I have been reading http://zorro-trader.com/manual/en/montecarlo.htm and I don't understand this part:



From what I learnt in probability and statistics course, the confidence level is the probability of the parameter being in the confidence interval. There are three variables: confidence interval, confidence level and number of experiments, if the number of experiments is fixed and you have a too wide confidence interval, you can narrow it by lowering the confidence level. Of course, the more experiments you perform, the more narrow the confidence interval for your parameter is and the more higher the confidence level.

Anyway, this has nothing to do with the probability of the parameter being in the interval in one particular sample:



http://en.wikipedia.org/wiki/Confidence_interval

So I don't understand from what reasoning did you arrive at these two statements:



Following the definitions I quoted and explained before, 50% confidence level means that in 50% of the experiments (the various equity curves generated -by I would like to know what procedure-) the parameter(s), in this case Anual Return, Max Drawdown and Capital Required were 202%,1940$ and 1760$ respectively.
How do you arrive at "half the simulations had a better and half a worse result" ?



Here I'm more puzzled, how do you derive that the likeliness of the parameter being at certain value with 100% confidence level is 1/n? From what I quoted, it can't be derived from confidence intervals ("After a sample is taken, the population parameter is either in the interval made or not; it is not a matter of chance").

I would greatly appreciate if you can shed some light on this, whether you are using another definition of Confidence Interval or what, Monte Carlo simulations are a great improvement to strategies but I want to understand how to use it properly. Thanks!

The confidence level is no confidence interval, it splits the simulations into two set of results. You can find many explanations of Monte Carlo simulation on the Internet. I've borrowed the description from here: http://www.adaptrade.com/Articles/article-mc.htm.

The "1/n" just results from the fact that the higher the confidence level, the less likely it is to get the same or a worse result. At 100% confidence level, only 1 of n samples was same or worse - that's your 1/n probability.

Thanks for that! I have done a course in which we used Monte Carlo methods, basically you generate many samples from a distribution (uniform, normal, etc) and then plot a bin graph. The amount of times a bin (which could be a value or a range of values) appear divided by the number of samples was the probability.

From what I read in the link you posted it is the same procedure. My confusion came from here:



As I thought, they mix the concept of probability with confidence level which have a subtle difference, but anyway what is important is to understand what we are talking about.

Actually, what is being described here is the probability of an interval (which is a set),

so when in the table in http://zorro-trader.com/manual/en/montecarlo.htm
it appears:


it means that in 90% of the samples:

1) the AR was at least 165%? or exactly 165%?
2) the DDmax was at most 3080$? or exactly 3080$?
3) the Capital required was at most 2580$? or exactly 2580$?

Please, if it at least/most, correct me if is at least or at most in each of 3.

If it is exactly then, how did you manage to arrive to an exact value? The bins from a Monte Carlo simulation would be a lot (consider the drunk walk problem that models prices)...Do you average them? For instance if you get AR of 163,164,165,166,167% they go to the 165% bin?



Ok, this is like what I put in the spoiler above, but shouldn't it be 99%? Look: (Confidence level/100) = 1 - alpha,

if Confidence level is 100% then alpha is 0 and P(better result) = 1-alpha = 1 , that is you are sure, and P(the same or worse result) = 1 - P(better result) = 1 - 1 = 0 which is never...

if Confidence level is 99% then alpha is 0.01 and P(better result) = 1-alpha = 0.99 , that is you are almost sure, and P(the same or worse result) = 1 - P(better result) = 1 - 0.99 = 0.01 which is almost never...If n = 100 then 1/100 is 0.01

So the 1/n example works with 99% of Confidence level or am I missing something?

I never had a statistics course, but I think your description of what you've learned in that course is correct. Only difference is that we have two variable bins here, not many fixed bins as in your course. Maybe that confused you.

I have reworded the online description a little to make it more clear. When you follow your probability interval definition, you can see that at confidence level 99%, the probability to get the same or worse result is (1/n + 1%). And at 100%, it's 1/n.