Trading behavior and price discovery during the S&P 500 rollover.
Recurring contract terminations provide an excellent laboratory to investigate the informational content of trades and price discovery in index futures. (1) We use high frequency transactions data from 1996 to 2001 and calculate several measures to take advantage of the peculiarities of this rollover period, which centers around the deterministic shift in volume from one contract to the next. These measures include effective bid/ask spread, volume, price volatility, price discovery across futures contracts, and market makers' income. While calculations of trading spreads, volumes, volatility, and income are straightforward, price discovery requires a more elaborate investigation. Hasbrouck (1995) defines the contribution to the price discovery process from related markets as the information share, which is the contribution from each price series to the variance of their common factor. Gonzalo and Granger (1995) use common factor components to measure price discovery. We calculate both Hasbrouck's information share and Gonzalo and Granger's common factor components in this study for different futures contracts during the rollover period to explore price discovery among the contracts.
In a paper closely related to ours, Kawaller, Koch, and Peterson (2001) examine the futures rollover period and find that the volume/volatility relationship is characterized by a surprising inverse relationship, looking across contract maturities. They also make the observation that there appears to be a corresponding shift of locals from trading the nearby to trading the next-out contract at the redesignation. Our empirical evidence builds on their findings, using a more detailed data set to both reaffirm and extend their basic results. Like Kawaller et al. (2001) we find a sizeable jump (as compared to a gradual change) in volume from the nearby to the next-out contract on the redesignation date, while volatility in the nearby contract also rises the moment it loses its lead status. Correspondingly, volatility falls and volume rises in the next-out contract the moment it is designated as the lead contract. There is also a jump in the number of locals from trading the nearby to trading the next-out contract at the redesignation, verifying the assertion of Kawaller et al. (2001).
These results confirm that our detailed data set and that used by Kawaller et al. (2001) do not conflict. The goal of this study, however, is to investigate the information content of trades and contracts during the futures rollover period. Kawaller et al. (2001) observe that the traditional information models indicate a positive volume and volatility relationship, and this is the puzzle that we are investigating. We further investigate the dynamics of price discovery across the nearby and next-out contract during the redesignation period, an analysis that extends Kawaller et al. (2001) in a natural direction. We also investigate some of the microstructural implications of the rollover period, in lieu of the informational role in microstructure models.
Based on our empirical evidence, both Hasbrouck's (1995) information shares and Gonzalo and Granger's (1995) common weights suggest that the nearby contract loses its price discovery leadership immediately upon redesignation. In other words, the designated lead contact is also empirically the price discovery leader. As a result, trading in the non-lead contract, which benefits from the price discovered in the same pit in the lead contract, should reveal less information asymmetry and by extension be subject to less of an information premium according to basic market microstructure. The premium would be exhibited in the bid ask spread, but we find little effect there. When market makers' per contract income is investigated, however, we find that market makers who specialize in trading the non-lead contract earn a high return from trading the non-lead contract. We are left with the argument that the bid ask premium comes directly from inventory issues associated with the non-lead contract rather than information asymmetry. Traders have an increased risk when trading the non-lead contract which is due to the infrequency of trading, rather than an asymmetric information problem. Thus, they earn higher per contract revenue from bearing the inventory risk. In other words, the increase in the liquidity premium (the inventory effect) overwhelms the decrease in any information premium so that there remains a high per contract income from high volume non-lead contract traders.
Our analysis hinges critically on the institutional structure of the S&P 500 futures market, especially the futures microstructure during our sample period. In this section we present an overview of that structure focusing on the description of the rollover period and the types of trading that will be occurring during the period. In addition, the description helps identify the mechanism that generates our data.
Every three months an S&P 500 futures contract matures, undergoing a final settlement and marking to market before disappearing from the Chicago Mercantile Exchange (CME). The contract ceases trading at 3:15 pm Chicago time on a Thursday afternoon, the day before the third Friday of the contract month. These maturing contracts are marked to market at the last-trading-day Thursday settlement price and then one last time on Friday when a final settlement is made for the contract (accomplished by marking any remaining open positions to market one final time and then closing them out). (2) This final mark-to-market, substituting for delivery to achieve convergence in the contract, uses a unique S&P 500 index value based on the Friday opening prices of the 500 S&P 500 stocks. (3) There are S&P 500 futures contracts maturing in March, June, September, and December. Contracts are listed for trading for a total of two years. Historically there has been extremely low volume in any particular S&P 500 index futures contract month until just a few weeks before the maturity of the prior contract or about 14 weeks prior to the last day to trade. In other words, while there are potentially eight contracts trading, on any day S&P index futures volume is highly concentrated in a single contract month.
Each day one S&P 500 contract month is designated by the exchange as the lead contract. Certain exchange rules are focused on the lead contract. For example, trading in the lead contract is subject to the top-step rule, which prohibits members from trading for a proprietary account in that contract month while standing on the top step of the trading pit. This would otherwise give proprietary traders a valuable view of the order flow from the trading desks. During our sample period, CME members who were actively trading the lead contract occupied the majority of the S&P 500 futures pit real estate. On the other hand, members offering to trade in non-lead contract months formed a mini-pit in a small section of the S&P 500 pit. During regular trading hours (8:30 am to 3:15 pm Chicago time in our data set) all S&P 500 futures trades other than E-mini trades were executed in the pit. (4)
Likewise E-mini proprietary trades are relegated to off-floor entry or, if on the floor, on electronic terminals off the top step and down in the pit. The top-step rule effectively results in the top step of the pit being reserved for commission brokers, who are CME members acting as agents. Traders executing proprietary trades, manually or using terminals for E-mini or lead month trading, are forced down in the pit or upstairs. The lead contract month is usually the contract month that is closest to maturity (the nearby contract). In the final week before the last trading day of a contract the bulk of trading in S&P 500 futures shifts to the next contract month (the next-out contract) as the CME redesignates this as the lead contract. Thus, the lead contract is sometimes the nearby and sometimes, for a very brief period, the next out.
