Memoria Descriptiva

We recognize that the volume clock is useful in analyzing certain problems, for instance, VPIN

(Easley, Lopez de Prado, and O’Hara 2012), and trade execution (Easley, Lopez de Prado, and

O’Hara 2015). However, testing jumps using price time series under volume clock may not be

First of all, one difficulty of using volume clock comes from the cross-sectional heterogeneity of

the volumes. In our data sample, there are liquid large market cap stocks such as Coca-Cola

(NYSE: KO), as well as low-priced small-cap stocks, such as JMP group (NYSE: JMP). The

volume of Coca-Cola is more than 500 times greater than JMP. We are not sure if it makes

sense to sample the prices of these two stocks based on same volume bucket, and compare the

volume-clock-based jumps of Coca-Cola and JMP. To be more specific, if we set the volume

clock in such a way that there are 360 volume minutes per calendar trading day for Coca-Cola,

its price is sampled at the minute frequency. Using the same volume bucket as the clock, one

calendar trading day of JMP is only considered as less than one volume minutes since the

volume of JMP is 500 times smaller. As a consequence, the price of JMP would be sampled at

the daily frequency. It completely contradicts our purpose of investigating the “flash crash” or

“mini flash crash” type of jumps. In this case, we essentially focus on testing the jumps in high

volume stocks while overlooking the jumps in thinly-traded stocks.

One may consider using different volume buckets to time Coca-Cola and JMP separately. But

now the concern becomes what is the sensible choice? It could be a quite arbitrary decision.

Moreover, if one needs to choose different volume buckets for each unique stock in the U.S.

markets, making economic sensible and convincing choice would be a challenge.

In our empirical analysis, the detected jumps in different stocks are compared cross-sectionally

based on stock characteristics. Because we are aware that the trading protocols, rules, and

technology are quite different now and ten years ago. Cross-sectional comparison mitigates the

issue of varying market conditions over the years. At any point in time, the cross-sectional

comparison among different characteristic buckets should be reliable.

Second, volume clock shifts out focus on the jumps in these high volume periods while overlook-

ing the jumps in normal market condition and the liquidity dry-up periods. Let’s consider the

market condition when the market liquidity dries up. At the moment, trading volume is low,

while the asset prices become very unstable. As the market liquidity dries up, the price insta-

bility can be caused by the unusually large price impact of the trade, or by the canceled quotes

as market makers are withdrawing their liquidity provision. In these scenarios, price jumps are

in companion with thin trading volume. If the clock based on volume bucket is adopted, we

dry-up periods would look more benign. From a different perspective, during liquidity dry-up

periods, since volume is low, we would downsample the price data points comparing to the

normal times (we would sample the data points at a much lower frequency because the volume

clock runs slower than the physical clock). As a result, there will be fewer jumps identified using

volume clock because there are fewer data points sampled during these extreme periods. On

the other hand, there are also very volatile times with high trading volume. If the volume clock

is adopted, we essentially focus on the jumps during high volume periods while overlooking the

jumps in normal market condition and the liquidity dry-up periods. But this deviates from our

aim to investigate all the transient and permanent jumps in the U.S. stocks.

What’s more concerned is that by dilating or shrinking the local time frame may completely

change the nature of the identified jumps. For instance, the econometric test identifies a jump

if there is a large sharp change in price relative to the local volatility. However, if the local time

frame is dilated (stretched), i.e., the volume clock runs much slower than the physical clock,

the sharp price change would look much milder and not so different from random walk. Then

the jump based on physical clock would not be classified as a jump using volume clock.

Third, testing the jump based on volume clock would run into some econometric difficulties as

well. As the current jump tests are all based on the price movements with the physical clock.

We are not sure if there is an econometrically sound way to test price jumps when the price is

timed with the volume-based clock.

Therefore, we think it makes more sense to simply using the physical clock, because this paper

aims to investigate the market stability from an average investor point of view. The time

experienced by the average investors is the physical time, not volume-bucket time artificially

introduce by researchers. Let alone to say, the actual meaning of volume clock is still a very

debatable issue (Andersen and Bondarenko 2014a, 2014b).

4.3

Literature Review

The research that is closest to ours is Gao and Mizrach (2016), which is recently referred to

To be more specific, they examine stocks whose bids (asks) move more than 10% at the NBBO

between 09:35 and 15:55 but recover within the trading day. There is a breakdown (or breakup)

of the limit order book happen if the national best bids (asks) fall (rise) 10% below (above)

the 09:35 price, and rebound within 2.5% of the 09:35 price at 15:55. They find that market

quality (in terms of the limit order book breakups and breakdowns) has improved since the

implementation of Reg.NMS, since mid-October 2007.

Although Gao and Mizrach (2016) share some similar starting points as our study, i.e., the

market stability issue, their research is completely different from ours in the following ways.

