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Monte Carlo Analysis

Monte Carlo analysis is a simulation technique for estimating future results of a trading system by analyzing past system performance. Through the use of Monte Carlo simulation, key system performance indicators: risk, equity, profit, draw-down and run-up can be predicted with reasonable accuracy.

By knowing future system performance, the trader can prepare for future drawdowns, know the amount of capital required, what lowest equity is expected and have a good idea of the profit range for a particular trading system during similar market conditions. Monte Carlo simulation significantly improves the accuracy of future system performance estimates over traditional back-testing, offering the trader an extremely beneficial tool for managing risk.

Using traditional back-testing, system performance results are only accurate for the specific order of trades tested. Monte Carlo simulation randomly selects historical trades, calculating system performance results for each trade and counting occurrences of these results within user defined ranges. Upon repeating for a specified number of simulations, total occurrences within each range are divided by the number of simulations to arrive at the probability of each performance result.

For example, 75 random selections from 75 historical trades are made. With each selection, risk, equity, profit, draw-down or run-up is calculated and the matching range is increased by one. For 1000 simulations, if 200 draw-down calculations fall within the range of $4000. - $4500., the probability of draw-down within this range is (200 / 1000) x 100 or 20%.

The STOPS implementation of Monte Carlo simulation is unique in that actual trading system performance results are analyzed, not hypothetical results from back-testing. This improves the accuracy of the simulation and greatly increases trader confidence and risk management.

STOPS Monte Carlo Simulation features:

  • Risk, equity, profit, draw-down, and run-up analysis.
  • User selected securities.
  • Long or short positions.
  • Gross or net equity.
  • User defined number of simulations.
  • User defined group increment.
  • Bar charting of results.
  • Fully integrated with all STOPS money management tools.

The following example illustrates STOPS Monte Carlo Simulation:

  1. To begin the Monte Carlo Simulation, the required analysis is selected on the reports screen.


The Reports screen provides quick access to all STOPS reports.   (View Full-Size)

In this example, Monte Carlo simulation equity analysis is selected.

  1. Simulation parameters are selected. Parameters include security date range, gross or net equity, long or short positions, number of simulations and group increment.


The Monte Carlo Simulation Parameters screen provides simulation flexibility.   (View Full-Size)

In this example, gross equity for all long and short positions opened between 5/5/05 and 9/8/05 will be analyzed. 5000 simulations will be run and performance results will be grouped in $500 ranges.

  1. The simulation is started. Upon completion, the probability percentage of each performance result group is charted. The largest and smallest results and their respective probabilities are tabulated.


Monte Carlo Simulation results are charted for easy interpretation.   (View Full-Size)

In this example, there is a 30% probability gross equity will be in the $2500 - $3000 range, 29% probability in the $500 - $1000 range, 24% probability in the $1500 - $2000 range, 14% probability in the $1000 - $1500 range and 10% probability in the $3000 - $3500 range.The Largest gross equity is $3500 at 10% probability and the smallest gross equity is $1000 at 30% probability.

 

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