Tick size and market quality: Simulations based on agent‐based artificial stock markets

• Published date: 01 July 2020
• Author: Xinhui Yang,Qing Ye,Jie Zhang
• Date: 01 July 2020
• DOI: http://doi.org/10.1002/isaf.1474

RESEARCH ARTICLE

Tick size and market quality: Simulations based on agent-based

artificial stock markets

Xinhui Yang|Jie Zhang|Qing Ye

International Business School Suzhou, Xi'an

Jiaotong–Liverpool University, China

Correspondence

Xinhui Yang, International Business School

Suzhou (IBSS), Business Building (BS), South

Campus, Xi'an Jiaotong–Liverpool University,

8 Chongwen Road, Suzhou Dushu Lake

Science and Education Innovation District,

Suzhou Industrial Park, Suzhou 215123, P. R.

China.

Email: xinhui.yang@xjtlu.edu.cn

Summary

This paper investigates the way that minimum tick size affects market quality based

on an agent-based artificial stock market. Our results indicate that stepwise and com-

bination systems can promote market quality in certain aspects, compared with a uni-

form system. A minimal combination system performed the best to improve market

quality. This is the first study to analyse tick size systems that remain at the theory

stage and compare four types of system under the same experimental environment.

The results suggests that a minimal combination system could be considered a new

direction for market policy reform to improve market quality.

KEYWORDS

agent-based modelling, artificial stock market, market quality, tick size

1|INTRODUCTION

Tick size is the minimal magnitude in the change of stock prices. Now-

adays, there are two main tick size systems used in stock markets

around the world. The first is the uniform tick size system, which is

operated in many stock exchanges, such as the New York Stock

Exchange (NYSE), Nasdaq, Hong Kong Stock Exchange, and Shanghai

Stock Exchange. Under the uniform tick size system, tick size is the

same for all stocks in the market. The second system is the stepwise

tick sizesystem. Forinstance, the TorontoStock Exchange(TSX) and

Singapore Stock Exchange (SGX) use a price stepwise tick size system,

in which tick size rises with increasing stock prices.

Proponents for smaller tick size believe this is an effective method

to narrow bid–ask spread, which can further encourage the price

competition in the market and decrease trading cost (Harris, 1997).

The US Securities and Exchange Commission (SEC), which held the

similar viewpoint, mandated US exchanges adopting penny tick size

for quoting and trading. Consequently, the NYSE and Nasdaq

decreased tick size from $1/8 to $1/16 in 1997 and again from $1/16

to $0.01 in 2001. The American Stock Exchange (AMEX) gradually

decreased tick size from $1/8 to $1/16 for all stocks over a 6 year

period (1992 to 1997) and reduced tick size further from $1/16 to

$0.01 in 2001. Reduction in tick size has also appeared in the price

stepwise systemmarkets,suchas intheTSX andSGX.

However, there are controversial arguments by some researchers

claiming that larger tick size still has a positive impact on market

liquidity in certain circumstances (Weild, Kim, & Newport, 2012). A

number of studies pointed out that smaller tick size might reduce the

profits for liquidity suppliers and further reduce the liquidity provision

in the limit order book (Angel, 1997; Harris, 1997). Also, some

researchers have found that the optimal tick size should be deter-

mined by the trading environment, such as firm size and trade volume

(Angel, 1997; O'Hara, Saar, & Zhong, 2019). Therefore, a unique tick

size may not be suitable for all stocks (O'Hara et al., 2019; Verousis,

Perotti, & Sermpinis, 2018). Accordingly, some stock markets impose

larger ticksizeforcertainstocks.Forexample,in2000,the Tokyo

Stock Exchange (TSE) raised tick size from ¥10,000 to ¥50,000 for

stocks with prices between ¥20 million and ¥30 million, and raised

tick size from ¥10,000 to ¥100,000 for stocks with prices above

¥30 million. The SEC implemented a three-phase pilot programme to

increasing tick size from $0.01 to $0.05 for approximately 1,200 small

capitalization stocks in 2016. In addition, based on the stepwise tick

size system, some stock markets attempted to determine the tick size

by using more variables besides price. For instance, the stepwise tick

size adopted in the London Stock Exchange (LSE) is not purely based

on price, but is also based on the daily number of transactions,

whereby stocks with a higher daily number of transactions have a

smaller tick size. In Asia, theTSE adopted a smaller magnitude of price

Received: 12 September 2019Revised: 15 March 2020Accepted: 5 May 2020

DOI: 10.1002/isaf.1474

Intell Sys Acc Fin Mgmt. 2020;27:125–141.wileyonlinelibrary.com/journal/isaf© 2020 John Wiley & Sons, Ltd.125

stepwise tick size for TOPIX100

1

constituent issues in 2014. As the

SEC stated, the three-phase pilot is used to ‘assess whether wider tick

sizes enhance the market quality of these stocks for the benefit of

issuers and investors—such as less volatility and increased liquidity’

(SEC, 2016), which indicates that some stock markets might have real-

ized the effects of the tick size system on market quality, yet the

various reforms suggest that markets are still undergoing a period of

trial and error.

