of the three specialist-owned firms from Section 6. The first merger took place on March 20, 2001 when Benjamin Jacobson & Sons was acquired by Spear Leeds Kellogg. On October 19, 2001, Bocklet & Company was acquired by LaBranche & Co. The final of the three mergers took place on March 1, 2004, with Van Der Moolen acquiring Lyden, Dolan, Nick & Company. The empirical strategy is straightforward. We first identify the set of stocks assigned to each specialist firm just prior to the merger. The same stocks are studied post-merger to see if there is a change in the sensitivity of spreads. Specifically, we define a dummy variable Post f,t for each date and specialist firm that is equal to one after a firm is merged and zero otherwise. We interact this dummy with each of the included revenue and inventory measures to see if there is an identifiable difference in sensitivities post-merger. For example, the specification with inventories alone on the right-hand side is: Spr f, t = t α 1 + α 2Post f, t 1 + β1 Inv f, t 1 + β 2 Inv f, t 1 Post f, t 1 + ε f,. (10) and the relevant null hypothesis is that β 2 = 0. The pre-merger period covers event days [-70, - 11], about three calendar months, and the post-merger period is defined symmetrically as event 19