MonteCarlo Wealth Lab

A sophisticated, browser-based Monte Carlo simulation tool for retirement planning and wealth accumulation analysis. This single-file HTML application models investment growth under uncertainty using correlated asset returns, tax considerations, and strategic cash management.

🎯 Overview

The MonteCarlo Wealth Lab helps investors and financial planners understand the probability distribution of future wealth outcomes by running thousands of simulated investment scenarios. It accounts for:

• Correlated asset returns across multiple investment funds
• Systematic investment plans (SIP) with step-up rates
• War chest strategy with tactical deployment rules
• Tax implications (LTCG calculations)
• Inflation adjustments for real purchasing power
• Age-based milestones and target corpus planning

🚀 Quick Start

1. Open the simulator: Simply open MonteCarlo.html in any modern web browser
2. Configure your inputs: Adjust the simulation parameters in the left sidebar
3. Set up your portfolio: Configure fund allocations, expected returns, and volatility
4. Run simulation: Click "RUN SIMULATION" to generate 5,000+ Monte Carlo paths
5. Analyze results: Review the comprehensive output including fan charts, probability curves, and milestone analysis

No installation required - this is a standalone HTML file that runs entirely in your browser.

📊 Key Features

Simulation Engine

• 5,000+ Monte Carlo simulations by default (configurable up to 50,000)
• Correlated asset modeling using Cholesky decomposition
• Seeded random number generation for reproducible results
• Monthly time-step resolution for accurate compounding

Investment Strategy Modeling

• Multi-fund portfolio allocation (up to 10 funds)
• Systematic Investment Plans (SIP) with customizable step-up rates
• War chest strategy with tactical deployment based on market drawdowns
• Age-based milestone tracking (20%, 50%, 80%, 100% of target age)

Financial Calculations

• LTCG tax calculations based on current Indian tax laws
• Inflation-adjusted real returns
• After-tax corpus projections
• Cost basis tracking for tax calculations

Comprehensive Visualization

• Fan chart showing percentile ranges over time
• Histogram distribution at target age
• Probability curves for hitting various wealth targets
• Milestone tables with detailed statistics
• Outcome distribution breakdown by wealth brackets

🛠️ User Guide

Simulation Parameters

Basic Settings

• Simulations: Number of Monte Carlo paths (500-50,000)
• Current Age: Your current age (20-50)
• Target Age: Age at which you want to achieve your target corpus (30-65)
• Random Seed: For reproducible results (1-999)

Starting Position

• Corpus: Initial investment amount in lakhs (₹L)
• War Chest Initial: Initial cash reserve in lakhs (₹L)

Monthly SIP Configuration

• Base SIP: Monthly investment amount in thousands (₹K)
• Step-up Rate: Annual percentage increase in SIP (0-30%)
• Step-up Every: Frequency of SIP increases in months (6-24)

War Chest Strategy

• Monthly Addition: Monthly cash addition to war chest in thousands (₹K)
• Parking Return: Annual return on parked cash (3-12%)
• Cooldown: Minimum months between deployments (1-18)
• Deployment Rules: Percentage of war chest to deploy at various drawdown levels (-5%, -10%, -20%, -30%)

Tax & Inflation

• LTCG Rate: Long-term capital gains tax rate (5-30%)
• Annual Exemption: Tax-free LTCG amount in thousands (₹K)
• Inflation Rate: Expected annual inflation (2-15%)

Target

• Target Corpus: Desired wealth at target age in crores (₹Cr)

Fund Configuration

The simulator supports up to 10 different investment funds:

1. Add/Remove Funds: Use the "Add Fund" button or remove existing funds
2. Weight Allocation: Each fund's percentage of total portfolio (must sum to 100%)
3. Expected Return: Annual expected return for the fund (5-35%)
4. Volatility: Annual standard deviation of returns (5-65%)

Note: The simulator includes a predefined correlation matrix to model realistic relationships between different asset classes.

Interpreting Results

Key Metrics

• Median @ Age: Most likely outcome at specified ages
• P(≥Target) @ Age: Probability of achieving your target corpus
• Worst 5%: Floor protection level (5th percentile)

Charts Explained

• Fan Chart: Shows wealth distribution over time with percentile bands
• Histogram: Distribution of final wealth outcomes
• Probability Curve: Likelihood of hitting various wealth targets
• Milestone Table: Detailed statistics at key ages

Risk Analysis

• Downside Risk: Probability of poor outcomes
• Outcome Distribution: Percentage of simulations in different wealth brackets
• Real vs Nominal: Inflation-adjusted purchasing power

🔧 Technical Documentation

Architecture Overview

The application is built as a single HTML file with three main components:

1. HTML Structure: Semantic markup with comprehensive styling
2. CSS Styling: Custom dark theme with responsive design
3. JavaScript Logic: Complete simulation engine and visualization

Mathematical Models

Monte Carlo Simulation

// Core simulation loop
for (let s = 0; s < numSims; s++) {
  let corpus = startCorpus;
  let wc = wcInit;
  
  for (let m = 1; m <= totalMonths; m++) {
    // Generate correlated returns
    const returns = generateCorrelatedReturns();
    
