The Impact of Tick Size on the Quality of a Pure Order-Driven Market: Evidence from the Stock Exchange of Hong Kong

Transcription

1 The Impact of Tick Size on the Quality of a Pure Order-Driven Market: Evidence from the Stock Exchange of Hong Kong K. C. Chan Chuan-Yang Hwang Department of Finance Hong Kong University of Science & Technology Clearwater Bay, Hong Kong Fax: (852) Phone: (852) October, 2001 We are grateful to the able research assistance provided by Gary Wong. We thank Roger Huang, Chu Zhang for useful discussion, and comments from participants in the research seminar at HKUST. Chan s address is kcchan@uxmail.ust.hk, and Hwang s is cyhwang@uxmail.ust.hk

2 The Impact of Tick Size on the Quality of a Pure Order-Driven Market: Evidence from the Stock Exchange of Hong Kong Abstract Most previous studies rely on the event-study technique to investigate the impact of tick size change on market quality. We take an alternative approach, by comparing the market quality of a set of stocks whose prices fall within two tight regions around the threshold prices across which tick size changes. We choose the Stock Exchange of Hong Kong for this study because of its three desirable features: (1) it is a pure-order driven market which allows us to contrast with results on the NYSE ; (2) it offers a wide range of tick sizes and threshold prices which allows us to gauge the differential impact on market quality of different degrees of trading cost savings due to the tick size reduction; (3) it displays limit orders beyond the inside quote which is essential for drawing a correct inference regarding the impact of tick size on market depth. In contrast to previous studies, we find that the market quality, defined in terms of spread and market depth, increases after a reduction in tick size. Furthermore, the volume increases with the reduction of tick size as well. The biggest improvement in the market quality is found in smaller stocks, which see more economically significant changes in tick size than larger stocks. 2

3 1. INTRODUCTION All markets have a minimum price increment (tick size) by which prices of assets are allowed to change. Recent years see many exchanges adopting smaller tick sizes in an effort to reduce transaction costs and attract trading volumes. The United States markets, which traditionally use ticks denominated in eighths or sixteenths, have also joined this move. Based on a mandate by the United Sates Congress (the Common Cents Stock Pricing Act of 1997), the Securities and Exchange Commission (SEC) requires that all United States exchanges begin to quote security prices in dollars and cents by June 30, On March 6, 2000, the NASD announced that the Nasdaq stock market would not have sufficient capacity to meet the target days for implementation, hence the June 30, 2000 deadline had been postponed to April 9, The decimalization is likely to be inevitable since SEC believes that decimal pricing could benefit investors by enhancing investor comprehension, facilitating globalization of U.S. markets, and potentially reducing transaction costs. 1 SEC's belief reflects the outcome of a debate over the optimal tick size among regulators, practitioners and academics. Although the actual changes taking place in many exchanges suggest that the proponents for tick size reduction seems to be winning the support, the debate over the merits for tick size reduction is by no means settled. At issue in the regulatory debate is whether a tick size reduction, say from the relatively large ones seen in the United States to decimal pricing, can improve market quality. Supporters argue that a lower tick size would promote competition among liquidity providers and reduce transaction costs, which will cause both transaction volume and market liquidity to increase. Others, such as Grossman and Miller (1988) and Harris (1997) caution that while a reduced spread may benefit liquidity demanders, it may lower the profitability of supplying liquidity. The tick size also offers protection to limit order traders and lowering it may reduce the supply of liquidity from them. Investors who place limit orders risk being front-run by other investors who step in front of the queue by offering price improvement on existing limit orders. A large tick size makes it costly to front-run existing limit orders. A lower tick size increases the possibilities of front- 1 See SEC's order dated January 28, 2000 which directs the exchanges and NASD to submit a decimalization implementation plan. 3

