## 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?

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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…

“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.