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Decimalization and market liquidity

Craig H. Furfine

On January 29, 2001, the New York Stock Exchange (NYSE) implemented decimalization. Beginning on that Monday, stocks began to be priced in dollars and cents, and price changes were allowed to be as small as 1 cent.1 Prior to this change, NYSE stocks were quoted in fractions of a dollar and traded in increments of 1/16, or 6.25 cents. Decimalization of stock markets is relevant for policymakers because it has the potential to affect market liquidity, and therefore the overall functioning of financial markets.

Advocates of the adoption of decimalization argue that the finer gradation of stock prices will benefit investors. This is because the pricing increment dictates the smallest possible bid?ask spread for a given stock. This spread represents the difference between the lowest price an investor can pay for a stock and the highest price an investor can receive for selling the same stock. Prior to decimalization, actively traded stocks often had a spread equal to the minimum price increment, or tick, of 6.25 cents. For instance, an investor might have faced a bid?ask spread of 50 1/2?50 9/16 for shares of stock in XYZ company on Friday, January 26, 2001. That is, abstracting from any transaction fees levied by brokers, an investor wanting to sell a round lot of 100 shares of XYZ could expect to receive $5,050 and an investor needing to buy 100 shares would have to pay $5,056.25. Following decimalization, however, the two investors might face a spread of 50.51?50.53. Thus, the seller of XYZ would receive an extra penny per share and the buyer of XYZ shares would save 3.25 cents per share.

However, decimalization may affect more than a stock's bid?ask spread. To understand this, consider the set of firms and individuals that stand ready to buy and sell the stock of XYZ company. For example, prior to decimalization, a dealer might have been willing to commit to buy 10,000 shares of XYZ company at 50 1/2 and to sell 10,000 shares at 50 9/16. In practice, these commitments may have been made by the dealer

placing a limit buy order for 10,000 at 50 1/2 and a limit sell order for 10,000 shares at 50 9/16. If these are the only outstanding orders for XYZ stock at these prices, then the stock will have a bid?ask spread of 1/16 and a so-called depth of 10,000 (at the bid price) by 10,000 (at the ask price) shares. With decimal pricing, the same dealer may have decided not to post limit orders of the same size at the new prices of 50.51?50.53. This is because the profitability of committing to be willing to both buy and sell a given stock, as measured by the bid?ask spread, has declined. Thus, the dealer might only be willing to offer depth of 1,000 by 1,000. From the perspective of a small investor, for example one wishing to trade only a few hundred shares, this reduction in depth at the bid?ask spread is not a concern. Depth at the best available prices will suffice. However, for large traders, for example those wishing to trade several thousand shares, quoted depth at the best-quoted prices may be insufficient to fill the desired order. For such trades, the effective transaction price lies somewhere outside the posted bid and ask.

In this article, I examine how various measures of stock market liquidity changed following decimalization. A stock's illiquidity measures the cost to a buyer or seller of transacting in shares beyond the true underlying value of the security. These costs arise from a lack of an infinite supply of shares that can be purchased and sold at the same price. That is, if investors could buy or sell any number of shares of XYZ stock at 50.52, then one would say that XYZ shares are perfectly liquid at that price. Bid?ask spreads and limited depth represent two departures from this situation and, thus, bid?ask spreads and depth are two measures of

Craig H. Furfine is an economic advisor at the Federal Reserve Bank of Chicago. The author would like to give special thanks to Bob Chakravorti and Helen Koshy for helpful comments.

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liquidity. Lower spreads and higher depth represent more liquidity. Higher spreads and lower depth signal less liquidity.

I document that decimalization did lead to smaller spreads and lower depth, and thus caused a theoretically ambiguous change to market liquidity. Thus, to empirically address whether and/or to what extent market liquidity was affected by decimalization, one must focus on a liquidity measure that is affected by both a finer pricing grid and lower depth. In this article, I examine the revision to a stock's price that follows a trade as a direct measure of a stock's liquidity. This is known as the price impact of a trade. By definition, perfect liquidity implies that a given trade should not affect the price.2 With imperfect liquidity, the size of the price revision following a trade is likely positively related to tick size, since any adjustment to prices must be at least as large as the minimum tick. Likewise, the price impact should be negatively related to market depth, since lower depth implies that a given (large) trade may have to travel through more prices in order to be filled.

