Liquidity is one of the core concepts of market quality since it determines implicit transaction costs for investors. It can be measured along different dimensions and empirical studies regularly analyze the bid-ask spread, representing transaction costs for small orders, and order book depth, which indicates how much liquidity denoted in euro volume is offered by passive orders on both sides of the book (Chordia et al.
2001). Specifically, we use the relative quoted spread
5, which is the quoted bid-ask spread (i.e., the difference between the best bid and best ask) divided by the midpoint (i.e., the price in between best bid and best ask) as shown in Eq. (
1). The subscripts
i and
t represent stock and point in time respectively. Using the relative instead of the absolute spread is meaningful in order to account for the different price levels of the stocks. Throughout the paper, we report the relative quoted spread in basis points (bps)
6.
$$\begin{aligned} Relative\,Quoted\,Spread_{i,t}= \frac{ BestAsk_{i,t}-BestBid_{i,t} } {Midpoint_{i,t}} \end{aligned}$$
(1)
Regarding order book depth, we use two different measures. First, L1-Volume (see Eq. (
2)) represents the euro volume available at the best bid and ask. Therefore, this measure indicates how much volume can be traded immediately without further market impact in terms of worse prices than the current best bid and ask. Second, we rely on the Depth(10) measure proposed by Degryse et al. (
2015) in order to measure liquidity that is provided on deeper levels of the order book, i.e., at worse prices than the current best bid and ask, but still within an appropriate range of ten basis points (bps) around the current midpoint. The calculation of the Depth(10) measure is provided in Eq. (
3). The subscript
l indicates the order book level. Order book levels and the euro volume provided on these levels are taken into account as long as the respective level’s bid (ask) limit is larger (smaller) than ten bps below (above) the current midpoint, which represents the fair value of a stock.
$$\begin{aligned} L1\text {-}Volume_{i,t}&= BestAsk_{i,t} \cdot Quantity^{BestAsk}_{i,t} \nonumber \\&\quad + BestBid_{i,t} \cdot Quantity^{BestBid}_{i,t} \end{aligned}$$
(2)
$$\begin{aligned} Depth\,Ask(10)_{i,t}&= \sum _{l=1}^L {Price^{Ask}_{l,i,t} \cdot Quantity^{Ask}_{l,i,t}} \cdot \mathbbm {1}_{\left\{ Price^{Ask}_{l,i,t} < Midpoint_{i,t} \cdot (1+10bps)\right\} } ,\nonumber \\ Depth\,Bid(10)_{i,t}&= \sum _{l=1}^L {Price^{Bid}_{l,i,t} \cdot Quantity^{Bid}_{l,i,t}} \cdot \mathbbm {1}_{\left\{ Price^{Bid}_{l,i,t} > Midpoint_{i,t} \cdot (1-10bps)\right\} }, \nonumber \\ Depth (10)_{i,t}&= Depth\,Ask(10)_{i,t}+ Depth\,Bid(10)_{i,t} \end{aligned}$$
(3)
Moreover, we analyze order imbalance similar to Chordia et al. (
2002) in order to evaluate whether asymmetries in the order book change when HFT is interrupted. Order imbalances in either direction, i.e., excess interest to buy or to sell a stock, imply lower levels of liquidity. We calculate order imbalance based on the difference in trading interest revealed in the order book. Specifically, we measure imbalances in the amount of buy and sell order volume based on the difference between the euro volume on both sides of the order book that is close to the midpoint (i.e., within ten bps in line with the Depth(10) measure). Possible values of the order imbalance measure specified in Eq. (
4) range between zero and one.
$$\begin{aligned} Order\,Imbalance_{i,t}= \frac{ |Depth\,Ask(10)_{i,t} - Depth\,Bid(10)_{i,t} |}{Depth(10)_{i,t}} \end{aligned}$$
(4)
Volatility is the second dimension of market quality analyzed in our empirical study. We differentiate between trade price volatility (
S.
D.
Price) and midpoint volatility (
S.
D.
Midpoint). As shown in Eq. (
5), trade price volatility is measured by the standard deviation of trade prices
\(p_{i,t}\) in a given time interval
T divided by the average trade price
\(\overline{p_{i,t}}\) in the same time interval to obtain the measure in relative terms to account for different price levels of the analyzed stocks. The variable
n represents the number of trades (midpoints) in time interval
T. Midpoint volatility is computed identically except that
\(p_{i,t}\) represents the midpoint of best bid and best ask and not trade prices. Due to the fast quoting behavior in today’s automated securities markets and particularly the fast quoting behavior of HFTs, it is of interest to differentiate between these two volatility measures (Haferkorn
2017). As the relative spread, both measures for volatility are provided in bps throughout the paper.
$$\begin{aligned} S.D.\,Price_{i,T}= \dfrac{ \sqrt{ \frac{ \sum (p_{i,t} - \overline{p_{i,t}})^2}{n-1}} }{\overline{p_{i,t}}} \end{aligned}$$
(5)
In order to rule out that our observations regarding changes in liquidity and volatility are only driven by mechanical changes in trading activity due to the potential absence of HFTs despite their possibility to revert to slower connections, we also incorporate measures for trading activity in our analysis. Trading
activity is regularly measured via the number of trades and the euro volume traded in a given period (Chordia et al.
2001). In particular with the emergence of HFTs, who often update their orders leading to a large number of orders relative to the number of executed trades, the number of quotes, i.e., changes of best bid and/or best ask, and the number of order submissions in a given time interval are also analyzed (Hasbrouck and Saar
2013).
In order to be able to run regression analyses with contemporaneous observations, we aggregate all measures of liquidity, volatility, and trading activity into one-minute intervals. This means, we average all liquidity measures in a given one-minute interval and sum up the observed number of trades, quotes, order submissions, as well as the trading volume, which indicate trading activity. Both volatility measures are calculated based on all observations of prices respectively midpoints in a certain one-minute interval. This results in 20,990 observations in total for the 70 stocks and 60 min on five trading days.
7 Due to order book data issues for three CAC40 stocks (ACCP.PA, BNPP.PA, and UNBP.AS), market quality measures that depend on full order book information (i.e., number of submissions, Depth(10), and order imbalance) could not be calculated for 180 observations. Thus, the final data set to investigate these measures consists of 20,810 observations.