Monte Carlo Simulation

Portfolio Monte Carlo Simulation Overview

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 multiple 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.

Simulation Model Configuration

Portfolio Type

Initial Amount

$ .00

Cashflows

Cashflows Amounts

Withdrawal Amount

$ .00

Inflation Adjusted

Withdrawal Percentage

Rolling Average Periods

Smoothing Rate

Withdrawal Frequency

Life Expectancy Model

Current Age

Simulation Period in Years

Tax Treatment

Investment Horizon

Federal Income Tax

Capital Gains Tax

Dividend Tax

Affordable Care Act Tax

State Income Tax

Simulation Model

Time Series Model

Risk-Free Rate

Use Historical Volatility

Use Historical Correlations

Correlation Matrix

Use Full History

Start Year

End Year

Bootstrap Model

Block Min. Years

Block Max. Years

Circular Bootstrapping

Distribution

Degrees of Freedom

Expected Return

Volatility

Sequence of Returns Risk

Inflation Model

Inflation Mean

Inflation Volatility

Rebalancing

Intervals

Percentile Intervals

Return Intervals

Portfolio Assets

Allocation

Mean

Volatility

Asset 1

Asset 2

Asset 3

Asset 4

Asset 5

Asset 6

Asset 7

Asset 8

Asset 9

Asset 10

Total

Monte Carlo Simulation Results Save

Monte Carlo simulation results for 5000 portfolios based on entered mean and historical asset correlations and volatility. Returns were modeled as correlated random samples from a multivariate normal distribution. The configured portfolio model had 4.22% annual mean return with 7.10% standard deviation. The simulation results are based on generated nominal returns and specified inflation adjusted withdrawals ($250,000 per year). The simulated inflation model used historical inflation with 2.55% mean and 1.20% standard deviation based on the Consumer Price Index (CPI-U) data from Jan 2010 to Dec 2023. 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 Vanguard Intmdt-Term Trs Idx Admiral (VSIGX) [Dec 2009 - Mar 2024].

Portfolio Model

Ticker	Name	Allocation
VTI	Vanguard Total Stock Market ETF	25.00%
SPHQ	Invesco S&P 500 Quality ETF	9.00%
XLU	Utilities Select Sector SPDR ETF	8.00%
VPU	Vanguard Utilities ETF	8.00%
VSIGX	Vanguard Intmdt-Term Trs Idx Admiral	50.00%
Save portfolio »

Performance Summary

Summary Statistics
	10th Percentile	25th Percentile	50th Percentile	75th Percentile	90th Percentile
Time Weighted Rate of Return (nominal)	2.72%	3.30%	4.01%	4.69%	5.31%
Time Weighted Rate of Return (real)	0.11%	0.70%	1.42%	2.10%	2.72%
Portfolio End Balance (nominal)	$0.00	$0.00	$6,456,801	$23,111,777	$43,423,227
Portfolio End Balance (real)	$0.00	$0.00	$1,835,115	$6,738,612	$12,606,883
Annual Mean Return (nominal)	2.95%	3.53%	4.26%	4.94%	5.57%
Annualized Volatility	6.63%	6.75%	6.89%	7.03%	7.15%
Sharpe Ratio	-0.33	-0.25	-0.15	-0.05	0.04
Sortino Ratio	-0.43	-0.33	-0.20	-0.07	0.05
Maximum Drawdown	-100.00%	-100.00%	-60.59%	-28.27%	-21.10%
Maximum Drawdown Excluding Cashflows	-26.76%	-22.85%	-19.05%	-16.13%	-14.12%
Safe Withdrawal Rate	1.91%	2.29%	2.76%	3.34%	3.87%
Perpetual Withdrawal Rate	0.13%	0.71%	1.42%	2.08%	2.66%
3164 portfolios out of 5000 simulated portfolios (63.28%) survived all withdrawals.

Portfolio Balance

Portfolio Survival

Notes and Disclosures

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 5000 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 (dollar amount withdrawal).
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 (percentage withdrawal).
The results assume annual rebalancing of portfolio assets.
Contributions and withdrawals are done at the end of each specified time period.
Sharpe and Sortino ratios are calculated against the specified 5.30% risk-free rate.

