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Extreme price clustering in the London equity index futures and options markets
Journal of Banking & Finance 22 (1998) 1193±1206
Extreme price clustering in the London equity index futures and options markets Owain ap Gwilym a, Andrew Clare b, Stephen Thomas a
a,*,1
Department of Management, University of Southampton, High®eld, Southampton S017 1BJ, UK b ISMA Centre, Department of Economics, University of Reading, UK Received 27 May 1997; accepted 18 March 1998
Abstract Price clustering and optimal tick sizes have recently been topics of substantial public policy interest, and this paper presents evidence which is relevant to both debates. Around 98% of quoted and traded prices for LIFFE stock index derivatives are found to occur at even ticks. We report that clustering increases with volatility and transaction frequency, and decreases with trade size, and ®nd that the proportion of odd ticks is signi®cantly lower near the market open and higher near the close. Further, an inverse relationship is reported between bid±ask spreads and the number of odd ticks, and spreads cluster at even-tick values. This evidence of extreme price clustering is the ®rst to be presented for ®nancial derivatives. The results support both the price resolution and the negotiation hypotheses of price clustering. Ó 1998 Elsevier Science B.V. All rights reserved. JEL classi®cation: G12 Keywords: Clustering; NASDAQ; Tick size; Bid±ask spreads; Intraday data
*
Corresponding author. Tel.: 44 1703 593068; fax: 44 1703 593844; e-mail: [email protected]. 1 This paper bene®ted considerably from the comments and suggestions of two anonymous referees. We are grateful for helpful comments from participants at the 1997 Cornell±Queen's Derivatives Securities Conference, the 1997 BNP-Imperial College Forecasting Financial Markets Conference, and the 1997 International Symposium on Forecasting. The authors also gratefully acknowledge the ®nancial support of the Leverhulme Trust (Grant F391/I). 0378-4266/98/$19.00 Ó 1998 Elsevier Science B.V. All rights reserved. PII S 0 3 7 8 - 4 2 6 6 ( 9 8 ) 0 0 0 5 4 - 5
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1. Introduction Price clustering is the occurrence of signi®cantly greater than 50% of quoted and/or traded prices at even price fractions, or of certain integers. This phenomenon has become a topic of substantial public policy interest following the publication of research ®ndings by Christie and Schultz (1994) that market makers in actively traded NASDAQ stocks may have implicitly colluded to maintain bid-ask spreads of at least $0.25 by avoiding odd-eighth quotes. Shortly after the Christie and Schultz (1994) results were publicised, dealers in a number of major stocks, including Apple and Microsoft, rapidly increased their use of odd-eighth quotes which led to a decline in mean inside and effective spreads of nearly 50% (see Christie et al., 1994). Evidence of price clustering has also been documented in other markets, e.g. Goodhart and Curcio (1991) for foreign exchange markets, Ball et al. (1985) for the gold market, and Grossman et al. (1996) for equity, foreign exchange and gold markets. However, no previous study has examined the phenomenon in ®nancial derivatives markets. Several theories have been proposed to explain the observation of price clustering. The attraction theory proposed by Goodhart and Curcio (1991) suggests that discrete trading prices are obtained from continuously distributed underlying values by rounding to the nearest available ®nal unit (as in Gottlieb and Kalay, 1985), but the basic attraction of each integer varies. Ball et al. (1985) suggest that clustering results from the achievement of the optimal degree of price resolution, i.e. the desired level of price accuracy. The negotiation hypothesis by Harris (1991) suggests that a smaller price set is chosen by market participants to limit the number of bids and asks that can be made and thus lowers the costs of negotiation. In this paper we ®nd evidence of extreme clustering in the quoted and traded prices of the equity index futures and options contracts traded on the London International Financial Futures and Options Exchange (LIFFE), and thus present the ®rst evidence of this phenomenon for ®nancial derivatives. We ®nd that although the minimum tick size for FTSE derivatives is half an index point, 98.3% of quotes and 98.4% of trades occur at even ticks (full index points) for the FTSE100 futures contract. Similar ®ndings are reported for options on the FTSE100 index and for the FTSE250 futures contracts, with additional clustering at the values 0 and 5 for the fourth index digit in the latter case. In general our results support the price resolution hypothesis by Ball et al. (1985) which implies that the price clustering in this market results from the achievement of the desired level of price accuracy. However, we also ®nd relationships between clustering and trade sizes and volatility which support the negotiation hypothesis by Harris (1991). The remainder of this paper is organised as follows. Section 2 outlines the market structure of LIFFE and the dataset, while Section 3 presents results on
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the extent of price clustering with interpretations in the light of existing theory. Section 4 examines intraday variability in price clustering, which has not previously been considered, and Section 5 concludes. 2. Market structure and the dataset Consideration of market structure is important because it has been argued that the high degree of clustering at NASDAQ was due to some defect in its market structure. LIFFE operates an open outcry trading system similar to those at US futures markets e.g. Chicago Mercantile Exchange (CME). At LIFFE, there are currently two futures contracts traded on equity indices. By far the most heavily traded is the FTSE100 stock index futures contract, which is based upon the top 100 UK companies by market capitalisation. A more recently introduced and less heavily traded futures contract is based upon the FTSE250, which is an index of the next 250 largest stocks by market capitalisation. LIFFE also trades both American- and European-style options on the FTSE100 stock index. Dependent on series and maturity, there can be up to ®fty price makers active at any time in the FTSE100 stock index futures and options markets, but often only two or three in the FTSE250 index futures. Trading in the FTSE100 futures market occurs by open outcry from 08:35± 16:10GMT, and by Automated Pit Trading (APT) from 16:32±17:30GMT. The vast majority of trading in this derivative occurs in the front month contract up to its last trading day, at which point a switch occurs to the immediately succeeding contract. The contract is currently valued at, £25 per index point, with a minimum price movement of 0.5 index points. At the average price for FTSE100 futures in our sample of 2966.4, the tick value is 1.7 basis points (12.5/(25 ´ 2966.4)). Most stocks in London are quoted in ticks of 1 pence and with an average price of around £4, this translates to 25 basis points. Pit trading hours for the options contract are the same as for the FTSE100 futures, while the FTSE250 futures market opens and closes ®ve minutes earlier. Tick size for the FTSE100 options and the FTSE250 index futures is half an index point, with a tick value of £5 for both contracts. The FTSE100 index futures and options are traded in two separate pits that are adjacent to one another to facilitate trading and hedging. Traders commonly delta hedge options positions using the index futures. All contract maturities are traded in the same pit by the same traders. Large orders are split among multiple buyers/sellers in the pit on a pro rata basis. The dataset includes all quotes and trades on the FTSE100 stock index futures contracts from 24 January 1992 to 30 June 1995 (consisting of 923,703 trades and 1,780,785 quotes). The source is the LIFFE Time and Sales data on CD-ROM, which contains information on the time to the nearest second, contract type, ¯oor or APT trading, commodity code, delivery month, price,
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transaction code (bid, ask or trade), and traded volume. Trades and quotes taking place during APT are not considered here. Similar data for the FTSE250 stock index futures contract is available from its inception on 25 February 1994 to 30 June 1995 (consisting of 1,358 trades and 7,512 quotes). Data on the American-style option on the FTSE100 stock index from 4 January 1993 to 31 March 1994 (consisting of 97,574 trades and 223,681 matched bids and asks) is obtained from a separate source. These options are chosen rather than the European-style equivalent due to greater liquidity. 3. Results 3.1. Clustering and the price resolution hypothesis Table 1 presents results for the number and percentage of trades which occur at odd and even ticks for the FTSE100 futures contract. Over the entire sample, 98.4% of trades on all contracts occur at even ticks, a result which is robust across sub-samples. Out of a total of 1.78 million bids and asks, only 30,222 (1.7%) occurred at odd ticks. The results in Table 1 are supportive of the price resolution hypothesis by Ball et al. (1985), i.e. the market does not seem to require the additional price re®nement of half index points. Splitting of large orders among multiple buyers or sellers in the pit could impact on the level of observed price clustering. The transaction record does not make any distinction between multiple trades at a given price based on a single order and multiple trades at a given price based on dierent orders. To account for this, we re-examined clustering frequencies following aggregation of all trades at the same price within one-minute intervals. 2 The results were materially unchanged: over the entire sample, 97.7% of trades occurred at even ticks, with little variation across sub-samples. The FTSE250 index futures contract also displays a high degree of price clustering, with 98.5% (99.4%) of trades in all contracts (front-month only) Table 1 Number and percentage of FTSE100 stock index futures trades occurring at odd and even ticks Sample Full sample 1/92±6/95
2
All contracts
Front month contract only
Even ticks
Odd ticks
Even ticks
Odd ticks
909005 98.41%
14698 1.59%
884918 98.81%
10614 1.19%
We are grateful to an anonymous referee for this suggestion.
