What position size will give X% Maximum drawdown?....Ultimately calculating the MAR ratio
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If I have an optimization result which gives a Maximum drawdown of 'x' during which the Risk Per trade was set at 'r' % of the account equity, then how do I calculate the size of 'r' that will produce a value for 'x' of 10%?
I'm not sure it is even possible at this stage....not without more information.....but I would like to be able to do this calculation from the info given in an optimization report.
I (not an expert so this may be way off) have almost come to the conclusion that the answer uses logarithms and/or the e constant......but I could be totally wrong.
If this CAN'T be done from the info given by an optimization, then what info would be required in order to do it?
If there is no possible way to do it except by trial and error, then is there at least a way to estimate it? For example, if a formula produced a value that actually ended up resulting in 9% or 11% maximum drawdown when run, then this would be acceptable considering there is no exact formula.
ULTIMATELY what am I doing?
Where this all comes from is that I use a metric of the ratio of the annual compounded ROR to the maximum drawdown (Annual ROR % / Maximum Drawdown %). This is actually the MAR ratio. Originally I had thought that this value would remain CONSTANT, even if the risk per trade were changed (because changing the risk per trade would change both the return and the maximum drawdown together). However, I have discovered that this is not the case. It seems that for a profitable strategy, that as the risk per trade is increased, so does the MAR ratio (increasing the risk per trade is increasing the annual ROR by MORE than it is increasing the maximum drawdown).
What would I like to be able to do?
Given a set of optimization results, where the maximum drawdown of each result differs, I would like to be able to reasonably estimate (correct to 2 decimal places.....unless exact is possible) what the MAR ratio of each WOULD be IF the maximum drawdown were 10% across the board (i.e. I want to be able to adjust the MAR ratio, so that I can see what it would be if the maximum drawdown were 10%.....instead of whatever the maximum drawdown is from the optimization report).
Currently the results range from a Maximum Drawdown of 1% to a Maximum Drawdown of 50%.
Well ladies and gentlemen, any ideas?