Monte Carlo Simulation
Probabilistic projections of portfolio growth using random sampling techniques.
Geometric Brownian Motion
GBM models asset prices as following a random walk with drift. It's the foundation of options pricing and portfolio simulation, capturing both expected growth and random fluctuations.
Ito Correction
The -σ²/2 term in the drift adjusts for the difference between arithmetic and geometric means. Without it, simulations would overestimate wealth, especially for volatile portfolios.
Percentile Projections
We run 1,000 simulations and report key percentiles: 5th (worst case), 25th (conservative), 50th (median), 75th (optimistic), and 95th (best case).
Probability of Loss
Calculated as the percentage of simulation paths where the final value is below the starting value. Lower probability of loss indicates a more conservative risk profile.