How to Mislead: Using Wrong Statistics

February 2, 2013

Investment Newsletter for the end of January, 2013

Today is about how to cheat with numbers. The wrong statistical tool, or the right tool used the wrong way, can be misleading. I am not necessarily implying evil intent. You may have just messed up.

I am absolutely certain that the market (The Dow) usually goes down the day before month end and usually goes up the day after month end. My investment management fees are lower as a result. I have been laughing with my wife for five years about the conspiracy to reduce my income.

My son works for me now. I had him prepare a data series for the last 10 years (actually 121 months). It was a huge amount of work and thank goodness I didn’t have to do it. And I am right. The Dow went down 56% of the last days of each month. It only went up 44% of the time. So where is my screw up? I ignored the size of the ups and downs. It turns out the average over the last 121 months was a net GAIN of 29 points. The ups were much bigger than the downs. Behaviorally, humans remember the number of good events and bad events but not the importance of each event.

What about the day after billing, the day after month end? I am absolutely certain that the market goes up. And, I am right. 74 times out of 121 months, 61% of the time, it went up. Am I making the same emotional mistake? It turns out I am not. The market averaged a gain of 79 points.

Lesson number one: The number of up and down periods is meaningless.

But what about that gain? Have I discovered something new? Can I time the market by buying on the last day of each month and selling on the next day? Ten years of statistics says yes. Even after commissions, I wouldn’t burn off 79 points. Now, I know full well that I haven’t discovered anything. I am using the tool incorrectly. Ten years is not a big enough sample. I can not prove that. But I will add another ten years (1992 to 2002) to the data series soon and report back to you. I would be shocked if the gains didn’t disappear with a longer sample.

Lesson number two: Sample size matters. Bigger samples are better than smaller ones. Short time periods are suspicious.

If it was true, the automatic trading programs that many firms use would buy the day before and sell on the first day, just like I am suggesting. The computers can certainly spot the trends. Because of all the buying, the price would go up more on the buy day. All the sales orders on the sell day would force the price down. The net effect would wipe out the 79 points before your alarm even rang in the morning. Remember the stock market is an auction where the price goes up or down because of supply and demand.

Lesson number three: If there was market inefficiency this obvious, it would disappear immediately.

It was excellent month in the market. Thank-you for your continued trust. Please call if you have any problems or questions. I will do everything I can for you. It is also now tax time. Call also with your tax questions.

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