Trade Execution Costs and Market Quality after Decimalization*

Transcription

1 Trade Execution Costs and Market Quality after Decimalization* Journal of Financial and Quantitative Analysis, forthcoming. Hendrik Bessembinder Blaine Huntsman Chair in Finance David Eccles School of Business 1645 E. Campus Center Drive University of Utah Salt Lake City, UT Comments Appreciated Initial Draft: November 2001 Current Draft: August 2002 *The author thanks the New York Stock Exchange for the provision of financial support and data for this study, and the Nasdaq Stock Market for the provision of data. The paper was improved by the comments of Kumar Venkataraman, Amy Edwards, Tim McCormick, an anonymous referee, and participants at the NYSE conference on Practices and Concerns of Institutional Equity Desks.

2 Trade Execution Costs and Market Quality after Decimalization Abstract This study assesses trade execution costs and market quality for NYSE and Nasdaq stocks before and after the 2001 change to decimal pricing. Several theoretical predictions are confirmed. Quoted bid-ask spreads declined substantially on each market, with the largest declines for heavily traded stocks. The percentage of shares receiving price improvement increased on the NYSE, but not on Nasdaq. However, those trades completed at prices within or outside the quotes were improved or disimproved by smaller amounts after decimalization, and trades completed outside the quotes saw the largest reductions in trade execution costs, as a class. Effective bid-ask spreads as a percentage of share price, arguably the most relevant measure of execution costs for smaller trades, averaged 0.33% on a volume-weighted basis after decimalization for both NYSE and Nasdaq stocks. There is no evidence of systematic intraday reversals of quote changes on either market, as would be expected if decimalization had damaged liquidity supply.

3 Trade Execution Costs and Market Quality after Decimalization I. Introduction The New York Stock Exchange (NYSE) replaced the system of fractional pricing that had been in use throughout its history in favor of decimal pricing on January 29, The Nasdaq Stock Market decimalized shortly thereafter, on April 9, Arguably more important than the change to decimal pricing per se, was the reduction in the minimum price increment, or tick size, to one cent on both markets. This study reports on measures of trade execution costs and market quality on both markets before and after decimalization. This study is of interest from three perspectives. First, academics or portfolio managers who wish to evaluate whether a proposed trading strategy can be implemented successfully need to know the cost of executing the required transactions. For example, Lesmond, Schill, and Zhou (2001) investigate whether investors can trade on the well documented momentum effect in stock prices, and conclude that trade execution costs render the apparent profits illusory. Analyses such as these require accurate estimates of trade execution costs for various categories of stocks, and these costs are likely to have changed in the wake of decimalization. Second, it is unclear a priori whether a smaller tick size will enhance market quality. The most obvious effect of a smaller tick size is that a narrower bid-ask spread can be quoted. However, as Harris (1994, 1997, 1999) has argued, a smaller tick size can inhibit incentives to provide liquidity, potentially damaging market quality. Previous tick size reductions on the Toronto Stock Exchange (from 12.5 cents to five cents for most stocks) and on the U.S. equity markets (from 12.5 cents to Each market shifted some pilot securities to decimal trading at earlier dates. On the NYSE, seven securities switched to decimal pricing on August 28, 2000, 57 securities on September 2, 2000, 94 securities on December 1

4 cents) were studied extensively (see Harris (1997) for a survey, and Jones and Lipson (2001) and Goldstein and Kavajecz (2000) for more recent evidence). In general, these studies found that a smaller tick size decreased quoted and effective bid-ask spreads, but also decreased liquidity provision. The economic arguments suggest that a non-zero optimal tick size may exist, implying that relations between tick size and variables such as bid-ask spreads, quote sizes, and limit order book depth are unlikely to be linear, and that simply extrapolating the results of the previous studies may be misleading. This study provides direct evidence on and tests of hypotheses regarding decimalization. The third issue on which this study provides perspective is that of optimal market structure. Several recent studies, including Huang and Stoll (1996), Bessembinder and Kaufman (1997), Bessembinder (1999), Stoll (2000), Weston (2000), and Securities and Exchange Commission (2001), have compared trading costs across the NYSE s specialist-auction market and Nasdaq s dealer market structure. In general these studies have reported higher trading costs on the Nasdaq market, though the cross-market differential has decreased steadily over time. This study provides updated empirical evidence on this comparison. The sample used here includes 300 common stocks from each market that are matched on the basis of market capitalization. 2 A matched sample comparison is more useful for cross-market 4, 2000, and 1 security (an exchange traded fund) on December 18, The Nasdaq stock market adopted decimal pricing for 14 securities on March 12, 2001 and for 197 securities on March 25, A natural question is whether key results of this study would vary if the Nasdaq and NYSE samples were matched by criteria other than market capitalization. The large sample sizes (360 million trades and quotes in the present sample) involved made sensitivity testing impractical. The available evidence indicates that the results of cross-market comparison studies are quite robust to reasonable alternative matching procedures. Chung, Van Ness and Van Ness (2000) match Nasdaq and NYSE samples based on share price, return volatility, and trading activity to compare trading costs in the wake of the 1997 Nasdaq market reforms, and obtain results very similar to those of Bessembinder (1999), who matched based on market capitalization. LaPlante and Muscarella (1997) 2

