Spreads, depths, and quote clustering on the nyse and Nasdaq: Evidence after the 1997 sec rule changes Kee H. Chung,a,* Bonnie F. Van Ness,b Robert A. Van Nessb

5. Quote clustering and its impact on spreads
5.1. Quote clustering

Christie and Schultz (1994) and Barclay (1997) show that the frequency of even-eighth quotes on Nasdaq is much higher than the corresponding figure on the NYSE. Based on this evidence, they suggest that there exists implicit collusion among Nasdaq dealers. Christie, Harris, and Schultz (1994), Bessembinder (1997) and Christie and Schultz (1999) provide additional evidence consistent with collusive behavior. Others argue that the higher frequency of even-eighth quotes does not necessarily imply covert collusion among market makers. For example, Grossman et al. (1997) suggest that the less-frequent use of odd-eighth quotes among Nasdaq dealers may be attributed to the natural clustering of price in competitive financial markets.¹⁸ They suggest that market participants use a coarser price grid as protection against informed traders, as compensation for increased inventory risk, and to minimize the cost of negotiation. In a similar vein, Furbush (1995), Kleidon and Willig (1995), Laux (1995), Godek (1996), and Huang and Stoll (1996) suggest that collusion is implausible in a market with many competitors and easy entry.

In this study, we compare the extent of quote clustering between Nasdaq-listed and NYSE-listed stocks using data after the implementation of the new SEC order handling rules and the new minimum tick size. The new SEC rules require that limit order quotes be displayed in the Nasdaq BBO when they improve market maker quotes and allow the public access to superior quotes in ECNs. These rule changes, together with the reduction in tick size from $1/8 to $1/16 on both the NYSE and Nasdaq, offer an excellent opportunity to re-evaluate the quotation behavior of liquidity providers and thereby shed light on the collusion hypothesis.

We report in Table 7 (see also Fig. 2) the proportion of Nasdaq quotes in each quote increment. The results show that the proportion of even-sixteenth quotes is significantly larger than that of odd-sixteenth quotes and about 72% of Nasdaq quotes are in even-sixteenths (see Panel B). We find that the proportion of even-eighth quotes among those quotes in eighths is only 55%, which is significantly smaller than the corresponding figure (84%) reported in Huang and Stoll (1996). Our results also show that the proportion of even-fourths among those quotes in quarters, and the proportion of whole numbers among those quotes in halves are slightly larger than 53%.

We find similar results for our NYSE stocks, although the degree of quote clustering is lower than that of our Nasdaq stocks. The proportion of even-sixteenth quotes is significantly larger than that of odd-sixteenth quotes and about 60% of NYSE quotes are in even-sixteenths (see also Fig. 2). We find, however, that the use of even quotes at larger grids is not as frequent as in the case of sixteenths. The proportion of even-eighth quotes among those quotes in eighths is about 53%. We find similar results in the use of even-fourths and whole numbers.

Overall, our results show that liquidity providers on Nasdaq (i.e., market makers and limit order traders) tend to quote more in even-sixteenths, even-eighths, even-fourths, and whole numbers than their odd-counterparts, and the tendency is particularly strong in the case of sixteenth quotes. Our results suggest that the avoidance of odd-eighth quotes by market makers reported in previous studies has largely been replaced by the avoidance of odd-sixteenths after the reduction in the minimum tick size. Our results also show that NYSE specialists quote significantly more in even-sixteenths than odd-sixteenths, although their use of even-eighths was only marginally higher when the minimum tick size was one-eighth (see Huang and Stoll, 1996).

