Monte Carlo Simulation: 🔑Key to Determining Your Trading Capital 📊

As a beginner trader, you might be eager to dive into the markets with your newly developed strategy. But have you ever wondered how much money you need to start trading effectively? One of the biggest challenges traders face is figuring out how much capital they need to trade a strategy successfully. It's not just about having enough money to place trades; it’s about having enough capital to survive the inevitable drawdowns and market volatility.

Starting with too little capital is a huge mistake, even if you have a solid strategy. Undercapitalization can lead to failure, but there’s a statistical method that can help you determine the right amount of capital to start with: it is called Monte Carlo simulations.

Introducing Monte Carlo Simulation

Monte Carlo simulations are a statistical tool used to understand the impact of risk and uncertainty in financial models. In trading, it's used to simulate different potential outcomes by randomly changing the order of your trades. This allows you to see the possible equity curve scenarios and determine how much capital you really need.

Why Trade Sequence Matters

When backtesting a strategy, traders often assume future trades will follow the same order as they did historically. However, the order of winning and losing trades can greatly affect your equity curve and drawdowns.

Consider this:

• Same Trades, Different Order: By reshuffling the order of trades, you can get very different equity curves, even though the total profit and average trade stay the same.

• Impact on Capital: If you start with losses early on, your capital might drop below the margin requirement, preventing you from making future trades.

Understanding Margin Requirements

Before diving into Monte Carlo simulations, it’s important to understand margin requirements. This is the minimum amount of capital you need to open a position.

For example, trading E-mini S&P 500 futures requires a margin of $16,060 per contract, while buying shares of Apple stock might require $2,263 for 10 shares. These margin requirements fluctuate based on the price and volatility of the instrument you're trading.

The Risk of Ruin

Risk of ruin is the point at which your account falls so low that you can no longer trade. It's not when your account hits zero, but when it falls below the margin requirement, stopping you from making new trades.

The goal is to ensure your capital stays above this critical threshold.

"When it comes to trading, Risk of ruin, is the level where you cannot trade anymore—it's not zero dollars in your account”

Using Monte Carlo Simulations

Monte Carlo simulations offer several options like adding noise to the trade results, replacing trades, or skipping trades. The simplest method is to shuffle all the trades to get different trade sequences, which is what we’ll focus on here.

By running thousands of simulations on the profit and loss results of a strategy, you can estimate:

• Optimal Starting Capital: The minimum capital needed to keep trading with acceptable risk.

• Probability of Drawdowns: How likely you are to experience a specific level of drawdown.

Step-by-Step Guide to Determine Your Capital Needs

Here’s how you can apply Monte Carlo simulations to find your minimum capital requirement or target drawdown:

1.     Collect Trade Data: Gather the historical trades from your strategy.

2.     Randomize Trade Sequence: Shuffle the order of trades to create different scenarios. Each scenario is one simulation.

3.     Run Simulations: Use tools like Excel, dedicated software, or AI tools like ChatGPT to run thousands of simulations.

4.     Calculate Probabilities: Analyze the results to determine the probability of your capital falling below the margin requirement at different starting capital levels.

Below are the equity curves of 10 simulations. Notice how the curves differ, even though they all start and end at the same point, because we’re using all trades in the simulation.

Remember that final Net PL and number of trades will not change, regardless of number of simulations in this type of simulation (shuffling exact number of trades).

Strategy Example

Let’s use an example strategy that trades the E-mini futures of the S&P 500, with a margin requirement of $16,060 for a single contract.

• Starting Capital: $17,500

• Margin Requirement: $16,060

• Number of Trades: 166

• Net Profit/Loss: $117,757

• Max Drawdown: $7,810

• Max DD %: 27.96% (highly depends on starting equity and when it happened)

• Risk of Ruin: 0%

We are interested in how many equity curves from the simulation will drop below the minimum margin requirement. If the equity falls below $16,060, it means we can’t trade anymore due to lack of capital, not because the account is at zero.

"It's a huge mistake to start with the minimum amount of capital to trade because even the most robust strategy will fail if it is undercapitalized."

After running 5,000 Monte Carlo simulations on the profit and loss data, we get the following results at different starting capital levels and confidence levels:

Based on the stats above, starting to trade this strategy with $17,500 where the margin requirement to trade a single contract is $16,060, the following statements are true:

• You have about a 30% chance of ending up unable to trade because the equity will fall below $16,060. It doesn’t mean the account is at zero, just that you don’t have enough funds to trade.

• You are 61% confident that your drawdown will stay under 25% and below $20,000.

• You are 98% confident that your drawdown will be under 48% and below $20,000.

If you increase the starting capital to $35,000, the results improve:

• You are almost 100% confident that your equity won’t dip below $16,060.

• You are 89% confident that your drawdown will be under 25% and below $20,000.

• There is an 80% chance that your drawdown will be under 22% and below $15,000.

If you want to ensure you never experience a drawdown of more than 25%, you would need to start with $70,000 to achieve a 100% confidence level.

More advanced simulations can introduce noise, like replace some trades, add/deduct from P&L, increase/decrease StDev, etc. with these added functions, we can build a probability for any metric that we want to target, like average trade, consecutive winners/losers, etc.

The more simulations you do the more accurate your probabilities will end up. Just keep in mind that simulations over 25,000 are over kill, and simulations under 100 are deceiving. 2,500 to 5,000 simulations are the sweet spot.

Conclusion

Proper capitalization is not just a safety net—it’s a fundamental part of any successful trading strategy or a portfolio of strategies. Monte Carlo simulations give you a statistical way to figure out how much capital you need to trade your strategy or portfolio effectively.

"Once you have a robust strategy, it's extremely important to be well-capitalized so that when you suffer that inevitable drawdown, you will have enough capital to cover the margin requirement for your next trade."

Don’t leave your trading success to chance. Use statistical tools like Monte Carlo simulations to make smart, informed decisions about your capital requirements. This proactive approach will significantly increase your chances of long-term success in trading.

P.S. If you want the link for the Excel Monte Carlo simulation or the ChatGPT script, reply to this email, and I’ll be happy to send it to you.