5 comparisons than using all stocks traded on the markets (as in Nasdaq (2001a) and NYSE (2001a)), because Nasdaq stocks are on average smaller and have lower share prices. The pre-decimalization sample covers the last three weeks before the NYSE decimalization. The post-decimalization sample is extended to twenty-one weeks after the Nasdaq market decimalized, to assess possible longer-term effects of the change in price increments. The sample includes 172 million trades and 187 million quotations in these 600 stocks, and includes trades completed both on and off the listing market. 3 Results are reported separately for large, medium, and small-capitalization stocks. The large stock sample includes the 100 largest Nasdaq stocks. Sample selection techniques are described in detail in Appendix A. Three measures of trading costs are considered: quoted bid-ask spreads, effective spreads (which allow for trades at prices other than the quote), and realized bid-ask spreads (which measure trading costs net of trades information content). The study also considers a limited set of market quality measures, including quote sizes, the competitiveness of quotes originating off the listing market, intraday return volatility, and the tendency for quote changes to be systematically reversed within the trading day. I also evaluate the sensitivity of overall conclusions to the weighting method used to obtain averages, focusing in particular on distinctions between results obtained when weighting each stock equally and when weighting by trading volume. Harris (1999) made several predictions regarding the impact of reducing the tick size to a penny. These predictions included reduced bid-ask spreads, especially for heavily traded stocks, reductions in quotation sizes, and an increase in price improvement rates for stocks traded in specialistinvestigate several alternatives to size-matching in their smaller scale (ten firms from each market) study of large trade execution costs, and report that results are insensitive to the use of alternative matching techniques. 3 The trade and quote observations are obtained from the Trade and Quote (TAQ) database, and must pass a series of error filters described in Bessembinder (2002). 3

6 auction markets. 4 The predicted spread reduction results from the removal of a potentially binding constraint on spread widths. The reduction is expected to be greater for heavily traded stocks since their equilibrium spreads are likely to be smaller and the constraint is more likely to be binding. Also, since large Nasdaq stocks are more heavily traded than large NYSE stocks, we anticipate a greater impact on quoted spreads for large Nasdaq stocks. The predicted reduction in average quotation size in conjunction with reduced spread widths is a consequence of an upward sloping liquidity supply curve. The increase in price improvement rates results from the enforcement of price-time priority rules. The tick size represents the cost of obtaining price priority, thereby stepping in front of existing quotes or limit orders. More frequent stepping ahead of the quote due to a lower cost of doing so increases the rate of price improvement for market orders, but decreases execution rates for the limit orders that often establish the quote. The NYSE enforces price-time priority, while Nasdaq does not. 5 As a consequence the price-improvement prediction is specific to the NYSE. If the increased rate of price improvement reflects a lower cost of stepping ahead of existing quotes and limit orders then we also anticipate a smaller magnitude of price improvement when it occurs. Each of these predictions is verified here. Quoted spreads decreased substantially after decimalization, on both markets, and for stocks in all market capitalization groups. The most striking reduction in average quoted spreads is for large-capitalization Nasdaq stocks, which decreased on a volume-weighted basis to 1.6 cents per share, or 0.096% of share price. Spreads on large capitalization NYSE-listed stocks also declined significantly, to 5.2 cents or 0.182% of share price. Quote sizes were 4 Harris also made several predictions that cannot be investigated here due to data limitations, including that large orders will be broken up more frequently, the ratio of market to limit orders will rise, electronic proprietary traders will become more profitable, payment for order flow will decrease, and large traders will increase their use of floor brokers and alternative trading systems. 5 The NYSE enforces price time priority for orders directed to it. Price time priority is not enforced across the various markets that trade NYSE stocks. Most order flow in Nasdaq stocks is directed according to pre-specified agreements that violate price and time priority. 4

7 reduced substantially on each market. Further, the percentage of shares receiving price improvement increased significantly on the NYSE, but was almost unchanged on the Nasdaq market, and the magnitude of price improvement when it occurred declines. Contemporaneous working papers, including Nasdaq (2001a) and Chung, Van Ness and Van Ness (2001), also compare trading costs across Nasdaq and the NYSE in the wake of decimalization. The former study reports lower quoted and effective spreads on the Nasdaq market, while the latter finds that execution costs on Nasdaq are still larger than on the NYSE after decimalization. This study shows how these conflicting results can be reconciled. Quoted and effective spreads for the majority of medium and small capitalization stocks remain narrower on the NYSE. Studies, such as Chung, Van Ness and Van Ness (2001), that include smaller stocks and weight results for each stock equally will tend to find higher trading costs on the Nasdaq market. But spreads for large stocks, which are also the most heavily traded, are narrower on Nasdaq after decimalization. Results that are based on volume-weighted average across stocks, as reported in NASD (2001a), will be more likely to find lower trading costs on Nasdaq. 6 The effective bid-ask spread (how close the trade price comes to the quote midpoint) as a percentage of share price is arguably the most relevant measure of trade execution cost. This study finds that the volume-weighted average effective bid-ask spread for sample Nasdaq stocks after decimalization is statistically indistinguishable from the corresponding pre-decimalization Nasdaq measure, or from the corresponding post-decimalization sample NYSE measure. This result reflects in 6 NYSE (2001a) also documents that conclusions as to which market has lower trade execution costs are sensitive to methodology, but focuses on (i) the method of averaging results across trades for a given stock, rather than methods of averaging across stocks, and (ii) spreads as a percentage of share price as compared to absolute spreads. The NYSE study uses all stocks listed on each market. The lower average share price resulting from including the many small-capitalization Nasdaq stocks will tend to lead to higher percentage spreads on the Nasdaq market, ceteris paribus. In contrast, this study focuses on a capitalization matched sample of NYSE and Nasdaq stocks. 5