Participants in the S&P 500 index futures market can be categorized in general terms by their fundamental reasons for trading, with a major distinction between members and non-members. Exchange members (owners or leaseholders) are able to execute trades for their proprietary accounts and are exclusively able to execute trades as agents for non-members. Traditionally, member proprietary trading in futures markets is considered to be market making, with, for example, rare overnight positions for proprietary trader accounts (Kuserk and Locke, 1993; Manaster and Mann, 1996).
Non-member trading in stock index futures arises primarily from institutional investors and securities broker dealers, with a small retail component, as well as options traders. This trading may be based on portfolio management, or may be based on arbitrage relationships. Some S&P 500 futures trading may be driven by index options or index futures options trading for hedging or arbitrage purposes. The securities and options based arbitrage trading in S&P 500 futures typically will occur in the lead contract month, as the bulk of options trading occurs place in shorter-term expirations.
Based on volume patterns, trading related to portfolio management also must be concentrated in the lead month, necessitating, for these traders, rolling forward at contract maturity if the portfolio management timing is not synchronized with the futures contract expiration cycle. As the last day to trade a contract nears, traders desiring to maintain the same S&P 500 futures exposure need to roll the position forward. In rolling, traders with long positions sell the nearby and buy the same number in the next-out contract, and traders with short positions buy the nearby and sell the next-out contract. These trades convey no information about the S&P 500 to the market, merely moving a position from one derivative to a nearly equivalent derivative. The timing of these trades is strategic, with traders searching for a situation when the combined cost of the two trades is minimized.
Several papers have examined the properties of intra-commodity spreads (month-to-month differences in the same commodity). Billingsley and Chance (1988) examine the efficiency of S&P 500 spreads using the cash index and proxies for the cost of carry. Similarly, Frino and McKenzie (2002) investigate how intramarket spreads in a comparable index futures market (the Australian All Ordinaries) vary over time using proxies for the cost of carry. Billingsley and Chance (1988) find that the S&P 500 contract spreads became increasingly efficient after the commencement of trading in 1982 with respect to their cost-of-carry proxies. Frino and McKenzie (2002) note that mispricing relative to their cost-of-carry proxies follows a pattern around contract maturity that is consistent with the liquidity effects of rolling the contract. Mispricing is defined by Frino and McKenzie (2002) as the difference between the spread between two successive futures contracts and the value calculated by using available interest rates and a perfect foresight dividend yield.
These papers do not examine the liquidity costs of each contract directly, as in measuring the bid ask spreads. Kawaller, Koch, and Peterson (2001) examine how the shift in volume from the nearby to the next-out contract affects the volatility of the two contracts, implying something about liquidity. The volume shift into the next-out contract lowers its volatility, suggesting that the volume is not based on information. In other words, if trading contained information, then more trading would mean more information flow, and hence more volatility. This study examines volume, volatility, rollover spread, and price discovery among futures contract to investigate their interactions.
Empirical Techniques Cointegration and Microstructure
Multiple contracts with different maturity dates trade in close proximity on the trading floor in futures markets. The prices of these different maturities are linked due to the relatively constant (intraday) rollover spreads and cannot diverge far before arbitrage trading will draw them together. Empirically, the prices of different maturities should share a common factor. The observed prices, after adjusting for the cost of carry, share in common the value of the underlying asset. In addition, each price has an idiosyncratic component that incorporates any microstructure effects and exhibits a zero-mean covariance-stationary process. Because these prices share a common factor and should be individually non-stationary, they should be cointegrated. With cointegrated price series we can estimate a vector error correction model (VECM) to uncover the dynamic relationship between the contract prices and the relative contributions to information.
We investigate the implied cointegration in several different ways using several different sampling methods. First, a sample of prices at five-minute frequencies from each contract month is taken to examine the cointegration of these unconditional prices. These are unconditional because we do not pay attention in this sample to whether a market maker is buying or selling. This would be a sample from prices observed to the world via price reporting, commonly known in futures trading as time and sales data. The vector error correction mechanism is given by:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
The price series [F.sub.1,t] and [F.sub.2,t] are the last prices observed in each maturity at the end of a five-minute window. The term [[mu].sub.uc] is the average level of the cost of carry between two maturities, a relatively constant number throughout one day.
Second, the role that arbitrage (or the threat of arbitrage) plays in constraining the spreads is considered. In particular, we assume that the process by which informational parity across contract months is enforced takes a particular form. We assume that the members on the floor executing proprietary trades will attempt to quote arbitrage-free prices. Unfortunately, these quotes are not recorded, but the identification of the principals behind each trade, ex post, is available in our data set. Thus, market maker (member proprietary trading) buys and sells can be identified ex post. Our paired arbitrage-free prices are market maker buy prices in one contact month and the sell prices in another contract month. Hence, our second cointegration model involves sampling these conditional prices, obtaining for each interval the last market maker buy and sell prices in each of the contract months, and pairing opposing buys and sells. This analysis is restricted to the nearby and next-out contracts, due to the trading infrequency in other contract months. (There are potentially eight contract months trading.) These two conditional price models are:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
[F.sub.1,t.sup.b] = The purchase price by market makers in the nearby;
[F.sub.1,t.sup.a] = The sales price by market makers in the nearby;
[F.sub.2,t.sup.b] = The purchase price by market makers in the next out; and
[F.sub.2,t.sup.a] = The sales price by market makers in the next out.
All series are generated by taking the last prices in each five-minute window. The terms [[mu].sub.ab] and [[mu].sub.ba] have two components: the cost of carry and a bid-ask spread component.
We estimate the vector error correction models (VECMs) daily for these three price pairs. We use these estimated models to calculate two representations of relative information from Hasbrouk (1995) and Gonzalo and Granger (1995). The pairs of disturbance terms ([u.sub.1,t] and [u.sub.2,t]; [u.sup.b.sub.1,t] and [u.sup.a.sub.2,t]; [u.sup.a.sub.1,t] and [u.sup.b.sub.2,t]) in the VECMs have zero means and a (2 x 2) covariance matrix, [OMEGA]. Hasbrouck (1995) defines the information share as the proportional contribution of a particular price series' innovation to the total innovation in the common efficient price. In other words, a price series' contribution to price discovery is its information share, the proportion of the efficient price innovation variance that can be attributed to that particular price series. In this sense the information share is a relative measure that allocates information to different price series and can be obtained by examining the covariance matrix, [OMEGA], of the errors from the estimated VECMs. If the price innovations are correlated (as they may well be), however, the estimated covariance matrix, [OMEGA], is not diagonal. In this situation, a lower triangular matrix F can be obtained such that such that [??] = FF'. The information share conditional on the ordering of the series is then defined as the following:
[IS.sub.i] = [([[[psi]F].sub.i]).sup.2]/[psi][??][psi]' (4)
[[[psi]F].sub.i] = The ith element of the row matrix [psi]F.
The vector [psi] is generated from the moving average representation of vector error correction models, which can be estimated by a numerical procedure (Hasbrouck, 1995). When the errors are correlated, each price's estimated information share using equation (4) is affected by the ordering of price series, with earlier placement in the ordering leading to a higher information share. Changing the order of the price series, the maximum and the minimum information share can be obtained. With only two price series, there are only two possible values. More prices would bring more potential information share values. The two information shares for each contract from these various orderings in the decomposition are calculated on a daily basis.
For each estimated VECM, the Gonzalo and Granger (1995) common factor components also are generated. Gonzalo and Granger (1995) propose a permanent/transitory model to analyze the contribution of each price series to the common factor components in the underlying asset. With the decomposition of a price series into permanent and transitory components, the contribution of price discovery from each price series is defined as the coefficients in the common factor components, which are the elements of the vector orthogonal to the error correction coefficients ([[lambda].sub.1], [[lambda].sub.2]) estimated in the VECM. In other words, the estimated common factor is
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
with the elements of [[lambda].sub.[perpendicular]] giving each price series' common factor weights. These weights typically are normalized to sum to one. Unlike the Hasbrouk measure, a particular Gonzalo Granger weight is unbounded. There is a unique (up to the normalization) [[lambda].sub.[perpendicular]] for each estimated VECM. When the innovations of the VECM are exactly uncorrelated, the Hasbrouk and Gonzalo Granger methods return equivalent information shares.
Data and Methodology
We use six years of high frequency transactions data, from 1996 through 2001, for the CME S&P 500 index futures market. The transactions records identify the contract, quantity, price of each trade, trade date and time to the second, trade direction (buying or selling), customer type (trade for the member's account, i.e., CTI1; for the house's account, i.e., CTI2; for another member on the floor, i.e., CTI3; or for a customer, i.e., CTI4), counterparty's customer type, delivery month of the contract (March, June, September, or December), and the floor trader's masked identification when executing proprietary trades. The data are provided by the U.S. Commodity Futures Trading Commission (CFTC). We omit the unfortunate maturation period for the September 2001 contract, leaving us with 23 quarterly contract maturities for analysis. (5)
Summary statistics about futures contracts during the rollover period are examined, including the trading volumes of different maturity contracts, the number of traders trading different contracts, and the volatilities of these contracts. Contract spreads are generated from traded prices during the contract rollover period to investigate the cost to rollover a long position and the cost to rollover a short position. The vector error correction models are estimated for the various price pairs to investigate price discovery among these contracts. The Hasbrouck (1995) method involves calculating information shares, while the Gonzalo and Granger (1995) method involves finding contributions to the common factor. These methods tend to provide similar results; both are presented.
To further investigate the relationship between trading revenues and information asymmetry of different contracts, we select relatively active dealers each quarter and examine their trading behavior. We define the pre-roll period as the seven days prior to the redesignation to one day prior to the redesignation. Similarly, the post- roll period starts from the redesignation date to the nearby contract maturity seven days later. Two groups of active traders are selected based on their total proprietary trading (CTI1) quantities in the pre-roll period. Members of the first group of dealers have the highest trading volume in the lead contract, i.e., the nearby contract before the redesignation. Members of the second group of dealers have the highest trading volume in the non-lead contract, i.e., the next-out contract before the redesignation. Per contract income is defined as the trading revenues divided by the total number of contracts traded. While most of these active dealers trade both the lead and the non-lead contracts in the pre-roll period as well as in the post-roll period, there appears to be specialization in the lightly traded non-lead contract. Per contract incomes are generated and compared between these two groups of active dealers when they trade either the lead or the non-lead contract, which also is related to the liquidity of each contract.
Trading Volume and Traders
We present the average daily volume of contracts ranked by nearness to maturity and the average number of market makers trading each contract in Table 1 by time to
(5) Given the September 11 event in 2001, the futures prices were affected by unusual factors. Many days during this rollover period are missing. Because we focus on the rollover period, we are forced to drop the third quarter of 2001 for our analysis. maturity of the nearby contract. Our time indicator is in calendar days; day -7 is a week before the last trading day for the nearby contract. We identify each day a maturity rank for all contracts that are trading by time to maturity. For example, in early March 1998, the nearby contract, which is the March 1998 contract, has a rank of one; June 1998, the next out, has a rank of two; September 1998 has a rank of three; and December 1998 has a rank of four. If there is March 1999 trading, that would have a rank of five, etc. The table presents the average volume and average number of traders by maturity rank (1 to 5) from days -14 to 7 across the 23 quarters in the dataset. Volume on the redesignation date (-7) jumps from the nearby to next out.
In addition, a general weekly pattern in volume is observable, with Monday (e.g., days -10, -3, and 4) volume much lower on average than the previous Friday (days -13, -6, and 1) or Tuesday (days -9, -2, 5). Chang, Jain, and Locke (1995) examine the day of week effect in the S&P 500 futures market and find higher trading volatility close to the market closing on Friday, which is similar to the weekend effect (Miller, 1988). Cornell (1985) finds that the mean return on Monday is lower for stocks, which is referred as the Blue Monday effect. Fisher, Gosnell, and Lasser (1993) find lower trading volume in stock markets on Mondays and also relate this finding to the Monday effect. Our finding of lower trading volume in S&P 500 futures on Mondays is consistent with Fisher, et al. (1993) as well as with Chang et al. (1995).
Kawaller, Koch, and Peterson (2001) describe a process by which the S&P 500 pit traders suddenly switch focus from trading the nearby to trading the next out on the redesignation date. Based on our transactions level data, we offer a direct empirical examination of this suggestion by calculating the average number of market makers trading in the nearby and next-out contract on any day. Our empirical result suggests that there is a huge jump in traders from the nearby to the next out at the redesignation, shown in Table 1, consistent with the assertion in Kawaller et al. (2001).
From the transactions data we sample six price series to use in subsequent analysis. The price analysis is limited to the nearby and next-out contracts and concentrates on the three weeks before redesignation and the final week before maturity. The last price in each five-minute bracket from 8:30 am to 3:15 pm (Chicago time) is first identified for the nearby and the next-out contracts. We refer to these as unconditional prices. Next, the last price at which a market maker buys a contract and the last price at which a market maker sells a contract in the nearby and next-out contracts are identified. We refer to these four price series as conditional prices. The advantage of using bid and offer prices, proxied by the ex post buy and sell prices, is that these series should not exhibit bid-ask bounce. The volatility of these conditional price series should reveal more of the intrinsic volatility than the unconditional price series. Thus, each day there are six sampled price series: two unconditional prices, market maker buy prices in two maturities, and market maker sell prices in two maturities.
Figure 1 presents the volatility of these six series with respect to time to maturity. Volatility is the standard deviation of returns (logarithmic price changes, multiplying by 1000) for each of the five-minute price series. The standard deviation for each Series each day is calculated and then averaged by calendar days to maturity. The next-out volatility is higher prior to redesignation (which occurs on day -7). In the pre-redesignation period, the buy-and-sell prices have about the same volatility as the unconditional series for the nearby contract, while the unconditional volatility is lower than the buy-and-sell series for the next out, reflecting the dampening effect of negative serial correlation in the unconditional data associated with a bid-ask bounce effect.
These results complement the findings of Kawaller, Koch, and Peterson (2001). In particular, focusing on the conditional price series, the evidence suggests that volatility falls in the next-out contract, as it is designated as the lead contract. In addition, volatility in the nearby contract rises dramatically after it loses its lead status. These are, as Kawaller et al. (2001) find, negatively correlated with the volume shifts. Because our measures attempt to eliminate informational effects, this is somewhat of a puzzling finding.
[FIGURE 1 OMITTED]
To consider these implications further, note that differences in futures in the lead contract have a lower volatility than differences in futures in the non-lead contract. As Kawaller, Koch, and Peterson (2001) observe, it is clearly not the volume of trading that generates volatility (the mixture of distributions theory), because the volume also shifts with the lead from the nearby to the next out. Instead, the institutional structure of the market means that the frequency and volume of trading are inversely associated with volatility. Thus, holding the institution (S&P 500 futures trading) constant and observing trading in the same location (the futures pit), the prices of contracts that simply trade less frequently are more volatile. Equally surprisingly, this result holds when restricting the analysis to bid or offer prices. The difference is statistically significant using the nonparametric Wilcoxon signed-rank test, with the results readily available from the authors.
As mentioned in the empirical techniques section, we consider the role that arbitrage plays in constraining the spread, which leads to our utilization of the paired arbitrage-free prices. More specifically, when we estimate the VECMs, we use two conditional prices, which are for rolling a long position and a short position. In addition, we also utilize these conditional prices to estimate the price volatility, arguing that the conditional prices reveal more of the intrinsic volatility and ought to be immune from the effects of bid-ask bounce. During the futures rollover period, an investor wishing to roll a long (short) position forward must sell (buy) the nearby and buy (sell) the next-out contract. The bid ask spreads of the two maturities are critically important to the decision to roll the contract, especially if the spread varies systematically over time. In particular this rollover cost will be critical to the strategic ability of some traders needing to time their rollover during the period near a contract maturity. We investigate the total costs of rolling long and short positions during the rollover period.
Figure 2 presents the intramarket spreads by time to maturity. There are two types of spreads represented: raw values and a relative (percentage) spread, as the S&P changed in value over our sample period. For each of these the two rollover spreads are calculated by comparing prices at which the market makers sell the nearby and buy the next out and prices at which the market makers sell the next out and buy the nearby. In addition, these same values are adjusted by dividing by the mean of the respective spread and multiplying by 1,000 to bring them to the same scale as the raw spreads. The four spread measures are calculated each day. Then averages are formed by time to maturity of the nearby contract. Other than the Monday (-10) four days before redesignation when the raw spreads drop a bit, there is no pattern to the spreads with respect to expiration. The difference between the market maker sell prices in the next out and buy prices in the nearby is on average greater than the difference between the buy prices in the next out and sell prices in the nearby. In other words, it costs more for a customer to rollover a short position than to rollover a long position. The difference is statistically significant when examined by the Wilcoxon signed-rank test, again with the results readily available from the authors.
[FIGURE 2 OMITTED]
The empirical evidence indicates that there is no pattern to the spreads with respect to expiration, with the exception that the raw spread drops a bit on the Monday before the redesignation. It seems that the cost of rolling a position is not affected by the information content of contracts during the rollover, as measured by volume, volatility, and price discovery. Instead, the cost of rolling over a position is affected more by a Monday effect (Fisher, Gosnell, and Lasser, 1993). This suggests that the best time to rollover a position during the contract rollover period is on the Monday before the redesignation. We also find that it costs more to rollover a short position than to roll a long position. In other words, the potential cost for roiling over a position is higher for short traders than for long traders during the futures contract rollover period.
Each day we estimate the vector error correction models for three pairs of prices. The first pair is the two unconditional price series, a five-minute price series for the nearby and next-out contracts. The second pair is the market maker buy price in the nearby and sell price in the next out. The third pair is the market maker sell price in the nearby and buy price in the next out. We estimate a separate model for each pair each day. Following Hasbrouk (1995), we calculate a maximum and minimum information share from each VECM by switching the rows in the covariance matrix of the residuals prior to find the 2 x 2 square root and proceeding with the information share calculation. This switching result is due to the bias induced by the top row status in the Cholesky decomposition. The information share is the percentage of the volatility of the common factor that is contributed by the respective price series. The mean of these two information shares is calculated each day. Also, for the common factor contributions, Gonzalo and Granger's (1995) methodology is followed, and the normalized (i.e., sum-to-one) vector that is orthogonal to the estimated error correction vector is computed. Essentially, Hasbrouck's information shares are variance-weighted Gonzalo and Granger contributions to the common factor, allowing for correlated errors (hence the need to shuffle the rows in Hasbrouk to obtain maximum and minimum values). Table 2 presents the average information shares and common factor component for the three pairs of price series, for the nearby and the next-out contracts, where the averages are calculated by calendar days to the next maturing contract.
Hasbrouck's information shares appear less extreme than Gonzalo and Granger's common factor components. Hasbrouck's shares are bounded between one and zero. The (normalized) Gonzalo Granger measures are unbounded, although, similar to Hasbrouck, the normalized Gonzalo Granger shares sum to one. (In odd conditions, one Gonzalo Granger share could be 115 percent and another -15 percent.) Hasbrouk shares are non-negative. Unlike volume and volatility, Hasbrouck's information shares show a gradual decline across the redesignation; that is, the nearby contract appears to lose its informational importance gradually prior to and after the redesignation. In a slight contrast, the common factor component for the nearby contract drops suddenly on the redesignation date when it is no longer the lead contract.
In addition to the unconditional price series, the zero-arbitrage pairs also are used to mitigate microstructure effects in the estimation, with results also shown in Table 2. (By design, microstructure effects should be tempered by the autocorrelation structures in the unconditional VECMs, but because there are conditional data available, this more direct analysis is included.) While these prices are sampled in an attempt to purge microstructure effects from the unconditional series, the results are similar to the conditional series. Again the Hasbrouck measures are less extreme than the Gonzalo and Granger measures. There is a gradual decline in the information share in the nearby and an abrupt decline in the Gonzalo Granger common factor contributions.
The difference of the price discovery shares between the lead contract and the non-lead contract is examined further by a Wilcoxon signed-rank test. With the results readily available from the authors, the lead contract's information share is significantly greater than the non-lead contract's. The same result is found when the common factor weights are examined. Despite the fact that these two contracts trade side by side in the futures pit in plain view of each other with some common traders, there is a pronounced difference in their estimated contribution to price discovery. The contract-designated lead (the contract with the highest volume) has a significant edge in price discovery. Further, this result holds after taking into account zero arbitrage conditions using market maker prices.
The evidence leads us to conclude that the result on price discovery is attributable simply to relative volumes. Certainly, the information known to traders entering orders to trade both contracts ought to be the same. Also, all market makers for both contract maturities are integrated into a large pit. Yet the empirical results suggest that there is much more price discovery in the lead contract. Of course, active bids and offers are not available in the data set, only prices at which market makers trade (in other words, ex post traded bids and offers). Insofar as the frequency of trading in the non-lead months is so much lower than the lead, these findings could simply reflect the relative frequencies.
Per Contract Income
Because the lead contract contains more information in the price discovery when compared to the non-lead contract, revenues generated by floor traders from trading these two different contracts are worth further examination. Because the redesignation date is seven days prior to the nearby contract maturity, a pre-roll period is defined from date -14 to date -8, and a post-roll period starts from -7 to 0. The lead contract in the pre-roll period is the nearby contract, while the lead contract in the post-roll period is the next-out contract. The trading volumes of the ten highest volume dealers who trade the lead or the non-lead contract in the pre-roll or in the post-roll are investigated and compared to total market proprietary trades, with the results shown in Table 3. The evidence suggests that the top ten non-lead contract traders account for more than 65 percent of the proprietary trades, while the top ten lead contract traders account for only about 20 percent of the proprietary trades.
We further select two groups of active traders. We select the first group of top ten dealers based on their total trading quantity on the lead contract (nearby) in the pre-roll period. Our second group of top ten dealers is selected based on their total trading quantity on the non-lead contract (next out) in the pre-roll period. Table 4 presents the mean and the median per contract income for these two groups of traders by their trading in both the non-lead and lead contracts by the calendar day to the nearby contract maturity. It appears that these traders make average positive per contract income in the lead contract. Non-lead contract income before redesignation is volatile. Recall that some trading may be designated spread trading. After the trade is complete, the traders place individual prices on the legs of the spread, with some latitude, as long as the leg prices differ by the agreed-to spread. Because of this, income per contract can be arbitrarily distributed between the lead and non-lead contracts when these leg prices are established; hence, the combination of positive and negative spreads coexisting makes some sense. The significance of the difference between the lead contract income and the non-lead contract income for these traders is examined by the Wilcoxon signed-rank test. Results are available from the authors. The result suggests that the difference is not significant. Many missing observations are found in the non-lead per contract income for these traders, suggesting that active lead contract traders do not necessarily trade the non-lead contract at the same time.
Because traders may be more likely to trade the non-lead contract for speculative purposes, per contract income for top dealers who trade the non-lead contract is investigated (Table 4). The results suggest that, on average, the non-lead contract income seems to be higher than the lead contract income. The difference is further examined by the Wilcoxon signed-rank test. It suggests that these non-lead contract traders generate a significant higher per contract income from the non-lead contract than from the lead contract. From the price discovery results, it seems that whatever information asymmetry exists is processed by the lead contract market makers. With little price discovery in the non-lead months, market makers in these contracts should not receive an asymmetric information premium. Nonetheless, the empirical result suggests that top dealers are still able to generate a high per contract income from trading the non-lead contract.
The relationship between volume and liquidity around the redesignation is interesting. As volume jumps from the nearby to the next out, the inventory cost (the holding time) associated with a market maker holding a position falls in the next out and rises in the nearby. On the other hand, any asymmetric information costs will be constant across these contracts across the redesignation. Thus, to the extent that a jump is observed in the bid ask spread on the nearby at the time of the redesignation, this is entirely due to inventory costs: with lower volume, there is simply less likelihood that an order of opposing sign will arrive in the pit soon. Traders have to carry inventory costs when trading the non-lead contract; thus, they earn a higher per contract revenue as an (il)liquidity premium. Our results suggest that a liquidity premium overwhelms the information effect so that we still see a high per contract income from high volume non-lead contract traders.
To investigate the argument that dealers trading the non-lead contract earn a higher income because of a higher liquidity risk, the relationship between per contract income and market liquidity is examined. Market liquidity is measured by the standard deviation of the market price in five-minute intervals on a daily basis. With the regression result shown in Table 5, there is a significant relationship between the market price standard deviation and per contract income on non-lead contracts in the post-roll period. In other words, the higher return on the non-lead contract in the post-roll is significantly related to its lower liquidity.
The informational events associated with the redesignation of the lead S&P 500 futures contract and the associated contract rollovers are examined. This recurring contract termination provides an excellent laboratory for identifying the information content of trades, because this natural periodicity requires hedgers to enter into informationless spread trading. Thus, some traders have a trading imperative, moving their position through time. Other traders continue to trade for traditional portfolio management reasons, strategically choosing the particular contract, nearby or next out, to trade. In addition, the facilitation of this rolling trading is handled by a small subset of floor traders, whose trading is examined directly.
The empirical results show that volume on the redesignation date (seven days before maturity) jumps dramatically from the nearby to the next-out contract. The number of market makers is also investigated. There is a huge jump in traders from the nearby to the next out at the redesignation, one week prior to maturity. These futures contracts also exhibit different volatility attributes. Volatility in the nearby contract rises dramatically after it loses its lead status. Volatility falls in the next-out contract as it is designated as the lead contract. The results suggest that the structure of the market, the frequency of trading, or the volume of trading is inversely associated with volatility.
For the rollover spread, the difference between the sell in the next out and buy in the nearby is on average greater than the difference between the buy in the next out and sell in the nearby. In other words, it costs more to rollover a short position than to rollover a long position. Nevertheless, on a percentage basis, these differences are small. Hence, there appears to be little arbitrage opportunity in intramarket spreading. This study uses Hasbrouck's (1995) information share and Gonzalo and Granger's (1995) common factor weights to investigate price discovery between these contracts. Hasbrouck's information shares show that the nearby contract loses its information share gradually prior to and after the redesignation. The common factor component for the nearby contract drops suddenly on the redesignation date when it is no longer the lead contract.
High volume traders' per contract incomes in the lead contract and in the non-lead contract are also investigated. Active lead contract traders are able to generate an average positive per contract income from the lead contract, while the income from the non-lead contract seems volatile around redesignation. Nonetheless, the difference between the lead contract income and the non-lead contract income is not significant. On the other hand, active non-lead contract traders seem able to obtain a significantly higher income from trading the non-lead contract than from trading the lead contract. We suspect that part of the income comes from the illiquidity of the non-lead contract. Traders have to carry inventory costs when trading the non-lead contract; thus, they earn a higher return as the liquidity premium. The liquidity premium overwhelms the information effect so that there is a high per contract income from trading the non-lead contract.
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[2.] Chang, E.C., P.C. Jain, and P.R. Locke, "S&P 500 Index Futures Volatility and Price around the NYSE Close," Journal of Business (January 1995), pp. 61-84.
[3.] Cornell, B., "The Weekly Pattern in Stock Returns: Cash versus Futures: A Note," Journal of Finance (June 1985), pp. 583-588.
[4.] Ferguson, M.F., and S.C. Mann, "Execution Costs and Their Intraday Variation in Futures Markets," Journal of Business (January 2001), pp. 125-160.
[5.] Fisher, R., T. Gosnell, and D. Lasser, "Good News, Bad News, Volume, and the Monday Effect," Journal of Business Finance & Accounting (November 1993), pp. 881-892.
[6.] Frino, A., and M.D. McKenzie, "The Pricing of Stock Index Futures Spreads at Contract Expiration," Journal of Futures Markets (May 2002), pp. 451-469.
[7.] Gonzalo, J., and C. Granger, "Estimation of Common Long-Memory Components in Cointegrated Systems," Journal of Business and Economic Statistics (January 1995), pp. 27-35.
[8.] Hasbrouck, J., "One Security, Many Markets: Determining the Contributions to Price Discover," Journal of Finance (September 1995), pp. 1175-1199.
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[11.] Kawalter, I.G., P.D. Koch, and J.E. Peterson, "Volume and Volatility Surrounding Quarterly Redesignation of the Lead S&P 500 Futures Contract," Journal of Futures Markets (December 2001), pp. 1119-1149.
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California State University Stanislaus
Texas Christian University
(1) Ferguson and Mann (2001), Kurov (2005), and Locke and Onayev (2007) investigate the relationship between trading and price on futures markets.
(2) This is termed cash settlement as opposed to the traditional futures delivery procedure, whereby deliveries of the commodity or security are made from the short to the long position, and cash is transferred from the long to the short. In cash settlement, only money changes hands after final settlement: positions that are in the money receive money from the clearinghouse, and positions out of the money pay money to the clearinghouse. In effect, there is one final daily marking to market before the positions are closed.
(3) The CME refers to this as the Special Opening Quotation, with additional rules for stocks that fail to open and other unusual conditions.
(4) The E-mini is similar to an odd-lot trade, identical to the S&P 500 futures in every respect except that the notional value is only $50 times the value of the S&P index versus $250 times the S&P for a regular S&P futures contract. A position of five E-mini contracts is identical to an S&P 500 futures contract. All E-mini trades are electronically executed on the Globex system. Only members may enter trades on Globex, similar to pit trading (although some orders may be automatically routed through member's trading architectures). E-mini trades are not included in our analysis.
Table 1--Contract Trading Volume and Number of Proprietary Traders Contract Expire -14 -13 -10 -9 -8 7 1st Volume 22,349 20,365 15,422 19,801 19,535 2,434 Traders 414 399 387 408 417 51 2nd Volume 451 480 549 688 1,098 20,679 Traders 25 26 28 33 36 409 3rd Volume 2 4 5 4 3 4 Traders 2 2 2 2 2 2 4th Volume 2 6 1 1 1 4 Traders 2 2 2 1 1 2 5th Volume 2 2 1 1 2 2 Traders 2 1 1 1 1 2 Total Volume 22,806 20,857 15,977 20,495 20,638 23,122 Traders 444 429 419 445 457 465 Contract -7 -6 -3 -2 -1 0 7 1st Volume 1,216 844 873 662 528 Traders 39 34 32 29 29 2nd Volume 19,073 18,388 20,593 20,867 18,984 15,055 Traders 391 391 413 408 400 351 3rd Volume 9 11 14 9 14 9 Traders 3 3 3 3 4 4 4th Volume 3 2 1 1 2 2 Traders 2 1 1 1 1 2 5th Volume 1 2 2 2 1 2 Traders 1 1 2 1 1 2 Total Volume 20,302 19,246 21,483 21,540 19,529 15,068 Traders 436 430 451 443 435 359 Contract 1 4 5 6 7 1st Volume Traders 2nd Volume 14,128 18,382 18,529 17,094 Traders 343 385 375 353 3rd Volume 16 17 24 12 Traders 4 5 5 5 4th Volume 2 1 2 3 Traders 2 1 2 1 5th Volume 2 2 5 1 Traders 1 3 2 1 Total Volume 14,147 18,403 18,560 17,110 Traders 350 394 383 361 The average daily volume by contract month rank and the average number of floor traders trading for their proprietary account each day in each contract month, by time to contract maturity (from -14 to 7) are presented, over the period from 1996 to 2001. The first contract is the contract which matures at day zero. The second contract is the contract which matures three months after day zero. The third contract is the contract which matures six months after day zero. The fourth contract matures nine months after day zero, and the fifth contract matures 12 months after day zero. Expire is the time to the first contract maturity. The data are S&P 500 futures trading on the CME from 1996 through 2001 Table 2--Information Shares and Common Factor Weights (in Percentage) Expire -14 -13 -10 -9 Unconditional HB Nearby 79.95 76.50 77.24 70.41 Prices Next Out 20.05 23.50 22.76 29.59 GG Nearby 94.36 98.89 91.10 95.29 Next Out 5.64 1.11 8.90 4.71 Conditional HB Nearby Buy 78.45 80.94 74.32 68.92 Prices Next Out Sell 21.55 19.06 25.68 31.08 GG Nearby Buy 94.14 103.58 89.33 92.25 Next Out Sell 5.86 -3.58 10.67 7.75 Conditional HB Nearby Sell 82.20 81.53 77.22 77.28 Prices Next Out Buy 17.80 18.47 22.78 22.72 GG Nearby Sell 93.60 96.07 86.14 100.47 Next Out Buy 6.40 3.93 13.86 -0.47 Expire -8 -7 -6 -3 -2 Unconditional Nearby 63.61 32.33 25.18 21.11 29.92 Prices Next Out 36.39 67.67 74.82 78.89 70.08 Nearby 85.41 2.12 5.87 1.94 10.30 Next Out 14.59 97.88 94.13 