4 running, diminishes the profit to liquidity providers and therefore their incentives to provide market immediacy. Consequently, the market depth and volume would decline. The empirical model in Harris (1994) predicts that, if the tick size at NYSE and AMEX were to decrease from $1/8 to $1/16, the bid-ask spread would decrease, volume would increase, but the depth at the inside bid/ask quotes would decrease. The AMEX reduced the tick size from $1/8 to $1/16 for stocks priced between $1 and $5 on September 3, Ahn et al. (1996) find that after the tick size reduction, the bid-ask spread decreased, without however significant changes in market depth and volume. The Toronto Stock Exchange (TSE) changed from a mixed decimal and fractional pricing to pure decimal pricing. The tick size was reduced from 5 cents to 1 cent for stocks priced between $3 to $5, and from $1/8 to 5 cents for stocks priced above $5. Bacidore(1997), Ahn et al. (1998), Huson et al. (1997), and Porter and Weaver (1997) find that the bid-ask spread decreased, but volume stayed at the same level, and the depth at the quotes decreased. These results are generally consistent with the prediction of Harris (1994). Furthermore, the dramatic decrease in spread has prompted the authors to argue that the smaller tick size had at worst no effect and at best a liquidity improving effect on the Toronto Stock despite a decrease in quoted depth. Ronen and Weaver (1998) study a more recent event of tick size reduction by AMEX in May 1997, they report results consistent with earlier empirical work. While these studies show that the market depth has decreased after the tick size reduction, it may be argued that there is a shortcoming in their data sets as they can only measure the depth at the inside quotes. As the tick size is reduced, the orders at the inside quotes represent a truncation of the original order queue, and this could account for why market depth was found to decrease after a tick size reduction in these studies. A recent study, which is not subject to this shortcoming, is Goldstein and Kavajecz (2000). They look into the changes in the depth on the entire limit order book from before to after the July 1977 tick size reduction on the NYSE. They find not only that the quoted spreads and the quoted depth decline after the change, but the depth throughout the limit order book declines as well. Like that study, this paper also looks at depth over the entire limit order book. But an important difference between the Goldstein and Kavajecz's study and ours is the difference in the market structure setting in the two studies. Goldstein and Kavajecz study the NYSE, where liquidity is provided by the specialist, limit order traders and floor traders. The strategic behaviors and competition between the three affect the supply of depth. In contrast, we study a pure limit order 4

5 market, where there are no specialists, dealers or market makers. It is important, in our view, to study how the tick size change would affect the market depth in a pure limit order setting, in order to isolate the effect of the strategic behavior in the NYSE-like market. The difference in our results versus the Goldstein and Kavajecz s, would suggest that the market microstructure does matter, and it highlights the importance of the adverse selection problem faced by liquidity providers due to the presence of specialists as modeled by Rock (1996) and Seppi (1997). All previously mentioned studies are event studies that try to measure any changes in market quality before and after a tick size reduction. Because tick size reduction is a rare event, the sample in most of this kind of studies consists of a single event. During this event period, market factors other than the tick size change may affect volume and depth, and there are not enough independent events to wash away these confounding factors. There is however a potentially powerful test of the tick-size impact on market quality which is suggested by Harris (1994) that is free of such problems. It is a transition study which studies stocks experiencing large changes in tick size as they cross from one price range to another price range to see if market quality changes with transition from one tick size to another. In a market with a fine schedule of tick size, such a test can be potentially powerful as it can be viewed to contain a large sample of independent tick size changes. Bessembinder (2000) adopts this approach to study the change in execution cost and liquidity for NASDAQ-listed stocks whose tick size changed as their share prices passed through $10 during He reports that there is no evidence of a damaging reduction in liquidity with the smaller tick size. Unfortunately, he focuses mainly on bid-ask spread and omits the analysis of the depth, perhaps due to not having access to the whole limit order book data. In this paper, we turn to Hong Kong market for conduct this transition study (with some modification for reasons to be explained in the methodology section), because Stock Exchange of Hong Kong (SEHK) is a pure-order driven market that allows us to contrast with Goldstein and Kavajecz's (2000) result. It is also because SEHK reports limit order book data up to four queues beyond the best quote which is essential to draw a correct inference regarding the impact of tick size change on market depth. Moreover, unlike the single transition point (threshold price) of tick size change as in Bessembinder's (2000) study on NASDAQ, SEHK offers a wide range of tick sizes and threshold prices which allows us to gauge the differential impact on market quality of different degree of trading cost savings due to tick size reduction. 5