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occurring at even ticks. Only 15 (0.2%) quotes occurred at odd ticks over this sample. For the American-style FTSE100 index options contract, we ®nd that 97.7% of bids, 98.1% of asks and 95.9% of trades occur at even ticks, once again supporting the hypothesis by Ball et al. (1985). Table 2 presents a more detailed analysis of this by contract moneyness and maturity. The largest proportion of odd ticks is for out-of-the-money, near-maturity options which is the lowest priced category. Clustering tends to decrease as maturity approaches and is less severe for out-of-the-money contracts. For in-the-money contracts with longer than a month to maturity, occurrence of odd ticks is close to zero. Overall, the observations which do occur at odd ticks tend to be in relatively low price option contracts, which is consistent with the evidence by Harris (1991) from the NYSE/AMEX markets that price clustering tends to increase with the price level. 3.2. The attraction hypothesis Given that odd ticks are so rare in the FTSE derivative contracts, we conduct further analysis based on the ®nal digit of the price (eectively assuming that the minimum price movement is one index point). In Table 3, traded and quoted prices are split into the ten possible integer values for the ®nal digit. For the FTSE100 stock index futures contract we ®nd little evidence of a preference for any integer values, with trades and quotes generally occurring approximately 10% of the time in each of the ten digits. The largest deviations are for the integers 1 and 9, discussed as the least popular digits in Goodhart and Curcio (1991). However, the FTSE250 futures and FTSE100 options show a dierent pattern. For the FTSE250 contract, 78% of bids and asks, and 69% of trades have either 0 or 5 as the ®nal digit, while 2 is the next most popular digit at 7% of trades. For the FTSE100 options, over 30% of trades occur at a ®nal digit of zero, with 5 being the next popular digit at 9.6%. Clustering is less severe in quotes, but there are still 28% with ®nal integers taking the values of 0 or 5. These two contracts thus oer strong support for the Goodhart and Curcio (1991) attraction hypothesis in the ®nal integers of the price. 3.3. The negotiation hypothesis The negotiation hypothesis by Harris (1991) suggests that a smaller price set limits the number of bids and asks which can be made and thus lowers the costs of negotiation; hence participants will tend to prefer a smaller price set. However, for larger trades market participants may ®nd it worthwhile negotiating on a wider range of prices. We examine the relationship between odd and even tick trades and the respective mean trade size for the FTSE100
99.1 97.8 82.7 97.3
97.0 95.5 76.2 94.7
100 99.5 93.3 98.7
Bid
99.1 97.4 78.8 96.7
2nd
Trade
Bid
Ask
Near
Maturity
99.9 99.6 94.7 99.0
Ask 99.1 98.7 89.2 97.6
Trade
Ask
Trade
100 100 100 99.7 99.8 99.0 96.1 96.3 91.5 98.9 99.0 97.4
Bid
3rd Ask
100 100 99.7 99.6 97.8 98.9 99.1 99.4
Bid
4th 99.0 98.0 92.9 96.7
Trade 99.9 99.8 98.6 99.3
Bid
Other 99.7 99.9 98.9 99.5
Ask
99.0 98.3 97.5 98.0
Trade
99.6 98.3 92.2 97.7
Bid
Total
99.5 98.6 93.7 98.1
Ask
98.0 96.8 87.4 95.9
Trade
This table presents the percentage of bid, asked and traded prices which occur at even ticks, classi®ed by moneyness and maturity. For American-style FTSE100 stock index options, the available expiry dates at any given time are June and December plus additional months such that the four nearest calendar months are always available for trading. The maturity categories used here re¯ect this, with the ®rst category de®ned as the nearest expiry, the second category is the second nearest expiry, and so on. The moneyness categories are de®ned as IN (in-the-money), AT (near-the-money) and OUT (out-of-the-money) according to the ratio of the underlying price to the exercise price (S/K) as follows: 0< S/K 6 0.95 is OUT for calls and IN for puts, 0.95 < S/K < 1.05 is AT for both calls and puts, and 1.05 6 S/K <1 is IN for calls and OUT for puts.
IN AT OUT Total
S/K
Table 2 Price clustering in American-style FTSE100 stock index options classi®ed by moneyness and maturity
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Table 3 Price clustering on fourth digit of index value for FTSE100 and FTSE250 stock index futures contracts, and ®nal whole digit of option price
0 1 2 3 4 5 6 7 8 9
FTSE100 futures
FTSE250 futures
FTSE100 options
Trades
Quotes
Trades
Quotes
Trades
Quotes
10.2 8.9 9.9 10.0 10.2 10.5 10.4 10.3 10.3 9.3
10.0 8.9 10.0 10.0 10.2 10.6 10.4 10.4 10.5 9.2
39.9 3.2 7.2 3.0 3.8 28.8 3.4 3.8 4.3 2.7
45.5 1.6 4.2 2.6 2.5 32.5 2.2 3.8 3.5 1.7
30.8 7.1 8.6 7.8 7.5 9.6 7.3 7.4 8.0 5.8
15.3 8.0 10.8 9.7 8.6 12.6 7.9 9.3 10.7 7.1
The table presents the percentages of traded and quoted price occurring at the ®nal whole digit of the price, i.e. eectively assuming a minimum price movement of one index point rather than half an index point.
futures contract. 3 If the negotiation hypothesis is valid we would expect to ®nd a higher probability of odd-ticks for trades of a larger size, and Table 4 presents direct evidence on this. For the limited number of trades that occur at odd-ticks in the FTSE100 futures market, mean trade size is far higher than for even-tick trades. For the entire sample, the average trade for even ticks is for 6.5 contracts, whereas for odd tick trades the equivalent value is 19.5 contracts, a result which is robust across sub-samples. These results are consistent with those of Brown et al. (1991) for COMEX silver futures. For the NASDAQ stocks in their sample whose market makers rarely use oddeighths, Christie and Schultz (1994) ®nd that large trades are far more likely to occur on odd eighths than are small trades. Such evidence suggests that the bene®ts of larger trades justify additional negotiation costs. Table 4 Mean trade sizes for FTSE100 stock index futures trades at odd and even ticks Sample
All contracts
Front month contract only
Even ticks
Odd ticks
Even ticks
Odd ticks
Full sample 1/92±6/95
6.50
19.47
6.17
14.31
3 There are too few odd-tick trades in the FTSE250 futures to conduct a similar meaningful analysis of the relationship between even and odd tick trades and trade size. In addition, volume data is not available for the FTSE100 options contract and therefore we cannot undertake the analysis for this contract either.
