1 – The zero return measure

7Lesmond et al. (1999) relate zero returns to illiquidity by arguing that zero returns (or zeros) occur when informed traders are not (or less) willing to trade. They also argue that less liquid stocks are more likely to exhibit zero volume days, hence zero returns. Following their reasoning, zero returns occur when the value of the new information set does not exceed the cost of trading. Therefore, informed traders do not react to the information signal. Lesmond et al. (1999) find that firm size is negatively related to the frequency of zero returns and positively related to both Roll (1984)’s measure and quoted spread. They intuitively argue that informed traders do not trade after the evaluation of the new information set’s value, which would lead to a zero return, as the effect of other types of traders is assimilated to noise.

8Their to bit model assumes that the unobserved true return on day t for the stock i (R^*_it) is given by: [2]

9

10with

11

12where R_mt is the market return for day t and ∈_it is a public information shock for stock i at day t.

13The threshold that the value of the new information set should exceed is denoted as α_1i ≤ 0 for negative information and α_2i ≥ 0 for positive information, for stock i. This model is estimated by maximum likelihood, using the function described in Lesmond et al (1999).

14This model follows the framework of Copeland and Galai (1983), Glosten and Milgrom (1985) and Kyle (1985) and implies that the arrival of new information is correctly valued by each informed trader as well as that their reaction timings are similar.

15Based on this limited dependent variable model, Lesmond et al (1999) build two types of measures. The first one is presented as the difference between the thresholds, α_2i - α_1i, and the second one is computed as the proportion of zero returns on a given time interval. These measures have been put in question in several papers. Goyenko et al. (2009) test the usefulness of these measures by comparing them to a large set of liquidity proxies, emphasizing that the frequency of zero returns does not constitute an accurate proxy for liquidity. Bekaert et al. (2007) use the frequency of zero returns to address the relationship between liquidity and asset pricing on emerging market data, since they only dispose on price series. They also discuss the limitations of this measure. Levine and Schmukler (2006) study the relationship between liquidity and cross-listing using the frequency of zero returns. Liu (2006) discusses and modifies the measure but Chang et al. (2010) assess that Liu (2006)’s modification is not significantly related to stock returns in the Japanese market, as opposed to zeros. Lang et al. (2012) apply the proxy to evaluate whether liquidity, transparency and valuation are related to each other.

2 – Zero returns and informed trading

16In a dealership market, Lesmond et al (1999)’s model may still hold since the market maker will probably widen the spread if new information comes and if informed traders have failed to stay hidden. In this type of market, the dealer acts as a counterparty for all order submissions. The dealer is a monopolist with regard to the determination of the bid and ask quotes. The detection of informed traders, or of their willingness to trade, forces the market maker to enlarge the spread, which in turn impacts the return that informed traders would have made without the dealer’s intervention. They are therefore not willing to trade anymore. The market becomes more illiquid and the probability of a zero return is higher. However, Lesmond et al (1999) use data from NYSE/AMEX individual stocks which are attributed designated market makers, also called specialists. The specialists may trade if all limit orders outstanding at the best quotes have been fulfilled. Traders are therefore more likely to trade with each other, as it is the case in a traditional limit order market.

17When we more closely examine the applicability of this model in a limit order book market, some hypotheses do not hold anymore. One of the main assumptions behind this model is that only informed traders move prices as zero returns are said to proxy zero “informed” volume. However, uninformed traders may also significantly influence prices and recent research evidence has shown that informed traders do not always trade aggressively, e.g. Bloomfield et al. (2005). Bekaert et al. (2007) also argue in favor of that point even if zero returns may still be considered as a measure of the lack of informed trading, in its most usual form. Mazza (2014) also confirms that there are less informed traders when opening and closing prices are very close, as measured by the PIN indicator of Easley et al. (1996). Lesmond et al (1999) did not test this hypothesis directly as it is a condition for their model to hold, i.e. the zero return is the consequence of informed traders’ non-willingness to trade after the upcoming of new information whose value does not exceed the threshold. Bekaert et al. (2007) nevertheless argue that news are associated to shocks which are related to excess volatility. As a consequence, if there are news that do not enable trading or no news, there is no excess volatility, which implies a higher liquidity. This has been suggested by Pagano (1989), among others, who identifies a positive relationship between illiquidity and volatility. This link is opposed to the proposition of Lesmond et al (1999) who argue that zero returns imply higher transaction costs, hence lower liquidity. Bekaert et al. (2007) also present cross-listing of firms as a serious limitation of the model, since local liquidity may be dramatically different from foreign liquidity.

