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
Statistical Returns - Simulate future returns based on the mean, volatility and correlations of portfolios assets
Forecasted Returns - Simulate future returns based on any forecasted mean and standard deviation of 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.

Portfolio Type

Initial Amount

$ .00

Periodic Adjustment

Cashflows Amounts

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Withdrawal Amount

$ .00

Inflation Adjusted

Withdrawal Percentage

Rolling Average Periods

Smoothing Rate

Withdrawal Frequency

Life Expectancy Model

Current Age

Simulation Period in Years

Simulation Model

Use Historical Volatility

Use Historical Correlations

Correlation Matrix

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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

Intervals

Percentile Intervals

Return Intervals

Asset 1

Select asset 1

Enter percentage allocation for asset 1 %

Expected return for asset 1 %

Expected volatility for asset 1 %

Asset 2

Select asset 2

Enter percentage allocation for asset 2 %

Expected return for asset 2 %

Expected volatility for asset 2 %

Asset 3

Select asset 3

Enter percentage allocation for asset 3 %

Expected return for asset 3 %

Expected volatility for asset 3 %

Asset 4

Select asset 4

Enter percentage allocation for asset 4 %

Expected return for asset 4 %

Expected volatility for asset 4 %

Asset 5

Select asset 5

Enter percentage allocation for asset 5 %

Expected return for asset 5 %

Expected volatility for asset 5 %

Asset 6

Select asset 6

Enter percentage allocation for asset 6 %

Expected return for asset 6 %

Expected volatility for asset 6 %

Asset 7

Select asset 7

Enter percentage allocation for asset 7 %

Expected return for asset 7 %

Expected volatility for asset 7 %

Asset 8

Select asset 8

Enter percentage allocation for asset 8 %

Expected return for asset 8 %

Expected volatility for asset 8 %

Asset 9

Select asset 9

Enter percentage allocation for asset 9 %

Expected return for asset 9 %

Expected volatility for asset 9 %

Asset 10

Select asset 10

Enter percentage allocation for asset 10 %

Expected return for asset 10 %

Expected volatility for asset 10 %

Total

Total allocation for portfolio %

Monte Carlo Simulation Results

Monte Carlo simulation results for 10000 portfolios with $1,000,000 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 8.52% mean return (8.14% CAGR) with 7.86% standard deviation of annual returns. The simulation results are based on generated nominal returns and specified inflation adjusted withdrawals ($40,000 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 - Aug 2019].
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Portfolio Allocation

Asset Class	Allocation
US Stock Market	50.00%
Total US Bond Market	50.00%
Save portfolio »

Summary Statistics

Summary Statistics
	10th Percentile	25th Percentile	50th Percentile	75th Percentile	90th Percentile
Time Weighted Rate of Return (nominal)	5.99%	7.03%	8.17%	9.29%	10.32%
Time Weighted Rate of Return (real)	3.33%	4.30%	5.39%	6.50%	7.52%
Portfolio End Balance (nominal)	$1,182,139	$2,397,658	$4,250,536	$6,761,756	$10,067,283
Portfolio End Balance (real)	$555,680	$1,120,256	$1,964,620	$3,114,693	$4,648,329
Maximum Drawdown	-41.16%	-30.12%	-22.83%	-18.33%	-16.23%
Maximum Drawdown Excluding Cashflows	-26.38%	-21.49%	-18.26%	-16.23%	-12.71%
Safe Withdrawal Rate	4.97%	5.78%	6.75%	7.84%	8.88%
Perpetual Withdrawal Rate	3.23%	4.13%	5.12%	6.11%	7.00%
9834 portfolios out of 10000 simulated portfolios (98.34%) 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. 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
Name	US Stock Market	Total US Bond Market	Inflation	CAGR	Expected Annual Return	Annualized Volatility
US Stock Market	1.00	0.07	0.01	9.76%	11.02%	14.99%
Total US Bond Market	0.07	1.00	-0.11	5.78%	5.85%	3.81%
Inflation	0.01	-0.11	1.00	2.60%	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
Percentile	1 Year	3 Years	5 Years	10 Years	15 Years	20 Years	25 Years	30 Years
10th Percentile	-1.41%	1.22%	2.88%	4.43%	5.11%	5.49%	5.78%	5.99%
25th Percentile	2.07%	4.78%	5.46%	6.26%	6.57%	6.78%	6.93%	7.03%
50th Percentile	9.89%	8.48%	8.28%	8.23%	8.20%	8.18%	8.18%	8.17%
75th Percentile	12.33%	11.87%	11.05%	10.16%	9.76%	9.57%	9.40%	9.29%
90th Percentile	20.22%	14.89%	13.40%	11.83%	11.21%	10.78%	10.52%	10.32%

Annual Return Probabilities

Annual Return Probabilities
Return	1 Year	3 Years	5 Years	10 Years	15 Years	20 Years	25 Years	30 Years
>= 0.00%	84.34%	93.27%	97.49%	99.71%	99.97%	99.99%	100.00%	100.00%
>= 2.50%	71.86%	85.87%	91.39%	97.15%	99.17%	99.66%	99.86%	99.94%
>= 5.00%	65.95%	73.95%	78.35%	86.32%	91.02%	93.41%	95.52%	96.76%
>= 7.50%	62.81%	57.14%	57.43%	59.77%	61.08%	62.76%	63.71%	65.20%
>= 10.00%	47.01%	37.58%	33.73%	26.87%	21.85%	18.75%	16.00%	13.90%
>= 12.50%	24.55%	21.16%	14.79%	6.34%	3.23%	1.57%	0.80%	0.38%

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%	29.10%	0.00%	49.35%	7.84%
>= 5.00%	20.02%	0.00%	41.43%	7.67%
>= 7.50%	15.94%	0.00%	33.53%	7.39%
>= 10.00%	10.77%	0.00%	26.75%	7.08%
>= 12.50%	6.36%	0.00%	21.91%	6.84%
>= 15.00%	5.58%	0.00%	19.12%	6.60%
>= 17.50%	4.85%	0.00%	16.60%	6.39%
>= 20.00%	1.50%	0.00%	13.80%	6.15%
>= 22.50%	0.81%	0.00%	11.76%	6.00%
>= 25.00%	0.33%	0.00%	10.13%	5.83%
>= 27.50%	0.23%	0.00%	8.82%	5.70%
>= 30.00%	0.17%	0.00%	7.57%	5.49%
>= 32.50%	0.06%	0.00%	6.77%	5.29%
>= 35.00%	0.03%	0.00%	6.16%	5.06%
>= 37.50%	0.02%	0.00%	5.70%	4.92%
>= 40.00%	0.02%	0.00%	5.29%	4.79%
Loss is measured against the original portfolio balance.