i am confused with all these probs. also, i am getting weird #s in my simulation and they seem to be dependent on the Stop value. examples of the prob ratios am getting: 6.6/1 or 5/1 depending on Stop value. i will check your solution and then re-simulate again.
Isn't this whole question just getting to the fact that the probability of getting stopped out is a function of the size of the stop vs. the standard deviation of the daily range, while the probability of making a similar gain would be a function of the size of the stop vs. the standard deviation of the daily returns? Effectively, this would make the ratio that answers your question a function of the ratio of the standard deviation of the daily range to the standard deviation of the daily returns, correct?
As an example from my previous post - if the stop is set at 1%, the standard deviation of the daily range is 2% and the standard deviation of the daily returns is 1%, the ratio in the original question would equal 1.94 : 1. That is, you'd get stopped out 30.85% of the time, and you'd get an end of day return of 1% or more 15.87% of the time. 30.85%/15.87% = 1.94:1 ratio of hitting the stop vs. getting a similar sized gain. Unfortunately, the math to convert the three inputs (stop, std dev of range and std dev of returns) into that ratio doesn't come naturally to me, but I'd love to see the derivation to see if my rusty AP calculus comes back to me... I confess to no longer being able to integrate functions of e.
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