Sunday, March 29, 2009

Regression to the Mean

Here is a statistical principle that, to me, works almost like magic when I looked at it the first time:

Regression to the Mean

According to an article on Wikipedia, if I know the mean or expected value of a random variable (coin flips, test results, etc), if I take a random result from the variable's sample space and it turns out to be far from the mean, (either beyond the 25-percentile on the distribution curve, or at a certain distance beyond the standard deviation), if I take another independent sample, the second value will be much closer to the mean, depending on how independent my second measurement is from the first.

Does regression to the mean occur in stock price movement? Or perhaps this is better applied to forex spot prices, due to its greater volatility which more closely approximates normal distributions (will have to find out whether this is true). If that's the case, one should simply go long when the price is far below the mean, and short when its above.

The key reason why this doesn't apply is because the range of values of the second price is almost always dependent on the first, since the price-time graph is continuous. But instead of being applied to the instrument price as a whole, we can use it to gauge the likelihood of more specific events which are more random, eg after the MACD crosses over and this indicator goes up and so-and-so, what is the average price behavior over the next 10 candlesticks? In this case we might simply open a position based on the average behavior, But if regression to the mean applies, we can also wait for a large deviation to occur in the negative direction, which according to the principle will increase the odds that this won't happen the next time.

This brings me to the question: what is the best way to model the price of a financial instrument as a random variable, and hence in a probability distribution graph?

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