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4. Intraday variability in price clustering 4.1. The intraday occurrence of odd ticks Though Grossman et al. (1996) report variation in clustering over time, previous studies have not considered the possibility of variability in the level of clustering on an intraday basis. If the negotiation hypothesis holds, we would expect to observe a greater proportion of odd ticks during low volume and low volatility periods. Previous studies (e.g. Ekman, 1992) document that the middle of the day tends to be a time of relatively low volume and volatility in stock index futures markets, with periods of high volume and volatility near the open and close. Fig. 1 plots the number of odd and even tick trades for the FTSE100 futures contract per 5-min interval during the day. The pattern for even-tick trades follows a familiar U-shaped intraday pattern in trading volume. Notable peaks occur during the intervals ending 09:35GMT, 11:35GMT, and 13:35GMT, which correspond to the principal UK releases in the period from Autumn 1993, UK releases prior to Autumn 1993, and principal US releases, respectively. 4 However, the pattern for odd-tick trades diers markedly in that there is an elevated number of trades in the last interval of the day only, which is approximately double the level for most of the rest of the day. 5 A relatively low percentage of odd-tick trades is found near the market open, with relatively high percentages around lunchtime (a period of low volume) and near the close of trading. Since negotiation costs would generally be higher in periods of high volume and volatility, the observation of few odd-ticks near the open lends additional support to the negotiation hypothesis. However, the observation of an increase in odd-ticks near the market close is clearly in con¯ict with this hypothesis. 6 The signi®cance of the low percentage of odd-ticks at the market open, and high percentage at the close is now tested for the FTSE100 futures contract. 7 4 During the sample period used for FTSE100 index futures in this paper, both the Central Statistical Oce (CSO) and the Bank of England changed the release time for announcements from 11:30GMT to 09:30GMT. All the main CSO releases were at 09:30GMT from the ®rst announcement day after 23 August 1993. The monetary statistics released by the Bank of England changed to a 09:30GMT release time from 3 September 1993. Labour market statistics were released at 09:30GMT from 18 November 1993. 5 The above was repeated for the FTSE250 futures contract. The even-tick trades showed a crude U-shaped pattern across the day, but there were too few odd-tick trades to produce any discernible pattern. 6 Similar patterns are observed for the quotes and trades in the American-style FTSE100 index option contract. 7 Data availability prevents us from undertaking similar analysis for the other two derivatives in our sample.
Fig. 1. Intraday distribution of odd and even tick trades FTSE100 index futures contract.
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We also examine the relationship between the percentage of odd-tick trades and trade size, price, transaction frequency and volatility (in line with Harris (1991)). Section 3 above reported that mean trade size was larger for odd-tick trades, implying an expected positive coecient here. Harris (1991) shows that a greater proportion of odd-ticks occurs in low priced trades, but as the index futures price only varies over a relatively narrow range such a relationship is not expected here. Harris (1991) also ®nds that clustering decreases with transaction frequency and uses the inverse square root transformation due to information-theoretic considerations, showing that price uncertainty is proportional to the inverse square root of the number of transactions. 8 This implies a negative coecient for this variable here. Clustering is expected to increase in periods of high volatility, and the coecient on mean absolute return is thus expected to have a negative coecient. The following regression is estimated: ODDt a b1 D1 b2 D2 c1 St c2 Pt c3 Tt c4 ARt t ;
1
where ODDt is the percentage of trades which occur at an odd tick for interval n n 1; . . . ; 23 on day i i 1; . . . ; 846; D1 is a (0, 1) dummy variable for the opening interval of the day; D2 is a dummy for the closing interval; St is the mean trade size in interval n on day i; Pt is the mean trade price in interval n on day i; Tt is the inverse square root of the number of transactions per 5 min (see below) in interval n on day i; and ARt is the absolute return across interval n on day i. 9 Table 5 reports the results, and shows a strongly signi®cant higher percentage of odd-tick trades near the close, and also the percentage of odd-tick trades near the open is signi®cantly lower than the rest of the day. There is a signi®cant positive relationship between the percentage of odd-tick trades and mean trade size, an insigni®cant relationship with the price level, and a strongly signi®cant negative relationship with volatility. Although the above results con®rm prior expectations, the strong positive relationship between the inverse of transaction frequency and odd ticks implies that odd ticks are used more frequently during quiet trading periods, a result which is in contrast to the evidence by Harris (1991). Although higher trading frequency is hypothesised to reveal greater price certainty (Harris, p. 402), it seems that in this open
8 Harris (1991) states: ``Suppose that each transaction conveys information about underlying value plus some noise. Underlying value estimators computed from the transaction sequence would then have standard errors that are proportional to the square root of the number of transactions observed''. The inverse transformation is also useful because clustering should not decrease without limit as transaction frequency increases because other factors also determine minimum tick sizes. 9 We only use front-month contracts for this regression, and due to the low frequency of oddticks it was necessary to use 20-min intervals across the trading day, with an opening interval of 15 min. The number of transactions per ®ve minutes is used due to this shorter opening interval.
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Table 5 The relationship between odd-tick trades and market closure, trade size, price, transaction frequency and volatility for FTSE100 stock index futures Variable
Coecient
t-statistic
a b1 (08:35±08:50) b2 (15:50±16:10) c1 c2 c3 c4
0.085 )0.156 0.571 0.049 0.001 2.668 )1.218
0.20 )2.06 5.23 2.98 0.87 7.36 )7.30
b a a
a a
The estimation is by Generalised Method of Moments (GMM) to ensure robustness to heteroscedasticity and autocorrelation. Intervals with no trade were omitted, resulting in estimation over 19,392 observations (846 days ´ 23 intervals (19458) minus 66 missing). Times are GMT. a Signi®cant at 1%. b Signi®cant at 5%.
outcry setting the use of odd ticks is cumbersome during busy periods and discussion with LIFFE sta con®rmed this proposition. 4.2. The relationship between bid±ask spreads and odd ticks A concern arising from the reporting of extreme clustering at NASDAQ was the implications for transactions costs in the form of wider spreads. The intraday pattern in odd tick frequency identi®ed here may be consistent with the existence of wide bid±ask spreads near the market open and a narrowing of spreads at the close. We examine the FTSE100 futures contract to gauge the impact of the avoidance of odd-tick quotes on bid±ask spreads. Since our dataset includes a complete record of bid and ask quotes, the quoted spread can be measured directly. We take the ®rst bid and ®rst ask of each day as the opening spread, and then split the remainder of the day into 5-min intervals. For each interval on each day, the last bid and last ask are used to compute the spread. Because trading in this contract is concentrated in the front-month contract through to expiry, this contract is used until the day before its expiry, when the series moves on to the next contract. With the exception of the opening and closing intervals, the mean spread for each interval is around 1.3 index points. The mean spread is far wider at the open than during the rest of the day, and this also corresponds with a period containing a signi®cantly low proportion of odd-tick trades as discussed above. Wide spreads at the open are likely to be due to a need for protection against overnight information. A narrowing of the spread observed in the closing interval is consistent with the increased proportion of odd-ticks discussed above. The closing interval is the only case where the mean spread is below one index point. Also, whereas spreads at the open are highly variable across days, closing spreads are consistently narrow.