18Another reason that puts the usefulness of the zero return measure in limit order markets in question resides in the connection between zeros and illiquidity. Lesmond et al (1999) establish the link by making the hypothesis that transaction costs are higher when informed traders do not want to trade after the arrival of a new information set because the value of this new information does not exceed the cost of trading. If we question this hypothesis, as we should for limit order markets with a public and visible order book, the model does not hold anymore. The only proposition that would still apply is that zeros are linked to less informed trading. Lesmond et al (1999), Bekaert et al. (2007) and Mazza (2014) agree on that point. Their reasoning only differ in the way informed trading is associated with illiquidity. Lesmond et al (1999) argue that a high level of transaction costs, hence an illiquid state of the order book, is what forces informed traders not to trade. Mazza (2014) however suggests that informed traders trade less because there is a consensus on the fair value of the security and prices are efficient. As informed traders do not participate to the current session, i.e. they do not trade to move the price towards the fundamental value, the order book presents a higher liquidity. There is an extensive literature on order submissions made by informed traders which suggests that the absence of informed trading should result in a higher liquidity. This argument is opposed to the reasoning of Lesmond et al (1999). For instance, Harris (1998) suggests that informed traders’ use of market orders is higher when they believe their information is short-lived. Harris (2003) further suggests that “their most important decision is whether to trade aggressively or not”. This decision implies the minimization of trading costs: If the stock is (not) liquid, they may (not) trade aggressively. If they know that their informational advantage will last long enough, they will prefer trading slowly to diminish their market impact. Anand et al. (2005) also empirically investigate the changes in the trading strategies of informed traders and find that they place liquidity-taking orders earlier in the day while they provide liquidity later in the same day.

19On that account, Mazza (2014) proposes some theoretical justifications to characterize the higher liquidity that occurs when there is a temporary consensus between buyers and sellers on the fundamental value of the security. He bases his reasoning on Bloomfield et al. (2005) who show that informed traders provide liquidity when they estimate their information has a low value, rather than consuming it from the book, as they do when they estimate this value as high. In their model, informed traders do not stop trading when the value of their information goes down, but submit aggressive limit orders to earn the spread. In the hypothesis of asymmetric information, they incur a lower risk when they submit limit orders as they do not bear the cost of trading against a better informed trader. Behaving as dealers when they cannot profitably trade on their information set is their best choice to make money. Bloomfield et al. (2005) also suggest that their profits are even higher in this last case. In addition, Harris (1998) and Bloomfield et al. (2005) demonstrate that liquidity traders are also most likely to change their way of trading throughout the day: They initially try to meet their target by submitting limit orders, which are less expensive, but they become more aggressive since their non-execution risk increases near the end of the day. As a result, they hit the liquidity offered by informed traders. These propositions are consistent with Anand et al. (2005). Furthermore, symmetrically informed traders will not trade with each others, as outlined by Harris (2003). This implies that trading activity is driven by liquidity or noise traders who pick informed traders’ pending limit orders off. Informed traders will try to gain price priority by reducing the spread and come closer to the fundamental value to increase the probability of being picked off by other traders. There is a competition effect that makes the order book more informative, more dense, and the spread narrower. Trading is reactivated when informed traders estimate that the spread is sufficiently low to hit the best opposite quote or when the fundamental value has changed, as explained in Mazza (2014). As a result, when a price discovery process has been sufficiently efficient to bring an agree menton the fundamental value of the security that is located inside the spread, informed traders provide liquidity to earn the spread.

20Furthermore, Lesmond et al (1999) use zero returns as low frequency liquidity proxies, aiming at measuring liquidity when volumes, trades and order data are not available. Based on high frequency data, we nevertheless argue that zero returns are not always related to less trading volume, since liquidity may abound on both sides of the book, implying that prices do not move before the outstanding liquidity has completely dried out at the best quotes. There is clearly a need to disentangle zero volume from zero returns for large as well as small caps.

