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## Are Stock Prices Random?

There is a lot of interesting mathematical debate about stock prices:  are they predictable?  Are they random?  Can you make money by identifying trends?  Can you beat the market and make a fortune?

Some (most?) mathematicians would tell you that stock prices are essentially random walks, that is, no more predictable than a coin flip.  The amount a price goes up or down at any given moment might follow some pattern (small movement is more likely than large movement, for example), but whether that movement is up or down is basically random.  Now, what random means to mathematicians can get kind of complicated, but you get the idea.

I thought it might be interesting to compare actual stock prices to a list of randomly generated numbers.  After messing around with a spreadsheet for a bit, I came up with the following:

One of these graphs represents 200 days of prices of the Dow Jones Industrial average; the other represents a a sequence of numbers that move up or down randomly.  (Figuring out how to get a good-looking random graph took some time, and is an interesting challenge in and of itself).

So, can you tell which is the Dow and which is a coin toss?  More importantly, how much would you be willing to bet on it?

www.MrHonner.com

1. September 28, 2010 at 8:51 pm

You’d be surprised at how often the gambler’s fallacy (the idea of randomness having memory) is applied to predicting the stock market. It’s exactly the same flaw in believing a coin must land on heads next if it has landed on tails several times in a row. However, at least in coin tosses, there’s a slight chance the coin may be weighted if it continues to land on one side, so that may have some merit…

2. October 2, 2010 at 5:28 pm

“No solution.” I guess.

A can be seen as a coin toss where the heads and tails switch randomly. It can also be seen as Dow, since the stocks rise and fall in the same fashion.

B can represent a “weighted” coin that’s landing on heads or tails repeatedly. It can also be seen as Dow with a very bad day.

Wait a minute, how would A and B show coin toss? It’s either Heads or Tails, unless you show how that total amount changes over time.

1. October 6, 2010 at 9:01 am