One might argue that the prevalence of even-sixteenths over odd-sixteenths on both Nasdaq and the NYSE is due to deliberate attempts by market makers/specialists to widen their spreads. As shown by Chung, Van Ness, and Van Ness (1999), the majority of NYSE quotes reflect the interests of limit order traders. Similarly, a significant portion of Nasdaq quotes may now reflect the interest of limit order traders. Consequently, attributing more frequent even-sixteenth quotes on the NYSE and Nasdaq to specialist/dealer behavior may be fallacious. As suggested by numerous researchers,¹⁹ the observed quote clustering on Nasdaq and the NYSE may be driven by reasons other than collusion. In the next section, we present an alternative explanation for quote clustering.
5.2. A behavioral explanation of quote clustering

Several recent studies find a significant increase in the frequency of odd-eighth quotes on Nasdaq after the public disclosure of Christie and Schultz's (1994) findings.²⁰ Some researchers (e.g., Christie, Harris, and Schultz, 1994) have interpreted the finding to imply that market makers stopped colluding due to pressures from the negative publicity and investigations by the DOJ and the SEC. Alternatively, it may reflect the attempts of non-collusive market makers to avoid being charged with collusion on the basis of mistaken interpretations of data. Indeed, Sherwood Securities, while settling the litigation by agreeing to pay a total of $9.2 million, maintained that it had not engaged in any improper conduct.

If one interprets the decrease in the use of even-eighth quotes as the manifestation of reduced dealer collusion, the prevalence (nearly 80%) of even-sixteenth quotes after the introduction of the new minimum tick size is puzzling. One may argue that market makers renewed their collusion by avoiding odd-sixteenths and thereby maintain bid-ask spreads at supra-competitive levels. This scenario does not appear to be plausible, given the negative publicity of Nasdaq collusion in the recent past. In addition, considering the size of the penalty associated with class-action lawsuits, the benefits of collusion appear to be smaller than the costs.²¹ These considerations suggest that the prevalence of even-sixteenth quotes (or the lack of odd-sixteenth quotes) might be driven by reasons other than collusion.

Harris (1991) offers an alternative explanation for quote clustering that is based on certain human behavior. He suggests that price clustering occurs because traders use a discrete set of prices to specify the terms of their trades. Harris maintains that traders use discrete price sets to lower the costs of negotiation.²² Following Harris (1991) and Grossman et al. (1997), we assume that traders and market makers have their own preferred price grids (i.e., whole numbers, halves, quarters, eighths, or sixteenths), and within each grid, they prefer even quotes to odd quotes.²³ Preferred price grids may be determined by the level of investor sophistication, the precision of information, habits, or conventions. For example, casual empiricism suggests that many traders use quarters or halves as their primary price grids and rarely use smaller grids when they submit limit orders. Hence, we can portray the preference structure of a representative liquidity provider with the following postulates:

(5a) Q₀  Q₈;
(5b) (Q₀, Q₈)  (Q₄, Q₁₂);
(5c) (Q₀, Q₄, Q₈, Q₁₂)  (Q₂, Q₆, Q₁₀, Q₁₄); and
(5d) (Q₀, Q₂, Q₄, Q₆, Q₈, Q₁₀, Q₁₂, Q₁₄)  (Q₁, Q₃, Q₅, Q₇, Q₉, Q₁₁, Q₁₃, Q₁₅);

where Q_j denotes quotes in j/16 and (Q_j, Q_k)  (Q_m, Q_n) indicates that quotes Q_j and Q_k are preferred to quotes Q_m and Q_n. Note, for example, that the expression (5c) represents the postulate that liquidity providers prefer even-eighths to odd-eighths and, similarly, the expression (5b) represents the postulate that liquidity providers prefer even-quarters to odd-quarters.²⁴

We can predict the relative frequencies of different sixteenths based on these postulates. First, from (5a), we predict that P₀ > P₈, where P_j denotes the proportion of quotes in j/16. Next, from (5b), we predict that P₈ > (P₄, P₁₂), where P_j > (P_m, P_n) indicates that the proportion of Q_j is larger than the proportion of Q_m or Q_n. From (5c), we expect that (P₄, P₁₂) > (P₂, P₆, P₁₀, P₁₄). Finally, from (5d), we obtain (P₂, P₆, P₁₀, P₁₄) > (P₁, P₃, P₅, P₇, P₉, P₁₁, P₁₃, P₁₅). By combining these relations, we have P₀ > P₈ > (P₄, P₁₂) > (P₂, P₆, P₁₀, P₁₄) > (P₁, P₃, P₅, P₇, P₉, P₁₁, P₁₃, P₁₅). Thus, our model predicts that whole numbers are more frequent than halves, halves are more frequent than odd-quarters, odd-quarters are more frequent than odd-eighths, and odd-eighths are more frequent than odd-sixteenths.