21In addition, if we consider the widely used Amihud illiquidity ratio, presented in Amihud (2002), which is defined as

22Given these limitations, we question the use of zero returns as a proxy for illiquidity or for higher transaction costs in a limit order market. In this paper, we analyze the connection between intraday zero returns and different order book-based and trade-based liquidity proxies. Our study focuses on intraday zero returns rather than daily to examine the justification of the proxy on lower time frames. Addressing the occurrence of zero returns and their implications towards market microstructure is different from the initial measure proposed by Lesmond et al (1999). Nevertheless, their justifications are grounded on the interpretation of each individual zero return that they aggregate to form a low-frequency proxy. As a result, their reasoning should also be verified on higher frequency data. The possible pitfall of moving to intraday intervals resides in the fact that intraday liquidity is U-shaped (Biais et al., 1995). In order to make our results robust, we take this U-shaped pattern into account in our event study methodology. To the best of our knowledge, this paper is the first to thoroughly analyze the information content of zero returns on an intraday time frame. As robustness checks, we consider different interval lengths and investigate whether the relationship does still hold for daily data.

1 – Data

23We test the relationship between zeros and liquidity using Euronext market data on 701 stocks. This unique and rich dataset contains all orders and trades for 61 trading days from February 1 to April 30, 2006. Since the implementation phase of MiFID starting in November 2007, volumes have been shifting from national exchanges to Multilateral Trading Facilities (MTF) due to cross-listing. The key advantage of this dataset is to avoid that phenomenon. In order to still be representative of market activity, more recent datasets must include sufficient information from MTF and market data, which has become extremely difficult in today’s decentralized trading environment. In addition, our dataset includes market members’ ID that we use to disentangle buyer-initiated and seller-initiated trades, without any error margin. Traditionally, in market microstructure studies, the Lee and Ready (1991) algorithm is used to categorize buyer and seller-initiated trades. This algorithm has proved to be sufficiently efficient but misclassification may still occur. In our case, we are able to precisely match the two orders that generate each transaction, by comparing the submission times and the type of orders. Finally, we are also provided with undisclosed data on hidden orders [3]. We build 15-minute-intervals from 9:00 AM to 5:30 PM (CET), which leads to 34 intervals per day. [4] In the robustness checks section, we investigate whether our findings still hold for different time frames.

24In our event study, we need to control for contagious events, i.e. more than one event in a window. An event is the occurrence of a zero return. In order to avoid contagion effects between events, we do not consider occurrences in the previous and next three periods around the occurrence of the zero return. We only consider [–3,+3] windows where there is only one event occurring at time t = 0. Before filters, the sample contains 671,843 zero returns. After filters, only 6,302 events remain. This is the consequence of non-trading that often affects small caps stocks. We split the complete database into three capitalization-based portfolios, motivated by Lesmond et al. (1999) who outline that firm size has an impact on the relationship between zero returns and liquidity. Large, mid, and small cap companies respectively exhibit a market capitalization larger than EUR 1 billion, between EUR 150 millions and EUR 1 billion, and below EUR 150 millions.

25Figure 1 shows the distribution of our events among the 34 intervals. The unfiltered sample displays a peak around midday which comes from non-trading that occurs around lunch time. We observe that the peak disappears after the filters have been applied. These figures further show that there is a wide dispersion of zero returns and that they are not supposed to occur at a particular moment during the day, excepted around noon.

Figure 1

Zero returns by interval

Zero returns by interval

This figure displays the number of events in each time interval. Panel (a) and (b) respectively present the distribution of the events before and after filters have been applied. The 34 intervals correspond to 15-minute intervals starting at 9:00 AM until 5:30 PM.

2 – Liquidity proxies

26We analyze the relationship between zero returns and liquidity proxies by measuring liquidity at the end of each 15-minute interval. This allows us to directly link liquidity to zero returns. We first analyze order book-based liquidity measures such as the relative spread and depth. We consider two levels of depth: Depth at the best quotes and depth beyond the best quotes up to the fifth limit. These variables are computed in numbers of shares. We then include dispersion and slope measures that are respectively presented in Næs and Skjeltorp (2006) and Kang and Yeo (2008). The dispersion measures how far from each other are the price limits: The more distant the quotes, the higher the dispersion. This proxy is computed as follows:

27

28where, for security i and interval t,

29The dispersion is a liquidity proxy as for a given large market order, the resulting transaction costs are lower if the book is more dense, i.e. less disperse. It is also a measure of traders’ willingness to provide liquidity. The book becomes more dense when traders compete to supply liquidity at the best quotes, and obtain price priority. This is an interesting measure as it combines both prices and quantities.

