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The Breakout Bulletin

The following article was originally published in the November 2003 issue of The Breakout Bulletin.

Intraday Statistics for the E-mini S&P

Day trading the S&P 500 futures is a goal for many traders. The daily range and volume of the S&P's -- either mini or full-size -- make them possibly the most attractive day trading vehicles available. The e-mini's are particularly popular because they're traded electronically and have low margin requirements and excellent liquidity. This month I'm going to present a number of intraday statistics for the e-mini S&P 500 futures. These statistics can reveal quite a bit about how the market trades throughout the day and will hopefully give you some ideas for exploiting these intraday tendencies. I'll end by illustrating how this might be done with a simple trading system.


Many traders use volume -- how many contracts are being bought and sold -- as a confirming indicator. Generally speaking, high volume tends to validate a move. On the other hand, big moves on light volume can be suspect. This raises the question: what constitutes high and low volumes? For example, when looking at an intraday (e.g., 5 min) chart, you might wonder if the current day's volume is above or below average for that time of day. To address this, I calculated the average daily volume at each 30 min interval over the date range 2/12/2001 to 10/22/2003. The results are shown below in Fig. 3. The horizontal axis is the time of day, Chicago (Central) time. The vertical axis is the day's total trade volume up through the time indicated. The error bars represent one standard deviation. The actual volume numbers for each time point are given in the table below the horizontal axis. For example, the average volume at 11:00 am (CT) is about 207,000 contracts. As an example of how to use this, you might look at the day's volume at 11:00 am and if it's much more than 207,000, you could consider that to be a high volume day. Any move that may have occurred at that point might be given more credence than if the volume was below average.

Average daily volume in e-mini S&P

Figure 3. Average daily volume throughout the trading day in the E-mini S&P.


To generate additional statistics on the trading day, I divided the day into three equal sessions of 2 hr, 15 min each (the entire day session is 6 hr, 45 min). On a chart, this gives us 135 min bars. The date range was the same as above: 2/12/01 to 10/22/03. I wrote a simple EasyLanguage system to accumulate the following data for each bar: volume, range (high - low), and point change (close minus prior bar's close). I wrote the data to a comma-delimited data file, which I opened in Excel for further processing. The advantage of 135 min bars is that it provides a morning session bar, a mid-day bar, and an afternoon bar. The morning bar is from 8:30 am to 10:45 am CT; the midday bar is from 10:45 to 1:00 pm CT; and the afternoon bar is from 1:00 pm to 3:15 pm CT. Below, I'll compare these different sessions and use the results to answer questions about how the different sessions relate to one another.


Some of the questions we can address with these data are:

  1. How differently does the market trade in the morning than in the afternoon or midday?
  2. Does the market tend to reverse at midday (the "midday slump")?
  3. Does the market action in the morning say anything about how the market trades in the afternoon?


Before we try to answer these questions, let's take a look at a few basic results. The table below lists the daily average volume, range, and point change (absolute value) for the morning ("AM"), midday ("Mid") and afternoon ("PM") bars. Note that the morning bar has the largest numbers in each category, and the midday bar has the smallest. For the point change numbers, I took the absolute value of the difference between one close and the close of the previous bar, then averaged those values over all days in the sample.


Table. Daily average volume, range, and point change for the E-mini S&P 500 futures, 135 min bars, 2/12/01 to 10/22/03.


     Session     Volume    Range     Change (abs.) 

         AM        195955      12.25          7.52

         Mid         88084        7.93          3.58

         PM        154548      10.56          5.57


We needn't limit ourselves to summary statistics, however. Figs. 4 - 6 show how the volumes, ranges, and point changes are distributed for each session over the days in the sample. It's a good idea to examine the statistical distributions in this case because the quantities in question are not normally distributed, as can be seen from the fact that the curves in Figs. 4 - 6 are not symmetrical, let alone bell-shaped. The most prevalent values for volume, range, and point change -- at the peaks of the distribution curves -- are less than the average values. For example, in Fig. 6, the most point changes in the AM occurred in the range from 2 to 3 points, which is well below the average AM point change of 7.52 points. Another interesting feature of the distribution curves is that the volume distribution curves appear to be bi-modal; that is, they have two major peaks. This means that trading days tend to be either high volume or low volume but days with average volume occur less frequently.


Distribution of trading volume, ES

Figure 4. Trading volume distribution for the E-mini S&P, 135 min bars, 2/12/01 to 10/22/03.
Distribution of trading range, ES
Figure 5. Range (high minus low) distribution for the E-mini S&P, 135 min bars, 2/12/01 to 10/22/03.
Distribution of absolute point changes, ES
Figure 6. Point change (close to close, absolute value) distribution for the E-mini S&P, 135 min bars, 2/12/01 to 10/22/03.


When probability curves are not normal, it's more difficult to perform significance tests. The usual method to determine if a value is higher or lower than normal is to look at how many standard deviations it is from the average. If it's more than, say, two standard deviations from the average, it can be considered an unlikely occurrence. You might use that approach to determine if the morning's volume was unusually high or low. Knowing that the volume was unusually high, for example, might be used to justify adding to your position later in the day if the market continues in your favor. However, when the probability distribution is not normal, using the standard deviation is not accurate. We could get a rough idea by simply comparing the volume to the average volume, but a better method is to look at the cumulative distribution of the volumes.


