## How Many Trades are Enough Trades? : Answering the Question of Trade Frequency From a Statistical Perspective

The first question we need to ask ourselves is: How do we determine statistical significance in trading? How do we determine what is meaningful and what is not? In trading the answer to this question comes from whether or not the outcome of a strategy can be derived from pure chance. Think about a strategy which has 10 trades during a 10 year period with 10 of these trades being profitable. If the strategy has a symmetrical risk to reward ratio then the chance of achieving 10 consecutive profitable trades by mere random chance is approximately 0.00097%. This means that there is a chance of about 1 in 1000 that the outcome of the system was the result of nothing but pure luck. But is this number too big or too small ? Since we want to make sure that a strategy’s outcome CANNOT be the result of random chance we have to choose a very low threshold for the probability of this being the case. In order to have a high confidence that results aren’t the result of random chance I usually only pick systems that show a probability of having a random analogue with the same results being inferior to 0.000001% or 1 in 100 thousand. A system which is built upon symmetrical, unrestricted logic rules which has such a low probability of being the result of random chance (taking into account out-of-sample results and being properly developed with accurate simulations) has a very high chance of actually exploiting an inefficiency on the market. But how many trades do we need then?

The number of trades that are a minimum depends on the characteristics of your strategy. In order to determine if a real-world strategy with X trades has enough we first need to determine the probability of a random strategy achieving the exact same profit results. However we need to make-up a random strategy with a similar distribution class population in order to make sure we’re comparing apples to apples. The easiest way to do this is to perform a Monte Carlo simulation using a distribution of return profile which closely resembles the one of the strategy you want to evaluate with the difference that classes have been equally-balanced to make the overall winning probably equal to the overall losing probability. After running this simulation you should calculate – within the random strategy Monte Carlo simulation – the probability to reach the profit level of your back-testing result.

However this is only the simplest way in which such a comparison could be made. We could also randomize the outcome of the evaluated strategy to know how many of these outcomes could potentially overlap with those which are the result of random chance. In order to do this we need to run a Monte Carlo simulation of both strategies and then see the maximum profit reached by the random strategy populations and how many of our evaluated system outcomes end up above this end-result. By doing this we could calculate the probability of the overall system outcomes falling into random chance, the lower the probability here the better our system is. Once you reach a trade number for which the shared region between final profits of the MC simulations for the evaluated and equalized-for-randomness distributions falls below 1% of a 100K iteration MC simulation you are within a number which is good enough.

As you can see the question of “minimum trade number”  is not answered simply by a number but by the inherent characteristics of your strategy and how many trades such a strategy needs to prove that it is significantly above the probability of these results being the mere outcome of random chance. By then evaluating the overall MC simulation result overlap between such a strategy and one equalized to have no edge we can see how good the quality of our distribution actually is against its partner with no market advantage. Definitely trading strategies that cannot be derived from simple chance is the most important objective of the “minimum trade number requirement” as this gives us a much higher confidence that we are trading a strategy which has an edge although whether or not this edge exists in reality also concerns the development procedure (simulation accuracy, out-of-sample testing, optimization procedure, simulation length, etc).

You can leave a response, or trackback from your own site.

### 3 Responses to “How Many Trades are Enough Trades? : Answering the Question of Trade Frequency From a Statistical Perspective”

1. McDuck says:

Daniel ,

when you say
“The easiest way to do this is to perform a Monte Carlo simulation using a distribution of return profile which closely resembles the one of the strategy you want to evaluate with the difference that classes have been equally-balanced to make the overall winning probably equal to the overall losing probability”

what do you mean with the last part of the statement “with the difference that classes have been equally-balanced to make the overall winning probably equal to the overall losing probability” ?.

The classes do not reproduce the original distribution?. It’s my understanding that the idea is like putting as many balls of a color/number in a basket as their frequency in the backtests. Later randomly one chooses a ball take note of its color/number and return it to the ball.

Best.

• admin says:

Hi McDuck,

Thank you for your comment :o) What we want here is to evaluate the strategy against a similar strategy which has NO edge (to evaluate for the probability of our strategy’s results to be the results of a similar but random strategy), therefore we need to evaluate it against a close but modified distribution in which the long term edge has been reduced to zero. The idea here is NOT to evaluate an MC simulation of our strategy but to simulate a random counterpart that could eventually lead to a similar outcome, again we are evaluating a RANDOM analogue with NO edge and NOT the distribution of our strategy. In order to do this the distribution classes need to be equalized in order to reduce the edge to zero while preserving some relative class proportions (we are evaluating the distribution of a DIFFERENT strategy, one which has NO edge but is SIMILAR to ours). I will make a video during the next few weeks about this in Asirikuy as I understand it to be confusing :o) Thanks again for posting,

Best Regards,

Daniel

2. McDuck says:

Hi Daniel,

What I don’t get is how you do the ‘equalizing’. Anyway, looking forward to you video to understand better the idea.
Best.