In this study, I examine the stocks of 1,339 companies that began decimal trading on the NYSE on January 29, 2001. I document what previous studies have found regarding the relationship between tick size, bid?ask spreads, and depth. I then estimate the price impact of a trade, distinguishing trades undertaken before decimalization from those after and further distinguishing large trades from small trades. I find that for both large and small trades, decimalization typically led to an improvement in liquidity as measured by a decline in the price impact of a trade for actively traded stocks. For less actively traded stocks, decimalization led to improved liquidity more often than it led to reduced liquidity. However, the most common empirical finding for infrequently traded stocks was that there was not a statistically significant change in liquidity following decimalization.

Selective literature review

I mention only a few contributions to the extensive literature on the effects of reducing tick sizes on various measures of market performance, including liquidity. In Seppi's (1997) theoretical framework, reduction in tick sizes leads to a reduction in the willingness of both small and large traders to supply liquidity through limit orders (depth). However, because retail investors require less depth to conduct trading, optimal tick size depends positively on typical trade size. That is, institutions that typically trade in large amounts prefer large tick sizes, whereas small investors prefer small tick sizes.

Harris (1994), using data from a time when the minimum tick was 1/8, fits a regression model estimating

the frequency at which spreads are at the minimum. Using this relationship, Harris estimates that the impact of reducing the minimum tick size to 1/16 would be accompanied by both lower bid?ask spreads and lower quoted depth. His results are therefore also consistent with the notion that optimal tick size is related to the size of a trade. They indicate that small traders would almost certainly benefit from smaller tick sizes, but that large traders might be hurt if the depth of the market were to fall sufficiently.

Goldstein and Kavajecz (2000) analyze the NYSE's reduction in tick size from 1/8 to 1/16 and address the relationship between minimum tick size, bid?ask spreads, and market liquidity. What is unique about this study is that these authors not only look at the depth reported at the best bid and ask prices, they also collect data on liquidity available at some distance away from the best bid and ask prices. This complete collection of prices and available depth is called the limit order book. They find that not only did depth at the best bid and ask decline, but cumulative depth similarly declined throughout the limit order book following the NYSE's previous reduction in minimum tick size. They found such declines in depth as far as 50 cents from the midpoint of the bid?ask spread. Using implied average price of a trade of a given size derived from the limit order book, these authors find that large traders were not made better off by the smaller tick sizes and were made worse off for infrequently traded stocks.

More recent work has examined changes in market liquidity for NYSE-listed stocks since decimalization. Chakravarty et al. (2001) study a small set of stocks that began trading in decimals as part of an NYSE pilot program in 2000. These authors find that decimalization has led to significantly lower spreads and also lower quoted depth. Bacidore et al. (2001) also study stocks in the decimalization pilot. These authors focus on whether decimalization leads to significant changes in order submission strategies. They find that there is no noticeable change in the use of limit versus market orders, but the size of limit orders has fallen and the frequency of limit order cancellation has increased since decimalization. Smaller limit orders and higher cancellation rates explain how lower depth materialized.

Bessembinder (2003) studies a larger sample of NYSE and Nasdaq (National Association of Securities Dealers Automated Quotation) stocks and documents that following decimalization, bid?ask spreads fell noticeably, with the largest declines seen for the most actively traded stocks. Bessembinder also reports an increase in the frequency of price improvement on the NYSE following decimalization. Price improvement

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occurs when a trade is conducted at a price inside the bid?ask spread. Higher rates of price improvement are consistent with the

TABLE 1

Average trading activity of sample stocks

fact that decimalization makes it easier for traders to step in front of the current best

Category

Average time between trades

Number of stocks

bid or ask to take the other side of a mar-

1

5?10 minutes

191

ket order.

2

1 minute?4 minutes, 59 seconds

722

3

30?59 seconds

237

Data, sample selection, and

4

15?29 seconds

108

summary statistics

5

5?14 seconds

70

6

Less than 5 seconds

11

For this study, I extracted stock mar-

ket trade and quote data from the NYSE TAQ (Trades and Quotes) database, cover-

Source: New York Stock Exchange, 2001, Trades and Quotes (TAQ) database, January 16?February 16.

ing the 24 trading days beginning Tuesday,

January 16, 2001, and ending on February 16, 2001.3 Following Hasbrouck (1991), I also impose a minimum price requirement on each company's stock. I require each stock to be trading for at least $5, on average, during the five-week sample period. I similarly impose a maximum price of $200. Also following Hasbrouck (1991), I require a minimum level of trading activity. I limit my sample to stocks that traded, on average, at least every ten minutes over these five weeks. Finally, I eliminate those stocks that were part of the NYSE pilot program and, therefore, traded in decimals prior to January 29, 2001. My final sample consists of 1,339 stocks.