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Table 6 The relationship between bid±ask spreads and odd-ticks, and market closure for the FTSE100 stock index futures contract Variable
Coecient
t-statistic
a b1 (08:35±08:40) b2 (15:55±16:10) c
1.381 1.267 )0.269 )0.056
321.30 13.27 )14.37 )12.55
a a a a
The estimation is by Generalised Method of Moments (GMM) to ensure robustness to heteroscedasticity and autocorrelation. Intervals with no bid and/or no ask were omitted, resulting in estimation for 24,921 observations (845 days ´ 31 intervals (26195) minus 1274 missing). Times are GMT. a Signi®cant at 1%.
We now test the signi®cance of the relationship between the spread and the frequency of odd-tick quotes, and the signi®cance of wide spreads at the open and narrow spreads at the close, by estimating the following regression 10 St a b1 D1 b2 D2 cODDt t ;
2
where St is the absolute quoted spread for interval n n 1; . . . ; 31 on day i (i 1, 845); and (0, 1) dummy variables are included for the opening (D1) and closing (D2) intervals of the trading day. 11 The variable ODDt represents the number of odd-tick quotes per 5-min interval for interval n on day i. 12 Table 6 presents the results, which con®rm prior expectations. The coecient on the dummy for the opening interval is signi®cantly positive, and the coecient for the closing interval is signi®cantly negative. The coecient for the number of odd-ticks is also signi®cantly negative, con®rming the hypothesis of an inverse relationship between the number of odd-tick quotes in an interval and the level of the bid±ask spread. Given the extreme price clustering at even-tick quotes documented for the FTSE100 futures contract, we also expect bid±ask spreads to cluster at even tick values, since an odd-tick value of the spread requires one side of the spread to be at an even-tick and the other to be at an odd-tick. We ®nd that 97.8% of spreads are at even-ticks, and almost two-thirds are at two ticks (one index
10 Due to the low frequency of odd-ticks, it was necessary to use 15-min intervals across the trading day. The opening spread was retained and associated with the number of odd-ticks in the ®rst 5-min interval of the day. The remainder of the day was split into thirty equal intervals of 15 min, with the spread being based on the last bid and last ask in an interval as above, and the number of odd-tick quotes was divided by 3 for consistency with the opening interval. 11 We have 845 days for quotes, while there were 846 days for trades, because the quotes data for 27 March 1992 is absent from the time and sales tape. 12 Following the comments of an anonymous referee, we re-estimated this equation replacing the opening spread with the spread at the end of the ®rst 5-min interval of the day. The coecients were virtually unchanged.
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point). Only 1.37% of spreads are at the minimum value of one tick. Similar results are found for the FTSE100 index options. 5. Summary and conclusions This paper is the ®rst to document price clustering in ®nancial derivatives. We ®nd that quotes and trades in the FTSE100 stock index futures and options contracts and the FTSE250 stock index futures contract are heavily concentrated at full index points despite a minimum tick of 0.5 index points. For each contract, around 98% of trades occur at full index points. The FTSE250 futures and FTSE100 options also exhibit clustering at the decimals 0 and 5 for the ®nal whole digit of price. The options contracts show a tendency for any trades and quotes at odd tick values to be for low priced contracts such as those which are out-of-the-money and/or nearing maturity, which is consistent with the evidence by Harris (1991) for US stocks. These results suggest that the market does not seem to require the additional price re®nement of half index points, and support the price resolution hypothesis by Ball et al. (1985). A major innovation of this study is the examination of clustering on an intraday basis. For the FTSE100 futures contracts, we report a signi®cant relationship between the percentage of trades at an odd tick and mean trade size. This is consistent with the negotiation hypothesis by Harris (1991) in that larger trade sizes justify the costs of negotiating prices. We also ®nd that the proportion of odd ticks is signi®cantly lower near the market open, and signi®cantly higher near the close. Clustering increases with volatility and with transaction frequency. The former supports expectations, but the latter is contrary to Harris (1991). A signi®cant inverse relationship is reported between the bid±ask spread and the number of odd ticks. Wide spreads at the open correspond with a low percentage of odd ticks, while narrow spreads near the close correspond with a relatively high percentage of odd ticks. This intraday pattern suggests that the use of odd ticks is driven more by the desired quoted spread than by volume of trading (which is high at both open and close). We also document clustering of the bid±ask spread, with 98% of spreads at even-tick values. The results support both the price resolution hypothesis by Ball et al. (1985), and to a lesser extent, the negotiation hypothesis by Harris (1991). We ®nd only limited evidence for the attraction hypothesis by Goodhart and Curcio (1991), speci®cally in the price clustering characteristics of the FTSE250 futures and FTSE100 options contracts. Although odd ticks are used rarely in these markets, those instances when they are used more frequently, for example at the close of trading and for larger volume trades, may be extremely important for a trader needing to unwind a position rapidly. Therefore, although an increase in the minimum tick to a full index point may reduce negotiation costs
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by reducing the available price set, this would be achieved at the expense of wider spreads at the close of trading and for relatively large trades. References Ball, C.A., Torous, W.A., Tschoegl, A.E., 1985. The degree of price resolution: The case of the gold market. Journal of Futures Markets 5, 29±43. Brown, S., Laux, P., Schachter, B., 1991. On the existence of an optimal tick size. Review of Futures Markets 10, 50±72. Christie, W.G., Schultz, P.H., 1994. Why do NASDAQ market makers avoid odd-eighth quotes? Journal of Finance 49, 1813±1840. Christie, W.G., Harris, J.H., Schultz, P.H., 1994. Why did NASDAQ market makers stop avoiding odd-eighth quotes? Journal of Finance 49, 1841±1860. Ekman, P.D., 1992. Intraday patterns in the S&P500 index futures market. Journal of Futures Markets 12, 365±382. Goodhart, C., Curcio, R., 1991. The clustering of bid-ask prices and the spread in the foreign exchange market. Discussion paper 110. London School of Economics, London. Gottlieb, G., Kalay, A., 1985. Implications of the discreteness of observed stock prices. Journal of Finance 40, 135±153. Grossman, S.J., Miller, M.H., Fischel, D.R., Cone, K.R., Ross, D.J., 1996. Clustering and competition in asset markets. A Lexecon report. Harris, L.E., 1991. Stock price clustering and discreteness. Review of Financial Studies 4, 389±415.
