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Thursday, September 2, 1999
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The Urge to Trade
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A few months ago I stumbled across the Yahoo! "Investment Challenge." It looked like risk-free fun so I entered. I told myself that I would use it as an avenue for releasing my pent-up stock trading impulses. This, I rationalized, would make it easier to focus my more sensible side on the investment of my real money. Little did I know then that I would actually learn something in the process. *Fade to the past...*

Now I'm no teenage yahoo, I tell myself, as I begin to consider my stock picks. I've done a little reading on investing and I have a knack for data, so I won't be surprised if I do pretty well. Armed with my burgeoning market prowess, then, I proceed to create a winning portfolio, "buy" the stocks, and then check on the portfolio value periodically throughout the month.

OK, I'll come clean: I check it every day! Sometimes I check it both in the morning and evening. And, on occasion, I even have to fight off the urge to check it again during the day. This experience brings to mind all that I learned about behavior shaping in my college basic psychology class. I'll never forget watching my lab rat go NUTS pushing on that lever when I made a simple change in his feeding schedule from one pellet every five pushes to "on average" one pellet every five pushes. In this one observation, I learned more about human nature than I had learned via the *Iliad* and *Odyssey* combined. Nothing motivates like the unpredictable pat on the back!

Which is exactly what I'm getting from Yahoo! (back to the story). My portfolio jumped around a lot, but, in the end, the ups overcame the downs and I ended up ahead 2% on the month. Not bad, but I wondered how this compares to the competition. So I hit the "Standings" link and my jaw drops to the floor.

Here, in front of me, is a top 20 composed entirely of "investors" who have earned over 300% in one month! How on earth? I ask. So I click on a few of these successful investors and review their trades. The pattern is always the same. Buy one extremely volatile stock at a time and pour all of your fake money into it. If it starts to drop, bail immediately. If it "pops," watch for the turn down and sell immediately. If it hovers flat, sell it and repeat step 1.

Now wait a minute, I think. If this isn't a "random walk" I don't know what is. With the number of trades these guys are making, their portfolio balance ought to be approaching "zero minus commissions," the expected value of the random walk, right? So I sit down to do something that I should have done 10 years ago -- work out the **standard deviation** of a random walk! Here's what I learned:

- The standard deviation of a random walk result (end point - starting point) gets
**bigger**with increasing n, not smaller! ( = sqrt(n) x sigma, where sigma = standard deviation of each incremental change ). Given that the computation of averages, and not sums, dominates most statistical practice, this reality takes a little getting used to. As n gets bigger, the range of typical values for the sum gets wider, not narrower as it does for averages. The sum does not necessarily "close in on zero," it just averages zero. - Assume, for the sake of argument, that the average day-trader does no better than a random process minus commissions. Lesson one then confirms that more day traders will lose money than make money, but it also says that a non-trivial number of them will make (or lose!) very large amounts of money, and that the amount of money they can hope to make, the high end, actually gets larger the longer they trade!
- To get a better feel for this, I set up MS-EXCEL to generate a random walk of size n=1000 and graph the result. Then I hit the
button over and over again to generate a series of these random walks. As predicted by the theory, many of the walks ended up much farther from zero than my intuition would have ever believed. Moreover, I could have shown many of the resulting graphs to my stock club and generated a long discussion about the underlying "pattern"! There really did appear to be "trends" in many of them, and I say this as a guy who looks at a lot of data. - If you flip a fair coin and get 100 heads in a row, what are your odds of heads on the 101st toss? You guessed it: 1/2. Similarly, no matter how far from zero a random walk finds itself, its current position will not impact its direction going forward. So odds favor its path, from this point forward, staying on the same side of zero that it currently finds itself.
- Put together a) the rat in the Skinner box, b) the non-trivial probability of striking it rich, and 3) the great difficulty in distinguishing skill from dumb luck, and you have all the ingredients for a very powerful human motivator -- namely day trading.

Push, push, push, push, pellet! Push, push, push, push, push (heard in the background: "Honey, time for dinner!") push, push, pellet! Push, push, pellet! Push, push ("Daddy?") push, push, push , push...

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