Monte Carlo Calculation

Monte Carlo Investment Growth Calculator

Use this calculator to simulate potential investment growth over time, accounting for the variability of annual returns using a Monte Carlo simulation.

// Helper function to generate a random number from a normal distribution (Box-Muller transform) function normalRandom(mean, stdDev) { var u = 0, v = 0; while (u === 0) u = Math.random(); // Converting [0,1) to (0,1) while (v === 0) v = Math.random(); var z = Math.sqrt(-2.0 * Math.log(u)) * Math.cos(2.0 * Math.PI * v); return z * stdDev + mean; } function calculateMonteCarlo() { var initialInvestment = parseFloat(document.getElementById('initialInvestment').value); var numSimulations = parseInt(document.getElementById('numSimulations').value); var numYears = parseInt(document.getElementById('numYears').value); var avgAnnualReturn = parseFloat(document.getElementById('avgAnnualReturn').value) / 100; // Convert percentage to decimal var stdDevAnnualReturn = parseFloat(document.getElementById('stdDevAnnualReturn').value) / 100; // Convert percentage to decimal var annualContribution = parseFloat(document.getElementById('annualContribution').value); // Input validation if (isNaN(initialInvestment) || initialInvestment < 0) { document.getElementById('result').innerHTML = 'Please enter a valid Initial Investment (non-negative number).'; return; } if (isNaN(numSimulations) || numSimulations 100000) { // Added upper limit for performance document.getElementById('result').innerHTML = 'Please enter a valid Number of Simulations (e.g., 100 to 100,000).'; return; } if (isNaN(numYears) || numYears <= 0) { document.getElementById('result').innerHTML = 'Please enter a valid Number of Years (must be greater than 0).'; return; } if (isNaN(avgAnnualReturn)) { document.getElementById('result').innerHTML = 'Please enter a valid Average Annual Return.'; return; } if (isNaN(stdDevAnnualReturn) || stdDevAnnualReturn < 0) { document.getElementById('result').innerHTML = 'Please enter a valid Standard Deviation of Annual Return (non-negative number).'; return; } if (isNaN(annualContribution) || annualContribution < 0) { document.getElementById('result').innerHTML = 'Please enter a valid Annual Contribution (non-negative number).'; return; } var finalValues = []; for (var i = 0; i < numSimulations; i++) { var currentValue = initialInvestment; for (var j = 0; j < numYears; j++) { var annualReturn = normalRandom(avgAnnualReturn, stdDevAnnualReturn); currentValue *= (1 + annualReturn); currentValue += annualContribution; } finalValues.push(currentValue); } // Sort final values to calculate percentiles finalValues.sort(function(a, b) { return a – b; }); // Calculate statistics var sum = finalValues.reduce(function(a, b) { return a + b; }, 0); var mean = sum / numSimulations; var stdDevSumSq = finalValues.reduce(function(a, b) { return a + Math.pow(b – mean, 2); }, 0); var stdDev = Math.sqrt(stdDevSumSq / numSimulations); // Calculate percentiles, ensuring indices are within bounds var percentile10 = finalValues[Math.floor(numSimulations * 0.10)]; var percentile50 = finalValues[Math.floor(numSimulations * 0.50)]; // Median var percentile90 = finalValues[Math.floor(numSimulations * 0.90)]; var resultHTML = '

Simulation Results:

'; resultHTML += 'Average Projected Final Value: $' + mean.toFixed(2) + "; resultHTML += 'Standard Deviation of Final Values: $' + stdDev.toFixed(2) + "; resultHTML += '10th Percentile (Worst 10% of outcomes): $' + percentile10.toFixed(2) + "; resultHTML += '50th Percentile (Median outcome): $' + percentile50.toFixed(2) + "; resultHTML += '90th Percentile (Best 10% of outcomes): $' + percentile90.toFixed(2) + "; document.getElementById('result').innerHTML = resultHTML; } .monte-carlo-calculator { font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif; background-color: #f9f9f9; padding: 25px; border-radius: 10px; box-shadow: 0 4px 12px rgba(0, 0, 0, 0.1); max-width: 600px; margin: 30px auto; border: 1px solid #e0e0e0; } .monte-carlo-calculator h2 { color: #2c3e50; text-align: center; margin-bottom: 20px; font-size: 1.8em; } .monte-carlo-calculator p { color: #555; line-height: 1.6; margin-bottom: 15px; } .calculator-inputs label { display: block; margin-bottom: 8px; color: #34495e; font-weight: bold; font-size: 0.95em; } .calculator-inputs input[type="number"] { width: calc(100% – 22px); padding: 10px; margin-bottom: 15px; border: 1px solid #ccc; border-radius: 5px; font-size: 1em; box-sizing: border-box; } .calculator-inputs button { background-color: #28a745; color: white; padding: 12px 25px; border: none; border-radius: 5px; cursor: pointer; font-size: 1.1em; font-weight: bold; display: block; width: 100%; margin-top: 20px; transition: background-color 0.3s ease; } .calculator-inputs button:hover { background-color: #218838; } .calculator-results { margin-top: 30px; padding: 20px; background-color: #e9f7ef; border: 1px solid #d4edda; border-radius: 8px; color: #155724; } .calculator-results h3 { color: #2c3e50; margin-top: 0; margin-bottom: 15px; font-size: 1.5em; text-align: center; } .calculator-results p { margin-bottom: 10px; font-size: 1.05em; } .calculator-results p strong { color: #0a3d15; }

