Christian Caron, PhD
Simulating Portfolio Growth Using Monte Carlo Methods
To explore the uncertainty of long-term investing, I used a Monte Carlo simulation—a technique that models thousands of possible outcomes by randomly sampling from historical data. By applying this method to S&P 500 returns from 1980 onward, I generated 1,000 potential 30-year investment paths for a portfolio with consistent yearly contributions. The charts below show both the range of final outcomes and how those outcomes unfold over time.
Distribution of Final Portfolio Values after 30 Years
This chart shows the results of a Monte Carlo simulation modeling 30 years of investing in the S&P 500. Using historical annual returns from 1980 to the present, I simulated 1,000 potential futures for a portfolio starting with $10,000 and adding $6,000 per year. Each simulation randomly samples past returns to reflect the ups and downs of real markets.
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The histogram shows the range of final portfolio values after 30 years:
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25% of simulations ended with less than $644,039
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50% of simulations ended between $644,039 and $1,570,275
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25% of simulations ended with more than $1,570,275
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The red dashed line marks the median outcome of $1,018,713.
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This distribution is right-skewed, indicating the potential for outsized gains in especially strong market environments. Even with consistent contributions, long-term outcomes can vary widely depending on the sequence of returns.
Monte Carlo Simulation Using Real S&P 500 Annual Returns (Sampled from 1980 to 2025)
Year-by-Year Investment Projections
This interactive fan chart builds on the Monte Carlo framework by tracing the full 30‑year trajectory of each simulated portfolio, instead of just the final outcome. It again uses historical S&P 500 returns (1980–present), with:
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$10,000 starting balance
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$6,000 annual investment
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1,000 simulations
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The shaded bands show how the range of potential values expands over time:
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The dark blue line represents the median portfolio value at a given point in time
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The steel blue band captures the middle 50% of outcomes (25th to 75th percentile)
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The light blue band spans the broader 80% range (10th to 90th percentile)
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The histogram and fan chart give both a snapshot of end‑values and a dynamic view of growth paths, illustrating the full spectrum of risk and reward in a long‑term equity investment.