The data are then adjusted according to procedures common in the microstructure literature. Following Hasbrouck (1991), I keep only New York quotes and consider multiple trades on a regional exchange for the same stock at the same price and time to be one trade. Then, I sort the trade data (for each company and day) by time, with the prevailing quote at transaction t defined to be the last quote that was posted at least five seconds before the transaction (Lee and Ready, 1991).

I group the 1,339 stocks into six categories according to their average trade frequency, with Category 1 stocks being the least traded and Category 6 stocks being the most frequently traded. The number of stocks in each category is shown in table 1. I first calculate the narrowest bid?ask spread witnessed by each stock and for each day. I then average these minimums across stocks within the same trading category. These average minimum values are plotted in figure 1. As is apparent from figure 1, minimum tick size strongly influences the extent to which bid?ask spreads can narrow within a day. Every stock in the four most actively traded categories experienced a bid?ask spread equal to the minimum tick size at least once on every day of the

size, suggesting that nearly all of the 722 stocks in that category experience minimum tick-sized spreads during each day. Even for those stocks trading only every five to ten minutes, average minimum spreads hover around 6.5 cents when the minimum tick size was 6.25 and fall to around 2 cents after decimalization.

Figure 2 plots the mean spread within a day averaged across stocks in a given trading category. As expected, more frequently traded stocks have lower spreads. For stocks in all categories, decimalization has led to a decline in average bid?ask spreads. This decline in mean spreads is most pronounced for the more actively traded stocks. For example, mean bid? ask spreads for stocks in Category 1 averaged 13.6 cents, about a penny over two ticks, in the two weeks prior to decimalization. Following decimalization, the average mean spread of these stocks fell to 10.5 cents. For the most actively traded stocks, average mean spreads were 11.3 cents before decimalization and fell to 7.0 cents after.

The narrowing of bid?ask spreads following decimalization illustrated in figures 1 and 2 has been accompanied by a decline in average depth at the posted prices. Figure 3 reports the mean of the bid and ask depth posted throughout a day, averaged across stocks in each category. The post-decimalization decline in posted depth was significant, especially for the most actively traded stocks that had previously had a very large number of shares committed to trade at the posted spread. For the least actively traded stocks, posted depth fell by half, from just under 6,600 shares to 3,300 shares on average. The most actively traded stocks experienced depth declines of more than two-thirds, from an average of 18,700 shares to slightly more than 6,000 shares.

sample period. For stocks in Category 2, that is, those Price impact of trading

trading every one to five minutes, minimum spreads were always within 1/10 of a cent of the minimum tick

The statistics reported in the previous section confirm that decimalization has led to both a decline

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FIGURE 1

Average minimum daily spread

0.07

0.06

0.05

0.04

0.03

0.02

0.01

0 1/15/01

1/22/01

1/29/01

2/5/01

2/12/01

Category 1 (least actively traded) Category 2

Category 3 Category 4

Category 5 Category 6 (most actively traded)

Source: NYSE TAQ database from January 16?February 16, 2001.

FIGURE 2

Average mean daily spread

0.16

0.14

0.12

0.10

0.08

0.06

0.04

0.02

0 1/15/01

1/22/01

1/29/01

2/5/01

2/12/01

Category 1 (least actively traded) Category 2

Category 3 Category 4

Category 5 Category 6 (most actively traded)

Source: NYSE TAQ database from January 16?February 16, 2001.

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FIGURE 3

Average daily quoted depth (in number of round lots)

300

250

200 150

100

50

0 1/15/01

1/22/01

1/29/01

2/5/01

1/12/01

Category 1 (least actively traded) Category 2

Category 3 Category 4

Category 5 Category 6 (most actively traded)

Source; NYSE TAQ database from January 16?February 16, 2001.

in spreads and a decline in depth. Thus, an investor making a relatively small trade generally faces improved liquidity, since the trade can be executed at a narrower spread. For institutional investors making large trades, however, the lower depth may imply that a large trade must travel through several prices before being fulfilled, and thus decimalization may not necessarily have led to better execution prices. To try to combine the effects of spread and depth in one framework, I examine a liquidity measure called the price impact of a trade, which was first motivated and estimated by Hasbrouck (1991). This is a measure of how much the price of a stock changes following a given trade as estimated in an autoregression framework. While other measures of liquidity are conceivable, price impact has the advantage of being influenced by both smaller price increments and lower depth. In particular, decimalization may cause the price impact to decline since prices can adjust by smaller increments, but it may also cause the price impact to rise since more prices must be exhausted because depth at any given price is lower.

In the price impact framework, the dependent variable of interest is the trade-to-trade return on a given stock. I denote this return rt and define it formally as the change in the natural logarithm of the midquote of a given stock that follows the trade at time t.4 That is,

1)

rt

=

100

ln

bidt

+1

+ askt+1 2

-

ln

bidt

+ askt 2

.