Understanding Monte Carlo Simulation for Investment Forecasting

The Monte Carlo simulation is a powerful computational technique that uses random sampling to obtain numerical results. It's particularly useful for modeling systems with many uncertain variables, allowing us to understand the range of possible outcomes and their probabilities, rather than just a single average result.

What is Monte Carlo Simulation?

At its core, a Monte Carlo simulation involves running a model thousands or even millions of times, each time using different random inputs drawn from a specified probability distribution. By observing the results of these numerous simulations, one can build a distribution of possible outcomes, which provides insights into the likelihood of various scenarios.

For example, instead of assuming a fixed annual return for an investment, a Monte Carlo simulation can model returns as a range of possibilities, reflecting market volatility. This provides a more realistic picture of potential investment performance.

How This Calculator Uses Monte Carlo for Investment Growth

This Monte Carlo Investment Growth Calculator applies the simulation technique to project the potential future value of an investment. Here's how it works:

1. Initial Investment: Your starting capital.
2. Number of Simulations: The number of times the entire investment period is simulated. More simulations generally lead to more accurate and stable results.
3. Number of Years: The duration over which the investment is projected.
4. Average Annual Return (%): The expected mean (average) annual return of your investment. This is the central tendency around which actual returns will fluctuate.
5. Standard Deviation of Annual Return (%): This measures the volatility or risk associated with your investment. A higher standard deviation means returns are expected to vary more widely from the average. In the simulation, annual returns are randomly generated from a normal distribution using this average and standard deviation.
6. Annual Contribution: Any additional money you plan to add to your investment each year.

For each simulation, the calculator randomly generates an annual return for each year based on the average return and standard deviation you provide. It then calculates the investment's growth year by year, including any annual contributions. This process is repeated for the specified number of simulations, creating a wide array of possible final investment values.

Interpreting the Results

The output of the Monte Carlo simulation provides a comprehensive view of your investment's potential future value:

• Average Projected Final Value: This is the mean of all the final values from every simulation. It represents the most likely outcome if the underlying assumptions hold true.
• Standard Deviation of Final Values: This indicates the spread or dispersion of the final values. A higher standard deviation suggests a wider range of possible outcomes, implying greater uncertainty or risk.
• 10th Percentile (Worst 10% of outcomes): This value means that 10% of the simulations resulted in a final value at or below this amount. It's a useful metric for understanding potential downside risk.
• 50th Percentile (Median outcome): This is the middle value of all simulated final outcomes. Half of the simulations resulted in a value above this, and half below. It can sometimes be a more robust measure than the mean, especially if the distribution of outcomes is skewed.
• 90th Percentile (Best 10% of outcomes): This value indicates that 10% of the simulations resulted in a final value at or above this amount. It helps visualize the potential upside of your investment.

Why Use Monte Carlo?

Traditional financial models often rely on single-point estimates (e.g., "your investment will grow by 7% annually"). While simple, this approach doesn't account for the inherent uncertainty and volatility of markets. Monte Carlo simulation offers a more robust approach by:

• Quantifying Risk: It provides a clear picture of the range of possible outcomes, helping you understand the best-case, worst-case, and most likely scenarios.
• Better Decision Making: By understanding the probability of different outcomes, investors can make more informed decisions about risk tolerance, savings rates, and investment strategies.
• Flexibility: It can incorporate various types of uncertainty and complex interactions between variables.

Example Scenario:

Let's say you have an initial investment of $10,000, plan to invest for 10 years, contribute an additional $1,000 annually, and expect an average annual return of 7% with a standard deviation of 10%. Running 1,000 simulations might yield results like:

• Average Projected Final Value: $35,000
• Standard Deviation of Final Values: $8,000
• 10th Percentile: $25,000 (meaning there's a 10% chance your investment could be $25,000 or less)
• 50th Percentile: $34,500
• 90th Percentile: $46,000 (meaning there's a 10% chance your investment could be $46,000 or more)

This example shows that while the average outcome is $35,000, there's a significant range of possibilities, from $25,000 in less favorable scenarios to $46,000 in more favorable ones. This insight is invaluable for financial planning.