Extreme price clustering in the London equity index futures and options markets Owain ap Gwilym a, Andrew Clare b, Stephen Thomas a
a,*,1
Department of Management, University of Southampton, High®eld, Southampton S017 1BJ, UK b ISMA Centre, Department of Economics, University of Reading, UK Received 27 May 1997; accepted 18 March 1998
Abstract Price clustering and optimal tick sizes have recently been topics of substantial public policy interest, and this paper presents evidence which is relevant to both debates. Around 98% of quoted and traded prices for LIFFE stock index derivatives are found to occur at even ticks. We report that clustering increases with volatility and transaction frequency, and decreases with trade size, and ®nd that the proportion of odd ticks is signi®cantly lower near the market open and higher near the close. Further, an inverse relationship is reported between bid±ask spreads and the number of odd ticks, and spreads cluster at even-tick values. This evidence of extreme price clustering is the ®rst to be presented for ®nancial derivatives. The results support both the price resolution and the negotiation hypotheses of price clustering. Ó 1998 Elsevier Science B.V. All rights reserved. JEL classi®cation: G12 Keywords: Clustering; NASDAQ; Tick size; Bid±ask spreads; Intraday data
*
Corresponding author. Tel.: 44 1703 593068; fax: 44 1703 593844; e-mail: [email protected]. 1 This paper bene®ted considerably from the comments and suggestions of two anonymous referees. We are grateful for helpful comments from participants at the 1997 Cornell±Queen's Derivatives Securities Conference, the 1997 BNP-Imperial College Forecasting Financial Markets Conference, and the 1997 International Symposium on Forecasting. The authors also gratefully acknowledge the ®nancial support of the Leverhulme Trust (Grant F391/I). 0378-4266/98/$19.00 Ó 1998 Elsevier Science B.V. All rights reserved. PII S 0 3 7 8 - 4 2 6 6 ( 9 8 ) 0 0 0 5 4 - 5
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1. Introduction Price clustering is the occurrence of signi®cantly greater than 50% of quoted and/or traded prices at even price fractions, or of certain integers. This phenomenon has become a topic of substantial public policy interest following the publication of research ®ndings by Christie and Schultz (1994) that market makers in actively traded NASDAQ stocks may have implicitly colluded to maintain bid-ask spreads of at least $0.25 by avoiding odd-eighth quotes. Shortly after the Christie and Schultz (1994) results were publicised, dealers in a number of major stocks, including Apple and Microsoft, rapidly increased their use of odd-eighth quotes which led to a decline in mean inside and effective spreads of nearly 50% (see Christie et al., 1994). Evidence of price clustering has also been documented in other markets, e.g. Goodhart and Curcio (1991) for foreign exchange markets, Ball et al. (1985) for the gold market, and Grossman et al. (1996) for equity, foreign exchange and gold markets. However, no previous study has examined the phenomenon in ®nancial derivatives markets. Several theories have been proposed to explain the observation of price clustering. The attraction theory proposed by Goodhart and Curcio (1991) suggests that discrete trading prices are obtained from continuously distributed underlying values by rounding to the nearest available ®nal unit (as in Gottlieb and Kalay, 1985), but the basic attraction of each integer varies. Ball et al. (1985) suggest that clustering results from the achievement of the optimal degree of price resolution, i.e. the desired level of price accuracy. The negotiation hypothesis by Harris (1991) suggests that a smaller price set is chosen by market participants to limit the number of bids and asks that can be made and thus lowers the costs of negotiation. In this paper we ®nd evidence of extreme clustering in the quoted and traded prices of the equity index futures and options contracts traded on the London International Financial Futures and Options Exchange (LIFFE), and thus present the ®rst evidence of this phenomenon for ®nancial derivatives. We ®nd that although the minimum tick size for FTSE derivatives is half an index point, 98.3% of quotes and 98.4% of trades occur at even ticks (full index points) for the FTSE100 futures contract. Similar ®ndings are reported for options on the FTSE100 index and for the FTSE250 futures contracts, with additional clustering at the values 0 and 5 for the fourth index digit in the latter case. In general our results support the price resolution hypothesis by Ball et al. (1985) which implies that the price clustering in this market results from the achievement of the desired level of price accuracy. However, we also ®nd relationships between clustering and trade sizes and volatility which support the negotiation hypothesis by Harris (1991). The remainder of this paper is organised as follows. Section 2 outlines the market structure of LIFFE and the dataset, while Section 3 presents results on
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the extent of price clustering with interpretations in the light of existing theory. Section 4 examines intraday variability in price clustering, which has not previously been considered, and Section 5 concludes. 2. Market structure and the dataset Consideration of market structure is important because it has been argued that the high degree of clustering at NASDAQ was due to some defect in its market structure. LIFFE operates an open outcry trading system similar to those at US futures markets e.g. Chicago Mercantile Exchange (CME). At LIFFE, there are currently two futures contracts traded on equity indices. By far the most heavily traded is the FTSE100 stock index futures contract, which is based upon the top 100 UK companies by market capitalisation. A more recently introduced and less heavily traded futures contract is based upon the FTSE250, which is an index of the next 250 largest stocks by market capitalisation. LIFFE also trades both American- and European-style options on the FTSE100 stock index. Dependent on series and maturity, there can be up to ®fty price makers active at any time in the FTSE100 stock index futures and options markets, but often only two or three in the FTSE250 index futures. Trading in the FTSE100 futures market occurs by open outcry from 08:35± 16:10GMT, and by Automated Pit Trading (APT) from 16:32±17:30GMT. The vast majority of trading in this derivative occurs in the front month contract up to its last trading day, at which point a switch occurs to the immediately succeeding contract. The contract is currently valued at, £25 per index point, with a minimum price movement of 0.5 index points. At the average price for FTSE100 futures in our sample of 2966.4, the tick value is 1.7 basis points (12.5/(25 ´ 2966.4)). Most stocks in London are quoted in ticks of 1 pence and with an average price of around £4, this translates to 25 basis points. Pit trading hours for the options contract are the same as for the FTSE100 futures, while the FTSE250 futures market opens and closes ®ve minutes earlier. Tick size for the FTSE100 options and the FTSE250 index futures is half an index point, with a tick value of £5 for both contracts. The FTSE100 index futures and options are traded in two separate pits that are adjacent to one another to facilitate trading and hedging. Traders commonly delta hedge options positions using the index futures. All contract maturities are traded in the same pit by the same traders. Large orders are split among multiple buyers/sellers in the pit on a pro rata basis. The dataset includes all quotes and trades on the FTSE100 stock index futures contracts from 24 January 1992 to 30 June 1995 (consisting of 923,703 trades and 1,780,785 quotes). The source is the LIFFE Time and Sales data on CD-ROM, which contains information on the time to the nearest second, contract type, ¯oor or APT trading, commodity code, delivery month, price,
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transaction code (bid, ask or trade), and traded volume. Trades and quotes taking place during APT are not considered here. Similar data for the FTSE250 stock index futures contract is available from its inception on 25 February 1994 to 30 June 1995 (consisting of 1,358 trades and 7,512 quotes). Data on the American-style option on the FTSE100 stock index from 4 January 1993 to 31 March 1994 (consisting of 97,574 trades and 223,681 matched bids and asks) is obtained from a separate source. These options are chosen rather than the European-style equivalent due to greater liquidity. 3. Results 3.1. Clustering and the price resolution hypothesis Table 1 presents results for the number and percentage of trades which occur at odd and even ticks for the FTSE100 futures contract. Over the entire sample, 98.4% of trades on all contracts occur at even ticks, a result which is robust across sub-samples. Out of a total of 1.78 million bids and asks, only 30,222 (1.7%) occurred at odd ticks. The results in Table 1 are supportive of the price resolution hypothesis by Ball et al. (1985), i.e. the market does not seem to require the additional price re®nement of half index points. Splitting of large orders among multiple buyers or sellers in the pit could impact on the level of observed price clustering. The transaction record does not make any distinction between multiple trades at a given price based on a single order and multiple trades at a given price based on dierent orders. To account for this, we re-examined clustering frequencies following aggregation of all trades at the same price within one-minute intervals. 2 The results were materially unchanged: over the entire sample, 97.7% of trades occurred at even ticks, with little variation across sub-samples. The FTSE250 index futures contract also displays a high degree of price clustering, with 98.5% (99.4%) of trades in all contracts (front-month only) Table 1 Number and percentage of FTSE100 stock index futures trades occurring at odd and even ticks Sample Full sample 1/92±6/95
2
All contracts
Front month contract only
Even ticks
Odd ticks
Even ticks
Odd ticks
909005 98.41%
14698 1.59%
884918 98.81%
10614 1.19%
We are grateful to an anonymous referee for this suggestion.
