#### Tim Folkerts

**Trusted Information Resource**

The I-Chart provides a standard way in Quality Engineering to look for changes in a process. A data point is recorded at regular intervals and various tests are performed to see if there has been a change in the process -- to see if hte process is "out of control".

In this case, the market forces shaping the S&P500 is the "process" and we are looking at the % change in the closing value from the previous day. (By using % change, we can more easily & effectively compare with other measures - like the DJIA - and also with previous decades when the closing values were much lower.)

Several tests are common for I-Charts to see if there has been a change in the process. Five tests were used to see if the process was "out of control"

- a single point more than 3 standard deviations from the mean

*looking for highly unusual single days* - 2 out of 3 points more than 2 standard deviations from the mean

*looking for a small cluster of fairly unusual days* - 4 out of 5 points more than 1 standard deviations from the mean

*looking for a week of moderately unusual days* - 15 points within 1 standard deviation of the mean

*3 weeks with unusually little change in the markets* - 9 points in a row on one side of the mean

*a 2 week run up or down*

Control limits were calculated using the first 100 days in each interval. When two or more of these oot-of-control conditions were detected in a short period of time, a shift was assumed to have occurred and new control limits calculated. The most common out-of-control conditions were the first (signaling increased variability) and the 4th (signaling decreased variability).

During the first half of the decade, there are two major periods.

- Up through April 2003, the market showed considerable variability. Several sub-intervals might be identified, but for the most part the control limits (the +/- 3 standard deviation limits) were around 4% to 5%. in other words, days when the closing valuechanged by 4 or 5 percent were not atypical.
- After April 2003, the control limits tightened considerably. Now the control limits were down near 2.4%. It is easy to see the change on the graph - the values are much mroe densly packed near the center.

The rest of the decade shows more trends. (Notice first of all that the scale is much different here, about twice as great on the y axis.)

- 2005 through mid-2007 continues the tight control limits a small daily variability.
- around July 2007, the variability increased - almost doubling. The process stayed at these limits for about a year
- October saw unprecedented variability. Never in the history of the S&P 500 was the variability as great. The data ends 23-OCT-2008, but, given the state of the markets (Mid NOvermber as this is being written) I expect the large control limits are still in effect.

*In the future, I plan to look at:*

*how other measures compare with these results -- for example the DJIA or foreign markets.**see if there are way to either predict the the changes, or to use the changes to predict other financial measures**Others??? We will see.*