30The slope is a measure of the elasticities

31

32

33p^B_τ and p^A_τ are the prices, respectively at the bid and at the ask, appearing at the quote τ. p₀ denotes the quoted midpoint. Finally, and are the natural logarithm of accumulated total share volume at the limit τ respectively for the bid and the ask sides. [5] In each equation, the first term represents the slope of the first line of the book to the midquote while the second one is the sum of the four remaining local slopes. The slope is then obtained by averaging both supply and demand elasticities. [6]

34Table 1 presents the descriptive statistics of these liquidity proxies, as well as information on market capitalization, volume and number of trades. We may observe that the distributions of these liquidity proxies are heavily skewed and leptokurtic.

Table 1

Descriptive statistics

Group Mean STD Median Skewness Kurtosis CV Market Cap (kEUR) Small Mid Large 66049.591 461084.347 11280287.064 42219.508 244309.592 18571741.538 60015.690 400465.334 4593171.461 0.416 0.596 3.764 –1.054 –0.843 17.913 63.921 52.986 164.639 Volume Small Mid Large 5583.599 6739.115 49681.859 77167.448 175117.735 215485.532 0.000 100.000 6080.000 55.419 204.604 30.373 4275.049 67361.596 2165.499 1382.038 2598.527 433.731 Number of trades Small Mid Large 2.751 4.973 49.198 10.824 14.277 79.122 0.000 1.000 22.000 17.321 26.460 6.741 521.367 1929.963 143.908 393.499 287.062 160.825 Depth BBO Small Mid Large 230983.000 462602.351 49579.580 1567896.644 6815596.565 311513.514 931.000 499.000 1986.000 10.211 16.820 9.492 126.613 290.320 107.840 678.793 1473.316 628.310 Depth 5 limits Small Mid Large 1133794.079 2400065.297 250027.301 7262446.241 37698131.568 1377816.872 7800.000 3780.000 12053.500 9.077 20.556 7.996 90.080 443.553 73.537 640.544 1570.713 551.067 Dispersion Small Mid Large 0.050 0.108 0.114 0.083 3.257 0.412 0.024 0.054 0.042 25.513 630.524 13.814 2090.019 399147.148 287.887 165.336 3020.423 361.015 Slope Small Mid Large 491.457 1003.658 3186.220 571.736 1120.889 2701.555 333.126 636.069 2485.429 5.549 3.584 1.436 48.892 17.940 2.036 116.335 111.680 84.789 Relative Spread Small Mid Large 1.279 0.590 0.211 2.078 0.979 0.412 0.867 0.410 0.111 8.009 87.427 279.359 76.363 17153.975 134775.222 162.405 165.875 195.705

Descriptive statistics

This table presents the descriptive statistics for market capitalization, volume, number of trades, as well as liquidity variables. These statistics are computed for each market capitalization segment: Small, mid and large caps. Market capitalization is computed in kEUR, volume in number of shares and the number of trades is the sum of the numbers of buyer and seller-initiated trades. Depth BBO denotes the depth at the first limit while Depth 5 limits is the sum of bid and ask quantities up to the fifth limit. The dispersion and slope measures are computed as in Kang and Yeo (2008) and Næs Skjeltorp (2006), respectively.

35Using these proxies, we establish different propositions that we test in our empirical analyzes. We also formulate assumptions on trading activity.

36Proposition 1. Depth is higher when a zero return occurs.

37As depth is positively related to liquidity, we expect this relationship to hold for each capitalization group. However, if the book is becoming more dense and the spread lower, the quantities outstanding at the best quotes may actually be smaller. This effect should be minimized for the largest stocks that are more followed by analysts.

38Proposition 2. The relative spread is lower when a zero return occurs.

39The spread is negatively related to liquidity and as a consequence, we expect it to drop when a zero return takes place. Again, it is appropriate to distinguish large caps from small caps, given the tick size effect, i.e. large caps obviously display a much narrower spread than small caps do. As a matter of fact, if this relation is verified for smaller caps, the trough must be sharper than for larger caps, since there is much more room for improvement when the spread is usually large.

40Proposition 3. The dispersion is lower when a zero return occurs.

41The competition driven by informed traders who are willing to earn the spread forces the spread to be lower when a zero return occurs. The density of the book becomes higher and quotes are very close to each other. This proposition is much related to Proposition 2.

42Proposition 4. The slope is steeper when a zero return occurs.