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occurring at even ticks. Only 15 (0.2%) quotes occurred at odd ticks over this sample. For the American-style FTSE100 index options contract, we ®nd that 97.7% of bids, 98.1% of asks and 95.9% of trades occur at even ticks, once again supporting the hypothesis by Ball et al. (1985). Table 2 presents a more detailed analysis of this by contract moneyness and maturity. The largest proportion of odd ticks is for out-of-the-money, near-maturity options which is the lowest priced category. Clustering tends to decrease as maturity approaches and is less severe for out-of-the-money contracts. For in-the-money contracts with longer than a month to maturity, occurrence of odd ticks is close to zero. Overall, the observations which do occur at odd ticks tend to be in relatively low price option contracts, which is consistent with the evidence by Harris (1991) from the NYSE/AMEX markets that price clustering tends to increase with the price level. 3.2. The attraction hypothesis Given that odd ticks are so rare in the FTSE derivative contracts, we conduct further analysis based on the ®nal digit of the price (eectively assuming that the minimum price movement is one index point). In Table 3, traded and quoted prices are split into the ten possible integer values for the ®nal digit. For the FTSE100 stock index futures contract we ®nd little evidence of a preference for any integer values, with trades and quotes generally occurring approximately 10% of the time in each of the ten digits. The largest deviations are for the integers 1 and 9, discussed as the least popular digits in Goodhart and Curcio (1991). However, the FTSE250 futures and FTSE100 options show a dierent pattern. For the FTSE250 contract, 78% of bids and asks, and 69% of trades have either 0 or 5 as the ®nal digit, while 2 is the next most popular digit at 7% of trades. For the FTSE100 options, over 30% of trades occur at a ®nal digit of zero, with 5 being the next popular digit at 9.6%. Clustering is less severe in quotes, but there are still 28% with ®nal integers taking the values of 0 or 5. These two contracts thus oer strong support for the Goodhart and Curcio (1991) attraction hypothesis in the ®nal integers of the price. 3.3. The negotiation hypothesis The negotiation hypothesis by Harris (1991) suggests that a smaller price set limits the number of bids and asks which can be made and thus lowers the costs of negotiation; hence participants will tend to prefer a smaller price set. However, for larger trades market participants may ®nd it worthwhile negotiating on a wider range of prices. We examine the relationship between odd and even tick trades and the respective mean trade size for the FTSE100
99.1 97.8 82.7 97.3
97.0 95.5 76.2 94.7
100 99.5 93.3 98.7
Bid
99.1 97.4 78.8 96.7
2nd
Trade
Bid
Ask
Near
Maturity
99.9 99.6 94.7 99.0
Ask 99.1 98.7 89.2 97.6
Trade
Ask
Trade
100 100 100 99.7 99.8 99.0 96.1 96.3 91.5 98.9 99.0 97.4
Bid
3rd Ask
100 100 99.7 99.6 97.8 98.9 99.1 99.4
Bid
4th 99.0 98.0 92.9 96.7
Trade 99.9 99.8 98.6 99.3
Bid
Other 99.7 99.9 98.9 99.5
Ask
99.0 98.3 97.5 98.0
Trade
99.6 98.3 92.2 97.7
Bid
Total
99.5 98.6 93.7 98.1
Ask
98.0 96.8 87.4 95.9
Trade
This table presents the percentage of bid, asked and traded prices which occur at even ticks, classi®ed by moneyness and maturity. For American-style FTSE100 stock index options, the available expiry dates at any given time are June and December plus additional months such that the four nearest calendar months are always available for trading. The maturity categories used here re¯ect this, with the ®rst category de®ned as the nearest expiry, the second category is the second nearest expiry, and so on. The moneyness categories are de®ned as IN (in-the-money), AT (near-the-money) and OUT (out-of-the-money) according to the ratio of the underlying price to the exercise price (S/K) as follows: 0< S/K 6 0.95 is OUT for calls and IN for puts, 0.95 < S/K < 1.05 is AT for both calls and puts, and 1.05 6 S/K <1 is IN for calls and OUT for puts.
IN AT OUT Total
S/K
Table 2 Price clustering in American-style FTSE100 stock index options classi®ed by moneyness and maturity
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Table 3 Price clustering on fourth digit of index value for FTSE100 and FTSE250 stock index futures contracts, and ®nal whole digit of option price
0 1 2 3 4 5 6 7 8 9
FTSE100 futures
FTSE250 futures
FTSE100 options
Trades
Quotes
Trades
Quotes
Trades
Quotes
10.2 8.9 9.9 10.0 10.2 10.5 10.4 10.3 10.3 9.3
10.0 8.9 10.0 10.0 10.2 10.6 10.4 10.4 10.5 9.2
39.9 3.2 7.2 3.0 3.8 28.8 3.4 3.8 4.3 2.7
45.5 1.6 4.2 2.6 2.5 32.5 2.2 3.8 3.5 1.7
30.8 7.1 8.6 7.8 7.5 9.6 7.3 7.4 8.0 5.8
15.3 8.0 10.8 9.7 8.6 12.6 7.9 9.3 10.7 7.1
The table presents the percentages of traded and quoted price occurring at the ®nal whole digit of the price, i.e. eectively assuming a minimum price movement of one index point rather than half an index point.
futures contract. 3 If the negotiation hypothesis is valid we would expect to ®nd a higher probability of odd-ticks for trades of a larger size, and Table 4 presents direct evidence on this. For the limited number of trades that occur at odd-ticks in the FTSE100 futures market, mean trade size is far higher than for even-tick trades. For the entire sample, the average trade for even ticks is for 6.5 contracts, whereas for odd tick trades the equivalent value is 19.5 contracts, a result which is robust across sub-samples. These results are consistent with those of Brown et al. (1991) for COMEX silver futures. For the NASDAQ stocks in their sample whose market makers rarely use oddeighths, Christie and Schultz (1994) ®nd that large trades are far more likely to occur on odd eighths than are small trades. Such evidence suggests that the bene®ts of larger trades justify additional negotiation costs. Table 4 Mean trade sizes for FTSE100 stock index futures trades at odd and even ticks Sample
All contracts
Front month contract only
Even ticks
Odd ticks
Even ticks
Odd ticks
Full sample 1/92±6/95
6.50
19.47
6.17
14.31
3 There are too few odd-tick trades in the FTSE250 futures to conduct a similar meaningful analysis of the relationship between even and odd tick trades and trade size. In addition, volume data is not available for the FTSE100 options contract and therefore we cannot undertake the analysis for this contract either.