6 SEHK employs a sliding scale of minimum tick size. The tick size currently ranges from (in Hong Kong dollars) $0.001 for stocks priced below $0.25, to $0.50 for those above $200. A change in the tick size schedule in 1994 suggests that tick size changes could be a controversial subject. In early 1994, the SEHK proposed to reduce the tick size by half, which immediately ran into opposition from the brokerage industry. The SEHK compromised and agreed to a four-month evaluation program, in which beginning on June 1, 1994 tick sizes were reduced across the board by 50%. Volume dropped in the evaluation period, and the SEHK was forced to revert to the original tick size schedule for the stocks trading below $10. This incident shows the pitfalls of relying on an event study to examine the impact of tick size change. Tick size changes are rare (one in this case) so it is always hard to rule out other factors causing the volume drop. Furthermore, in the case of Hong Kong, the drop in volume could be contaminated by the gaming behavior of the brokerage industry. There were reports in the popular press that brokers purposely cut back trading among themselves to affect the total volume during the evaluation period. In our study, we compare the difference in market quality for stocks priced around the thresholds on the tick size schedule. Stocks that cross thresholds experience large relative changes in tick size. For example, the tick size is $0.025 for stocks below $5 and is $0.050 for stocks above $5. The tick size doubles for virtually identical prices. The large number of cases around the thresholds offer a sizable data set of significant tick size changes that could allow for a powerful test. SEHK reports limit orders up to four queues beyond the inside quote. Using these limit order data we reconstruct the comparable measures of depth from the both sides of the price thresholds. These provide more accurate measures of market depth than the orders at the inside quote used in previous empirical studies. In contrast to previous studies, we conclude that a reduction in the tick size does improve market quality. The effect is especially strong for stocks priced below $5, where the tick size amounts to more than 0.5% of the stock price. The spreads of these stocks decrease, and both market depth and volume increase from the high tick-size region to the low tick-size region. For stocks where the tick size is smaller than 0.5% of the stock price, the improvement in market quality is not as strong. Market depth increases for these stocks, but with no increase in trading volume. Our finding that market depth increases with a tick size reduction is in marked contrast from previous studies. We attribute this in part to differences in market depth 6

7 measures used. Previous studies, except most notably Goldstein and Kavajecz (2000), measure depth at the inside quotes, for both before and after the tick reduction, while we make use of the full range of limit orders. Another major difference is the event study nature of these earlier studies and the cross-sectional nature of ours. However, we believe the difference in the market structure between the NYSE and the Hong Kong Stock Exchange, which is the main interest and motivation for this study, is responsible for the difference in results. The Hong Kong market is a pure limit order market, while the NYSE is a hybrid market of a monopoly specialist and public limit orders. The strategic behavior of the specialist and the adverse selection problem faced by liquidity providers who places limit orders in the NYSE, as modeled in Rock (1990) and Seppi (1997) are very important in explaining the drop in depth on the limit order book that is not seen in Hong Kong. The remainder of this article is organized as follows. Section 2 discusses effects of the tick size change on the market quality. Section 3 describes the trading structure at Hong Kong Stock Exchange. Section 4 contains the discussion of methodology and the data used in this paper. Section 5 presents and interprets the results. Section 6 concludes the paper. 2. Issues For and Against Tick Size Reduction When considering what should be the minimum increment of price variation, it is well recognized that it should be a function of valuation differences among traders. If one trader thinks a stock is worth $10.0, and another thinks it is worth $10.2, trade will not take place if the tick size is $0.50. However, if the tick size is too small, say $0.01 in the example, there could be rounds of bargaining between traders which increase the execution time and trading costs. The optimal tick size is a balance between being small enough that allows trading to take place and large enough to discourage endless rounds of negotiation. It is intuitive thus to think the tick size should be related to the level of the price and the volatility. Harris (1997) contains an excellent survey of the arguments for and against decimalization, or a reduction in tick size. Supporters for the tick size reduction argue that it can lead to more competition between traders and lead to smaller bid-ask spreads. A trader who wants to compete for orders must make quote improvement in the increments of a tick size, thus large tick size prevents this competition. Reduction in tick 7

8 size will encourage more traders to offer competitive quotes, resulting in a tighter spread between the best bid and ask offers which were previously constrained by the larger tick size. However, as Harris (1994) points out, while this is good for the liquidity demanders, it reduces the profitability of the liquidity suppliers, and the market liquidity will decline as a result. The total impact of the smaller bid ask spread and lower market liquidity may affect traders differently. Smaller trades may benefit because of the reduction of the bidask spread, while larger trades may suffer because of the decline in market depth. Harris (1994), Seppi (1997) and others point out that the magnitude of the tick size offers a protection to existing limit orders, which is a source of liquidity in the market. In a market where time priority is observed, a trader who wants to step in front of existing limit orders must improve on the price by at least one tick. Traders who have good information of order flows can use their information to front-run less informed traders who have posted limit orders. For example, if a trader believes that a stock s price will rise, he or she can offer a slight improvement on the current best bid and get the shares ahead of the existing buy order. If the price indeed rises, the trade will be profitable. If the price does not go up, the trader can in turn sell it to the existing buy order. A larger tick size offers protection to limit orders against this front-running strategy. If the tick size is reduced, liquidity suppliers who post limit orders will seek protection from front running by quoting a smaller number of shares, which may cause a decrease in the market depth. For the market as a whole, if the cumulative depth decreases as a result of a tick size reduction, the market may be less liquid even if the bidask spread narrows. There is additional evidence on how tick size may affect market quality from the stock splits literature. The common practice of stock splits may indicate a desire on the part of listed companies to choose a relative tick size. In the United States market where the tick size is usually 1/8, the relative tick size increases after a stock split. Angel (1997) provides a model that argues that splits are intended to move the relative tick size to an optimal level. A number of studies, including Arnold and Lipson (1997) and Schultz (1998), study the effects of stock splits on trading costs and market quality. Schultz (1998) finds that trading costs increase after splits and suggest that this is consistent with splits acting as an incentive to brokers to promote stocks. However, he does not find evidence that the larger tick size leads to larger market depth. 8

