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# statistical analysis

1. 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. 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. Beats me. Thanks for the reply.

Unfortunately, I never took statistics in college.

4. 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).

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"

regards

7. 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. 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. 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. 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.

11. So is Characteristic A, that they are in the group of 29. Is Characteristic B, that they are profitable in the direction of the trend?

If that is so, then Characteristic B does not seem to really be a selectable criteria for use in filtering trades.

Perhaps you mean that the stock initially going down/up so that it can cross back through the open is one of your Characteristics?

12. 29 STOCKS IS SIMPLY THE SAMPLE THAT I HAVE AT THE MOMENT. EACH DAY I MAY OR MAY NOT FIND ANOTHER THAT MATCHES MY CRITERIA.

IF STOCK IS GREATER THAN THE OPENING PRICE AND MOVING UP AT THE OPEN, THE TRADE IS LONG. IF THE PRICE MOVES BELOW THE OPENING PRICE, THE TRADE IS SHORT. ONLY THE OPENING 2 TRADES ARE CONSIDERED. AFTER THAT, I'M OUT.

13. What you want is the joint distribution of your two characteristics (i.e. random processes).

You don't give us enough information on the characteristics of these process for us to give a closed form solution for the joint distribution.

Without making assumptions on the processes, you need to empirically compute the joint distribution with past data and hope that the distribution is stationary.
If the distribution isn't stationary the problem becomes very difficult.

Ninna

14. If I knew how to do all that, I wouldn't be asking any questions.

I had a great short play this morning but my trade was rejected.
God's laughing his ass off at me again.

15. I haven't been able to express when the Original Poster is missing, but at best, this situation is prone to the The Monte Hall Paradox.

The problem is ill-posed, but I will try again.

The 29 stocks are the sample universe. Stocks are in group A if it goes above the opening price. Knowing this, there is a 76% chance that a long trade entered at that point will eventually be profitable. Stocks are in group B if within the first few minutes, the price is below the open. Knowing this, there is a 75% chance that a separate short trade entered at that point will be profitable.

I have probably misunderstood. If not, most of the 29 stocks will probably be in A and B, and without alot of missing detail how can both a long and a short trade initiated seconds apart both have a high rate of success?

Trying to be helpful, but doubting that this is helping.

16. Easy

Lets say the stock moves up from the open and a long trade is made that is profitable. Then later on, the stock moves below the opening price and a short trade is made and it is profitable. Of course this happens frequently.

Now lets say that the probable percentage advantage is that it will make a short profitable trade. Since for this instance, the long trade is ignored and only the short trade is taken because it has a much higher probability of working.

Does it make sense now.

17. Made a nice buy on sfsf today at the open. My number one pick of the day.

18. There's what's not advised, right there. Sure search for "joint probability distribution". However, to trade just 1 stock is far from ideal. I'm not sure what the real rule of thumb is, but personally I'd trade at least 16. Otherwise you're missing the real benefit of having statistical information.

19. On any particular day, I can't find more than one or two stocks that meet these two criteria.

20. Seems unlikely that a 75% profitable signal would be consistent if sampled at a rate of one stock per day. There has been a nice run-up in stocks lately. I would guess that a characteristic like having 'C' in the symbol has had an open to close profit most of the time for the last three months. I know you are smarter than that, hoodooman, but consistency of profitability is a fleeting thing.

21. Yes you are right and yes, I've already thought of that.