Probability of Next Trade

Quote from MAESTRO:

I am sorry, but none of you above are correct what so ever. The solution is in Bayes' theorem and the most vivid illustration of it is presented via the Monty Hall paradox. Please educate yourself.

MAESTRO

http://en.wikipedia.org/wiki/Monty_Hall_problem
http://en.wikipedia.org/wiki/Bayes'_
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Hmmm, I had a couple of questions --

Is it necessary, to apply Bayes theorem, to assume that the OP's 65% winning rate has wins randomly distributed throughout the time series, and continuing forward?

In the material I've studied on Bayes theorem, the examples usually have conditions that exist at the same time (eg, false or positive test result and having or not a disease; choosing from 3 doors with a prize behind). Does it also apply to sequential events?

Do we have to assume the 65% win rate is somehow real or constant, and not overstated by an issue like small sample size?

Bayes theorem is based on conditional probability, but wouldn't trade outcomes be independent?
I suppose to test independence we'd have to see if these are true:
P(next trade wins | previous trade lost) = P(next trade wins) ??
P(next trade loses | previous trade won) = P(next trade loses) ??

thanks
 
Quote from zedDoubleNaught:

Hmmm, I had a couple of questions --

Is it necessary, to apply Bayes theorem, to assume that the OP's 65% winning rate has wins randomly distributed throughout the time series, and continuing forward? ...
More...

Just consider a simple example of tossing a biased coin. 65% probability of tails and 35% probability of heads. If you had n consecutive heads the probability of the next toss being a tail or head is still 65/35. Therefore, there is no advantage of "waiting". The only help is to increase the frequency of trading so that a win comes sooner. However, there is always a chance of ruin. You can have 100 losing trades on a row and still have 65/35 expectation of the winning trades. There is no guarantee of this winning expectation to exhibit itself in a fixed ( small or large) set of trades. However, there is a non-trivial method of improving the overall trading system using the Monty Hall paradox, but I am not about to tell you how to implement it. You would have to figure that out for yourself.

Cheers,
MAESTRO
 
This is a good example of what is wrong with posts on message boards: "I have a great secret but I am not going to tell you."

Your example does not apply to many trading systems because the returns are autocorrelated.

Quote from MAESTRO:

Just consider a simple example of tossing a biased coin. 65% probability of tails and 35% probability of heads. If you had n consecutive heads the probability of the next toss being a tail or head is still 65/35. Therefore, there is no advantage of "waiting". The only help is to increase the frequency of trading so that a win comes sooner. However, there is always a chance of ruin. You can have 100 losing trades on a row and still have 65/35 expectation of the winning trades. There is no guarantee of this winning expectation to exhibit itself in a fixed ( small or large) set of trades. However, there is a non-trivial method of improving the overall trading system using the Monty Hall paradox, but I am not about to tell you how to implement it. You would have to figure that out for yourself.

Cheers,
MAESTRO
More...
 
Depends on your strategy. With some strategies, such as always-in strategies for example, the outcome of one trade can influence the probable outcome of the next trade, so it may make sense to change position size accordingly.

With a trading system that is more opportunistic, and trades only when certain conditions are met, and isn't in the market most of the time, the probability that there is an exploitable dependency between the trades is smaller.

Quote from bearmountain:

Unfortunatly statistics is not my strong suit. I have a question about probability of win/loss of the next trade after a loss or losing trade.

A system is profitable 65% of the time.

When I drill down to the Losing series of trades (consecutive losing trades). 90% of the time, after 2 losing trades there is a winning trade. About 75% of the time there is a winning trade after one losing trade.

So my question is, what about just taking a trade after waiting for one or two losing trades?

So trade one profit, trade two profit, trade three loss.
Why not just wait to take a trade after trade three?

In black jack when the card count is high, the odds favor a player to bet big. Isn't the same true here?

I am sure I am not the first person to think of this, what are the issues involved with such a strategy?

Thans very much.
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Quote from MAESTRO:

... However, there is a non-trivial method of improving the overall trading system using the Monty Hall paradox, but I am not about to tell you how to implement it. You would have to figure that out for yourself.

Cheers,
MAESTRO
More...

Would you mean, implementing it by skipping some of the system's trades, or reversing the direction of some of the trades?
 
Quote from MAESTRO:

I am sorry, but none of you above are correct what so ever. The solution is in Bayes' theorem and the most vivid illustration of it is presented via the Monty Hall paradox. Please educate yourself.

MAESTRO

http://en.wikipedia.org/wiki/Monty_Hall_problem
http://en.wikipedia.org/wiki/Bayes'_
More...

I know it seems silly to even consider any trade has anything to do with the next, but if someone wants to backtest it, it may be fun to see the results.

It seems like most of us here are in agreement that a winning system should just be traded, rather than being analyzed trade for trade.
 
Quote from zedDoubleNaught:

Would you mean, implementing it by skipping some of the system's trades, or reversing the direction of some of the trades?
More...

None of the above. You need to create a dependency of the trade's outcome to the next trade entry to enjoy Bayes's methods. If the trades do not have a feed back or "memory" it would not work. One needs to attenuate the system's variety (W.R. Ashby) to improve it's decision making ability.

Cheers,
MAESTRO
 
Quote from MAESTRO:

None of the above. You need to create a dependency of the trade's outcome to the next trade entry to enjoy Bayes's methods. If the trades do not have a feed back or "memory" it would not work. One needs to attenuate the system's variety (W.R. Ashby) to improve it's decision making ability.

Cheers,
MAESTRO
More...

And what makes you think there is memory in all systems? When I run my automation tomorrow, why does BRCD care about what GS did a few minutes ago?

I mean no disrespect, and you are miles ahead of a lot of us mathematically. But intuitively I just can't grasp it. We are obviously running completely different systems, but your statements evidently imply correlations which I just don't deal with anymore. Couldn't make them work. Congrats to you since you obviously have.

I understand bayes and the monty hall problem, but it would seem as though the answer to the OP is that it depends on what type of system you are running.
 
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