9 3. Description of the Hong Kong Stock Exchange As of 1997, 638 companies are listed on the Stock Exchange of Hong Kong (SEHK) with a total capitalization of US$410.6 billion, which is about five percent of the NYSE's capitalization and was the 8th largest in the world. The annual trading volume at SEHK is US$485.7 billion, greater than that of the Toronto Stock Exchange and is about one-tenth of that at NYSE. SEHK employs a sliding scale of tick size, in which the tick size varies with the stock price. As presented in Table 1, the tick size ranges from $0.001 for stocks trading below $0.25 to $0.50 for those trading above $100. In terms of percentage of the price, the largest tick size (2%) occurs for the stocks barely above $0.25, and the smallest tick size (0.17%) occurs for the stocks slightly below $30. There are no designated market makers or specialists at SEHK. Investors place their orders with brokers who in turn enter the orders into the Automatic Order Matching and Execution System (AMS). AMS is completely order driven, and the orders are executed on the basis of strict price/time priority. AMS displays quotations with the aggregate order size of all orders represented in any one of the five queues. This facility enables brokers and investors alike to determine the actual depth of the market through the displayed price queues. The first seller queue represent the quotation at the best ask, while the next four queues represent the quotation which are one to four tick size higher than the best ask. Similarly the first buyer queue reflects the quotation at the best bid, while the other four queues each represent the quotation at the price one tick size below the previous queue. There are several direct costs of transaction on the SEHK, including a fixed commission of 0.25% charged by brokers, and a stamp duty of 0.125% and a transaction levy of 0.01% charged by the Hong Kong government. All these costs have to be paid by every trader for both sides of the trade. As a result, it is very costly to act as market makers in the Hong Kong market. 4. DATA AND METHODOLOGY 4.1 The data The intra-daily data used in this paper are from two separate files published by the Stock Exchange of Hong Kong: the Trading Record file and the Bid and Ask Record file. The Trading Record file includes all transaction price and volume records with a time 9

10 stamp to the nearest second. The Bid and Ask Record file records the time, bid and ask information for five buyer queues and seller queues at 30 second intervals. The buyer queues information includes the number of shares, and number of orders waiting to be executed at the best bid and at each of the four consecutive lower ticks. The seller queue information includes the number of shares, and number of orders waiting to be executed at the best ask and at each of the four consecutive higher ticks. In this paper, we use the data in a period from May 1996 till December Empirical Proxies for Market Quality At the heart of the debate of whether tick size should be changed is whether the change will affect market quality. Existing studies on this subject generally focuses on three proxies of market quality: bid-ask spread, market depth and trading volume. Bid-Ask spread A lower bid-ask spread implies a lower transaction cost for traders. Holding other factors constant, a lower bid-ask spread indicates a better market quality. A tick size reduction could lower the bid ask spread if the original tick size is a binding constraint on the posted spread. Since the posted spread cannot be smaller than the tick size, the observed spread may be larger than the amount that would be freely determined by the market. A reduction in tick size in this case can result in a lower spread. On the other hand, if the current tick size is not binding (i.e. the current quoted spread is already greater than one tick,) the reduction is tick size would have no impact on the bid-ask spread. Market depth Market depth is measured as the number of shares or number of orders waiting to be executed at different prices as in the limit order book. In a deep market, a market order has a small price impact as it will be absorbed by a large pool of limit orders. While the data available allow us to construct a picture of complete limit order depth, we concentrate on the depth close to the inside quotes, as this is the depth that matters the most. As we have seen, a tick size reduction can affect the incentives for the supply of market depth. The limit order suppliers, who are providing liquidity to the market, risk being taken advantage by front runners. A smaller tick size increases the risk of front 10

