Monte Carlo simulations illustrate how year-to-year fluctuations in rates of return can impact long-term investment outcomes. This technique uses a mathematical model to generate a wide range of potential results by running numerous trial runs—known as simulations—based on random variations in key inputs. The goal is to approximate the probability of different outcomes and assess the potential variability of results under uncertain market conditions. YCharts' Monte Carlo simulations are generated by running 1,000 independent simulations, each using randomized return sequences within defined parameters. YCharts uses a Geometric Brownian Motion (GBM) model, which incorporates assumptions about drift (expected return), volatility, and random market shocks to simulate asset price behavior over time.
To improve performance and maintain consistency across analyses, Monte Carlo simulations are precomputed using randomized return paths and stored for reuse. These stored simulations preserve the statistical properties of the original model, including randomness, variability, and asset class correlations. During each analysis, results are drawn from the stored simulations, optionally reordered to create a more dynamic user experience while maintaining the mathematical integrity of the simulation process. YCharts' Monte Carlo simulations are based on 1,000 projection paths per asset class, each representing a plausible future return sequence derived from randomized outcomes within defined parameters.
YCharts’ simulation model projects future returns based on broad asset classes, rather than the historical performance of individual securities. Simulations are driven by capital market assumptions—specifically, estimated return, standard deviation and correlation values—for each asset class. These assumptions are based on the historical performance of representative market indices, not actual investment products. To simulate future returns for funds and hypothetical portfolios, YCharts maps the fund or portfolio’s asset class weightings to the corresponding capital market assumptions.
The indices and time periods used to represent each asset class are:
- Stocks: S&P 500 - 01/03/2000 to 12/31/2024
- Bonds: Bloomberg US Aggregate - 01/03/2000 to 12/31/2024
- Cash: Bloomberg US Treasury Bills (1-3 Month) - 01/03/2000 to 12/31/2024
Preferred stocks are classified as bonds, convertible bonds are split between stocks and bonds and allocations to "Other" are distributed proportionally across stocks, bonds, and cash for Monte Carlo analysis. The return, volatility and correlation asset class assumptions used are shown in the table below.
Simulation results are displayed by percentile, representing the estimated likelihood of achieving various wealth levels based on the inputs and assumptions used in the projection:
- 5th Percentile (Worst-Case Scenario): This shows what could happen if things go poorly. Only 5 out of 100 simulations had results worse than this, which means most outcomes were better.
- 50th Percentile (Median Scenario): This is the middle of the road. Half of the simulations had lower results, and half had higher. It gives you a sense of the most typical or expected outcome based on the assumptions used.
- 95th Percentile (Best-Case Scenario): This shows what might happen in a very good market. Only 5 out of 100 simulations had better results than this, meaning it reflects a strong but less likely outcome.