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:
- Historical Returns - Simulate future returns by randomly selecting the returns for each year based on available historical returns
- Forecasted Returns - Simulate future returns based on any forecasted mean and standard deviation of assets
- Statistical Returns - Simulate future returns based on the mean, volatility and correlations of portfolios assets
- Parameterized Returns - Simulate future returns based on the specified statistical distribution
You can choose from several different withdrawal models including:
Fixed annual withdrawal or contribution - Apply a fixed annual withdrawal or contribution.
Yearly inflation adjustments are by default done for the specified withdrawal or contribution amount based on the selected model.
Fixed annual percentage - Withdraw a fixed percentage of the portfolio balance annually.
This model ensures that the portfolio never runs out, but the annual spending amount varies based on the portfolio growth.
The percentage based withdrawal can be smoothed by using the rolling portfolio average or a geometric spending rule.
Life expectancy based annual withdrawal - This model withdraws a variable percentage of the portfolio
balance based on life expectancy. This is the RMD approach where the withdrawal percentage is 1 / Life Expectancy.
Custom sequence - Import custom sequence of periodic cashflows from a file.
To simulate multiple stages such as career and retirement with detailed cashflow goals use the Financial Goals planning tool.
Monte Carlo Simulation Results
Monte Carlo simulation results for 10000 portfolios with $1.00 initial portfolio balance using the normal distribution with 7.00% mean and 12.00% standard deviation for annual returns. The simulation results are based on generated nominal returns and specified inflation adjusted contributions ($41,806 per year). The simulated inflation model used historical inflation with 3.91% mean and 1.30% standard deviation based on the Consumer Price Index (CPI-U) data from Jan 1972 to Dec 2021. The generated inflation samples were uncorrelated with simulated asset returns.
|10th Percentile||25th Percentile||50th Percentile||75th Percentile||90th Percentile|
|Time Weighted Rate of Return (nominal)||-0.21%||2.85%||6.32%||9.92%||13.37%|
|Time Weighted Rate of Return (real)||-4.25%||-1.17%||2.30%||5.90%||9.34%|
|Portfolio End Balance (nominal)||$226,284||$243,517||$265,849||$291,310||$316,578|
|Portfolio End Balance (real)||$187,250||$201,642||$219,353||$239,897||$260,302|
|Maximum Drawdown Excluding Cashflows||-25.46%||-19.94%||-15.22%||-11.67%||-9.29%|
|Safe Withdrawal Rate||17.14%||19.03%||21.35%||23.89%||26.46%|
|Perpetual Withdrawal Rate||0.00%||0.00%||2.26%||5.58%||8.54%|
Notes on results:
- IMPORTANT: The projections or other information generated by Portfolio Visualizer regarding the likelihood of various investment outcomes are hypothetical in nature, do not reflect actual investment results and are not guarantees of future results. Results may vary with each use and over time.
- The results do not constitute investment advice or recommendation, are provided solely for informational purposes, and are not an offer to buy or sell any securities. All use is subject to terms of service.
- Investing involves risk, including possible loss of principal. Past performance is not a guarantee of future results.
- Asset allocation and diversification strategies do not guarantee a profit or protect against a loss.
- Hypothetical returns do not reflect trading costs, transaction fees, commissions, or actual taxes due on investment returns.
- The results are based on information from a variety of sources we consider reliable, but we do not represent that the information is accurate or complete.
- Refer to the related documentation sections for more details on terms and definitions, methodology, and data sources.
- A Monte Carlo simulation is a mathematical technique used to provide a range of possible outcomes and to approximate the probability of certain outcomes by running multiple trial runs, called simulations, using random variables. The simulation results are displayed by percentile, a 5th percentile result means that 5% of the simulated portfolios did worse and 95% of simulated portfolios did better for the given return or risk metric. At the median point (50th percentile), half of the simulated portfolios did better and half did worse.
- The results are based on the total return of assets and assume that all received dividends and distributions are reinvested.
- Compound annualized growth rate (CAGR) is the annualized geometric mean return of the portfolio. It is calculated from the portfolio start and end balance and is thus impacted by any cashflows.
- The time-weighted rate of return (TWRR) is a measure of the compound rate of growth in a portfolio. This is calculated from the holding period returns (e.g. monthly returns), and TWRR will thus not be impacted by cashflows. If there are no external cashflows, TWRR will equal CAGR.
- The money-weighted rate of return (MWRR) is the internal rate of return (IRR) taking into account cashflows. This is the discount rate at which the present value of cash inflows equals the present value of cash outflows.
- Real return and balance are inflation adjusted values and show the growth of the purchasing power of the portfolio. Nominal return and balance show the portfolio gains without accounting for inflation.
- Standard deviation (Stdev) is used to measure the dispersion of returns around the mean and is often used as a measure of risk. A higher standard deviation implies greater the dispersion of data points around the mean.
- Correlation measures to what degree the returns of the two assets move in relation to each other. Correlation coefficient is a numerical value between -1 and +1. If one variable goes up by a certain amount, the correlation coefficient indicates which way the other variable moves and by how much. Asset correlations are calculated based on monthly returns.
- A drawdown refers to the decline in value of a single investment or an investment portfolio from a relative peak value to a relative trough. A maximum drawdown (Max Drawdown) is the maximum observed loss from a peak to a trough of a portfolio before a new peak is attained. Drawdown statistics are calculated from simulated monthly returns.
- All risk measures for the portfolio and portfolio assets are calculated based on monthly returns.
- The results are based on simulating 10000 portfolio return paths.
- The probability of success is based on the number of simulations the portfolio survives with a positive end balance.
- 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.
- Contributions and withdrawals are done at the end of each specified time period.
Expected Annual Return
Expected Annual Return
|Percentile||1 Year||3 Years||5 Years|
Annual Return Probabilities
Annual Return Probabilities
|Return||1 Year||3 Years||5 Years|
|Loss||Loss Probability Excluding Cashflows||Loss Probability Including Cashflows|
|Within Time Period||End of Time Period||Within Time Period||End of Time Period|
|Loss is measured against the original portfolio balance.|