11 running, and traders may become more reluctant to submit limit orders, or if they submit, they will not show their full demand. As a result there would be a reduction of limit orders and a decrease in the market depth. Furthermore, if a reduction of tick size also leads to a reduction in bid-ask spread, the compensation to the market makers would also decrease. They will tend to quote a smaller quantity in their limit order books to protect themselves against trading with informed traders. This will lead to a decrease in market depth. On the other hand, if the tick size reduction leads to a lower trading cost and increased participation in the market, and if this effect dominates other negative effects mentioned previously, the depth may actually increase. This prediction may be valid for a market where the main liquidity providers are not market makers, such as in the Hong Kong Stock Exchange. Volume Looking at changes in trading volume between two tick size regions can help corroborate the findings based on the spread and depth. This can clarify the questions that cannot be answered by looking at the quoted market depth alone. For example, when the tick size is reduced, we may observe a large reduction in the size of displayed quotes, because traders may be so concerned with front running that they seek to protect themselves by displaying smaller orders. But this may overstate the reduction in the market depth, as other traders who do not display their quotes may step in to augment the size at inside quotes. As the displayed depth is only a snapshot of the market, it does not tell us the total depth of the that will materialize during a period of time. Suppose the displayed depth measured in the 30-second interval shows a decrease from 50 shares to 40 shares after the ticks tick size reduction, but, say, volume increases from 10 shares to 30 shares during the same interval. While the market depth at any point in time may seem to drop, the higher level of volume indicates that the depth is greater than what the snap shot indicates. This simple example illustrates that market quality cannot be assessed with quoted depth alone. The need to take volume into consideration in judging the impact of tick size reduction on market depth change highlights the advantage of the non-event study and cross-sectional approach we have taken our approach in this paper. This is because volume is most susceptible to change in market conditions which are unrelated to the change of tick size. If we take the event study approach, and proceed to measure volume before and after a tick size change, we will have no way to know whether we can control 11

12 other factors that occur during the time period that affects volume. In the cross-sectional approach we take in our paper, we do not need to control for factors that may affect changes in volume over time. If the tick size reduction increases volume via lower trading costs, it follows that volume is likely to be affected in cases where trading costs are high in the first place. This suggests we should focus on the relative size of trading costs, i.e. trading costs as fraction of price, to test the trading cost explanation. In addition, the reduction of trading costs would be less significant in a market where market makers are the monopolistic liquidity provider. In a market, such as the Hong Kong Stock Exchange, where there are no market makers and where liquidity is provided competitively, a reduction in the tick size may have a less ambiguous effect on trading. 4.3 Methodology Since the tick size changes discretely, the maximal impact of tick size change on market quality would occur when a stock crosses a price threshold that effects the ticksize change. For example, when the price of a stock at SEHK rises slightly from $4.975 to $5, the tick size doubles. It would be natural to imagine a powerful test as suggested by Harris (1994), which is to compare the market quality of a sample of stocks that have risen or fallen through the threshold prices. However, such a test may yield possibly contaminated results. In a test like this, tick size increase is always conditioned on a rise in price and tick size reduction is always conditioned on a fall in price; since factors that lead to price changes may also affect measures of market quality, it would then be erroneous to conclude that any changes in market quality are due to tick size changes. Consequently, in this study we adopt an unconditional approach. We compare the market quality of all stocks whose prices fall within two sides equidistant from the threshold prices, regardless how they get there. There are eight threshold prices at SEHK that effect tick-size changes, as shown in the table above. In addition, to check the experimental design for our test, we also use the $10 and $20 levels as control, because the tick sizes around these two price levels remain at $0.05 in our sample period. If our methodology is sound, then the market quality for the stocks around these control levels should not be different. To test whether the tick size has any impact on market quality, we compare and test for a difference in the market quality (e.g. the bid-ask spread, depth and trading volume) of stocks whose prices fall within two comparison price regions with equal 12

13 dollar ranges around the threshold price. The regions are chosen tightly around the threshold prices and yet wide enough to yield a meaningful number of observations. When the tick size increases in multiples, each comparison price region is chosen to cover ten larger ticks. For cases where tick sizes increase by 2.5 times such as those around $2 and $50, the width of the comparison price region is chosen to be twenty larger ticks, as we cannot create a region of ten larger ticks with a multiple of smaller ticks. For each quote (trade) in the database, we record the bid-ask spread, the depth measures up to five queues (volume), and associate them with a particular large tick within which the price of this quote (trade) falls. From these records, we first generate the frequency distribution of bid-ask spread in term of number of tick size that we report in Table 2. Next we calculate the daily average of the market quality measures for each stock within each large tick; each of these averages is treated as an independent observation in the comparison tests. The measurements of bid-ask spread and trading volume are straightforward. The bid-ask spread is the difference between the inside bid and ask quotes. Trading volume is measured as the number of shares traded. A bit more explanation of the market depth measure is required. Ahn et al. (1996) study a 1994 event that AMEX changed the tick size from $1/8 to $1/16 for low price stocks. They find that market depth is not much affected with the change of tick size. On the other hand, both Ahn et al. (1998) and Bacidore (1997) study the impact of decimalization on market quality at Toronto Stock Exchange in 1996, and both find that the market depth become smaller after decimalization. The depth measure in all of these studies is the depth as the inside bid and ask quotes. However, a decrease in the depth at the inside quote does not necessarily indicate a decrease in market depth. A simple comparison of the depth at the inside quote under two different tick sizes is not correct. For example, suppose traders are willing to sell 200 shares at $20 and 200 shares at $19.95, but are forced to quote selling 400 shares at $20 because the $19.95 quote is infeasible. Now if tick size is reduced such that quoting at $19.95 becomes feasible, then the quote to sell 200 shares at $19.95 would become the inside quote. Comparing only the depth at the inside quote will lead one to conclude that market depth has decreased from 400 shares (at $20) to 200 shares (at $19.95) after the tick size reduction, when in fact the aggregate market depth has not changed shares at $19.5 and 200 shares at $20. Furthermore, depth is supposed to measure the number of shares available to absorb incoming orders without changing the price. The inside quote under a $0.05 tick size shows the depth to absorb incoming orders without changing the 13

