This ultra-advanced Monte Carlo simulation includes professional-grade features:
Real markets don't follow perfect bell curves. Advanced models capture fat tails (crashes), jumps (sudden shocks), and regime changes (bull/bear cycles).
Classic assumption: returns are symmetrically distributed around the mean.
Heavier tails → captures rare but severe crashes.
Returns are skewed to the right. Common in finance since prices can't go below zero.
Combines smooth drift + sudden jumps (e.g., market crashes).
Markets alternate between bull (high return, low vol) and bear (low/negative return, high vol).
Volatility changes over time (volatility clustering).
The Scenario Manager lets you:
Investing a fixed amount regularly (e.g., 200 EUR/month) regardless of market conditions.
Investing 200 EUR/month for 25 years at 8% annual return:
The Expected Yield is the average return you anticipate per month. It's the central tendency around which random returns fluctuate.
Volatility measures how much returns fluctuate around the average. High volatility = big swings up and down. Low volatility = stable returns.
Higher volatility means:
Each simulation is one possible future. Running many simulations creates a probability distribution of outcomes, giving you confidence intervals.
Higher simulation counts take longer to compute:
The Degrees of Freedom (DF) is a parameter that controls the "thickness" of the tails in the Student-t distribution.
Real financial markets have fat tails (more extreme events than the normal distribution predicts):
The Student-t distribution was discovered by William Sealy Gosset (pen name "Student") in 1908 while working at Guinness Brewery. It's one of the most important distributions in statistics!
The Jump Intensity (λ) is the average number of sudden jumps (crashes or spikes) per year in the Jump Diffusion model.
Financial assets don't move smoothly. They experience:
In each month of simulation:
| Asset Type | Recommended λ |
|---|---|
| Government Bonds | 0.05 - 0.1 |
| Large-Cap Stocks | 0.1 - 0.2 |
| Growth Stocks | 0.2 - 0.4 |
| Small-Caps / EM | 0.4 - 0.7 |
| Cryptocurrencies | 0.8 - 2.0 |
Jump Intensity (λ) and Jump Magnitude work together:
The Jump Magnitude is the average size of sudden moves (in percentage) when a jump occurs in the Jump Diffusion model.
You can also model positive jumps for sudden rallies:
Markets tend to:
| Jump Intensity (λ) | Jump Magnitude | Scenario |
|---|---|---|
| Low (0.1) | Large (-20%) | Rare catastrophes |
| Moderate (0.3) | Moderate (-10%) | ⭐ Realistic (stocks) |
| High (0.7) | Small (-5%) | Frequent corrections |
| Very High (1.5) | Very Large (-40%) | Crypto chaos |
In reality, not all jumps are the same size. The model assumes:
After running the simulation, check:
The middle value when all outcomes are sorted. 50% of simulations are above this, 50% below.
Only 10% of scenarios are worse than this. Think of it as a "bad luck" scenario.
Only 10% of scenarios are better than this. Think of it as a "good luck" scenario.
The arithmetic mean of all outcomes. Can be skewed by extreme values.
The extreme outcomes. Useful for understanding the full range of possibilities.
The difference between P10 and P90 shows your uncertainty:
VaR 5% = The 5th percentile outcome. 95% of scenarios are better than this.
Example: VaR 5% = 50,000 EUR means there's only a 5% chance you'll end up with less than 50,000 EUR.
% of simulations where you end up with less than you invested (no gains, or losses).
Lower is better. Ideally <5%.
Your expected return as a percentage of total invested capital.
Also called Expected Shortfall. Average loss in the worst 5% of cases.
More conservative than VaR (used by Basel III banking regulations).
Largest peak-to-trough decline during the investment period.
Shows the worst loss you'd experience before recovery.
Risk-adjusted return. Higher is better (>1 is good, >2 is excellent).
Like Sharpe Ratio but only penalizes downside volatility.
Annual return divided by maximum drawdown. Higher is better.
Maximum Drawdown (MDD) is the largest percentage drop from a peak to a trough in your portfolio value.
A tornado diagram shows which input parameters have the biggest impact on your final portfolio value.
A heat map visualizes portfolio outcomes across different combinations of Expected Return (X-axis) and Volatility (Y-axis).
A correlation matrix shows how different metrics are related to each other. Values range from -1 to +1.
The Efficient Frontier is a curve showing the best possible return for each level of risk (volatility).
Invented by Harry Markowitz (Nobel Prize 1990), the Efficient Frontier represents portfolios that offer:
Stress testing simulates how your portfolio would perform under extreme market conditions (crashes, recessions, bull markets).
Severe market crash (like 2008 Financial Crisis or COVID-19 initial shock).
Moderate economic downturn (typical recession).
Baseline scenario with no additional shock.
Strong economic growth (like 2020-2021 recovery).
Banks and institutions are required by law (Basel III, Dodd-Frank) to perform stress tests to ensure financial stability. You're using the same professional techniques!
This chart shows how long it takes (in months/years) to reach your target portfolio value across all simulations.
Percentage of simulations that reached the target within the time horizon.
The middle value: 50% of successful simulations reached the target faster, 50% slower.
If many simulations don't reach your target, you can:
The Sharpe Ratio measures risk-adjusted return. It answers: "How much return am I getting per unit of risk?"
Instead of calculating one Sharpe Ratio for the entire period, we calculate it over moving 12-month windows.
Hedge funds and institutional investors use rolling Sharpe Ratio to: