Trading the program can therefore move a disproportionate number of stocks towards one of the quotes, causing a bid-ask bounce in the index. A typical stock in the S&P 500 has a quoted spread of about 0.5 percent.3 So the spread for the index is also about 0.5 percent. Since quotations often change between trades (possibly several times), the current mean quotation should be closer to the underlying true value of the index than the index of quotations of the last trade.4 The latter is a measure of the value of the index of the last trade. abstracting from the rebound of supply and demand.
The remaining component in (1), the current mid-quotation index, QCt, is a proxy for the unobserved true value of the index. The data set from June 1989 uses individual stock trading prices and quotes to construct the index breakdown described above.” The breakdown is then used to evaluate the importance of the bid-ask rebound and the components of asynchronous trading. In the June 1989 sample, the one-minute standard deviation of the last traded index is 54 percent greater than that of the last traded midpoint index.
The last trade's intermediate bid is the average of the bid and ask bids valid at the time of the last trade. Programmatic trading occurred in only 17 percent of one-minute intervals in the entire sample.
Empirical Event-Study Methods
The regression model includes five one-minute leads of the program trading time series to characterize how program trading lags the analysis variables. 30 one-minute lags of the program trading time series are included to characterize the lagged relationship between the analysis variables and program trading. Given the lag structure of the regressions and this study's exclusive focus on intraday relationships, program trades that occurred in the first 30 and last 5 minutes of the trading day are dropped from the sample.15.
This regression event study method is not designed to determine causality, which cannot be determined by correlations alone. Regressions are designed simply to represent, as clearly as possible, the average relationship between program trading and the analysis variables of interest after accounting for grouped effects. Therefore, we refer to this analysis as an event study analysis rather than a transfer function analysis.
Event Analysis of the June 1989 Sample
On 22 trading days in June 1989, except for those trades occurring in the first 30 minutes and the last 5 minutes of the trading day. They represent the average value of the basis associated with the trading of the program after the effects of grouping have been removed. In both cases, the average event time inflation starts to move from zero before the reported time of trade submission.
The event and time base estimates are calculated without estimating the carrier mantle component. Estimates plotted are regression coefficients of the arbitrage sell index (plus intercept) obtained from minute-by-minute time series regressions of the basis and index components on the 5 leading and 30 lag index arbitrage buy-sell and non-arbitrage trades with the buy-sell program. The basis is the last traded value of the NYSE S&P 500 minus the price of the nearest S&P 500 futures contract plus an estimate of expected carrying costs.
The plotted estimates are regression coefficients (plus the intercept) obtained from regressions of the minute-by-minute time series of the number of trades of 5 leads and 30 lags of index arbitrage buy-and-sell and non-arbitrage buy-and-sell program trades. To measure the importance of the latter factor, we calculated event survey averages of the index bid-ask spread around the different types of program trades. As expected, it rises to an absolute peak shortly after the submission of the program trade.
These results suggest that some of the program transactions are executed almost immediately, or that some of the transaction submission times are reported late. The root mean sum of squares of the predicted values from the regressions of index changes on leads and lags of the four types of program trades measure the variation in index returns correlated with program trading. The estimates are obtained from regressions of the intraday time series of S&P 500 futures and one-minute spot index returns on 5 leads and 30 lags of index arbitrage buy-and-sell and non-arbitrage buy-and-sell program trades.
The sample includes all program trades reported by member firms to the NYSE on the 505 trading days in the two-year period 1989 through 1990, excluding trades that occurred in the first 30 minutes and the last 5 minutes of the trading day.
Event-Study Analysis of the Full Sample
The sample includes all program trades reported to the NYSE by member firms over 505 trading days over a two-year period from 1989 to 1990, excluding those trades that occurred in the first 30 minutes and the last 5 minutes of the trading day. 0.166). Event cumulatives in futures prices lead cumulatives in the money index by three to four minutes around index arbitrage trades. In the case of the futures price, however, most of the price change occurs within five minutes before the order is placed.
Perhaps the most notable feature/ of the event-time cash index and futures prices is the absence of large cumulative reversals in the 30 minutes after program trading. In the latter case, the cash index peaks five minutes after the reported order if time, followed by a slight reversal of about a third of the maximum change. The change in the futures price reaches a peak one or two minutes after the order if time and is followed by a more pronounced reversal than in the case of the cash index.
Estimates plotted are regression coefficients (plus intercepts) obtained from minute-by-minute time series regressions of the 5-way basis and 30-lag index arbitrage and non-arbitrage buy and sell program trades. The relationship between program trades and prices may depend on the timing of the trade within its episode. Estimates are obtained from intraday time series regressions of 5-way 1-minute returns and 30-lag index arbitrage and non-arbitrage buy and sell program trades.
Since program trading episodes are groups of events, the event regression study method is essential to distinguish the effects of the first and subsequent program trades. Cumulative event-time changes in the money index and the futures price surrounding non-arbitrage program trades are significantly different for the first and subsequent program trades (Figure 7, bottom). The actual average basis for subsequent trades is the time-weighted sum of the coefficients estimated for the first trade and for subsequent trades.
The estimates are obtained from regressions of intraday time series of one-minute S&P 500 futures and cash index returns on 5 leads and 10 lags of index arbitrage buy-and-sell and non-arbitrage buy-and-sell program trades classified by their position in a program trading "episode". An episode is defined as all sequences of the same type of program action. The estimates plotted arc regression coefficients (plus intercept) obtained from regressions of minute-by-minute time series on a basis of 5 leads and 10 lags of index arbitrage buy-and-sell and non-arbitrage buy-and-sell program trades classified according to their position in a program trading "episode". An episode is defined as all sequences of the same type of program trades (buy index arbitrage, buy nonarbitrage, sell index arbitrage, sell nonarbitrage) separated by more than five minutes without program trading. A similar analysis of the basis for nonarbitrage trades (not presented) shows very little difference in the effect on the basis between the first and subsequent trades in an episode.
Conclusion
The relationships between program transactions and cash and futures returns are stable over the two-year period under investigation. Second, the event plots and the estimates of the average price change around program trades are based on linear regressions. Third, only 30 minutes after individual program trades are studied to determine whether price reversals follow program industries.
Finally, all results presented in this article apply only to intraday program trades that took place 30 minutes after the opening and 5 minutes before the close of the trade. Program trades near or at the opening and closing—which includes most expiration day trading—can also be related to index changes, possibly in different ways. Program trades take somewhat longer because they are composed of many orders that must be sent sequentially.
In addition to the daily program trade reports, the NYSE estimates the timing and volume of SuperDot submitted program trades using an artificial intelligence program called the Program Traffic Locator (PTL). PTL scans the SuperDot order stream for patterns known to be associated with program trades. PTL-identified program trades and SuperDot program trades reported by member firms generally match [see Nair (1991)].
Trades with incomplete information about the direction of the trade and about the underlying strategy are also excluded. Spatt, 1994, "An Empirical Analysis of the Limit Order Book and the Order Flow in the Paris Bourse," working paper, Carnegie Mellon University. A Survey of the Issues and the Evidence,” working paper, Board of Governors of the Federal Reserve System.
Goetzman, 1988, "The Effect of the 'Triple Witching Hour' on Stock Market Volatility," Federal Reserve Bank of Atlanta Economic Review, 73, 2-15.
