# Timing the High/Low of the Day

### The Study

The purpose of this study is to ascertain when the high or low of the day (for the ES) will most probably occur. This study uses 1 minute open, high, low, close data for the S&P emini (Symbol: ES) from 1March1998 to 9June2004.

The ES had a value of around 1120 at the beginning of the study period and a value of around 1130 at the end of the study period showing a 0.9% gain over the 6 year period. During this period it reached a high of 1574.25 on 24/03/2000 at 10:58 EST and a low of 767.25 on 10/10/2002 at 09:58 EST.

Number of trading days observed in the study:

 Mondays 320 Tuesdays 320 Wednesdays 319 Thursdays 320 Fridays 307 Total days 1586

### Table of Probabilities

For practical purposes I have put the Table of Probabilities on a separate web page so that you can print it off or save it and use it as a reference tool while trading during the day. [You can also download the Excel spreadsheet (complete with charts) here.]

The study splits the day into 27 equal segments of 15 minutes each (numbered 0 through 26) and looks at the RTH trading day from 09:30 to 16:15 EST. [All times are EST which is GMT/UTC - 5.]

If you have a look at the Table of Probabilities you will see that the most likely segment for a high of day (HOD) to occur is from 09:30 to 09:45 on a Friday and most likely segment for a low of day (LOD) is from 09:30 to 09:45 on a Monday. In fact each of these HODs and LODs has a probability of around 20% which means that it should happen every 1 out of 5 Fridays and Mondays respectively. The least likely times for high and lows are in the middle of the trading session.

If the HODs/LODs were randomly distributed then we would expect the probability of each segment to be 3.7% (1/27). This is clearly not the case.

### Practical Uses

How can we practically use this table while trading the ES?

I have it printed out and stuck on the wall next to me. I also have a shortcut on my desktop to bring the table up on one of my screens. If my system gives me a buy/sell signal then I check the table for the likeliness of a HOD/LOD to be taking place in that segment and use it in 3 ways:

• Determine the number of contracts I trade that signal.
• Help with position how wide the stop will be.
• Help weigh the probability that a trade in that direction will be successful.

### Charts

As I've done with the table I have also produced charts for each day of the week on the following web pages.

The last page in this article shows all of the charts for all the days of the week and the average at the bottom.

### Further Analysis

I have taken a look outside of RTH and I have re-run the study using a time period of 10 hours from 06:15EST to 16:15EST divided into 40 x 15 minute segments. This is the chart of that study and here you can download the spreadsheet with the data and the chart: 10 hour study

### 24 hour study

Subsequent to the 10 hour analysis above I ran the same study across a 24 hour time period using 60 minute segments starting the study at midnight on Sundays and finishing at the close of trading on Fridays. Here is the chart of that study and you can download the spreadsheet with the result data and chart: 24 hour study

Unfortunately this particular study (the 24 hour one) has a shortfall and that is that the ES continuous contract does not run from midnight on Sundays to midnight on Fridays. Monday's trading session is actually from around 17:00 EST on Sunday to 16:15 EST on Monday and so on. This means that this particular study ignores the data generated on Sunday evenings and will have no data for Fridays after 16:15 EST when trading closes for the weekend. This can be seen in the spreadsheet. I still believe that there is value in this study despite the shortfalls.

### Final Note

In writing the software to create this study/analysis I only took into account the first segment in which the HOD/LOD occurred. If for example the HOD happened twice in both segments 4 and 8 then only segment 4 is counted.