14 price by $0.05, while the inside quote under a $0.1 tick shows the depth available to absorb an incoming order without affecting the price by $0.1. The reason that depth at the inside quotes is often used in the empirical literature even when different tick sizes are involved is due to lack of complete limit order book data. Using data from Singapore, Lau and McInish (1995) study a 1994 event that Singapore Stock Exchange lowered the tick size from $0.50 to $0.10 for the stocks trading above $25. They find that the sum of all the quoted sizes is reduced after the tick size is reduced. 2 However, summing of all the quote sizes may not be the right way to measure the depth either, because the depth at the quotes closest to the prevailing market prices should be more relevant because those quotes are the most likely to be filled. In this study, we consider two market depth measures. We define an aggregate depth measure which covers the same price range from both side of the tick size threshold. This is our primary measure of depth. We also compute the usual depth at the inside quotes on both sides of the threshold for comparison. Our aggregate depth measure is defined as follows. On the side with a larger tick size, we continue to measure depth at the best limit order price. But, on the other side with a smaller tick size, we collect limit orders form the inside quotes down to the next queues, so that we measure the market depth from the price range that is equal to larger tick size. This is defined as aggregate depth. It equals the number of shares needed to trade to move the dollar price by the same amount as the larger tick size. We also measure depth in terms of number of orders sitting in the limit order queue. To illustrate, suppose we use n1, n5 to denote the market depth, either as the numbers of shares or as number of orders waiting to be executed, at current best ask (bid) and at other four consecutive ticks higher (lower) ask prices. For the threshold price across which tick sizes double, such as the $30 level, the aggregate depth measure for the stock above $30 will be measured as n1 equal to the depth at inside quote in this case. The aggregate depth measure for stocks below $30 will be measured as n1+n2. For the threshold price where tick size quintuples such as the one at $0.25, the aggregate depth for stocks above $0.25 will be measured as n1, while it will be measured as n1+n2+n3+n4+n5 for stocks trading below $0.25. We also have cases where tick size become 2.5 times greater when stocks pass through the threshold prices such as the ones at $2 and $50. In these cases, the 2 Unfortunately, their results may be hampered by the small size and short period of the data (4 firms and 4 days before and 5 days after the event.) 14

15 aggregate depth will be measured as n1 for the stocks above the threshold and as 1/2(n1+n2+n3)+1/2(n1+n2) for the stocks below, half-way between two and three smaller ticks. The depth measure described above shows the depth at the inside quotes on the large-tick size and the equivalent depth on the small-tick size. We also go deeper into the limit order book and measure depth at the second larger-tick from the inside quote and the equivalent depth from the small-tick side. We do not go deeper into the limit order book as the orders further away from the inside quotes may be more subject to cancellations and do not reliably describe depth. 5. Empirical Results 5.1 Bid-ask spread Table 2 shows the frequency distribution of the bid ask spread for stocks whose prices fall within the comparison regions around the threshold prices. For example, for the $5 threshold price, we tabulate the occurrences that any stock with the best ask prices between $ 4.8 and $5.0 which has a dollar bid ask spread of $0.001 (1 tick), $0.002 (2 ticks) up to $0.01 (10 ticks). Similarly we keep track of occurrences that any stocks with the best bid prices between $5.0 and $5.2 having a dollar spread of $0.005 (1 tick), $0.010 (2 ticks) up to $0.05 (10 ticks). Same procedure is repeated for other threshold prices. The frequency distribution may allow us to see whether the current tick sizes are binding on the bid ask spread or not, which can shed some light on the question of whether the tick sizes at the SEHK are too large or too small. We observe that the onetick spread occurs with high frequency, which would suggest that traders in the Hong Kong market make use the full range of prices in submitting limit orders. 3 The last two columns are the frequency-weighted averages of the dollar spread and the percentage spread. One clear finding is that the spreads decrease dramatically when the tick size is reduced. The magnitude of the spread reduction depends on the threshold price as well as on the magnitude of the tick size reduction. Among the stocks whose tick sizes are cut in half, the average spread reduction ranges from 32% (1-0.28/0.41) for the $30 threshold to 48% (1-0.26/0.50) for the $200 threshold. For the whole sample, the largest spread reduction, which is 66% (1-0.94/2.79), occurs for stocks 3 In other words, the practice of avoiding, say, odd-eighths, as Christie and Schultz (1994) find for the NASDAQ market does not occur in Hong Kong. 15

