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# statistical analysis

Discussion in 'Strategy Development' started by hoodooman, Feb 6, 2011.

1. ### hoodooman

Let's assume that I have a specific sample of stocks.

75% of the time, I can pick the correct direction to trade because they correlate with a certain characteristic.

With this same sample of stocks, I can pick the correct direction to trade 75% of the time because they also correlate with another characteristic.

Now if I pick one of these stocks that correlates with both characteristics do
I enhance my probability of success and if so, by how much.

Replies will be sincerely appreciates.

2. ### rdg

Isn't it a function of the correlation of the 2 characteristics? In the degenerate case where corr(characteristic1,characteristic2)==1, the probability should still be 75%, right?

3. ### hoodooman

Beats me. Thanks for the reply.

Unfortunately, I never took statistics in college.

4. ### rdg

That makes sense though, right? The real degenerate case is where characteristic1 is the same as characteristic2. Clearly, taking the same characteristic into account twice won't change your probabilities.

Think about the characteristics as adding or removing information. If the system is comprised of information (a,b,c,d) and both characteristic 1 and characteristic 2 contain information (a,b,c), then you can take either (or both) into account and know (a,b,c) about the system. If, on the other hand, characteristic 1 contains information (a,b) and characteristic 2 contains information (c,d), then taking both into account gives you full knowledge of the system (a,b,c,d).

5. ### gtor514

P(A,B) = (0.25, 0.75)
P(X,Y) = (0.27,0.75)

P | A B
----------------------
X | 0.1875 0.5625
Y | 0.5625 0.9375

search "joint probability distribution"

6. ### hoodooman

regards

You can use the law of addition of probabilitites but the asumption is that the two processes are independent. If the processes are dependent it does not apply:

P(A+B) = P(A)+P(B) - P(A)P(B) = .75+.75 - .75x.75 = 0.9375

However, I doubt that in the markets you can find two uncorrelated processes of that kind.

8. ### hoodooman

Thanks for the reply. I tried two very high probability trades today.
One short and one long and they both went in the wrong direction.

If I didn't make God laugh his ass off every day then I would been dead a long time ago.

9. ### Steven.Davis

Determining the degeneracy of the two characteristics is easily determine by counting the sample set. Take 100 stocks. Categorize how many have A and separately B.

If almost all of the stocks are either both A and B or neither A nor B, then your characteristics are degenerate and your odds are still just 75%.

If most of the stocks are A or B, but not both, then for your 75% estimate to be true, you have a killer combination.

Just sort them out to see.

10. ### hoodooman

For a specific sample of 29 stocks:
76% will trade long for a profit
62% will trade short for a profit
89% will trigger a winning trade in the direction of the trend.
The trade is triggered when the price crosses the opening price.
Only the first two price crosses of the opening price are considered.

#10     Feb 8, 2011
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