8 part the declining relevance of quotations after decimalization. 7 The combined effect of more outside the quote executions, less inside the quote executions, and declining share prices fully offsets the effect of narrower quoted spreads for Nasdaq stocks. The data supports the overall conclusion that trade execution costs are quite similar across NYSE and Nasdaq stocks of matched capitalization in the wake of decimalization. This paper is organized as follows. Section II reviews several contemporaneous studies of decimalization and describes the general research methods employed. Section III reports on several measures of trading costs before and after decimalization, for the full sample and several subsamples. Section IV reports on changes in a limited set of market quality measures after decimalization. Section V summarizes the evidence as to whether decimalization has improved the trading environment. II. Related Studies, and Research Methods The decimalization of the U.S. stock markets has attracted considerable contemporaneous research attention. Chakravarty, Harris, and Wood (2001a) and Bacidore, Battalio, and Jennings (2001a) study NYSE stocks that switched to decimal trading in pilot studies before the market-wide adoption of decimal trading, and Chakravarty, Harris, and Wood (2001b) study fourteen Nasdaq stocks involved in a pilot decimalization study on that market. Chung and Chuwonganant (2002) report that the percentage of quote revisions that involve spread changes increased substantially after decimalization on the NYSE. Jennings (2001) investigates the extent to which new quotes tend to improve on prior quotes by the minimum one-cent increment after decimalization. Bacidore, Battalio, and Jennings (2001b), NYSE (2001b) and Nasdaq (2001b) conduct before versus after studies of 7 Edwards (2001) makes the point that quoted depths continue to be informative after decimalization, however, as the statistical forecast power of quote depths for actual trade prices did not decline after decimalization. 6

9 market quality, the first two for NYSE stocks and the last for Nasdaq stocks, each using relatively short samples comprised of a few weeks of data. NYSE (2001a), Nasdaq (2001a), and Chung, Van Ness, and Van Ness (2001) each provide comparisons of trading costs across Nasdaq and the NYSE using short samples drawn from the period after Nasdaq decimalized its markets. This study includes a longer post-decimalization sample, from the April 9 Nasdaq decimalization until August 31, The pre-decimalization sample focuses on the last three weeks of trading prior to the NYSE adoption of decimals on January 29, Where overlap exists, the results of this study tend to support similar conclusions as the contemporaneous working papers noted above. Exceptions are noted. In addition, this study provides weekly analysis of market quality over a longer sample interval, reconciliation of the apparently contradictory findings reported in some other papers, analysis of inside and outside the quotation trade executions, analysis of market quality, including return volatility and intraday variance ratios, and both cross-market comparisons and before versus after comparisons. Overall conclusions as to which market has the lowest trading costs are sensitive to the method used to average across individual observations within a stock and across stocks. This study considers two procedures. In the first, each trade in a stock is weighted equally to compute the mean for the stock, and the mean for the market is obtained as the simple average across stocks. In the second, the number of shares transacted weights each trade and the overall mean for the market is computed as the share volume weighted average of the stock means. The former method gives results that pertain to an average trade in an average sample stock. The latter method gives results that pertain to an average share transacted in the sample. With the exception of return volatility measures, statistical significance is assessed using a standard t-test for equality of means. Results are obtained in three stages. First, each mean is computed on a stock-week basis. Second, results are aggregated across weeks to obtain a mean for each stock. Finally, results are aggregated across stocks to obtain a final mean for the market. Statistical significance is assessed at the final stage, based on cross-sectional variation in the stock- 7

10 specific means. In most instances differences in means across markets are statistically significant. To reduce clutter, the Tables in this paper note only when a Nasdaq mean is not statistically different (pvalue >.01) from the corresponding NYSE mean or when a post decimalization mean is not statistically different from the corresponding pre decimalization mean. Since average volatility measures are known to not conform well to the t distribution, I instead report the median volatility measure for each market, and assess whether median volatilities are equal by use of the Wilcoxon rank sum test. III. Trade Execution Costs A. Quoted Bid-Ask Spreads Figures 1A, 1B, and 1C display average post-decimalization bid-ask spreads in cents per share for individual large, medium, and small capitalization stocks, respectively. The average spread for each stock is obtained by weighting each quote by the elapsed time before it is updated. Results are based on the best (national best bid or offer, or NBBO) quotation available in any market at each point in time. 8 Quoted spreads as displayed have been sorted from the narrowest average spread to the widest on each market. The data displayed on these Figures helps to illustrate the reasons that overall conclusions are sensitive to the weighting mechanism used to average across stocks. Figure 1A shows that quoted spreads for large Nasdaq stocks are remarkably narrow after decimalization. Twenty nine of the 100 large Nasdaq stocks have mean quoted spreads of less than two cents per share and seventy have quoted spreads of less than four cents per share. Quoted spreads are 8 The TAQ database reports quotations from the NYSE and the five regional exchanges, individual dealer quotes for NYSE stocks from the NASD market, and the best Nasdaq dealer quotes for Nasdaq stocks. The NBBO is recreated from this quotation data in two stages. First, the best bid and offer in effect for NYSE stocks among individual NASD dealers is assessed, and is designated as the NASD bid and offer. Then, the best bid and offer in effect across the NYSE, the five regional exchanges, and NASD dealers are determined and are designated as the 8

