Monte Carlo Simulation

This Monte Carlo simulation tool provides a means to test long term expected portfolio growth and portfolio survival based on withdrawals, e.g., testing whether the portfolio can sustain the planned withdrawals required for retirement or by an endowment fund. The following simulation models are supported for portfolio returns:

You can choose from several different withdrawal models including:

To simulate multiple stages such as career and retirement with detailed cashflow goals use the Financial Goals planning tool.

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Monte Carlo Simulation Results

Monte Carlo simulation results for 10000 portfolios with $875,000 initial portfolio balance using available historical returns data from Jan 1987 to Dec 2018. The historical return for the selected portfolio for this period was 9.05% mean return (8.53% CAGR) with 9.22% standard deviation of annual returns. The simulation results are based on generated nominal returns and specified inflation adjusted withdrawals ($45,000 per year). The simulated inflation model used historical inflation with 2.61% mean and 1.12% standard deviation based on the Consumer Price Index (CPI-U) data from Jan 1987 to Dec 2018. The generated inflation samples were correlated with simulated asset returns based on historical correlations. The available historical data for the simulation inputs was constrained by Total US Bond Market [Jan 1987 - Jul 2019].
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Portfolio Allocation

Asset Class Allocation
US Stock Market 60.00%
Total US Bond Market 40.00%
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Summary Statistics

Summary Statistics
10th Percentile25th Percentile50th Percentile75th Percentile90th Percentile
Time Weighted Rate of Return (nominal)5.98%7.23%8.57%9.88%11.05%
Time Weighted Rate of Return (real)3.32%4.52%5.82%7.08%8.22%
Portfolio End Balance (nominal)$0.00$892,355$2,716,290$5,389,722$8,903,123
Portfolio End Balance (inflation adjusted)$0.00$414,267$1,261,643$2,490,493$4,119,046
Maximum Drawdown-100.00%-48.74%-31.78%-24.13%-19.17%
Maximum Drawdown Excluding Cashflows-33.61%-27.40%-22.58%-19.17%-16.36%
Safe Withdrawal Rate4.88%5.86%7.05%8.35%9.64%
Perpetual Withdrawal Rate3.22%4.32%5.50%6.61%7.60%
8673 portfolios out of 10000 simulated portfolios (86.73%) survived all withdrawals.
   
Notes on results:
  • Monte Carlo simulation uses historical data and thus assumes that the future will, to some extent, mimic the past. The actual future results may vary.
  • The probability of success is based on the number of simulations the portfolio survives with a positive end balance.
  • Maximum drawdown statistics are calculated from simulated monthly balances.
  • Safe withdrawal rate is the percentage of the original portfolio balance that can be withdrawn at the end of each year with inflation adjustment without the portfolio running out of money.
  • Perpetual withdrawal rate is the percentage of portfolio balance that can be withdrawn at the end of each year while retaining the inflation adjusted portfolio balance.
  • The results assume annual rebalancing of portfolio assets at the end of each year. Taxes and transaction fees are not taken into account.
  • Past performance is not a guarantee of future returns and data and other errors may exist. See Disclaimer and Terms of Use
  • Contributions and withdrawals are done at the end of each specified time period

Simulated Assets - Correlations and Returns

Simulated Assets - Correlations and Returns
NameUS Stock MarketTotal US Bond MarketInflationCAGRExpected Annual ReturnAnnualized Volatility
US Stock Market1.000.070.019.76%11.02%14.99%
Total US Bond Market0.071.00-0.115.78%5.85%3.81%
Inflation0.01-0.111.002.60%2.61%1.12%
Asset correlations and return vs. risk statistics are based on monthly returns from Jan 1987 to Dec 2018

Expected Annual Return

Expected Annual Return
Percentile1 Year3 Years5 Years10 Years15 Years20 Years25 Years30 Years
10th Percentile-3.20%0.49%2.35%4.11%4.92%5.36%5.70%5.98%
25th Percentile2.18%4.72%5.50%6.27%6.73%6.94%7.06%7.23%
50th Percentile10.25%9.08%8.81%8.63%8.59%8.60%8.61%8.57%
75th Percentile17.39%13.07%11.95%10.92%10.47%10.19%10.02%9.88%
90th Percentile22.33%16.47%14.62%12.92%12.16%11.64%11.29%11.05%

Annual Return Probabilities

Annual Return Probabilities
Return1 Year3 Years5 Years10 Years15 Years20 Years25 Years30 Years
>= 0.00%78.53%91.28%95.81%99.13%99.90%99.95%99.99%100.00%
>= 2.50%72.06%84.48%89.54%95.77%98.15%99.23%99.64%99.78%
>= 5.00%66.08%73.94%77.87%84.97%89.47%92.26%94.39%96.02%
>= 7.50%62.91%59.66%60.90%62.86%65.13%66.97%68.86%70.48%
>= 10.00%50.56%43.95%39.85%34.44%30.65%27.71%25.31%23.15%
>= 12.50%40.85%28.12%21.24%12.60%7.93%4.98%3.22%2.24%

Loss Probabilities

Loss Probabilities
LossLoss Probability Excluding CashflowsLoss Probability Including Cashflows
Within Time PeriodEnd of Time PeriodWithin Time PeriodEnd of Time Period
>= 2.50%43.38%0.00%63.22%24.48%
>= 5.00%26.06%0.00%55.81%24.13%
>= 7.50%20.95%0.00%50.44%23.91%
>= 10.00%16.79%0.00%45.04%23.63%
>= 12.50%11.82%0.00%39.10%23.31%
>= 15.00%7.46%0.00%35.43%23.10%
>= 17.50%6.05%0.00%32.79%22.83%
>= 20.00%5.18%0.00%30.75%22.50%
>= 22.50%2.83%0.00%28.64%22.16%
>= 25.00%1.86%0.00%26.98%21.72%
>= 27.50%1.24%0.00%25.05%21.39%
>= 30.00%0.83%0.00%23.77%21.05%
>= 32.50%0.53%0.00%22.67%20.71%
>= 35.00%0.46%0.00%21.67%20.32%
>= 37.50%0.33%0.00%20.95%20.01%
>= 40.00%0.09%0.00%20.46%19.78%
Loss is measured against the original portfolio balance.