Monte Carlo Simulations in Trading

Ever wonder if you should move your stop loss to break even? Or how to even evaluate the efficiency of your strategy? Is it enough if your historical trading statistics point to positive expectancy? This is where one of my favorite free tools come in.

HowToTrade.com has a free Monte Carlo simulation tool, which you can access here. Here's what HowToTrade has to say about the Monte Carlo method:

The Monte Carlo Method is an automated technique that is used to project a trader’s different profit & loss outcomes. Through running Monte Carlo Simulations, individuals can estimate the efficacy of their trading strategies.

Our Monte Carlo tool is designed to help you accurately measure the variance of your profit & loss. Simply input strategic variables such as initial balance, risk percentage, risk vs reward ratio, win percentage, and a number of trades — the Monte Carlo Simulator does the rest!

Backtesting one's strategy is a great way to see how well it would've worked in a pre-defined period of time. Monte Carlo simulations stack on top of that by essentially stress testing your strategy.

For example, let's say you flip a coin 100 times. The first 100 times might result in heads 58% of the time. If you flip the same coin again another 100 times, it might only land on heads 49% of the time.

Rather than flipping the coin 100,000 times to gauge best and worst case scenarios, you can run a Monte Carlo simulation. While the long run expectancy is expected to be 50% heads and 50% tails, it does stress test how many times in a row the coin could land on heads. The keyword here is "could." It's not a guarantee, but it can help reveal the true maximum drawdown.

I recommend playing with the tool a little bit before reading my next section below.

Let's say you have a strategy that is showing positive expectancy. This implies you will be profitable in the long run. However, let's stress test this.

Scenario 1: Trend Scalping

Strategy description: scalp in the direction of the trend by taking small but consistent quick wins (high win rate but low reward-to-risk ratio)
Initial balance: $5,000
Risk % per 1 trade: 1%
Winning trade %: 75%
Break even trades %: 0%
Average number of trades per month: 20
Total months: 12
Take profit/stop loss ratio: 0.5

Here's the simulation graph in this scenario:

Here's where things get interesting. When you have a high win rate, you typically have a very tight take profit and perhaps a slightly larger stop loss (hence the 0.5 reward-to-risk ratio).

While the expectancy calculation may be positive, you can still have negative outcomes (red line on graph). Here are the stats below.

Worst Case Outcome:

Initial balance: $5,000
Result balance: $4,799
Return % after whole period of trading: -4.0%
Maximum drawdown: -16.3%
Max consecutive losses: 4
Max consecutive wins: 13

Best Case Outcome:

Initial balance: $5,000
Result balance: $8,455
Return % after whole period of trading: 69.1%
Maximum drawdown: -3.9%
Max consecutive losses: 3
Max consecutive wins: 15

Using more realistic stats from my trend following approach, I was able to use HowToTrade's Monte Carlo simulation tool to help me determine whether or not I should move my stop loss to breakeven after a trade goes in profit.

Some traders such as Tom Dante are very much against moving a stop loss to breakeven since it leads you to trade your P&L. In other words, you see it as a "free trade." However, there's also a psychological relief where you might be able to let your winners run knowing that you can't lose.

Scenario 2: Trend Following

Strategy description: swing trade momentum in the direction of the trend without exiting trades at breakeven
Initial balance: $5,000
Risk % per 1 trade: 1%
Winning trade %: 30%
Break even trades %: 0%
Average number of trades per month: 20
Total months: 12
Take profit/stop loss ratio: 4

In scenario 2, I'm going to assume an average reward-to-risk ratio of 4 and a lower win rate of only 30%.

Worst Case Outcome:

Initial balance: $5,000
Result balance: $6,417
Return % after whole period of trading: 28.3%
Maximum drawdown: -20.2%
Max consecutive losses: 13
Max consecutive wins: 3

Best Case Outcome:

Initial balance: $5,000
Result balance: $30,741
Return % after whole period of trading: 514.8%
Maximum drawdown: -16.7%
Max consecutive losses: 16
Max consecutive wins: 5

Scenario 3: Trend Following with Breakeven

Strategy description: swing trade momentum in the direction of the trend but 20% of the trades that do not pan out are now exited at breakeven
Initial balance: $5,000
Risk % per 1 trade: 1%
Winning trade %: 30%
Break even trades %: 20%
Average number of trades per month: 20
Total months: 12
Take profit/stop loss ratio: 4

Worst Case Outcome:

Initial balance: $5,000
Result balance: $9,335
Return % after whole period of trading: 86.7%
Maximum drawdown: -12.3%
Max consecutive losses: 15
Max consecutive wins: 3

Best Case Outcome:

Initial balance: $5,000
Result balance: $50,811
Return % after whole period of trading: 916.2%
Maximum drawdown: -8.7%
Max consecutive losses: 9
Max consecutive wins: 4

In Scenario 3, I specified that, on average, 20% of my trades will be stopped out at breakeven. You can see that this halved my drawdown despite no significant change in my max consecutive losses.

It's important to keep in mind that real-world trading conditions and environmental factors will change. However, the trading statistics collected can continuously be stress tested as I have done here.

These simulations also tell a few other realities of trading:

Losses are inevitable and you will enter periods of consecutive losses
Drawdowns are inevitable so your trading strategy should be stress tested against worst case scenario drawdown scenarios
The worst case scenario simulations can help you think about your strategy to navigate really turbulent market conditions where things do not go your way