Monte Carlo Simulation

Monte Carlo simulation, named after the casino, generates a large number of random paths — typically 5,000 to 100,000 — to estimate the distribution of an outcome that is too complex to solve analytically. In portfolio analysis it answers questions of the form: "given my asset mix and my assumed return model, what is the probability that my €100k becomes €X over T years?".

The basic procedure

1. 1.Estimate the joint return distribution from historical data (mean, covariance, sometimes skew/kurtosis).
2. 2.Draw a random sample from that distribution for each asset, each period of the horizon.
3. 3.Rebalance to target weights and compound the portfolio return path.
4. 4.Repeat N times. The output is N portfolio paths.
5. 5.Read percentiles: P5 (5% worst), P50 (median), P95 (5% best). The P5-P95 envelope is the "fan chart".

Common assumptions and their dangers

• ·Geometric Brownian Motion: log-returns Gaussian, constant μ and σ. Simple but ignores fat tails — real losses worse than the model predicts.
• ·Bootstrap: re-sample historical returns with replacement. Preserves the empirical distribution including tails, but cannot project beyond the worst observed event.
• ·Regime-switching: alternate between calm and crisis distributions. Closer to reality, harder to calibrate.

Reading a P5-P95 fan chart

The width of the fan is the strategy's outcome uncertainty. A narrow fan with a median above benchmark is a strong signal. A wide fan with a positive median can still be terrifying — the P5 path is your "bad 1-in-20 scenario" and is often within the band of historical drawdowns.

How MEDGE Capital uses Monte Carlo

Monte Carlo runs at 10,000 paths using geometric Brownian motion calibrated on the backtest window. The fan chart shows P5, P25, P50, P75, P95 over the user-selected forward horizon, and the "probability of reaching €X" widget converts the path distribution into a direct answer to the financial planning question.