    // Apply investment strategy
    corpus = corpus * (1 + blendedReturn) + monthlySIP;
    wc = wc * (1 + parkingReturn) + monthlyWCAddition;
    
    // Tactical deployment logic
    if (marketDrawdown > threshold && cooldownPeriodPassed) {
      deployFromWarChest();
    }
  }
}

Correlation Modeling

The simulator uses Cholesky decomposition to generate correlated random variables:

function cholesky(C) {
  const n = C.length;
  const L = Array.from({length:n}, () => new Float64Array(n));
  // Cholesky factorization implementation
  return L;
}

Tax Calculations

LTCG tax is calculated as:

Taxable Gain = Gross Corpus - Cost Basis
Tax = max(0, (Taxable Gain/15 - Exemption)) * LTCG Rate * 15
After-Tax = Gross - Tax

Code Structure

Core Functions

• runMonteCarlo(): Main simulation engine
• generateCorrelatedReturns(): Multi-asset return generation
• calculateMilestoneMonths(): Age-based milestone calculation
• renderResults(): Visualization and output generation

Utility Functions

• mulberry32(): Seeded random number generator
• boxMuller(): Normal distribution sampling
• pct(): Percentile calculation
• mean(), std(): Statistical functions

Chart Integration

Uses Chart.js for all visualizations:

• Line charts for fan plots and probability curves
• Bar charts for histograms and distributions
• Custom styling to match the application theme

Performance Considerations

• Chunked Processing: Simulations run in chunks to prevent browser freezing
• Web Workers: Could be implemented for very large simulation counts
• Memory Management: Charts are destroyed and recreated to prevent memory leaks
• Responsive Design: Charts resize automatically on window changes

💡 Use Cases & Examples

Retirement Planning

Scenario: 30-year-old investor targeting ₹10 crore by age 60

• Initial corpus: ₹0
• Monthly SIP: ₹50K with 10% annual step-up
• War chest: ₹25K monthly addition
• Portfolio: 60% equity funds, 40% debt funds

Analysis: The simulator shows probability of success, median outcomes, and downside protection.

Wealth Accumulation

Scenario: 35-year-old with existing ₹50L corpus targeting ₹5 crore in 15 years

• Starting corpus: ₹50L
• Monthly SIP: ₹30K
• Step-up rate: 8% annually
• War chest strategy for market timing

Analysis: Compare different asset allocations and step-up strategies.

Education Fund Planning

Scenario: Parent planning for child's education in 18 years

• Target: ₹2 crore
• Time horizon: 18 years
• Conservative portfolio allocation
• Regular monthly contributions

Analysis: Assess probability of meeting education funding goals.

⚠️ Limitations & Assumptions

Model Limitations

• Normal Distribution: Returns are modeled as normally distributed (real markets have fat tails)
• Constant Correlations: Correlation matrix is static over time
• No Black Swans: Extreme market events are not explicitly modeled
• Tax Simplification: Actual tax calculations may be more complex

Financial Assumptions

• Constant Inflation: Inflation rate is assumed constant over the simulation period
• No Additional Contributions: Beyond SIP, no lump sum additions are modeled
• No Withdrawals: No systematic withdrawals during the accumulation phase
• Fixed Asset Allocation: Portfolio weights remain constant over time

Technical Constraints

• Browser Limitations: Very large simulation counts may cause performance issues
• Single-threaded: JavaScript runs on main thread (no parallel processing)
• Memory Usage: Large simulation counts consume significant browser memory

🔍 Troubleshooting

Common Issues

Simulation Won't Start

• Cause: Fund weights don't sum to 100%
• Solution: Adjust fund allocations to total exactly 100%

Slow Performance

• Cause: Too many simulations (over 10,000)
• Solution: Reduce simulation count or use a more powerful device

Charts Not Displaying

• Cause: Browser blocking external script loading
• Solution: Ensure Chart.js CDN is accessible or use offline version

Unexpected Results

• Cause: Extreme input values (very high returns or volatility)
• Solution: Use realistic input parameters based on historical data

Validation System

The simulator includes comprehensive input validation:

• Age ranges and relationships
• Financial input reasonableness
• Fund allocation constraints
• Extreme parameter warnings

🤝 Contributing

While this is a single-file application, contributions are welcome for:

1. Bug Reports: Issues with calculations or visualizations
2. Feature Requests: New simulation capabilities or chart types
3. Documentation: Improvements to this README or inline code comments
4. Performance: Optimizations for large simulation counts

📄 License

This project is provided as-is for educational purposes. Users should consult with qualified financial advisors before making investment decisions.

🙏 Acknowledgments

• Chart.js: For excellent charting capabilities
• Mulberry32: For high-quality seeded random number generation
• Financial Modeling Community: For established Monte Carlo methodologies

📞 Support

For questions about using the simulator:

1. Check the troubleshooting section above
2. Review the input parameter explanations
3. Ensure all validation requirements are met
4. Start with the default configuration and make gradual changes

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⚠️ Disclaimer: This tool is for educational purposes only. It does not constitute SEBI-registered investment advice. Actual investment returns may differ significantly from simulated results. Always consult a qualified financial advisor and tax professional before making investment decisions.