a trading problem for mathematicians

[Steven.Davis]

Quote from ksmetana:

The correct answer is: Not enough information given.

Not enough information is right.

With additional assumptions such as A winning and B losing = wash, there is still an important question as to how often each gives a signal.

A simple Excel Monte Carlo analysis shows that the likelihood of getting a signal is a significant factor in applicability:

A Likelihoo   A Trades      A Net Net % Wins JoinTradin  Joint Net Net % Wins
       100%       5502        990        18%       2889       1001        35%
        90%       4974       1004        20%       2309        881        38%
        80%       4410        806        18%       1832        700        38%
        70%       3823        811        21%       1418        514        36%
        60%       3273        619        19%       1021        363        36%
        50%       2785        555        20%        685        279        41%
        40%       2225        363        16%        467        163        35%
        30%       1665        357        21%        272         94        35%
        20%       1053        215        20%        114         52        46%

Taking three samplings

                   Sample 1   Sample 2   Sample 3   
     A Prob        Net % Win  Net % Win  Net % Win  Std Dev    
          1          35%        39%        40%      0.028
        0.9          38%        41%        39%      0.015
        0.8          38%        38%        42%      0.023
        0.7          36%        39%        37%      0.014
        0.6          36%        42%        40%      0.033
        0.5          41%        42%        36%      0.032
        0.4          35%        36%        33%      0.015
        0.3          35%        36%        39%      0.023
        0.2          46%        36%        38%      0.051

So under these additional assumptions the Net % Win is 36-41% instead of 20%, but depending upon the frequency of trades, you are passing up 99% of your opportunities.

The assumption of uncorrelated returns is also a killer, bad assumption.

 

[trend2009]

i guess you did not understand the question. what extra information you need?

Quote from ksmetana:


The correct answer is: Not enough information given.

 

[Random.Capital]

Profit & Loss -> trading

"Winning" percentages -> math

Are you looking for a math answer, or a trading answer?

 

[MathAndLogic]

Quote from euclid:

You need a crystal ball to tell that going long and short at the same time will result in no profit? I think you need a new alias.

Iff A and B trade the same stock. Indeterminate if A and B trade different asset classes.

 

[ksmetana]

Assuming both methods are operating on the same time frame and on the same instrument...

You enter a trade on method A. Properly backtested 60% chance of reaching your target. You have an asssumed 60% chance of reaching your target on this trade.

You enter a trade on method B. Properly backtested 60% chance of reaching your target. You have an assumed 60% chance of reaching your target on this trade.

So, what is the question?

Because the signals overlap you have a higher probability? Incorrect.

The question is flawed due to lack of information.
However, if we give the question any merit, the REAL answer is to BACKTEST the success of overlapping signals. This will tell you how well the methods sync.

I promise you, if any idiot thinks he has solved this problem with any amount of conviction, the backtest will differ from his result.


When the methods overlap, it could result in 90% failure due to the nature of the methods. Similarly, they could result in 90% success.

 

[ForexQuant]

I agree with ksmetana. System C which is a combination of system A & system B is a complete new independent system. The combination of the systems may or may not increase the accuracy of prediction.

To find out the winrate of system C, you have to measure it directly, there is no other way.