The relative fractions of different sixteenths predicted by our behavioral model are exactly identical to the empirical distribution of Nasdaq quotes reported in Table 7: For the combined quotes of bid and ask, we find that integers (P₀ = 0.1151) are more ubiquitous than halves (P₈ = 0.0976); halves are more frequent than odd-quarters (P₄ = 0.0913 and P₁₂ = 0.0934), odd-quarters are more common than odd-eighths (P₂ = 0.0818, P₆ = 0.0781, P₁₀ = 0.0768, and P₁₄ = 0.0835), and odd-eighths are more common than odd-sixteenths (P₁ = 0.0396, P₃ = 0.0333, P₅ = 0.0325, P₇ = 0.0345, P₉ = 0.0338, P₁₁ = 0.0343, P₁₃ = 0.0340, and P₁₅ = 0.0406).²⁵ Our results indicate that there are distinct clusters of quotes on Nasdaq. We find a cluster of odd-sixteenth quotes (i.e., eight observations on the lower left corner of Fig. 3), a cluster of four odd-eighth quotes, a cluster of odd-quarter quotes, the halve quote, and the integer quote on the upper right corner. We observe similar results in the distribution of NYSE quotes.²⁶

Although the simple behavioral model of quote clustering offers an excellent prediction on the relative frequency of different quotes, the proposed model has limitations. First, it is an ad hoc model and thus it lacks sound economic rationale. It is not clear why traders prefer even numbers. Second, it cannot explain why Nasdaq exhibits a higher degree of quote clustering than the NYSE.²⁷ Third, it fails to provide predictions on the exact proportion of each quote. Nonetheless, the above result shows that quote clustering can be driven by certain human behavior, not necessarily by dealer collusion.
5.3. Impact of quote clustering on spreads

Previous studies show that stocks with a higher proportion of even quotes exhibit wider spreads.²⁸ In this section, we examine whether the same pattern exists after the 1997 SEC rule changes. Specifically, we analyze how the quoted, effective, and realized spreads are related to the extent of quote clustering and other determinants of spreads. We measure the extent of quote clustering (QC) by the weighted sum of four measures of clustering:²⁹

(6) QC = (1/16)D₁₆ + (1/8)D₈ + (1/4)D₄ + (1/2)D₂,

where D₁₆ = the difference in the proportions of even- and odd-sixteenths (i.e., D₁₆ = P₀ + P₂ + P₄

+ P₆ + P₈ + P₁₀ + P₁₂ + P₁₄ - P₁ - P₃ - P₅ - P₇ - P₉ - P₁₁ - P₁₃ - P₁₅),

D₈ = the difference in the proportions of even- and odd-eighths (i.e., D₈ = P₀ + P₄ + P₈ + P₁₂ - P₂

- P₆ - P₁₀ - P₁₄),

D₄ = the difference in the proportions of even- and odd-quarters (i.e., D₄ = P₀ + P₈ - P₄ - P₁₂), and

D₂ = the difference in the proportions of even- and odd-halves (i.e., D₂ = P₀ - P₈).³⁰

The first column of Table 8 shows the results when we regress the quoted spread of Nasdaq stocks against the four stock attributes and the extent of quote clustering. The second column shows the results of the same regression for NYSE stocks. Our explanatory variables jointly account for about 65% of the variation in spreads for our sample of Nasdaq stocks and nearly 91% of the variation in spreads for our NYSE sample. The results show that the quoted spread is significantly and positively related to the extent of quote clustering on both the NYSE and Nasdaq. The positive relation between quoted spreads and the degree of quote clustering is consistent with the findings of previous studies.

To examine whether the differential extent of clustering between Nasdaq and NYSE quotes can explain the difference between NYSE and Nasdaq spreads, we estimate the following regression model using data for our paired sample of 482 Nasdaq and NYSE stocks:
(7) Spread^N - Spread^Y = ₀ + _i(X_i^N - X_i^Y) + ₅(QC^N - QC^Y) + ;

where X_i (i = 1 to 4) represents one of the four stock attributes, N and Y refer to Nasdaq and NYSE, respectively,  denotes the summation over i = 1 to 4, QC represents the extent of quote clustering, and  is an error term. We expect ₅ to be positive and significant if the differential degree of clustering between Nasdaq and NYSE quotes can explain the difference between Nasdaq and NYSE spreads.

