Monte Carlo Simulation

📊 Purpose

Monte Carlo simulation uses random sampling to model the uncertainty in investment returns. Instead of a single projection, it generates thousands of possible scenarios to show the range of potential outcomes.

⚙️ How It Works

1. Random Returns: Each month, the simulation generates a random return based on your expected yield and volatility
2. Compounding: Returns accumulate over time with monthly investments added
3. Repetition: This process repeats 1,000+ times to create a distribution of outcomes
4. Analysis: Statistical analysis reveals probabilities (e.g., 90% chance of reaching X amount)

✅ Key Advantages

• Realistic: Captures market volatility and uncertainty
• Probabilistic: Shows likelihood of outcomes (not just one forecast)
• Risk-aware: Identifies worst-case and best-case scenarios
• Actionable: Helps adjust strategy based on confidence levels

📈 What Is Dollar-Cost Averaging (DCA)?

Investing a fixed amount regularly (e.g., 200 EUR/month) regardless of market conditions.

✅ Advantages

• Reduces timing risk: You buy more when prices are low, less when high
• Discipline: Automates investing, removes emotions
• Accessible: No need for large lump sum
• Compound growth: Early investments grow the longest

📐 Definition

The Expected Yield is the average return you anticipate per month. It's the central tendency around which random returns fluctuate.

📊 Definition

Volatility measures how much returns fluctuate around the average. High volatility = big swings up and down. Low volatility = stable returns.

📈 Typical Values (Annual)

• Cash/Bonds: 2-6%
• Balanced Portfolio (60/40): 10-12%
• Global Stocks (S&P 500): 15-20%
• Cryptocurrencies: 60-100%+

🎯 Why Multiple Simulations?

Each simulation is one possible future. Running many simulations creates a probability distribution of outcomes, giving you confidence intervals.

📊 How Many Do You Need?

• 100-500: Quick test, rough estimate (±5% accuracy)
• 1,000: Standard (±2% accuracy) → Recommended
• 5,000: High precision (±1% accuracy)
• 10,000+: Academic/professional use (±0.5% accuracy)

📈 Key Metrics Explained

1️⃣ Median (50th Percentile)

The middle value when all outcomes are sorted. 50% of simulations are above this, 50% below.

2️⃣ 10th Percentile (Pessimistic)

Only 10% of scenarios are worse than this. Think of it as a "bad luck" scenario.

3️⃣ 90th Percentile (Optimistic)

Only 10% of scenarios are better than this. Think of it as a "good luck" scenario.

📊 Key Risk Indicators

1️⃣ Value at Risk (VaR) 5%

VaR 5% = The 5th percentile outcome. 95% of scenarios are better than this.

2️⃣ Loss Probability

% of simulations where you end up with less than you invested (no gains, or losses).