43This is a corollary of Proposition 3, as the shape of the book is linked with its dispersion. We expect a steeper slope at the moment of the zero return, since a steep slope denotes a high level of agreement among analysts and traders about the fair value of the security, as previously mentioned.

44Proposition 5. There is less trading activity when a zero return occurs.

45If liquidity is effectively higher and the number of analysts and traders following the stock constant, a zero return should result in lower trading activity, since informed traders submit passive limit orders inside the existing quotes and do not trade aggressively anymore. We measure trading activity with the number of buyer and seller-initiated transactions that we classify after having matched orders and trades.

46Proposition 6. Volatility is lower when a zero return occurs.

47This proposition may seem trivial but is inferred from two phenomena. First, liquidity is inversely related to volatility. So, we expect volatility to be lower. Second, a zero return is also characterized by a lower volatility. Price excursions outside the close-open range should also be reduced as passive limit orders are submitted by informed traders around the quotes to absorb larger trades. We measure volatility by using the high-low range.

1 – Methodology

48To verify whether the assumptions of Lesmond et al. (1999) are correct, we first run an event study of liquidity proxies around zero returns. Our event is a dummy variable that equals 1 when the return is zero and 0 otherwise.

49The event study is built using abnormal measures of the different liquidity measures presented in the previous section. We consider a [–3,+3] window containing seven 15-minute intervals: The event as well as three period before and after the event.

50We compute the abnormality for liquidity proxy l and stock i at interval t as follows:

51

52where

53This approach has also been tested in Boudt and Petitjean (2014) and Mazza (2014). The median is more robust to represent the central tendency of the distribution, since the distributions of liquidity proxies are heavily skewed and leptokurtic as shown in Table 1. The mean is much more affected by extreme values.

54After the computation of the abnormality for each proxy, we quantify the distance between the current observation and the abnormal measure. We then aggregate the events to form graphs for each liquidity proxy. We finally test whether a particular type of pattern occurs during the [–3,+3] window and check if abnormality is significantly different from zero. As in Mazza (2014), we use a standard non parametric sign test since it does not need any assumption about the shape of the distribution. The null hypothesis specifies that the abnormal measure has a median equal to zero. The alternative hypothesis postulates the opposite. The M test statistic is computed as:

55We then analyze the p-values of each time interval of the window and check whether there are significant differences. If the p-value at the event interval is significant, the identified abnormal value is significantly different from zero, meaning that zero returns are associated to the corresponding configuration of the limit order book. If p-values are significant before the event, the zero return may be the consequence of a particular state of liquidity. If p-values are significant after the zero return, it may be the cause of the current state of liquidity, as measured by a given proxy.

2 – Results

56The results of the event study of liquidity proxies are presented in Figure 2.

Figure 2

Abnormal liquidity around zero returns

Abnormal liquidity around zero returns

These lines represent the intra-window median pattern for abnormal liquidity for the three market capitalization groups: Small, mid and large caps. Triangles (?), squares (?), and circles (?) indicate a rejection of the null hypothesis of the sign test respectively at the 99%, 95% and 90% confidence levels. All the abnormal measures of each liquidity proxy are statistically significant at the 95% level in the window [t – 2, t + 2].

57The relative spread drops more significantly for small caps, since they are less likely to display a narrow spread unlike large caps. As a consequence, the sharp drop in the abnormal relative spread for small caps is much more pronounced. The relationship between zero returns and liquidity is also very strong as the recovery to normal values takes place quickly, implying that zero returns are associated to liquidity shocks that are short-term and highly resilient.

58The dispersion drops sharply when the event occurs and is somehow anticipating the trough in t – 1. The shock also reverts very quickly to normal values in t + 1. This confirms our intuition that the competition among traders effectively takes place when a zero return is observed. A smaller spread, a higher dispersion and more depth confirm the hypothesis of an increased presence of informed traders in the supply of liquidity.

59The relationship for depth measures is not verified for small caps. It seems however that there is a significant increase in these proxies when a zero return occur as far as large cap stocks are concerned.

60Zero returns also affect depth calculated with the outstanding quantities of the five best limits. The slope also increases significantly when a zero return occurs, confirming the outcomes of the dispersion.

61These results do not confirm the explanation that stands behind the proxy presented in Lesmond et al. (1999). They rather point to the contrary: Informed traders act as market makers to profit from their informational advantage and earn the spread that liquidity and noise traders are willing to pay to meet their needs. These results are in line with the expectations we built in Propositions 1 to 4.