11 narrower for the Nasdaq stock compared to the NYSE stock in 99 of the 100 ranked large-capitalization stock pairs. By comparison, Huang and Stoll (1996) reported that quoted spreads for large capitalization Nasdaq stocks in a sample drawn from 1991 averaged over fifty cents per share. Figure 1B displays quoted spreads for medium-capitalization Nasdaq and NYSE stocks. The Nasdaq quoted spread is narrower than that of the equally ranked NYSE stock in only 38 of 100 pairs. Figure 1C shows that quoted spreads for small-capitalization Nasdaq stocks are almost always wider than for NYSE stocks. Since the majority of sample Nasdaq stocks have wider post-decimalization quoted spreads it can be anticipated that results obtained by weighting each sample stock equally will show wider average spreads on the Nasdaq market. Trades are not distributed randomly across stocks, but tend to be concentrated in a few, generally larger, stocks. For example, the 50 most active stocks account for 74.5% of postdecimalization sample volume in NYSE stocks and the 50 most active Nasdaq stocks account for 82.0% of Nasdaq volume, despite comprising only 16.7% of the sample. The simple average quoted spread after decimalization across the fifty most active Nasdaq stocks is 2.6 cents, compared to 5.6 cents for the fifty heavily traded NYSE stocks. The lower average spread for heavily traded Nasdaq stocks implies that volume-weighted averages will tend to show narrower quoted spreads for Nasdaq stocks. Table 1 reports on average quoted spreads for the full sample and for market-capitalization subsamples, pre and post-decimalization. Panel A relies on equal weighting across stocks, while Panel B relies on trading volume weights. Quoted spreads narrowed on each market after decimalization, for the full sample and for each subsample. These results are consistent with those reported in shorter samples for Nasdaq stocks by Nasdaq (2001b) and Chakravarty, Harris, and Wood (2001b), and for NYSE stocks by Bacidore, Battalio, and Jennings (2001b) and Chakravarty, Harris, and Wood (2001a). NBBO quotations. Quotes for NYSE-listed stocks originate at all five regional markets and at the NASD, as well as at the NYSE. For Nasdaq-listed stocks only Nasdaq and the Chicago Stock Exchange provide quotes. 9

12 As predicted by Harris (1999) the largest spread reductions are for the heavily traded large stocks, and the spread reduction for large stocks is greater on the Nasdaq market. The single most visible result is the decrease in volume-weighted spreads for large Nasdaq stocks, from 5.2 cents to 1.6 cents after decimalization. The volume-weighted spread for large NYSE-listed stocks also decreased substantially, from 10.6 cents to 5.2 cents. Volume-weighted spreads for the full sample are greatly influenced by the large capitalization stocks, and show similar declines post-decimalization. Equally weighted spreads decreased from 16.5 cents to 10.9 cents for the full NYSE sample, and from 17.5 cents to 13.4 cents for the full Nasdaq sample. As anticipated, Nasdaq spreads are narrower than NYSE spreads in the post decimalization sample on a volume-weighted basis, but are wider on an equally weighted basis. Each cross-market differential is statistically significant (p-value less than.01). Investors might be more concerned with trading costs as a percentage of share prices than with the absolute amount per share. Percentage trading costs will be affected by changes in share prices as well as changes in spreads. Panels C and D of Table 1 display average transaction prices for the full sample and for market-capitalization subsamples, for the pre and post-decimalization samples. The average share price for each stock is obtained by weighting each sample trade equally. Panel C reports final means obtained when weighting equally across stocks, while Panel D reports final means obtained when weighting stocks by their trading volume. Average share prices for sample NYSE stocks were little changed after decimalization, rising from $27.36 to $28.01 on an equal weighted basis, and declining from $33.90 to $32.89 on a volume weighted basis. Average Nasdaq share prices, in contrast, fell from $31.85 before decimalization to $26.80 afterward on an equally weighted basis, and from $40.98 before to $26.49 after on a volumeweighted basis. 9 These share price declines mirror the decrease in the Nasdaq composite index from 9 Note that the effects on study results that stem from the decrease over time in average Nasdaq share prices cannot be avoided by alternate sample selection techniques such as matching stocks on the basis of average share price at a point or over an interval of time. 10