We report the regression results in the third column of Table 8. The results show that the differential spread is significantly and positively related to the difference in quote clustering between Nasdaq and NYSE stocks after controlling for the cost-based spread determinants (i.e., share price, number of trades, trade size, and return volatility).³¹ Note that the estimated intercept (0.0010) when the clustering variable is included in the regression is significantly smaller than the corresponding figure (0.0025) when the clustering variable is not included in the regression (see Table 2). This result suggests that the difference in quoted spreads between Nasdaq and NYSE stocks can be attributed, at least in part, to the difference in quote clustering.

The significant and positive intercept indicates that the differential use of even quotes accounts for only a part of the difference between Nasdaq and NYSE spreads. At least a portion of the difference between Nasdaq and NYSE spreads is due to factors other than quote clustering and the four stock attributes. To assess the relative importance of the differential quote clustering in explaining the differential spread between the two samples, we calculate measures of quote clustering for our Nasdaq and NYSE samples. We find that mean values of QC^N and QC^Y are 0.0568 and 0.0310, respectively. Since the estimate of ₅ is 0.0574, the difference between NYSE spreads and Nasdaq spreads that is attributable to differential quote clustering is approximately 0.0015 [0.0574 x (0.0568 - 0.0310)]. The average quoted spread of our Nasdaq sample is 0.0024 greater than the corresponding figure for our NYSE sample. Hence, we infer that 63% (0.0015/0.0024) of the difference between Nasdaq and NYSE spreads is due to the differential use of even quotes between the two markets. The remaining 37% is due to other factors.

Also, we report the regression results for the effective and realized spread in Table 8. We find that both the effective and realized spreads are significantly and positively related to quote clustering. We also find that differences in both effective and realized spreads between Nasdaq and NYSE stocks are significantly and positively related to the difference in quote clustering between the two samples. The positive intercepts in both regressions indicate that both the effective and realized spreads are narrower on the NYSE after controlling for the cost-based determinants of spreads and differential quote clustering. To assess the portion of the differential effective spread that can be attributed to the differential quote clustering, note that QC^N = 0.0568, QC^Y = 0.0310, and ₅ = 0.0381. Hence, the difference between NYSE effective spreads and Nasdaq effective spreads that can be accounted for by differential quote clustering is 0.001 [0.0381 x (0.0568 - 0.0310)]. Finally, because the difference in the effective spread between the two samples is 0.0021, we conclude that 48% (0.001/0.0021) of the difference between Nasdaq and NYSE spreads is due to the differential use of even quotes between the two markets. The remaining 52% is due to other factors.³²

Our findings suggest that Nasdaq stocks have, on average, wider spreads than comparable stocks on the NYSE, even after controlling for their differences in stock attributes and quote clustering. The wider spread on Nasdaq may indicate that limit order traders on Nasdaq play less significant roles in establishing spread quotes compared to limit order traders on the NYSE. In addition, as pointed out by Huang and Stoll (1996) and others, there may be several structural factors that deter price improvement on Nasdaq. Internalization is one likely source of the lower price improvement rate on Nasdaq. Investors who place retail orders with a firm that has both brokerage and dealer operations will likely have their orders executed within that firm. Dealers must honor the best displayed quote (i.e., BBO) at the time the order is executed, independent of their own posted quotes. However, the order is "captured" in the sense that it will be executed within the firm. To the extent that dealers at this broker-dealer firm do not have to compete for the order flow using their own quotes, there is little incentive for them to offer price improvement.