62Figure 3 presents the outcomes of the event studies on trading activity measures.

Figure 3

Abnormal trading activity around zero returns

Abnormal trading activity around zero returns

These lines represent the intra-window median pattern for abnormal trading activity for the three market capitalization groups: Small, mid and large caps. Triangles (?), squares (?), and circles (?) indicate a rejection of the null hypothesis of the sign test respectively at the 99%, 95% and 90% confidence levels. All the abnormal measures of each trading activity proxy are statistically significant at the 95% level in the window [t – 2, t + 2].

63These graphs show that a drop appears at time t = 0, when the zero return occurs, for both trading activity and volatility proxies, even if the patterns are clearer for sell trades than buy trades. Panel (c) shows that volatility drops when a zero return occurs. The high-low range is smaller at that time, which is a clue on the consensus between buyers and sellers on the fundamental price. In addition to generate a higher liquidity in the order book, this consensus, also defined by the absence of informed trading and price discovery process, seems to be related to a significant drop in price volatility, indirectly supporting the negative relationship between volatility and liquidity, even at very particular moments, like zero-return intervals. [7] The graphs also emphasize that trading activity tend to be lower for all capitalization groups, which may be an additional clue of the absence of aggressive trading from the informed traders. The higher the market capitalization, the lower the magnitude of the variation. As the number of trades is lower, the liquidity that informed traders provide seems not to be totally hit by liquidity traders and noise traders.

64All in all, the event study clearly indicates that zero returns are much more related to liquidity than to illiquidity, as previously suggested by Lesmond et al. (1999). In the next section, we confirm the results of this non-parametric analysis by estimating fixed-effects logit regressions, with the occurrence of zero returns as the binary response variable.

65The event study analysis reveals that liquidity is effectively higher when an intraday zero return occurs, whatever the market capitalization group. Relative spread, slope and dispersion confirm this outcome. For the depth proxy, the results are less clear but are more significant for the largest caps. We therefore accept Propositions 1 to 4. Regarding trading activity and volatility, we also validate Propositions 5 and 6. Trading activity is significantly lower for the two proxies when a zero return takes place. Volatility is also significantly dropping in t = 0.

1 – Methodology

66In a second step, we run logit regressions on the unfiltered sample with ZR_i,t, the occurrence of zero returns for stock i at interval t, as the dependent variable:

67

68where ZR_i,t is the response variable, x’_i,t is a 1 × (k + 1) vector of the k explanatory variables (including intercept), β is a (k + 1) × 1 vector of coefficients (including intercept), c_i is the unobserved time invariant effect of stock i and

69

70In this equation, RS_i,t stands for the relative spread of stock i for interval t, Q5_i,t for depth at the five best limits, Dispersion_i,t for the dispersion, Slope_i,t for the slope and Volume_i,t for the volume. IT_i,t is a dummy variable that captures the presence of informed trading through trade imbalance. It is equal to one when the absolute trade imbalance is higher than 50% and 0 otherwise. The absolute value of the trade imbalance is computed as:

71Table 2 presents Pearson’s correlation coefficients between each non-dummy variable of the model. The values clearly indicate that the measures are not correlated.

Table 2

Correlation matrix

Volume RS Q5 Dispersion Slope Volume 1.00 ?RS –0.01 1.00 ?Q5 0.07 0.07 1.00 ?Dispersion –0.01 0.01 0.00 1.00 ?Slope 0.12 –0.08 –0.02 –0.02 1.00

Correlation matrix

This table presents Pearson’s correlation coefficients between the non-categorical variables of the model. Volume denotes the volume. Q5 denotes the quantity outstanding at the five best limits. Slope and Dispersion respectively denote the slope and dispersion proxies.