13 early 2001 though mid-year, and the larger decline in volume-weighted Nasdaq share prices reflects that large and actively traded Nasdaq stocks saw greater share price decreases over the sample interval. Panels E and F of Table 1 report average percentage quoted spreads, where individual observations are computed as the absolute spread relative to the midpoint of the bid and ask quotes. Panel E reports results that have been equally weighted across stocks while Panel F reports volumeweighted results. Despite Nasdaq share price declines, overall conclusions are similar to those obtained when examining absolute spreads: percentage spreads decreased on each market, with the equalweighted average after decimalization lower for NYSE stocks (0.58% compared to 0.73% on Nasdaq) and the volume-weighted average after decimalization lower for Nasdaq stocks (0.11% on Nasdaq compared to 0.22% on the NYSE). However, decreases in Nasdaq spreads are smaller when expressed as a percentage of share price. For example, the volume-weighted average absolute spread for Nasdaq stocks decreased by 75.3% (from 7.17 cents to 1.77 cents), while the volume weighted average percentage spread for Nasdaq stocks decreased by 49.5% (from 0.21% to 0.106%). B. Executions Inside and Outside the Quotations A potentially important shortcoming of the quoted bid-ask spread as a measure of trade execution costs is that trades are often executed at prices better or worse than the quotes. Harris (1999), among others, predicts that this issue will become more acute after decimalization. Price improvement occurs because orders are not always executed immediately at the best quotation. As Ready (1999) describes, the NYSE specialist has discretion to stop orders and seek prices better than the standing quotation from the crowd on the NYSE trading floor. Decimalization reduces the cost of obtaining a market order by improving on the standing quote to one cent per share. This gives members of the trading crowd incentives to refrain from publicizing their trading interest in the form of a limit order (which would be disseminated as the quotation if it were at the best price), but to instead retain the option to selectively step ahead of others limit orders. This is likely to result in an increased tendency for market orders to execute at prices better than the public quotation on the NYSE. On Nasdaq, time priority is not enforced, and institutional traders were able to negotiate trade prices inside 11

14 the quotes both before and after decimalization. Hence, the effect of decimalization on Nasdaq price improvement rates is unclear. Separately, because quote sizes are expected to decline with decimalization, it is anticipated that more large trades will execute at prices outside the quotes. Table 2 reports on executions at prices within the contemporaneous bid and ask quotes. 10 Results reported Panel A are based on computing the percentage of trades in each stock that receive price improvement, and then weighting equally across stocks. Results reported on Panel B are based on computing the percentage of shares traded in each stock at a price within the quotes, and then weighting across stocks based on trading volume. The former measure can be interpreted as the likelihood that a random trade in a random sample stock will execute at a price within the quotes. The latter measure can be interpreted as the likelihood that a randomly selected share traded in a sample stock will execute at a price within the quotes. Results reported on Panel A of Table 2 indicate that a larger percentage of trades receive price improvement after decimalization. The increase is from 30.6% to 39.9% of trades on the NYSE and from 20.1% to 26.9% on Nasdaq. Increases in the percentage of trades receiving price improvement are observed for each market capitalization sample. Results reported on Panel B of Table 2 indicate an increase in the percentage of traded shares receiving price improvement on the NYSE after decimalization, from 20.8% to 29.3%. On Nasdaq, in contrast, a smaller percentage of shares (7.9%) received price improvement after decimalization as compared to before (8.2%), but the change is not statistically significant. Finding increased rates of price improvement on the NYSE is consistent with the prediction that active traders will step ahead of the quote more often with a smaller tick size on markets that enforce price-time priority. For Nasdaq, 10 All results reported here are based on comparisons of trade prices to quotations reported in the TAQ database as contemporaneous with the trade time. Although some authors (e.g. Lee and Ready (1991)) have recommended adjusting time stamps to allow for trade reporting lags, recent evidence presented by Bessembinder (2002), Ellis, 12

15 which does not enforce price-time priority, results are mixed with more trades but less shares being executed at prices within the quotes. Panels C and D of Table 2 report on the percentage of trades and percentage of shares executed at prices outside the contemporaneous quotations. More trades are executed outside the quotes after decimalization, on both markets and for all capitalization based samples. On an equal-weighted basis the increase is from 1.7% of trades to 3.0% of trades on the NYSE and from 7.2% of trades to 10.9% of trades on Nasdaq. 11 Increases in the percentage of shares executed outside the quotes are more dramatic, reflecting that larger trades are more likely to execute outside the quotes. For NYSE-listed stocks the increase is from 8.0% of shares executed outside the quotes before decimalization to 13.6% after decimalization. Remarkably, more than a third (38.9%) of the shares traded in sample Nasdaq stocks after decimalization are at prices outside the quotes, compared to 20.8% before decimalization. 12 The increase in outside the quote executions on both markets indicates the declining relevance of quotations for trade execution costs in the wake of decimalization. The results reported on Table 2 indicate that more trades are completed at prices other than the bid or ask quotes after decimalization. However, the higher rate of non-quote executions may or may not equate to greater price improvement or disimprovement in dollar terms. Before decimalization, trades completed away from the quote typically had to improve or disimprove by at least 6.25 cents per Michaely, and O Hara (2000), and Peterson and Sirri (2002) indicates that contemporaneous comparisons are likely to provide more accurate results. 11 By comparison, Nasdaq (2001b) reports that 18% of Nasdaq trades completed in the first two weeks after decimalization occurred outside the quotes. 12 Some outside-the-quote executions for large Nasdaq trades reflect a newly adopted practice whereby brokerage firms add (subtract) a "commission-equivalent" to prices for institutional customer buy (sell) orders. (See Chapman (2001)). The markups are a response to decreasing bid-ask spreads, and are charged in lieu of a commission. Unfortunately, these trades are not identified in the available databases. 13

