Drive the Monte Carlo to Consistent Trading Profits

With backtested trade results in hand for the SPY VIX system, Monte Carlo simulation can help me determine how much capital I can safely trade with the system.

Some approaches to position sizing are based on maximum drawdown (MDD).  In Day Trading Futures Online (2000), Larry Williams suggests dividing account balance by margin per contract plus (1.5 x MDD) to determine number of contracts.

Monte Carlo simulation is a technique that can offer more statistical clarity about potential results.   Rather than simply assuming the worst future DD to be 50% worse than the backtested MDD, Monte Carlo simulation uses multiple trials and randomization to determine probabilities.

Historically, Monte Carlo simulation was first used by scientists working on the atom bomb.  The technique was named for the Monaco resort town renowned for its casinos where games of chance rule the day and has been used in many fields including engineering, insurance, the environment, and finance.

In trading system development, Monte Carlo simulation generates equity curves by randomizing the order of backtested trades thousands of times (or more).  The sample distribution of system statistics can then be studied.   By using the MDD seen in any randomly shuffled backtest rather than just one specific ordering of historical data, I can quantify my confidence level about future system statistics such as MDD.

Monte Carlo simulation suggests the ordering of outcomes in the past is just one possible history out of an infinite number of equally possible histories.  Position sizing based on the average(s) or extreme would serve me best.  Out of 10 trades with win loss sequence W-L-W-L-W-W-W-L-W-W, I could have seen W-W-L-L-L-W-W-W-W-W in which case the DD would have been much worse.  Monte Carlo analysis will tell me the probability of this taking place.