72We may not estimate this panel model by likelihood maximization as it is usually done for logit regressions. In nonlinear models, the fixed effects, c_i, are not removed by differenciation, like in linear models. In addition, maximum likelihood estimators are valid only asymptotically. This assumes that the number of parameters does not increase as the sample gets larger. This is not the case with panel data, since the number of individuals increases when we consider more records in the dataset. Estimating the c_i results in biased β estimators too. The biases are even greater when the number of time points per individual is small. This is called the incidental parameters problem (Neyman and Scott, 1948; McFadden, 1973; Chamberlain, 1980). One method to deal with this concern is to apply conditional maximum likelihood estimation which basically consists in conditioning the traditional likelihood function on the change of the state of the dependent variable ZR_i,t between all time periods of the sample. The “sufficient statistic” of the conditional logit model is

73Conditional logit controls for firms’ fixed effects without estimation biases but presents some drawbacks. First, it does not evaluate the impact of variables that are constant over time, e.g. market capitalization. This is a major concern since Lesmond et al. (1999) outlines that market capitalization is inversely related to the occurrence of zero returns. We bypass this disadvantage by running conditional logit regressions on three subsamples based on the market capitalization: Small, mid and large caps. Another drawback of this method that does not affect our study is that individuals are discarded if they display the same response variable level across all time periods of the subsample. This is not influential in our study since at least one zero return occurs for each stock.

2 – Results

74The results of the conditional logit regressions are displayed in Table 3.

Table 3

Conditional logit regressions

Variable Small Mid Large Estimate Odds Estimate Odds Estimate Odds RS 0.316*** 1.371 –0.029*** 0.971 –0.208*** 0.812 Q5 0.000*** 1.000 0.000*** 1.000 0.000*** 1.000 Dispersion –0.501*** 0.606 –0.090*** 0.914 –0.078*** 0.925 Slope 0.050*** 1.052 0.090*** 1.094 0.094*** 1.098 IT –2.521*** 0.080 –1.984*** 0.137 –0.681 0.506 Volume –0.002*** 0.998 –0.001*** 0.999 –0.010*** 0.990 This table presents the results of the estimation of the conditional logit model The model is estimated using three subsamples based on the market capitalization. The maximum likelihood estimation is made under the assumption that the state of the response variable ZRi,t changes for each stock across all time periods of the sample. We use Newton-Raphson’s optimization algorithm for likelihood maximization. Both parameter estimates and odds-ratio are shown. *, ** and *** respectively denote 90%, 95% and 99% confidence levels for the parameter estimates.

Conditional logit regressions

75These outcomes clearly confirm the findings of the event study. There are very few differences due to the fact that the whole sample of zero returns is used. For example, the significantly positive coefficient for the spread for small caps is most probably the consequence of non-trading.

76All variables behave consistently with the expectations presented in Propositions 1 to 4. First, as in Lesmond et al. (1999), we observe some variation in the parameter estimates across the different subsamples, even if the sign are always consistent, except the relative spread for small caps stocks. The relative spread and the dispersion display negative and highly significant estimates while depth and slope exhibit positive and highly significant parameter estimates, even if they are very low. As a result, positive modifications in spread and dispersion proxies negatively affect the log-odds of a return equal to zero, while positive variations in depth and slope positively influence the log-odds of a zero return.

77All these findings indicate that, in a limit order market such as Euronext, intraday zero returns are more likely to occur in liquid states of the book, rather than in illiquid states as proposed by Lesmond et al. (1999). Since liquidity is inversely correlated with transaction costs, we expect them to be lower when zero returns appear.

78Nevertheless, we confirm that the occurrence of zero returns is an indicator of the absence of aggressive informed trading, given that IT presents significantly negative estimates. We agree with Lesmond et al. (1999), Bekaert et al. (2007) and Mazza (2014) on this point. For small caps, the difference in odds-ratio is expected to be 0.08 when the trade imbalance is higher than 50%, all else equal. For large caps, the odds-ratio moves to 0.506. [10]

79In a nutshell, there is less informed trading when a zero return occurs. However, informed traders may still be present as our measure only captures the impact on trade imbalances that informed traders create, such as the PIN indicator. However, as outlined by Bloomfield et al. (2005), informed traders may still be present in the order book, trying to earn the spread that liquidity traders would agree to pay, even if they do not generate excess trade imbalance.

3 – Robustness checks

80In this section, we test whether the results of the conditional logit regressions obtained on 15-minute intervals still hold for other interval lengths. We apply the same methodology to 20, 30 and 60-minute intervals. The outcomes are presented in Table 4.

