The power of Monte Carlo Simulation

Path dependence

Trading profits do not just depend on getting from here to there. Profits also depend on the path taken.

This is not only true for some exotic options but also for plain vanilla trading. The problem is the account size.

In playing the marble game we are dealing with a mathematical abstraction where any number is a valid price. For instance with a %Risk method, equity can never reach zero. Consider starting with $1,000 and risking 20% on each trade. After a run of 5 losing trades equity is $253. Five more gets $85.90. The point is that it never reaches zero. Lose forever and zero will be approached arbitrarily close but never reached. (This is one of the problems with optimal-f risk calculations which are inherently a %Risk method.)

Real trading does not permit trading small sums. It simply becomes impractical because of commissions and the discrete size of acceptable orders. Show me a broker that will allow $2.34567 to be traded. But more important, before this level of equity is reached, there is likely a margin call. Day trade 2 S&P e-minis with a staring equity of $4,500 and the method better be good because current margin requirement is $3,937.50.

One of the truly powerful features on Monte Carlo simulation is that it handles this problem with ease. In TradeSim starting equity and minimum equity can be set. During any trial if equity falls below the minimum, then 'trading' is suspended for the rest of the trial and this shows up clearly in the statistical results.

For example here is the equity probability curve for a profitable method with two values of minimum equity. StartEQ=$1,000, MinEq = 0 and $910.

It is very clear that the minimum equity is too close to the starting equity and results in about 12% chance of halting trading. A greater margin between starting and minimum equity is needed.

One of the main strengths of Monte Carlo Simulation is that it allows flexibility in applying both risk strategies and it allows boundary conditions to be placed on the path that equity curve takes.


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Copyright 2002, Larry Sanders

Last update 2002.04.16