Take a look at Figs. 7 - 9, which plot the cumulative distributions of volume, range, and point change for our 135 min bar data. The cumulative distributions tell us what percent of the time the quantity in question is less than or equal to the value on the curve. For example, in Fig. 7, the volume in the morning session (blue line) at the 50% mark is about 197,000. This means that 50% of the time the volume is less than 197,000. At the 90% mark, the volume in the morning session is about 330,000. So, about 90% of the time, we can expect that the volume at the end of the first 2 hr, 15 min of trading will be less than 330,000. If it's more than that, we know it's an unusually high volume day. In fact, there's only a 1 in 10 chance that the volume will be greater than that at the end of the morning session.


Cumulative distribution of trading volume, ES

Figure 7. Cumulative distribution of trading volumes for the E-mini S&P, 135 min bars, 2/12/01 to 10/22/03.
Cumulative distribution of range, ES
Figure 8. Cumulative distribution of point ranges for the E-mini S&P, 135 min bars, 2/12/01 to 10/22/03.
Cumulative distribution of absolute point changes, ES
Figure 9. Cumulative distribution of point changes (absolute value) for the E-mini S&P, 135 min bars, 2/12/01 to 10/22/03.


As another example, consider Fig. 9. The absolute value of the point changes in the midday session is given by the red curve. The fact that this curve is to the left of the curves for the AM and PM sessions indicates that the market moves less in the middle of the day. In fact, following the 75% value on the vertical axis to the red curve in Fig. 9, we can see that 75% of the time, the change from the AM to the midday session is less than or equal to 4.75 points. For the afternoon session (green curve), this value is much larger. 75% of the time, the change from the midday to the PM session is less than or equal to 7.75 points. The 75% value for the AM session (blue curve) is 10.5 points.


Whether we look at volume, range, or point change, the midday curve in Figs. 7 - 9 is always to the left of the PM curve, which is to the left of the AM curve. This tells us that the morning session is the most active -- in terms of volume, point change, or range -- followed by the afternoon session. The midday session is the least active. Remember the three questions posed above? The observation just made addresses question 1: the morning session is different than the afternoon or midday in that it sees higher volume, greater range, and more point change. The midday session sees the least. What about question 2, the midday slump? Some traders expect a reversal of the morning trend in midday. Is this borne out by the data? Certainly, the middle of the day sees a drop off in volume coinciding with less volatility. However, if we look at the direction of the close of the midday bar relative to the direction of the morning close, we find that only 47% of the time does the midday bar close opposite to the AM close. In other words, if the morning bar closes up relative to the close of the previous bar, the midday bar closes down relative to the morning bar, or if the AM bar closes down, the midday bar closes up. This happens less than 50% of the time, which suggests that there is no midday slump in the S&P.


In question 3, I asked if the morning session has any predictive value for the afternoon. Based on the data collected from the 135 min bars, here are few statistics that may help answer that question:

  1. The average daily point change (absolute value) is 10.63 points.
  2. The average AM session point change is 71% of the average daily point change (using the absolute value of point change).
  3. The direction of the point change in the AM session is the same as the day's point change direction 75% of the time.
  4. The PM session closes in the same direction as the AM session 55% of the time.
  5. When the midday session closes in the same direction as the AM session, the PM session also closes in that direction 57% of the time.


There are probably at least several different ways these results could be used in trading. I'll illustrate one application by focusing on item #5, which suggests the following simple trading system:

  1. Buy the midday bar at its close if the morning bar closed up and the midday bar closes higher than the morning bar.
  2. Sell the midday bar at its close if the morning bar closed down and the midday bar closes lower than the morning bar.
  3. Exit at the day's close.


This is basically a trend-following system that takes advantage of the fact that when the market trades in the same direction in both the morning and midday, it's likely to continue to trade in that direction in the afternoon. According to result #5, this system should have a winning percentage of 57%. Here are the results as given by the TradeStation performance report:


    Net Profit:  $16,063

    Number of Trades: 287

    Percent Profitable: 57%

    Ave. Trade:  $56.00

    Profit Factor: 1.54

    Ratio Ave. Win/Ave. Loss: 1.02

    Max. Consec. Losers: 5


These results are without deducting slippage and commissions, so it would probably not be tradable in practice due to slippage on the exit. However, I haven't included a money management stop with this system. Adding better exits, such as a money management stop and/or a profit target, might turn this into a winning system. Also, the equity curve for the system as written is almost a 45 degree line, which is a good indication that there's something there to be exploited. As with any system, it should be tested out-of-sample to make sure it's not over-fit to the data. The fact that this system is based on a simple observation that makes intuitive sense increases the odds that it will hold up in the future.


Hopefully, the data and results I've presented will be food for thought for your own efforts in developing an intraday trading system, either for the E-mini S&P or your own market of interest. Once you collect some good, raw data, there are endless questions that can be posed and answered with a few simple, spreadsheet manipulations. Just make sure any system you come up with based on this type of analysis is tested out-of-sample, either in the past or in real-time tracking before committing real money. And don't get too carried away with complex data manipulations and complicated patterns or you could end up trying to exploit a statistical anomaly that isn't likely to repeat itself.

That's all for now. Good luck with your trading.


Mike Bryant

Breakout Futures