Portfolio End Balance Histogram

Maximum Drawdown Histogram Excluding Cashflows

Simulated Assets - Correlations and Returns

Simulated Assets - Correlations and Returns
Name	Ticker	VTI	SPHQ	XLU	VPU	VSIGX	^CPIU	Expected Annual Return	Annualized Volatility
Vanguard Total Stock Market ETF	VTI	1.00	0.96	0.44	0.48	-0.06	-0.02	7.00%	15.30%
Invesco S&P 500 Quality ETF	SPHQ	0.96	1.00	0.46	0.50	-0.00	-0.05	7.00%	13.92%
Utilities Select Sector SPDR ETF	XLU	0.44	0.46	1.00	1.00	0.26	-0.04	7.00%	14.02%
Vanguard Utilities ETF	VPU	0.48	0.50	1.00	1.00	0.25	-0.04	7.00%	13.80%
Vanguard Intmdt-Term Trs Idx Admiral	VSIGX	-0.06	-0.00	0.26	0.25	1.00	-0.20	1.50%	4.19%
Inflation	^CPIU	-0.02	-0.05	-0.04	-0.04	-0.20	1.00	2.55%	1.20%
Asset correlations are based on monthly returns from Jan 2010 to Dec 2023. Historical volatility is used with specified expected annual returns. CAGR is estimated from the expected mean return and volatility.

Expected Annual Return

Expected Annual Return
Percentile	1 Year	3 Years	5 Years	10 Years	15 Years	20 Years	25 Years	30 Years	40 Years	50 Years
10th Percentile	-4.84%	-1.23%	-0.13%	1.00%	1.56%	1.93%	2.17%	2.30%	2.52%	2.72%
25th Percentile	-0.94%	1.06%	1.73%	2.43%	2.73%	2.89%	2.98%	3.07%	3.23%	3.30%
50th Percentile	3.81%	3.78%	3.81%	3.99%	3.96%	3.98%	3.98%	3.97%	4.00%	4.01%
75th Percentile	8.68%	6.66%	6.06%	5.51%	5.27%	5.11%	5.00%	4.87%	4.78%	4.69%
90th Percentile	13.43%	9.34%	8.06%	6.88%	6.43%	6.08%	5.85%	5.70%	5.46%	5.31%

Annual Return Probabilities

Annual Return Probabilities
Return	1 Year	3 Years	5 Years	10 Years	15 Years	20 Years	25 Years	30 Years	40 Years	50 Years
>= 0.00%	70.38%	82.94%	89.14%	95.92%	98.56%	99.46%	99.84%	99.94%	99.96%	100.00%
>= 2.50%	57.44%	62.40%	65.88%	73.92%	78.48%	82.30%	84.76%	87.04%	90.36%	93.32%
>= 5.00%	43.38%	38.62%	36.30%	32.38%	29.80%	27.22%	24.98%	22.38%	19.36%	15.80%
>= 7.50%	30.68%	19.68%	13.44%	6.28%	3.26%	1.72%	0.98%	0.36%	0.04%	0.02%
>= 10.00%	19.80%	7.78%	3.28%	0.56%	0.06%	0.02%	0.00%	0.00%	0.00%	0.00%
>= 12.50%	12.54%	2.62%	0.56%	0.04%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%

Loss Probabilities

Loss Probabilities
Loss	Loss Probability Excluding Cashflows		Loss Probability Including Cashflows
Loss	Within Time Period	End of Time Period	Within Time Period	End of Time Period
>= 2.50%	54.78%	0.00%	81.38%	56.00%
>= 5.00%	36.06%	0.00%	73.86%	55.48%
>= 7.50%	23.36%	0.00%	68.48%	55.08%
>= 10.00%	14.42%	0.00%	64.38%	54.80%
>= 12.50%	8.86%	0.00%	61.02%	54.38%
>= 15.00%	5.76%	0.00%	58.70%	53.80%
>= 17.50%	3.34%	0.00%	56.68%	53.28%
>= 20.00%	2.00%	0.00%	55.10%	52.88%
>= 22.50%	1.02%	0.00%	54.00%	52.46%
>= 25.00%	0.64%	0.00%	52.94%	52.00%
>= 27.50%	0.38%	0.00%	52.18%	51.48%
>= 30.00%	0.16%	0.00%	51.44%	51.04%
>= 32.50%	0.12%	0.00%	51.04%	50.66%
>= 35.00%	0.06%	0.00%	50.40%	50.12%
>= 37.50%	0.04%	0.00%	49.84%	49.70%
>= 40.00%	0.00%	0.00%	49.10%	48.98%
Loss is measured against the original portfolio balance.