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4. Intraday variability in price clustering 4.1. The intraday occurrence of odd ticks Though Grossman et al. (1996) report variation in clustering over time, previous studies have not considered the possibility of variability in the level of clustering on an intraday basis. If the negotiation hypothesis holds, we would expect to observe a greater proportion of odd ticks during low volume and low volatility periods. Previous studies (e.g. Ekman, 1992) document that the middle of the day tends to be a time of relatively low volume and volatility in stock index futures markets, with periods of high volume and volatility near the open and close. Fig. 1 plots the number of odd and even tick trades for the FTSE100 futures contract per 5-min interval during the day. The pattern for even-tick trades follows a familiar U-shaped intraday pattern in trading volume. Notable peaks occur during the intervals ending 09:35GMT, 11:35GMT, and 13:35GMT, which correspond to the principal UK releases in the period from Autumn 1993, UK releases prior to Autumn 1993, and principal US releases, respectively. 4 However, the pattern for odd-tick trades diers markedly in that there is an elevated number of trades in the last interval of the day only, which is approximately double the level for most of the rest of the day. 5 A relatively low percentage of odd-tick trades is found near the market open, with relatively high percentages around lunchtime (a period of low volume) and near the close of trading. Since negotiation costs would generally be higher in periods of high volume and volatility, the observation of few odd-ticks near the open lends additional support to the negotiation hypothesis. However, the observation of an increase in odd-ticks near the market close is clearly in con¯ict with this hypothesis. 6 The signi®cance of the low percentage of odd-ticks at the market open, and high percentage at the close is now tested for the FTSE100 futures contract. 7 4 During the sample period used for FTSE100 index futures in this paper, both the Central Statistical Oce (CSO) and the Bank of England changed the release time for announcements from 11:30GMT to 09:30GMT. All the main CSO releases were at 09:30GMT from the ®rst announcement day after 23 August 1993. The monetary statistics released by the Bank of England changed to a 09:30GMT release time from 3 September 1993. Labour market statistics were released at 09:30GMT from 18 November 1993. 5 The above was repeated for the FTSE250 futures contract. The even-tick trades showed a crude U-shaped pattern across the day, but there were too few odd-tick trades to produce any discernible pattern. 6 Similar patterns are observed for the quotes and trades in the American-style FTSE100 index option contract. 7 Data availability prevents us from undertaking similar analysis for the other two derivatives in our sample.
Fig. 1. Intraday distribution of odd and even tick trades FTSE100 index futures contract.
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We also examine the relationship between the percentage of odd-tick trades and trade size, price, transaction frequency and volatility (in line with Harris (1991)). Section 3 above reported that mean trade size was larger for odd-tick trades, implying an expected positive coecient here. Harris (1991) shows that a greater proportion of odd-ticks occurs in low priced trades, but as the index futures price only varies over a relatively narrow range such a relationship is not expected here. Harris (1991) also ®nds that clustering decreases with transaction frequency and uses the inverse square root transformation due to information-theoretic considerations, showing that price uncertainty is proportional to the inverse square root of the number of transactions. 8 This implies a negative coecient for this variable here. Clustering is expected to increase in periods of high volatility, and the coecient on mean absolute return is thus expected to have a negative coecient. The following regression is estimated: ODDt a b1 D1 b2 D2 c1 St c2 Pt c3 Tt c4 ARt t ;
1
where ODDt is the percentage of trades which occur at an odd tick for interval n n 1; . . . ; 23 on day i i 1; . . . ; 846; D1 is a (0, 1) dummy variable for the opening interval of the day; D2 is a dummy for the closing interval; St is the mean trade size in interval n on day i; Pt is the mean trade price in interval n on day i; Tt is the inverse square root of the number of transactions per 5 min (see below) in interval n on day i; and ARt is the absolute return across interval n on day i. 9 Table 5 reports the results, and shows a strongly signi®cant higher percentage of odd-tick trades near the close, and also the percentage of odd-tick trades near the open is signi®cantly lower than the rest of the day. There is a signi®cant positive relationship between the percentage of odd-tick trades and mean trade size, an insigni®cant relationship with the price level, and a strongly signi®cant negative relationship with volatility. Although the above results con®rm prior expectations, the strong positive relationship between the inverse of transaction frequency and odd ticks implies that odd ticks are used more frequently during quiet trading periods, a result which is in contrast to the evidence by Harris (1991). Although higher trading frequency is hypothesised to reveal greater price certainty (Harris, p. 402), it seems that in this open
8 Harris (1991) states: ``Suppose that each transaction conveys information about underlying value plus some noise. Underlying value estimators computed from the transaction sequence would then have standard errors that are proportional to the square root of the number of transactions observed''. The inverse transformation is also useful because clustering should not decrease without limit as transaction frequency increases because other factors also determine minimum tick sizes. 9 We only use front-month contracts for this regression, and due to the low frequency of oddticks it was necessary to use 20-min intervals across the trading day, with an opening interval of 15 min. The number of transactions per ®ve minutes is used due to this shorter opening interval.
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Table 5 The relationship between odd-tick trades and market closure, trade size, price, transaction frequency and volatility for FTSE100 stock index futures Variable
Coecient
t-statistic
a b1 (08:35±08:50) b2 (15:50±16:10) c1 c2 c3 c4
0.085 )0.156 0.571 0.049 0.001 2.668 )1.218
0.20 )2.06 5.23 2.98 0.87 7.36 )7.30
b a a
a a
The estimation is by Generalised Method of Moments (GMM) to ensure robustness to heteroscedasticity and autocorrelation. Intervals with no trade were omitted, resulting in estimation over 19,392 observations (846 days ´ 23 intervals (19458) minus 66 missing). Times are GMT. a Signi®cant at 1%. b Signi®cant at 5%.
outcry setting the use of odd ticks is cumbersome during busy periods and discussion with LIFFE sta con®rmed this proposition. 4.2. The relationship between bid±ask spreads and odd ticks A concern arising from the reporting of extreme clustering at NASDAQ was the implications for transactions costs in the form of wider spreads. The intraday pattern in odd tick frequency identi®ed here may be consistent with the existence of wide bid±ask spreads near the market open and a narrowing of spreads at the close. We examine the FTSE100 futures contract to gauge the impact of the avoidance of odd-tick quotes on bid±ask spreads. Since our dataset includes a complete record of bid and ask quotes, the quoted spread can be measured directly. We take the ®rst bid and ®rst ask of each day as the opening spread, and then split the remainder of the day into 5-min intervals. For each interval on each day, the last bid and last ask are used to compute the spread. Because trading in this contract is concentrated in the front-month contract through to expiry, this contract is used until the day before its expiry, when the series moves on to the next contract. With the exception of the opening and closing intervals, the mean spread for each interval is around 1.3 index points. The mean spread is far wider at the open than during the rest of the day, and this also corresponds with a period containing a signi®cantly low proportion of odd-tick trades as discussed above. Wide spreads at the open are likely to be due to a need for protection against overnight information. A narrowing of the spread observed in the closing interval is consistent with the increased proportion of odd-ticks discussed above. The closing interval is the only case where the mean spread is below one index point. Also, whereas spreads at the open are highly variable across days, closing spreads are consistently narrow.