16 around the $0.25 threshold where tick size is reduced from $0.005 to $ The large reduction occurs even though more than 50% of the stocks would be quoted with a spread more than one tick when the tick size is $0.001, compared to 22.5% of such cases when the tick size is $ The frequency distribution of the spread in Table 2 also suggests that the tick size of $0.25 for stocks between $50 and $100 and the tick size of $0.50 for stocks between $100 and $200 may be too high. This inference is drawn from the observation that when tick sizes are reduced by half, the smaller tick is still binding for a majority of stocks. Between 91.18% to 96.31% of the stocks in the $50 to $100 range are quoted with a onetick spread. The corresponding figures for the $100 to $200 range are between 97.82% to 99.12%. We do not have a theory or model to guide us on the optimal frequency of the one-tick spread, but the empirical data shows a preponderance of one-tick spread in these price ranges when compared with the lower-price ranges. There seems to be case for a reduction of tick size for these large- price stocks. 5.2 Market depth The results of the market depth are contained in Table 3 and Table 4. In these tables, only the results for the depth at ask quotes are presented, since the results for those at the bid quotes are very similar. These tables present the daily average of depth measures from comparison regions involving different tick sizes. For each day in the sample period, and for each large price tick (and equivalent range of small ticks), we collect stocks whose prices or best quotes occur at least once at that tick. The average depth (however defined) of that stock on the day is taken as an observation in the tables. The tests on the differences on means are conducted over these observations. Since a comparison region comprises a number of ticks, a stock can enter repeatedly into the sample on any day. This, however, should not introduce a bias to the test because same methodology is used in constructing the samples from both sides of the price thresholds. Table 3 presents the daily averages of depth at the inside quote under different tick sizes. The picture is similar whether we measure depth in terms of number of shares or number of orders. With the exception of the $100 threshold price, we can see a significant decrease in depth at inside quote on the side of smaller tick around all the threshold prices. This result indicates when the tick size is reduced, the depth at the inside 16

17 quote would also decreases which is consistent the finding in Ahn et al. (1997) and Bacidore (1997). The results with the aggregate depth measures are presented in Table 4 and they offer a very different picture. The aggregate depth on the side of a small tick is larger than the depth at the inside quote on the side of the large tick at all threshold prices except at $200 threshold where only a few observations exists. The differences are very significant, with t statistics ranging from 2.07 at $50.00 threshold to at $2.00 threshold. We also compare the aggregate depth in the limit order book further away from the best quotes. On the side of the large tick size, this is the limit order depth quoted at the second order queue. On the side of the small tick size, it is the aggregate depth defined over the corresponding price range. For our data, this comparison is only possible at threshold prices across which tick size doubles. In other words, we compare n2, the depth at the second queue, of the large tick and the n3+n4, sum of the third and fourth queue, for the smaller tick. Again ignoring the results at $200 threshold due to its small number of observations, we find that the depth away from the best quote at the side of small ticks are in general no different if not larger than thatat the side of larger ticks. In summary, we find that the aggregate market depth increases when the tick size is reduced. This implies that a smaller transaction cost due to the reduction of tick size may encourage more traders to submit limit orders and this effect more than offsets the decline in market depth resulting from the heightened concern of being quote matched when the tick size becomes smaller. It is comforting to see in both tables 3 and 4 that our methodology produces no change of market depth at the control threshold ($10 and $20) across which tick size does not change. This suggest that our methodology is sound and the depth change we observe at other thresholds are indeed the results of tick size changes. Our results are different from those obtained by Goldstein and Kavajecz (2000), who find a decrease in limit order depth in the NYSE following its tick reduction. A possible explanation for the different conclusions drawn by the two studies may be due to fact that their study is an event study, while ours is a cross-sectional transition study. In an event study surrounding a significant change such as a tick reduction, it is possible that in the post-event period the market was still learning to adapt to the new structure, or that the time period is affected by other market factors. But there is another and what we believe is even a likelier explanation. In the NYSE, as modeled by Rock (1990) and Seppi (1997), liquidity is provided by a specialist with market power and competitive limit orders. The limit order liquidity providers face an adverse selection problem due to 17