98.06 89.70 Conditional Nearby Buy 64.40 35.65 30.28 29.90 29.17 Prices Next Out Sell 35.60 64.35 69.72 70.10 70.83 Nearby Buy 88.35 8.51 6.73 11.35 8.83 Next Out Sell 11.65 91.49 93.27 88.65 91.17 Conditional Nearby Sell 69.73 35.33 33.28 25.97 28.89 Prices Next Out Buy 30.27 64.67 66.72 74.03 71.11 Nearby Sell 94.81 -0.99 11.53 5.25 10.59 Next Out Buy 5.19 100.99 88.47 94.75 89.41 Expire -1 0 Unconditional Nearby 19.45 12.46 Prices Next Out 80.55 87.54 Nearby 5.32 2.66 Next Out 94.68 97.34 Conditional Nearby Buy 21.23 18.37 Prices Next Out Sell 78.77 81.63 Nearby Buy 4.14 6.12 Next Out Sell 95.86 93.88 Conditional Nearby Sell 21.17 20.12 Prices Next Out Buy 78.83 79.88 Nearby Sell 1.25 5.36 Next Out Buy 98.75 94.64 The table presents the median Hasbrouck (HB) information share and common factor component (GG) for the nearby and the next-out contracts for unconditional prices series and for conditional price series, with prices sampled at five-minute frequencies. Each day a VECM is estimated for the three price series. The daily HB information share is calculated as the average of the minimum and maximum shares. Then medians of the HB and GG values are calculated across quarters, holding calendar days to maturity constant Table 3--Market Shares for Top Dealers Pre-Roll Period Post-Roll Period Rank Nearby Next Out Nearby Next Out 1 2.45% 15.72% 11.67% 2.53% 2 2.14% 13.04% 10.39% 2.23% 3 1.95% 10.99% 9.32% 2.06% 4 1.87% 8.94% 8.29% 1.89% 5 1.75% 7.37% 6.98% 1.78% 6 1.66% 5.62% 5.60% 1.72% 7 1.57% 4.34% 4.81% 1.64% 8 1.51% 3.65% 4.24% 1.57% 9 1.46% 3.10% 3.78% 1.50% 10 1.40% 2.62% 3.40% 1.42% Total 17.75% 75.38% 68.48% 18.34% The top dealers are selected based on the total trading quantity for each contract in each period; i.e., top dealers might be different for these four contracts. The percentage is the dealer's trading quantity divided by the total CTII trading quantity for the same contract in the same time period. Top dealers are selected for each contract each quarter. The statistics represent the average percentage of shares across 23 quarters Table 4--Per Contract Income Trader Contract Expire -14 -13 -10 -9 Lead Traders Lead Mean 348 225 -41 -23 131 Median 253 181 44 21 105 Non-Lead Mean -360 -2,185 -645 1,023 -637 Median -738 -1,321 170 1,296 -530 Non-Lead Traders Lead Mean 507 -976 -644 449 72 Median 597 -654 105 538 -37 Non-Lead Mean 492 192 1,053 1,654 953 Median 408 -440 251 1,343 643 Trader -8 -7 -6 -3 -2 -1 Lead Traders Lead 211 -51 174 255 299 -149 281 16 -32 31 77 -48 Non-Lead -172 542 -4,038 1,205 -180 -552 407 -1,013 -2,058 770 699 -172 Non-Lead Traders Lead 16 -310 1,202 -198 1,192 533 817 276 318 359 331 317 Non-Lead -975 -178 759 1,180 1,716 1,145 -540 -69 136 91 864 820 The first group of top ten dealers are selected based on their total trading quantity on the lead contract (nearby) in the pre-roll (-l4 to -8) period. The second group of top ten dealers are selected based on their total trading quantity on the non-lead contract (next out) in the pre-roll (-14 to -8) period. The per contract income is computed as following: Income = [(P*Q(sell)- P*Q(Buy))+(Q(buy)-Q(sell))* Settle Price]/Max(Q(Buy),Q(Sell)). The settle price is the last trading price in the pre-roll period and in the post-roll period for the contract. Top ten dealers are selected each quarter. Per contract income for top dealers each quarter is investigated and the mean and the median statistics across 23 quarters are presented Table 5--The Relationship Between Per Contract Income and Liquidity Dependent Variable: Nearby Contract Income in Pre-roll Period (Lead Contract) R-square F value Pr > F 0.0357 3.93 0.050 Parameter Estimate Std Dev T value Pr > |t| Intercept 729.91 482.03 1.51 0.1329 Volatility -248.33 125.19 -1.98 0.0499 Dependent Variable: Next-out Contract Income in Post-roll Period (Lead Contract) R-square F value Pr > F 0.0000 0.00 0.978 Parameter Estimate Std Dev T value Pr > |t| Intercept 382.50 692.90 0.55 0.5818 Volatility 4.47 159.12 0.03 0.9776 Dependent Variable: Next-out Contract Income in Pre-roll Period (Non-Lead Contract) R-square F value Pr > F 0.0080 0.90 0.346 Parameter Estimate Std Dev T value Pr > |t| Intercept 1260.29 478.53 2.63 0.0097 Volatility -108.38 114.51 -0.95 0.3460 Dependent Variable: Nearby Contract Income in Post-roll Period (Non-Lead Contract) R-square F value Pr > F 0.1336 20.97 0.000 Parameter Estimate Std Dev T value Pr > |t| Intercept -1603.05 569.67 -2.81 0.0056 Volatility 561.77 122.66 4.58 <.0001 The independent variable is the market price standard deviation in five-minute intervals each day, while the dependent variable is the per contract income generated by active non-lead contract trades from trading the lead contract or the non-lead contract in the pre-roll or in the post-roll period
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|Author:||Huang, Tzu-Man; Locke, Peter|
|Publication:||Quarterly Journal of Finance and Accounting|
|Date:||Sep 22, 2009|
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