16 share. 13 The one-cent minimum price increment in effect after decimalization allows improvement or disimprovement as small as a penny. Harris (1999) predicts that discretional liquidity providers will view the smaller tick size as a lower cost of stepping in front of the existing quote or limit order. If so, we might expect the higher rate of price improvement for market orders to reflect more instances where the improvement is only a penny. Section III.E below investigates magnitudes of price improvement and disimprovement before and after decimalization. Some trades completed at prices outside the quotes are larger than the size of the corresponding quote (ask for buy, bid for sell) at the time of the trade. These trades need not be expected to execute at the quote, but might have to walk the book. However, some trades execute outside the quotes even though their size is less than or equal to the quote size. For NYSE-listed stocks these trades comprise apparent trade through violations. 14 Regarding outside the quote executions for Nasdaq stocks, Smith, Selway, and McCormick (1998, page 30) note: Unlike the ITS for exchange-listed securities, Nasdaq has no trade through rule. That is, market participants are not explicitly prevented from trading at prices inferior to the best quoted prices. Nasdaq rule 2320 does require (Smith, Selway, and McCormick (1998, page 30)) any transaction with a customer be at a price that is favorable relative to the best prevailing inter-dealer market, subject to market conditions and the nature of the transaction. Panels E and F of Table 2 report results analogous to those of Panels C and D, except that the analysis is restricted to those trades with a size less than or equal to the corresponding quote size. The key result is that even trades that are smaller than quote sizes are completed at prices outside the quotes 13 The assertion is not strictly true for Nasdaq stocks, where trade prices (as opposed to quotations) could be negotiated at fine increments even before decimalization. 14 A trade through is a violation of ITS agreements, but not necessarily of a SEC rule. The SEC firm quote rule is violated only if a market executes a trade at a price worse than its own quote. I refer to these trades as apparent violations, as some may actually be attributable to imperfect matching of the time stamps in the trade and quote databases. Errors in the time alignment of trades and quotes can make a trade that occurs just after a quote update appear to be executed outside the quotes when it was not. 14

17 more often after decimalization, implying that the overall increase in the rate of outside the quote executions is not fully attributable to declining quote sizes. For NYSE-listed stocks the rate of apparent trade through violations remains relatively small, at 1.5% of trades and 1.9% of shares. 15 For Nasdaq-listed stocks the issue looms larger, as 8.7% of trades smaller than the quote size and 17.3% of shares in trades smaller than the quote size are executed at prices outside the quotes. Nasdaq (2001b) notes that the apparent increase in outside the quote executions after decimalization might reflect rapid trading and rapid quote updates, resulting in increased difficulty in accurately matching trade prices with quotes prevailing at the trade execution time. 16 If so, it is reasonable to presume that investors will also have increased difficulty assessing whether their trades have received favorable execution prices. C. Effective Bid-Ask Spreads The finding that the percentage of trades completed at prices better or worse than the quotes has increased since decimalization implies that changes in trading costs could be greater or less than that implied by changes in quoted spreads. A potentially more precise measure of trading costs is the effective bid-ask spread, defined for each trade as twice the absolute difference between the trade price and the midpoint of the contemporaneous bid and ask quotes As elsewhere in this report, these figures pertain to all executions in NYSE-listed stocks, whether they occur at the NYSE, at a regional exchange, or on the NASD dealer market. The corresponding figures for NYSE executions are that 0.9% of trades and 1.3% of shares in transactions smaller than the quote size involve apparent trade through violations.- 16 Quote updates increased in frequency by 32.5% (from 2528 quote updates per stock day to 3350) for sample Nasdaq stocks after decimalization, while quote updates for sample NYSE stocks increased by 62.6% (from 1362 quote updates per stock day to 2215). 17 Multiplication by two converts the measure to an equivalent round-trip cost. This definition is equivalent to defining the effective spread as 2I(P-M), where P is the trade price, M is the quote midpoint, and I is a trade direction indicator assigned by the Lee and Ready (1991) algorithm. All results in this report were also replicated 15

