Monday, August 11, 2014

Don't Bother, Mr./Ms. Business Reporter

Dear Mass Media,
Unless the stock exchanges change by more than 2% in any given day, don't bother to report it, including you guys on my favorite business reports, Marketplace Money on NPR. The variation is due to random change. (And hey, Mr./Ms. Business Leader, pay attention to this analysis with regard to your own financial metrics like revenues, revenue changes, gross margins, etc. You might want to get a lot less excited by one-month changes in your reports.)  Since the late 1890's, the daily change has varied +/-1% three out of the five days in each week. If you hear about changes that are half-percent or less on any day, that's possible nearly 2.5 days of the week. Only once per month will the change exceed 2%. Once per year will the change exceed 3%. If that happens, please feel free to report it and look for some sort of assignable (or special) cause. Otherwise, read a book or go see a movie and write a review about it.
Dogs of the Dow - Dow Daily Percent Change Histogram
Point of Interest - Most striking is that this chart approaches a normal distribution (Bell Curve) thereby suggesting that the daily changes in the Dow are random. TheDow Weekly Percent Change Histogram has similar characteristics. For those of you that actually remember that statistics course we have a few numbers. The mean (average daily gain) is .026% demonstrating the upward bias of the Dow. The standard deviation is 1.07% and translated to English this means that 68% of the time the Dow has a daily change between ±1.1%; 95% of the time the Dow has a daily change between ±2.1%; and 99% of the time the Dow has a daily change between ±3.2%. So if you see that the Dow has dropped well over 2% you shouldn't be to surprised as as it would be expected that the Dow fluctuate more than ±2.1% five percent of the time which equals one trading day out of the month. All this hopefully provides you with a little perspective as to the Dow's daily fluctuations.


This is true of long-term variation. You could be a little more discerning on short-term variation. Hey, here's an idea, business reporter. Plot a control chart on the changes in the Dow or other stock exchanges and analyze it for statistically significant changes. I've done one here using the last 4 years' worth of data. I used 100 days of changes to set the control limits to avoid any quarter-end effects. You can see that even though 2010 had some volatility, the last four years have been steady with an average daily increase of 0.1% and a range of -2.4% to +2.5%. With this large a picture, it's how to see any 'out of control' (statistically significant) trends.

Let's just look at the last 120 days, nearly all of this year, with its unprecedented run-ups to new highs.

Here you can see there aren't any signals that the 'system' is out of control or doing anything statistically significant with regard to its daily changes: 1) there are no points outside the control limits (the UCL and the LCL); 2) there are not 8 points consecutively on one side of the center line (Average); 3) there are not 6 to 8 points continually trending up or continually trending down; 4) there aren't 2 out of 3 points near the control limits. At a glance, there aren't any unusual number of runs (times the Daily line crosses the Average line, e.g.) or any of the other indicators.

Now that you've seen this and any of the stock exchange indices tick up or down a percent or two, just say, "Ho-hum, another normal day on Wall Street" and go back to sipping your coffee or tea. Don't go looking for a reason; there isn't one. Today's results are just what we all expected. It's not because Apple, Best Buy, Amazon, IBM or anyone else did anything special. It's not because of what's happening in the Ukraine, Israel, the Brazilian rain forest or anywhere or with any one company.

Pick up the business book and start writing your review.

I tell you this so your work will also have significance when you report on something that really is worth paying hearing or reading about. I will thank you because your normal practice of reporting changes to stock indices every two to 8 hours is a pet peeve of mine.

Your friend,
The Compassionate Curmudgeon and Practical Business Radical

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