18 the advantages enjoyed by specialists. This is because specialist has access to market order information and can trade with very low costs, which is similar to having a valuable trading option against the limit order traders. The larger tick size makes it more costly to the specialist to trade ahead of the limit orders. When the tick size is reduced, the trading option given to the specialist becomes more valuable. In other words, when the tick size is reduced, the adverse selection problem faced by the limit order liquidity providers becomes more severe, and they respond by decreasing their supply of liquidity. In contrast, Hong Kong has a pure limit order market, with no traders having the special market power or unique access to order flow information. The limit order traders demand for protection from front running in this market may not be as severe as that in the NYSE, and thus a tick size reduction does not cause a decline in the limit order depth. This sharp contrast between Goldstein and Kavajecz s (2000) result and ours suggest that the adverse selection problem modeled by Rock (1996) and Seppi (1997) are quite important and relevant. 5.3 Volume Table 5 presents the evidence of the impact of tick size change on trading volume. The samples are constructed in the same way as the depth measures in earlier tables. Table 5 shows that volume increases when the tick size is reduced at all threshold prices. However, the increase is statistically significant only for stocks trading below $10, where the original tick size represents a significant amount (more than 0.5%) of the share price. Consequently, a tick size reduction would save a significant amount of transaction cost and encourage more trading. In contrast, one tick represents less than 0.5% of the price for stocks above $10, a further reduction of the tick size would not make too much difference to the trading cost, thus the increase in trading volume is not as significant as those happening at smaller price stocks. This finding corroborates the results related to market depth, showing that the larger depth accompanying smaller tick sizes is translated into trading volume. Many previous studies have either found that volume decreased after a tick size reduction, or that there is no relation between the two. Our results provide consistent evidence that a tick size reduction results in an improvement of market quality. Our findings contribute to the debate for the decimalization at US equity markets. Since the current tick size US$1/8 seems economically significant for stocks trading below US$25 (more than 0.5% of the share price), the improvement in trading volume 18

19 would be most significant for these stocks. The impact on trading volume may be minimal for stocks trading above US$25 as the currently adopted US$1/8 tick size represents less than 0.5% of the stock prices. Furthermore, our results suggest that the SEHK was right to reduce the tick size for stocks above $10 after the 1994 evaluation program, and perhaps it should have also reduced the tick size for those below $10 as well. Our results suggest that a reduction in tick size based on the current schedule does not significantly affect volume for stocks priced at and above $10, indicating that the current tick size is about right as far as volume is concerned. But for smaller-price stocks, our results show that a tick size reduction from the current level increases trading volume, suggesting that the SEHK should have keep the valuation program intact by not reverting to the original tick size for the stocks below $10 after the program ended in October Conclusion In contrast to previous studies which uses the event study technique to study the impact of tick size change on market quality, we take a more powerful approach by examining the market quality of a large set of stocks that are subject to different tick sizes. The SEHK data offers three desirable features for the study of tick size: (1) it contains a limit order book of up to five queues, and (2) it is a pure-order driven market where there are no specialists or market makers, and (3) it provides a wide range of threshold prices and tick size, The first feature is important in correctly assessing the impact of tick size change on the market depth. Because of data limitation, previous studies with the exception of Goldstein and Kavajecz s (2000) can only compare the depth at the inside quote and conclude that the depth is reduced after the tick size being reduced. With the SEHK data, we show that the depth increase after the tick size is reduced which is different from Goldstein and Kavajecz s (2000). This sharp contrast along with the second desirable feature of the SEHK allow us to conclude that the adverse selection problem faced by the limit order liquidity providers as modeled by Rock (1996) and Seppi (1997) is very important. The third desirable feature of the SEHK data allows us to gauge the differential impact for different degree of tick size reduction. We find that when tick sizes become smaller, the trading volume increases but the increase is limited only to the stocks trading 19

20 below $5. The bid-ask spread decreases and market depth improves for almost all of the tick size and price ranges, with a slightly more impact for stocks trading below $5. The possible explanation for the observed pattern is that the current tick sizes for small stocks are generally large in economic terms, so a reduction of tick size would lower trading cost significantly and induce more trading volume. On the other hand, the current tick size of larger-price stocks are perhaps small enough now, so that a reduction does not yield much difference to the trading volume. If the Hong Kong experience can shed some light on the United States market, our findings suggest that after the decimalization in US markets, the trading volume would increase significantly only for stocks trading below US$25. 20

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