18 Table 3 reports on average effective bid-ask spreads. Panels A and B report results based on equally weighting across trades in each stock, and then weighting results equally across stocks. Panels C and D report results based on share weighting across trades in each stock (so that large trades receive more weight) and then weighting results across stocks based on trading volume. Panels A and C report effective spreads in cents per share, while Panels B and D refer to effective spreads as a percentage of share price. Figures 1A to 1C also display average effective bid-ask spreads after decimalization for individual stocks in the large, medium, and small capitalization samples, respectively. Figure 1A reveals that effective bid-ask spreads for large Nasdaq stocks are generally greater than quoted bid-ask spreads, reflecting the large numbers of shares executed at prices outside the quotations. 18 Figure 1B shows that quoted and effective spreads are generally quite similar for medium capitalization Nasdaq stocks, while Figure 1C shows that effective spreads are generally less than quoted spreads for small Nasdaq stocks. In contrast to the variation in results for Nasdaq stocks, but in keeping with results of several studies conducted in earlier data, effective bid-ask spreads for large, medium, and small capitalization NYSE-listed stocks are generally less than quoted bid-ask spreads, reflecting price improvement possibilities. By most measures, effective bid-ask spreads are significantly lower after decimalization than before, on both markets. On a simple average basis effective spreads declined from 11.3 cents (0.65% of share price) to 7.3 cents (0.39% of share price) for NYSE-listed stocks, and from 14.7 cents (0.73% while using an alternate trade direction indicator algorithm suggested by Ellis, Michaely, and O Hara (2000). Results using the alternate algorithm indicate slightly smaller trade execution costs on both markets, pre and post decimalization. Overall conclusions are unaffected by use of the alternative algorithm. The effective spread remains an imperfect measure of trade execution costs in the absence of data on the customer orders that underlie trades, as some trades are incorrectly classified by any algorithm. 18 Nasdaq (2001b) also reports that average effective spreads exceed average quoted spreads for Nasdaq stocks after decimalization. That study also breaks down results by order size. Interestingly, average effective spreads exceed average quoted spreads even for small orders of less than 500 shares. 16

19 of share price) to 10.5 cents (0.58% of share price) for Nasdaq listed stocks. Decreases in simple average effective spreads are observed for each market capitalization sample. Effective spreads also declined on a volume-weighted basis on each market, from 12.7 cents (0.52%) to 7.5 cents (0.33%) for NYSE stocks and from 12.7 cents (0.35%) to 5.8 cents (0.33%) for Nasdaq stocks. One result here is particularly noteworthy. The volume-weighted average effective spread in percent after decimalization for Nasdaq stocks is 0.33%, which is not statistically different from the corresponding pre-decimalization spread for Nasdaq stocks of 0.35% (p-value =.104) or from the corresponding spread for NYSE stocks of 0.33% (p-value =.797). The increase in outside the quote executions in combination with the decrease in share prices for heavily-traded Nasdaq stocks together offset completely the striking decrease in quoted spreads for large Nasdaq stocks, leaving effective trading costs in percentage terms unchanged. Results reported to this point have not differentiated on the basis of trade size. Harris (1999) predicts that large traders might be disadvantaged by decimalization. The lower cost of stepping ahead of existing limit orders could inhibit incentives to post limit orders, thereby reducing the effective supply of liquidity for large orders. Consistent with this reasoning, Goldstein and Kavajecz (2000) report reductions in limit order book depth and Jones and Lipson (2001) report increased trading costs for institutional investors after the NYSE tick size was reduced from one eighth dollar to one sixteenth dollar. Bacidore, Battalio, and Jennings (2001a) report that traders reduced the size of their limit orders and cancel limit orders more frequently in stocks that adopted decimal pricing during NYSE pilot studies. The TAQ database does not contain data on orders. It is possible to obtain indirect evidence on whether large traders have been disadvantaged, by examining trade execution costs as a function of 17

20 trade size. 19 Table 4 reports on average effective spreads for small (less than 1000 shares), medium (1000 to 9999 shares), and large (10,000 or more shares) trades. The results reported on Table 4 generally do not provide support for the reasoning that large traders have been harmed by the market-wide change to decimal pricing, which is consistent with the conclusion reached by Bacidore, Battalio, and Jennings (2001a) for NYSE pilot stocks. On the NYSE the average effective spread for large trades decreased from 12.9 to 8.7 cents on a simple average basis, and from 11.5 to 8.7 cents on a volume weighted basis. On Nasdaq the average effective spread for large trades decreased from 23.5 cents to 15.5 cents on a simple average basis and from 19.8 cents to 10.9 cents on a volume weighted basis. Share price decreases do affect the Nasdaq comparison, however, and the volume-weighted average effective spread for large Nasdaq trades rose on a percentage basis, from 0.56% to 0.68%. Effective spreads for large trades generally exceed those for small trades on both markets, both before and after decimalization. Trade execution costs for small trades are particularly low after decimalization: the volume weighted average effective spread for small trades is just 0.16% on the NYSE and 0.12% on Nasdaq. Thus, while the analysis of effective spreads provides no evidence that large traders were harmed by decimalization, it does support the conclusion that small traders benefited most. D. Realized Spreads The greater effective spreads paid by large traders reflect, in part, the greater likelihood that large traders possess non-public information regarding stock values. Some observers (e.g. Seppi 1997) have argued that trading costs should be measured based on trades temporary or non-informational price impact. The realized bid-ask spread is such a measure. It is defined as twice (to capture the implied round trip cost) the amount by which prices for customer buy orders exceed, or prices for 19 Trade size does not directly reflect order size, since large orders might be broken into smaller segments for execution. 18