On Nasdaq, competition is also limited by the practice of preferencing customer order flow. Preferencing is a reciprocal arrangement between dealers and retail firms that are not dealers. Under a preferencing arrangement, retail firms direct their customer orders to a particular dealer in return for various services or cash payments (i.e., payment for order flow). If a large fraction of the retail order flow is preferenced, there is little incentive for a dealer to offer price improvement. In many cases, a dealer that offers price improvement does not increase his share of the order flow because the order flow is already preferenced.³³
6. Determinants of quote clustering

In this section, we examine how quote clustering varies with security characteristics. Our empirical model is based on the price resolution hypothesis advanced by Ball, Torous, and Tschoegl (1985) in their study of gold price clustering. These authors maintain that traders use discrete price sets to lower the costs of negotiation.³⁴ Negotiation costs will be low if traders use a coarse price set. If the price set is too coarse (i.e., the set does not include a price that is acceptable to both parties), however, lost gains from trade will be large. Ball, Torous, and Tschoegl suggest that the extent of clustering depends on the tradeoff between negotiation costs and lost gains from trade. They suggest that lost gains from trade are likely to be large if little dispersion exists among traders' reservation prices, such as when the underlying security values are well known. Based on these observations, the authors predict that traders will use a fine set of prices when the underlying security values are well known.

Following Harris (1991), we proxy the reservation-price dispersion with both return volatility and the number of trades. We expect stocks with a higher return volatility to have a larger reservation-price dispersion because information is not uniformly distributed and interpreted when events cause values to change widely. In contrast, we expect stocks with more frequent trading to have a smaller reservation- price dispersion because trading tends to reveal stock values by aggregating the information possessed by different traders. We conjecture that stocks with larger trade sizes have smaller reservation-price dispersions because large trades may indicate traders' confidence on the value of underlying securities. We predict that high-price stocks exhibit larger price variations (and hence more clustering) than low-price stocks because traders are likely to use discrete price sets on the basis of minimum price variations that are constant fractions of price.

We report the regression results in Table 9. The four explanatory variables account for nearly 40% of the cross-sectional variation in quote clustering for our Nasdaq sample. As predicted, we find that the extent of quote clustering is positively associated with share price, and negatively with the number of trades. We find, however, that the effects of trade size and return volatility on quote clustering are not significant. We find similar results for the NYSE sample, although the model explains only a small portion (about 10%) of the cross-sectional variation in quote clustering.

To examine whether differences in the extent of clustering between Nasdaq and NYSE quotes are due to differences in the attributes between Nasdaq and NYSE stocks, we run the following regression:

(8) QC^N - QC^Y = ₀ + _i(X_i^N - X_i^Y) + ;

where QC represents the extent of quote clustering, X_i (i = 1 to 4) represents one of the four stock attributes, N and Y refer to Nasdaq and NYSE, respectively,  denotes the summation over i = 1 to 4, and  is an error term. The results (see Table 9) show that the above regression model explains only a very small fraction (i.e., less than 3%) of the cross-sectional variation in the differential quote clustering. Also, the estimated intercept is positive and highly significant. Therefore, our findings suggest that the differential quote clustering between Nasdaq and NYSE stocks is largely due to factors other than the four stock attributes. This result rules out the possibility that the positive relation between the differential spread and differential quote clustering between Nasdaq and NYSE stocks discussed in Section 5.3 is a spurious correlation emerging from their respective correlations with the four stock attributes.
7. Summary and conclusion

Numerous studies suggest that execution costs on Nasdaq are significantly greater than those on the NYSE. Some researchers maintain that Nasdaq dealers implicitly collude to set larger spreads than their counterparts on the NYSE. Both academic research and anecdotal evidence suggest that execution costs for Nasdaq issues have declined significantly since the phased implementation of the new SEC order handling rules. In this study, we perform a post Nasdaq market reform comparison of Nasdaq and NYSE trading costs and depths.

Our empirical results show that the quoted spreads of Nasdaq stocks are wider than those of comparable NYSE stocks. While the negative publicity and legal action against Nasdaq market makers and subsequent SEC rule changes have exerted a significant impact on Nasdaq quotes, Nasdaq market makers still quote wider spreads than NYSE specialists. Our empirical results also show that the average quoted depth for Nasdaq stocks is significantly smaller than the corresponding figure for NYSE stocks. In addition, we find that Nasdaq stocks have wider effective and realized spreads than NYSE stocks. We find that there is a significant difference in quote clustering between Nasdaq-listed and NYSE-listed stocks and the difference accounts for at least a part of the disparity between Nasdaq spreads and NYSE spreads.