### Table of Probabilities

Segment Time Mon High Mon Low Tue High Tue Low Wed High Wed Low Thu High Thu Low Fri High Fri Low Average High Average Low
0 09:30 18.8% 21.9% 16.6% 16.3% 16.9% 14.7% 13.1% 15.0% 20.5% 15.6% 17.2% 16.7%
1 09:45 10.3% 8.4% 8.4% 4.1% 6.9% 5.6% 8.8% 6.6% 7.8% 9.1% 8.4% 6.8%
2 10:00 4.4% 7.5% 8.4% 5.9% 4.1% 7.2% 9.7% 8.8% 7.2% 6.5% 6.8% 7.2%
3 10:15 4.7% 2.8% 2.8% 7.2% 2.8% 6.3% 3.4% 6.3% 3.3% 5.2% 3.4% 5.6%
4 10:30 3.4% 4.1% 1.9% 3.4% 4.4% 3.1% 2.8% 3.1% 3.6% 3.6% 3.2% 3.5%
5 10:45 3.4% 2.5% 1.9% 2.8% 4.1% 3.1% 3.4% 2.8% 3.3% 4.9% 3.2% 3.2%
6 11:00 3.8% 2.8% 3.1% 0.9% 3.1% 3.1% 2.2% 1.6% 3.6% 1.6% 3.2% 2.0%
7 11:15 4.4% 1.9% 2.5% 2.8% 0.9% 2.8% 2.2% 1.9% 2.6% 0.7% 2.5% 2.0%
8 11:30 0.9% 1.6% 2.5% 1.6% 1.6% 3.1% 1.9% 1.9% 1.3% 2.3% 1.6% 2.1%
9 11:45 1.9% 2.5% 0.3% 1.3% 3.1% 1.3% 2.2% 0.9% 0.7% 2.3% 1.6% 1.7%
10 12:00 1.3% 1.3% 1.3% 0.9% 1.3% 2.5% 0.9% 1.9% 0.7% 1.0% 1.1% 1.5%
11 12:15 0.6% 0.6% 0.3% 0.9% 1.6% 0.9% 0.6% 2.8% 2.6% 2.0% 1.1% 1.4%
12 12:30 0.9% 1.3% 1.3% 0.9% 1.9% 0.6% 2.2% 1.6% 1.0% 1.0% 1.5% 1.1%
13 12:45 0.6% 1.6% 0.9% 1.3% 1.3% 1.9% 0.9% 0.9% 1.3% 2.9% 1.0% 1.7%
14 13:00 1.3% 0.6% 1.6% 1.3% 0.6% 0.3% 1.9% 1.9% 1.6% 1.6% 1.4% 1.1%
15 13:15 0.3% 0.9% 2.2% 1.3% 1.3% 1.3% 1.6% 0.3% 0.7% 0.3% 1.2% 0.8%
16 13:30 1.3% 2.5% 1.3% 0.9% 0.9% 0.9% 1.9% 3.1% 2.3% 1.6% 1.5% 1.8%
17 13:45 2.2% 0.3% 2.5% 0.6% 1.3% 1.9% 0.9% 0.6% 0.3% 2.3% 1.4% 1.1%
18 14:00 0.0% 1.3% 4.4% 2.8% 2.2% 2.5% 2.2% 0.9% 1.3% 1.3% 2.0% 1.8%
19 14:15 0.9% 2.8% 2.8% 3.1% 3.1% 1.3% 1.9% 2.5% 2.6% 1.0% 2.3% 2.1%
20 14:30 2.2% 1.9% 1.9% 2.5% 3.1% 1.3% 1.3% 3.4% 3.3% 2.3% 2.4% 2.3%
21 14:45 2.5% 0.9% 2.2% 2.2% 2.5% 2.8% 0.9% 3.4% 1.3% 2.6% 1.9% 2.4%
22 15:00 5.6% 4.4% 3.1% 5.0% 3.8% 3.8% 1.6% 2.8% 4.9% 3.9% 3.8% 4.0%
23 15:15 5.0% 5.3% 2.8% 3.8% 6.0% 5.3% 5.0% 4.4% 1.6% 4.9% 4.1% 4.7%
24 15:30 2.5% 5.0% 5.9% 8.4% 5.3% 5.3% 6.9% 5.3% 2.9% 6.8% 4.7% 6.2%
25 15:45 4.1% 5.3% 6.6% 10.3% 5.0% 5.6% 5.9% 5.3% 5.5% 4.2% 5.4% 6.1%
26 16:00 12.8% 8.1% 10.6% 7.5% 11.0% 11.3% 13.8% 10.0% 12.4% 8.5% 12.1% 9.1%