The best way to understand MCS is to look at an example. Say we
have a system that has 87 trades. Each trade is either a winner or a
loser. We take 87 ping pong balls, write upon them the profit or
loss of each trade and put them in a sack. Then we begin a process
of sampling the data by pulling balls out of the sack. We pull out
one ball, write the profit/loss of the ball down on our paper, and
put the ball back in the sack. We continue this process until we
have 87 theoretical trades written down on our pad. We tally up the
theoretical trades and calculate the drawdown from the simulation.
We have now completed one simulation. We repeat this process 1,000
times until we have 1,000 different simulations with 1,000 different
theoretical drawdowns.
If the process of drawing balls is truly random, then we will
have some drawdowns that are much lower and some that are much
higher than the TradeStation Summary Report calculation. We will
also have a great many simulations somewhere in the middle. We can
picture what the entire exercise looks like by creating bins for
each increment. If our increment is 1000, then we would have bins
labeled 01000, 10012000, 20013000, ...1900120000 etc.
Every time we get a drawdown between 4001 and 5000 we increase the count in the bin labeled 5000. Likewise if we get a drawdown of 13,520, we increment the count in bin 13,00114,000. If we tally the count in each bin, we would get a bell shaped curve of some sort. The figure below shows what a typical plot of this distribution looks like. I ran the Monte Carlo Simulation 1000 times, printed the results to a file, imported it into Excel, and graphed the bins on our Using MCS Software pages.
Interpreting the Results
There is a peak in the curve at the 6000 bin,
but there is a very long tail to the right. This indicates the
possibility of having much higher drawdowns than reported by
TradeStation. We can then calculate the theoretical probability of
achieving drawdowns greater than 7,000, or any other number for that
matter by counting occurrences in the bins to the right of a
particular bin.
Below, we have provided in spreadsheet format the data that
appears in the charts. In addition, we have added one extra column
that measures probabilities. Column 2, which measures the number of
drawdowns in each of the bins, adds up to 1,000. This is because we
set the MCS to run 1,000 simulations, and they are all represented
in the bins listed to the right. We can then pick any bin, add up
the "Counts" in the bins below it, divide by 1,000 and multiply by
100 to get the "Probability of Greater Drawdown." For instance, bin
2000 is empty so there is a 100% chance that the drawdown will be
greater than $2,000. From the listing we can see that there is a
48.8% chance that the drawdown will be greater than $7,000.
Similarly, there is a .1% chance that the drawdown will exceed
$22,000.