First of all, Gao and Mizrach (2016) interest in the breakdowns/breakups of the limit order book

while we are interested in the transient jumps that last from 5 minutes to 1 hour. To be more

specific, Gao and Mizrach (2016) study bids and asks separately for identifying breakdowns

in bids and breakups in asks. They focus on the dysfunction of the limit order book and

scrutinize every change in the NBBO. In contrast, our research aims to differentiate transient

price jumps from instantaneous volatility and market microstructure noise: we sample mid

prices at a lower frequency (2.5 minutes) and mitigate the market microstructure noise with

pre-averaging procedure. Second, their definition of breakdown (breakups) does not differentiate

transient extreme price movements from high volatility: when simulating the whole day’s price

path using random walks, one would generate many realizations of price paths that satisfy the

breakdown/breakup conditions, especially when the volatility is high. In other words, the bids

“breakdown” to a level lower than 10% of 09:35 price and come back within 2.5% of the 09:35

price do not necessarily mean dysfunction or instability of the markets, although it does contain

the events of market instability as its subset. While our transient jump test aims at identifying

the jumps using econometrically rigourous method, then test if the subsequent price movements

after the jump come back inside the volatility cone within 1 hour. Last but not least, although

the sample period of their data (1993-2013) is similar as ours, the conclusions of their study are

quite different from ours: Gao and Mizrach (2016) reports the breakdown frequency in all U.S.

stocks aggregately, while we document that the jump properties depend on stock characteristics.

Moreover, the event in their study is the implementation of Reg.NMS in October 2007, while

we focus on the implementation of auto-quote in early 2003, around which the major structural

With respect to other relevant studies, Hendershott, Jones, and Menkveld (2011) use the imple-

mentation of auto-quote on NYSE in 2003 to study the effect of algorithmic trading on market

liquidity. They find that the market liquidity, the quoted and effective bid-ask spread, improves

after the introduction of auto-quote for the large market cap stocks, while there is no significant

effect on market liquidity for small market cap stocks. Additionally, they show the reduction

in trading cost is driven by a reduction in adverse selection component of the bid-ask spread.

Note that Hendershott, Jones, and Menkveld (2011) exclude the stocks with price smaller than

5 dollars, for which we find that the transient jumps increase dramatically after 2003. Consid-

ering that the low-priced stock is usually the stocks with small market capitalization and low

market liquidity, the dataset of Hendershott, Jones, and Menkveld (2011) excludes these stocks.

Boehmer, Fong and Wu (2012) obtain similar findings based on a wide range of countries.

Interestingly, they find cross-sectional variations in the effect of algorithmic trading (AT): while

AT improves liquidity and informational efficiency for the large market cap and high-priced

stocks, greater AT reduces liquidity and worsens the volatility for the smallest capitalization

stocks. In line with Boehmer, Fong and Wu (2012), we also document completely different

effects of algorithmic trading on the large cap high-priced stocks and small cap low-priced

stocks. The difference is that Boehmer, Fong and Wu (2012) focus on market liquidity and

volatility, while our paper is about market stability, especially the transient price jumps that

are not information driven.

A related topic is the effect of algorithmic trading (AT) on volatility. However, the empirical

findings are rather mixed. Hasbrouck and Saar (2013) use the number of linked messages as a

proxy for algorithmic trading and find a negative effect of AT on volatility. Using the ban on

short-sales in the U.S. markets for about three weeks in September and October 2008, Brogaard

(2011) finds a negative effect of HFT on volatility. However, Boehmer, Fong and Wu (2012)

document a positive association between their measure of algorithmic trading and volatility,

based on their international sample of stocks.

Brogaard et al. (2016) study the extreme price movements and the behavior of HFTs. The

extreme price movements (EPMs) are defined as the 10-second absolute midquote returns that

belong to the 99.9th percentile of the return distribution. Brogaard et al. (2016) find that HFTs

non-high frequency traders (nHFTs). But this observation is limited to EPMs in single stocks.

When several stocks experience simultaneous EPMs, HFT liquidity demand dominates their

supply.

Menkveld and Zoican (2017) investigate the case when the trading platforms reduce their la-

tency, the market liquidity could be hurt because the market makers are more likely to meet

the high frequency bandits and less likely to meet the liquidity traders. The argument is rel-

evant to our study on market stability. The implementation of auto-quote on NYSE reduces

latency, thus the manual market makers, who have greater long-term risk-bearing capability are

more likely to meet the high frequency arbitragers (bandits). This creates an adverse selection

problem for the slow market makers who would be crowded out of the market by HFTs. In the

extreme market conditions, the absence of slow market makers could impair the resilience of

the market (Biais and Foucault 2014, and the references therein).

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