Table 4

Conditional logit regressions: Robustness checks

Variable Small Mid Large Estimate Odds Estimate Odds Estimate Odds Panel A: 20-minute intervals RS –0.009 0.991 –0.082*** 0.921 –0.204*** 0.815 Q5 0.001*** 1.001 0.000*** 1.000 0.000*** 1.000 Dispersion –0.429*** 0.651 –0.114*** 0.892 –0.070*** 0.933 Slope 0.016 1.016 0.073*** 1.076 0.094*** 1.098 IT –2.303*** 0.100 –1.791*** 0.167 –0.624*** 0.536 Volume 0.006*** 1.006 –0.002*** 0.998 –0.008*** 0.992 Panel B: 30-minute intervals RS 0.087*** 1.091 –0.237*** 0.789 –0.111*** 0.895 Q5 –0.000*** 1.000 0.000*** 1.000 0.000*** 1.000 Dispersion –0.404*** 0.667 –0.222*** 0.801 –0.091*** 0.913 Slope 0.066*** 1.068 0.052*** 1.053 0.106*** 1.112 IT –1.905*** 0.149 –1.487*** 0.226 –0.532*** 0.588 Volume –0.008*** 0.992 –0.001*** 0.999 –0.007*** 0.993 Panel C: 60-minute intervals RS –0.015* 0.985 –0.057*** 0.944 –0.003 0.997 Q5 0.000*** 1.000 0.000*** 1.000 0.000 1.000 Dispersion –0.263*** 0.768 –0.039 0.962 –0.039 0.962 Slope 0.004 1.004 0.027*** 1.028 0.014*** 1.014 IT –0.424*** 0.654 –0.213*** 0.808 –0.050*** 0.951 Volume –0.002*** 0.998 –0.000** 1.000 –0.001*** 0.999 This table presents the results of the estimation of the conditional logit model, where . Panel A, B and, C respectively present the results obtained with 20, 30 and 60-minute samples. The model is estimated using three subsamples based on the market capitalization. The maximum likelihood estimation is made under the assumption that the state of the response variable ZRi,t changes for each stock across all time periods of the sample. We use Newton-Raphson’s optimization algorithm for likelihood maximization. Both parameter estimates and odds-ratio are shown.*, ** and *** respectively denote 90%, 95% and 99% confidence levels for the parameter estimates.

Conditional logit regressions: Robustness checks

81These results clearly indicate that the relationships outlined using 15-minute intervals are validated when changing interval lengths. The vast majority of the estimates exhibits the same signs and significance levels as the core analysis. Even if the relationship seems to deteriorate for large caps for 60-minute intervals, the measure may still be considered as a proxy for the absence of aggressive informed trading, as outlined by Lesmond et al. (1999) and Bekaert et al. (2007).

4 – Daily zero returns

82Lesmond et al. (1999) use zero returns to characterize the state of liquidity on a daily basis. Even if intraday zero returns seem to point to a higher liquidity, this relationship has to be tested on daily frequencies in order to provide a complete analysis of the proxy. Table 5 presents the results of the conditional logit regressions estimated on daily data that cover the same sample of stocks.

Table 5

Conditional logit regressions: Daily data

Variable Small Mid Large Estimate Odds Estimate Odds Estimate Odds RS –0.135*** 0.874 –0.095 0.910 –0.180 0.835 Q5 0.001*** 1.001 0.000** 1.000 0.001* 1.001 Dispersion –3.028** 0.048 0.096 1.101 –0.012 0.988 Slope –0.070 0.932 0.111*** 1.118 0.093*** 1.097 IT –0.020 0.980 –0.083 0.920 0.145 1.156 Volume –0.003*** 0.997 –0.000 1.000 –0.001*** 0.999 This table presents the results of the estimation of the conditional logit model, where . The model is estimated using three subsamples based on the market capitalization. The maximum likelihood estimation is made under the assumption that the state of the response variable ZRi,t changes for each stock across all time periods of the sample. We use Newton-Raphson’s optimization algorithm for likelihood maximization. Both parameter estimates and odds-ratio are shown. *, ** and *** respectively denote 90%, 95% and 99% confidence levels for the parameter estimates.

Conditional logit regressions: Daily data

83The results suggest that the relationship to liquidity is much weaker than for intraday datasets. However, these outcomes do not point to illiquidity. The relative spread, the depth, the dispersion and the slope display some significance, in particular for small caps. Interestingly, we observe that the relationship to the IT variable seems to no longer hold. This may also be explained by the scarcity of high trade imbalance on daily data.

84In a nutshell, these findings indicate that daily zero returns are also not associated with higher illiquidity in the order book, as opposed to Lesmond et al. (1999).