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Table 6 The relationship between bid±ask spreads and odd-ticks, and market closure for the FTSE100 stock index futures contract Variable
Coecient
t-statistic
a b1 (08:35±08:40) b2 (15:55±16:10) c
1.381 1.267 )0.269 )0.056
321.30 13.27 )14.37 )12.55
a a a a
The estimation is by Generalised Method of Moments (GMM) to ensure robustness to heteroscedasticity and autocorrelation. Intervals with no bid and/or no ask were omitted, resulting in estimation for 24,921 observations (845 days ´ 31 intervals (26195) minus 1274 missing). Times are GMT. a Signi®cant at 1%.
We now test the signi®cance of the relationship between the spread and the frequency of odd-tick quotes, and the signi®cance of wide spreads at the open and narrow spreads at the close, by estimating the following regression 10 St a b1 D1 b2 D2 cODDt t ;
2
where St is the absolute quoted spread for interval n n 1; . . . ; 31 on day i (i 1, 845); and (0, 1) dummy variables are included for the opening (D1) and closing (D2) intervals of the trading day. 11 The variable ODDt represents the number of odd-tick quotes per 5-min interval for interval n on day i. 12 Table 6 presents the results, which con®rm prior expectations. The coecient on the dummy for the opening interval is signi®cantly positive, and the coecient for the closing interval is signi®cantly negative. The coecient for the number of odd-ticks is also signi®cantly negative, con®rming the hypothesis of an inverse relationship between the number of odd-tick quotes in an interval and the level of the bid±ask spread. Given the extreme price clustering at even-tick quotes documented for the FTSE100 futures contract, we also expect bid±ask spreads to cluster at even tick values, since an odd-tick value of the spread requires one side of the spread to be at an even-tick and the other to be at an odd-tick. We ®nd that 97.8% of spreads are at even-ticks, and almost two-thirds are at two ticks (one index
10 Due to the low frequency of odd-ticks, it was necessary to use 15-min intervals across the trading day. The opening spread was retained and associated with the number of odd-ticks in the ®rst 5-min interval of the day. The remainder of the day was split into thirty equal intervals of 15 min, with the spread being based on the last bid and last ask in an interval as above, and the number of odd-tick quotes was divided by 3 for consistency with the opening interval. 11 We have 845 days for quotes, while there were 846 days for trades, because the quotes data for 27 March 1992 is absent from the time and sales tape. 12 Following the comments of an anonymous referee, we re-estimated this equation replacing the opening spread with the spread at the end of the ®rst 5-min interval of the day. The coecients were virtually unchanged.
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point). Only 1.37% of spreads are at the minimum value of one tick. Similar results are found for the FTSE100 index options. 5. Summary and conclusions This paper is the ®rst to document price clustering in ®nancial derivatives. We ®nd that quotes and trades in the FTSE100 stock index futures and options contracts and the FTSE250 stock index futures contract are heavily concentrated at full index points despite a minimum tick of 0.5 index points. For each contract, around 98% of trades occur at full index points. The FTSE250 futures and FTSE100 options also exhibit clustering at the decimals 0 and 5 for the ®nal whole digit of price. The options contracts show a tendency for any trades and quotes at odd tick values to be for low priced contracts such as those which are out-of-the-money and/or nearing maturity, which is consistent with the evidence by Harris (1991) for US stocks. These results suggest that the market does not seem to require the additional price re®nement of half index points, and support the price resolution hypothesis by Ball et al. (1985). A major innovation of this study is the examination of clustering on an intraday basis. For the FTSE100 futures contracts, we report a signi®cant relationship between the percentage of trades at an odd tick and mean trade size. This is consistent with the negotiation hypothesis by Harris (1991) in that larger trade sizes justify the costs of negotiating prices. We also ®nd that the proportion of odd ticks is signi®cantly lower near the market open, and signi®cantly higher near the close. Clustering increases with volatility and with transaction frequency. The former supports expectations, but the latter is contrary to Harris (1991). A signi®cant inverse relationship is reported between the bid±ask spread and the number of odd ticks. Wide spreads at the open correspond with a low percentage of odd ticks, while narrow spreads near the close correspond with a relatively high percentage of odd ticks. This intraday pattern suggests that the use of odd ticks is driven more by the desired quoted spread than by volume of trading (which is high at both open and close). We also document clustering of the bid±ask spread, with 98% of spreads at even-tick values. The results support both the price resolution hypothesis by Ball et al. (1985), and to a lesser extent, the negotiation hypothesis by Harris (1991). We ®nd only limited evidence for the attraction hypothesis by Goodhart and Curcio (1991), speci®cally in the price clustering characteristics of the FTSE250 futures and FTSE100 options contracts. Although odd ticks are used rarely in these markets, those instances when they are used more frequently, for example at the close of trading and for larger volume trades, may be extremely important for a trader needing to unwind a position rapidly. Therefore, although an increase in the minimum tick to a full index point may reduce negotiation costs
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by reducing the available price set, this would be achieved at the expense of wider spreads at the close of trading and for relatively large trades. References Ball, C.A., Torous, W.A., Tschoegl, A.E., 1985. The degree of price resolution: The case of the gold market. Journal of Futures Markets 5, 29±43. Brown, S., Laux, P., Schachter, B., 1991. On the existence of an optimal tick size. Review of Futures Markets 10, 50±72. Christie, W.G., Schultz, P.H., 1994. Why do NASDAQ market makers avoid odd-eighth quotes? Journal of Finance 49, 1813±1840. Christie, W.G., Harris, J.H., Schultz, P.H., 1994. Why did NASDAQ market makers stop avoiding odd-eighth quotes? Journal of Finance 49, 1841±1860. Ekman, P.D., 1992. Intraday patterns in the S&P500 index futures market. Journal of Futures Markets 12, 365±382. Goodhart, C., Curcio, R., 1991. The clustering of bid-ask prices and the spread in the foreign exchange market. Discussion paper 110. London School of Economics, London. Gottlieb, G., Kalay, A., 1985. Implications of the discreteness of observed stock prices. Journal of Finance 40, 135±153. Grossman, S.J., Miller, M.H., Fischel, D.R., Cone, K.R., Ross, D.J., 1996. Clustering and competition in asset markets. A Lexecon report. Harris, L.E., 1991. Stock price clustering and discreteness. Review of Financial Studies 4, 389±415.