21 customer sell orders fall short of, the estimated post-trade value of the asset. 20 As such, it measures the post-trade price reversal. Since buy (sell) orders lead on average to upward (downward) revisions in values, realized spreads are generally smaller than effective spreads. To provide additional evidence on the trading costs borne by large and small traders, Table 5 reports on average realized bid-ask spreads, in cents and on a percentage basis, for various trade size categories. The realized spread is measured for each trade, and overall averages are computed on both an equal and a volume-weighted basis. Averaged across all trade sizes, realized bid-ask spreads decreased on each market after decimalization, and are substantially lower on the NYSE than on Nasdaq. The simple (weighted) average realized spread on the NYSE is 1.9 (2.4) cents after decimalization, compared to 5.6 (5.2) cents on Nasdaq. Realized spreads for large trades are greater than for small and medium-sized trades on both markets, both before and after decimalization. For example, the volume-weighted average realized spread is 0.117% of share price for large NYSE trades after decimalization, compared to 0.027% for medium and 0.025% for small trades. The remarkably small realized spread estimates for small and medium NYSE trades imply that liquidity is being supplied even though the net gain to the liquidity provider after allowing for trades information content is near zero. One possibility is that liquidityoriented traders are submitting limit orders even in response to very small spreads, since their alternative is to pay the spread by use of market orders Results reported here use the Lee and Ready (1991) algorithm to sign trades, and the midpoint of the quotes in effect 30 minutes after the trade, or the 4 p.m. midpoints for trades executed after 3:30, as the proxy for post-trade value. 21 To assess robustness of the key results obtained here, I also estimated bid-ask spreads in the present sample by use of the Roll (1984) method, which does not require the matching of trades with quotes or that trade direction be assigned. The results (not reported) confirm that bid-ask spreads declined after decimalization on each market, for stocks in all market capitalization groups. However, the average Roll-based spread estimates obtained for Nasdaq-listed stocks were substantially larger than the corresponding average effective bid-ask spreads, a result 19

22 By most measures, realized spreads for large trades declined after decimalization. On Nasdaq, the simple (volume-weighted) average realized spread for large trades decreased from 28.8 (23.9) cents to 18.1 (12.3) cents. On the NYSE, the simple average realized spread for large trades increased slightly from 2.7 to 3.4 cents, but the change is not statistically significant, while the volume-weighted average realized spread decreased from 3.1 to 2.9 cents; also a statistically insignificant decrease. Since realized spreads for large trades decreased significantly on Nasdaq and did not change significantly on the NYSE, this analysis does indicate any degradation of market quality for large trades after decimalization. E. Effective and Realized Spreads for Price Improved and Disimproved Trades. Section III.B. documents that more trades are completed both inside and outside the quotations after decimalization, on both markets. However, a higher rate of price improvement (disimprovement) after decimalization need not imply lower (higher) execution costs, because the differential between the execution price and the quote can be smaller when the tick size is reduced. In particular, if discretionary liquidity providers step in front of existing quotes and limit orders by improving the price by the minimum increment, then we would expect smaller price improvement with the smaller tick size, even though a greater percentage of market orders receive some improvement. Anecdotal evidence indicates that large traders who use limit orders increasingly complain of being pennied by liquidity providers who improve the price by the minimum increment. 22 which contrasts with those obtained by Schultz (2000) and Bessembinder (2002) for earlier samples. Ascertaining why the serial covariance based Roll procedure gives larger spread estimates than other methods for Nasdaq stocks in the 2001 data comprises an interesting issue for future research. 22 Jennings (2001) discusses this complaint in more detail. Consistent with the reasoning that pennying is an issue, Jennings (2001) reports an increase in the frequency with which new quotes improve on the prior quote by one tick after decimalization. Note, though, the distinction between that finding and the increased rate of price improvement documented here. Jennings documents an increase in the frequency with which firm quotes improve 20

23 To investigation this issue, I compute quoted spreads, effective spreads, and realized spreads for three categories of trades: those completed outside the quote, those completed at a price matching the quote, and those completed at a price within the quotes, before and after decimalization. In addition, I compute the amount of price improvement for each trade as half (to recover a one-way rather than round trip measure) the distance between the quoted and the effective spread. Results computed on an equal weighted basis are reported on Table 6A, while results that are averaged across trades based on trade size and across stocks based on trading volume are reported on Table 6B. On the NYSE, the amount of price improvement for trades within the quotes decreased after decimalization by more than 60%, from 8.5 (7.3) cents to 3.4 (2.3) cents on an equal (volume) weighted basis. On Nasdaq, the decrease in the amount of price improvement for those trades completed within the quotes was from 7.4 (4.2) cents to 3.5 (1.5) cents on an equal (volume) weighted basis. Those trades completed outside the quotes are disimproved by a smaller amount after decimalization. On a volume-weighted basis average price disimprovement declined from 12.6 cents to 9.1 cents on the NYSE, and from 15.4 cents to 5.5 cents on Nasdaq. The magnitudes of both price improvement and price disimprovement are smaller after decimalization. Price improvement tends to occur in stocks or at times when quoted spreads are wider. The simple average quoted spread at the time of trades that receive price improvement in the postdecimalization NYSE sample is 12.9 cents, compared to 7.9 cents for trades completed at the quote and 9.0 cents for trades executed outside the quote. On Nasdaq the corresponding figures are average quoted spreads of 15.3 cents at the time of price-improved trades, 10.2 cents at the time of trades completed at the quotes, and 8.5 cents at the time of trades at prices outside the quotes. Observing that price improved trades tend to occur when spreads are wide and that trades executed within the quotes receive a smaller amount of price improvement after decimalization implies on existing quotes by a penny, while the evidence here concerns non-expressed liquidity that is made available in real time to execute trades at prices better than the publicly expressed quotes. 21