Similar to the reforms in stock markets, the empirical evidence

regarding the effects of tick size systems on market quality is also

complex. Previous research mainly focused on market liquidity,

especially bid–ask spread, market depth, and trade volume. Although

most studies have found that bid–ask spread increases and market

depth decreases with smaller tick size, there is no consistent result for

trade volume. Harris (1994) used cross-sectional regression to deter-

mine that, in the AMEX and NYSE, after adopting a smaller tick size,

bid–ask spread and market depth decreased, whereas trade volume

increased. On this basis, Harris (1997) further explained that a smaller

tick size indicates fewer costs for liquidity demanders, which means

that this benefits traders in the stock market. However, a smaller tick

size also indicates smaller benefits for liquidity suppliers. A small tick

size can attract liquidity demanders to the stock market and improve

market liquidity; however, when the tick size is extremely small, liquid-

ity suppliers have less enthusiasm to supply liquidity to the market.

Therefore, Harris (1997) concluded that there is an optimal non-zero

tick size in stock markets. Goldstein and Kavajecz (2000) sought to

test the relationship between tick size and liquidity provision based

on data from the NYSE. They found that a smaller tick size would

increase or maintain benefits for small investors yet damage the bene-

fits of traders who submit larger orders in infrequently traded stocks,

especially for low-priced stocks. Based on these findings, they

suggested that smaller tick sizes be set for frequently traded stocks

and low-priced stock (we refer to this as ‘combination stepwise’for

the rest of this paper). However, to the best of our knowledge, no

study has empirically investigated the effect of this combination

stepwise system on stock markets.

Previous empirical studies on tick size mainly employed two types

of event studies. The first ones investigated events of tick size reform

in stock markets. Researchers compared market quality variables in

the pre-reform period with those in the post-reform period (e.g. Ahn,

Cai, Chan, & Hamao, 2007; Ahn, Cao, & Choe, 1998; Ahn, Charles, &

Hyuk, 1996; Bollen & Whaley, 1998; Crack, 1994; Goldstein &

Kavajecz, 2000; McInish & Lau, 1995; Niemeyer & Sandas, 1994;

Porter & Weaver, 1997; Ronen & Weaver, 1998). The second method

compared stocks' statistical properties when their prices moved across

bands in a price stepwise market (e.g. Bessembinder, 2000; Chan &

Hwang, 2001; Harris, 1996). The empirical studies that used actual

data from financial markets suffered from several limitations. First,

event studies can only compare two tick sizes or two tick size systems

at a time, which means it is difficult to find the optimal tick size

system among various tick size systems that exist in the market or

which are still at the theoretical stage. Second, market quality may be

influenced by exogenous factors, such as the macroeconomics, which

might compromise the results of empirical studies. Third, some tick

size systems (such as the combination system) that have been

suggested in previous literature are currently not used in practice;

those systems lack empirical results. In this paper, we employ an artifi-

cial stock market (ASM) to investigate the influence of tick size on

market quality to overcome the limitations of empirical studies. First,

an ASM can effectively control the experimental environment and

ensure that tick size is the only changing variable in different experi-

ments. Second, an ASM allows us to build various tick size systems,

which further helps us to investigate the effect of those systems,

especially those that have been suggested in the literature but not

adopted in actual stock markets.

Nowadays, the agent-based model is a prevalent approach to

investigate research questions in financial markets, especially for

those questions that cannot be addressed by empirical methodolo-

gies (e.g. Phelps & Ng, 2014; Jaffé, 2015; Veryzhenko, Arena,

Harb, & Oriol, 2017; Bajo, Mathieu, & Escalona, 2017). As an impor-

tant part of the agent-based model, the ASM has been widely used

to study tick size policy in previous studies (e.g. Darley and

Outkin, 2007; Mizuta, 2019), even though their research questions

are quite different from this study. Based on the Nasdaq market

simulation, Darley and Outkin (2007) found tick size reduction has a

negative impact on the price discovery process and could increase

trade volume. However, as discussed by Mizuta (2019), there are

too many parameters in the Darley and Outkin model, which does

not allow them to isolate the direct effect of tick size from other

factors. To address this issue, Mizuta (2019) built an ASM to

reinvestigate the tick size policy by controlling the tick size as the

unique variable in the market. He found low liquidity when the tick

size is larger than volatility. We expand this line of studies by pro-

posing four types of tick size systems: uniform tick size, price step-

wise tick size, volume stepwise tick size, and combination stepwise;

and we examine the impact of these on market qualities. We find

that, first, although a smaller tick size can generally improve market

quality, an extremely small tick size can hinder market quality;

second, among the four systems, the best market quality is

observed in the combination stepwise tick size system.

Our study provides two contributions. First, we investigate sev-

eral combinations of stepwise tick size systems that have theoretical

foundations yet have not yet been applied in actual stock markets.

The results verify the effectiveness of the tiered tick size system

proposed in Goldstein and Kavajecz (2000), which is a combination

stepwise system based on both trading activity and price level.

Second, we compare market quality under the uniform tick size sys-

tem and three stepwise tick size systems. To the best of our knowl-

edge, this is the first study that has undertaken such comparisons.

The results offer an intuitive perspective on the performance of dif-

ferent tick size systems and make it possible to determine the best

tick size system. Overall, our studies fill theoretical gaps and provide

policy implications for policymakers.

1

TheTOPIX100consistsof stocksinthe TOPIXCore 30and TOPIXLarge 70.TheTOPIX

Core 30 is the 30 most liquid and highly market-capitalized stocks, and theTOPIX Large 70 is

the 70 most liquid and highly market-capitalized stocks after the Core 30.

126 YANG ET AL.