The use of midquotes eliminates price changes

caused by the bid?ask bounce, that is, the alternating

arrival of buys and sells transacting at the ask and bid

price, respectively. Following Hasbrouck (1991), I de-

fine the variable x as an indicator of the direction of t

the trade occurring at time t. If the trade is initiated by

the buyer, the variable xt = 1. If the trade is initiated by the seller, then the variable xt = ?1. I assume trades at a transaction price greater than the midquote were

buyer-initiated and trades below the midquote were

seller-initiated. For trades at the midquote, xt is assigned to equal zero. Defining Dt as an indicator that equals 1 if trade t occurs during the first 30 minutes

of the trading day and dect as an indicator that equals 1 if trade t occurs during the decimal period after

January 29, 2001,5 I estimate the regression

5

[ ] 2) rt = Dt xt + i + i dect-i rt-i i =1 5 [ ] + i + i dect-i xt-i + t i=0

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4Q/2003, Economic Perspectives

for each stock in my sample.6 The price impact of a trade in this framework is equal to the sum of the i coefficients during the pre-decimalization period and equal to the sum of the i + i coefficients after decimalization. Because purchases should put upward pressure on prices, I expect that i should be positive for some or all of the trade lags i. This prediction follows from traditional microstructure theory. In Glosten and Milgrom (1985), for example, market makers set a positive bid?ask spread as compensation for trades made with counterparties with superior information. As a sequence of sell orders arrives, market makers lower bid prices, incorporating the probability that the order flow implies that better-informed investors believe the previous price was too high. The reverse occurs when a sequence of buy orders arrives. This type of dynamic quote adjustment leads to the prediction of a positive value of the i coefficients. The i coefficients may be either positive or negative depending on whether the stock has become less or more liquid (higher or lower price impact of a trade) since decimalization.

Table 2 summarizes the results from these 1,339 regressions. Each row of table 2 corresponds to stocks in different trade activity categories. The numbers reported in the first column represent the average value of the sum of the i coefficients across all stocks in the given category. These coefficients measure the price impact of a trade in the two weeks prior to decimalization. For instance, the first entry in the first column reports that the average price impact of a trade during this time is 9.2 basis points for stocks in the least actively traded category. Put another way, 11 trades in the same direction move an infrequently traded stock's price by 1 percent. As the numbers in the first column indicate, liquidity as measured by price impact

increases with trading activity, since trades of more actively traded stocks move prices less. For example, a trade of a stock of a very actively traded security moves the stock's price by just over 1 basis point. The numbers in the second and third columns summarize the statistical significance of the price impact results. The second and third columns report the fraction of stocks in the given category whose price impact estimate was positive and statistically significant (at the 5 percent level) and negative and statistically significant, respectively. As the numbers in columns two and three indicate, none of the stocks in the sample had a negative and significant price impact of a trade, whereas virtually all of the sample stocks had significantly positive price impacts.

The last three columns summarize the results for the decimalization period. A comparison of the fourth column with the first indicates that for stocks in all categories, the average price impact of a trade declined following decimalization. That is, stocks became more liquid on average. However, the numbers reported in the final two columns suggest that this result is not as uniform as the positive price impact result reported for the pre-decimalization period. For stocks in the least actively traded category, only one-quarter saw a statistically significant decrease in price impact following decimalization. Around two-thirds of the stocks in category two had statistically significant increases in liquidity. For the more actively traded stocks, that is, those that on average trade at least once per minute, more than 95 percent witnessed an increase in liquidity (decrease in price impact) following decimalization. The magnitude of the increased liquidity is fairly large, with the typical decline in price impact following decimalization being close to 40 percent.

TABLE 2

Average price impact of a trade: Before and after decimalization

Trade category

Average price impact

(sum of i)

Before decimalization

Share of stocks with

positive and sig. i

Share of stocks with

negative and sig. i

After decimalization

Average price impact

(sum of i + i )

Share of stocks with

positive and sig. i

Share of stocks with

negative and sig. i

1

0.092

0.974

0.000

0.074

2

0.070

0.999

0.000

0.045

3

0.043

1.000

0.000

0.025

4

0.032

1.000

0.000

0.019

5

0.023

1.000

0.000

0.014

6

0.011

1.000

0.000

0.006

5

5

Based on the regression equation rt = Dt xt + [ ] i + idect-i rt-i + [ ] i + idect-i xt-i + t .

Note: Sig. indicates significant.

i =1

i =0

0.016 0.007 0.008 0.000 0.014 0.000

0.251 0.652 0.945 0.954 0.957 1.000

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