Comparison of Monte Carlo Retirement Calculators

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This article was posted on December 9, 2002.

There are several Monte Carlo Retirement Withdrawal Simulators available on the web. Three of the most readily available programs are compared below.

T. Rowe Price (TRP) Retirement Income Calculator (Cost: Free)

Mutual Fund Company T. Rowe Price (TRP) has an interesting Monte Carlo-based withdrawal calculator on it's website. See link:

http://www3.troweprice.com/ric/RIC/

Like most Monte Carlo calculators, the T. Rowe Price model yields a lower safe withdrawal rate than a straight-up historical analysis. The results of any Monte Carlo analysis are very sensitive to the assumptions made. The fact that the calculator assumes relatively high-fee mutual funds probably reduces the calculated inflation-adjusted safe withdrawal rates by 0.40% to 0.50% versus similiar investments in a Vanguard fund.

From the T. Rowe Price web site:

"For each asset class, we deducted from their simulated performance the following expense ratios based on the mean averages for each comparable Lipper no-load mutual fund category:

Corporate Debt A rated .72% (Investment-Grade Bond)

Growth 1.09% (Large-Cap Stock)

High Yield .82% (High-Yield Bond)

International Equity 1.21% (International Stock)

International Fixed Income .96% ((International Bond)

Small-Cap 1.17% (Small-Cap Stock)

Short-Term Investment Grade .61% (Short-Term Bond) "

Here's a summary of the results for various asset allocations and length of pay out periods (45 years was the longest retirement period the TRP calculator would accommodate) along with the results from the REHP study for the same asset allocations and pay out periods.

T. Rowe Price Retirement Calculator Initial 99% Survivable Inflation-Adjusted Withdrawal Rates 40-year-old single retiree, $1 million starting portfolio, expense ratio = 1.00%
Asset Allocation Stocks/Bonds/Cash	30-Year Pay Out	40-Year Pay Out	45-Year Pay Out
5/25/70	3.00%	2.40%	2.16%
15/35/50	3.36%	2.64%	2.40%
25/40/35	3.36%	2.64%	2.52%
40/40/20	3.36%	2.64%	2.52%
60/30/10	3.24%	2.52%	2.40%
80/20/0	3.00%	2.52%	2.28%
100/0/0	2.64%	2.16%	2.16%

Portfolio Survival Simulator (Cost: $14.95)

The Portfolio Survival Simulator (PSS) web site http://www.portfoliosurvival.com/ offers an Excel spreadsheet that performs two types of Monte Carlo simumlation along with traditional historical safe withdrawal analysis. Unlike the T. Rowe Price calculator, it also allows the user to input his own investment expense ratio. One problem with the PSS program is that it doesn't include less than 40-year periods that cause the 40-Year withdrawal rate to fail. If 3.26% is the most you can take for 30 years, you can't take a 3.35% withdrawal for 40 years.

Here's a summary of the results for selected asset allocations and expense ratios.

Portfolio Survival Simulator Initial 99% Survivable Inflation-Adjusted Withdrawal Rates 40-year-old single retiree, $1 million starting portfolio RHS=Rolling Historical Simulations, MC=Monte Carlo, MC/BS=Monte Carlo with Bootstrap Sampling
Asset Allocation Stocks/Bonds/Cash	30-Year Pay Out			40-Year Pay Out
Simulation Type	RHS	MC	MC/BS	RHS	MC	MC/BS
60/30/10 (1.00% exp. ratio)	3.26%	2.78%	2.50%	3.35%	2.00%	2.00%
60/30/10 (0.20% exp. ratio)	3.65%	2.96%	3.03%	3.81%	2.70%	2.60%
80/20/0 (1.00% exp. ratio)	3.35%	2.68%	2.50%	3.65%	2.05%	2.00%
80/20/0 (0.20% exp. ratio)	3.71%	3.01%	2.67%	4.05%	2.37%	2.40%

Gummy's Monte Carlo Retirement Withdrawal Spreadsheet (Cost: Free)

Retired university professor Peter Ponzo has a wonderful web site at Gummy stuff. Among the offerings is an easy to sue Monte Carlo-based retirement withdrawal simulator, see link: http://home.golden.net/~pjponzo/sensible_withdrawals.htm

Gummy's Monte Carlo simulator allows users to enter their own investment return data and has room for as many as 10 different asset classes. It appears to ignore investment expenses, so there is no easy way to vary this parameter.

Gummy's Monte Carlo Spreadsheet Initial 99% Survivable Inflation-Adjusted Withdrawal Rates 40-year-old single retiree, $1 million starting portfolio, expense ratio = 0.00% Monte Carlo results based on 1,000 iterations
Asset Allocation Stocks/Bonds/Cash	30-Year Pay Out	40-Year Pay Out
80/20/0	2.18%	2.10%
60/30/10	2.45%	2.45%
Note (1): Asset Allocations: Stocks = S&P500, Bonds = 5-Year US Treasury Notes, Cash = US Treasury bills

Retire Early Safe Withdrawal Spreadsheet (Cost: Free)

Retire Early Safe Withdrawal Spreadsheet--Version 1.61 100% Historical Survivable Rate (Retirement starting on 9/16/1929.)
Asset Allocation Stock/Cash	30-Year Pay Out	40-Year Pay Out
60/40 (0.20% exp. ratio)	3.91%	3.54%
60/40 (1.00% exp. ratio)	3.52%	3.13%

Comparison of Four Retirement Withdrawal Calculators

Comparison for 60% stock/40% fixed income portfolio 1.00% investment expense ratio
Calculator Name	30-Year Pay Out	40-Year Pay Out
T. Rowe Price	3.24%	2.52%
Portfolio Simulator Historical	3.26%	3.35%
Portfolio Simulator Monte Carlo	2.78%	2.00%
Portfolio Simulator Monte Carlo with Bootstrap	2.50%	2.00%
Gummy Site Monte Carlo (assumes 0% exp. ratio)	2.45%	2.45%
Retire Early Excel Spreadsheet	3.52%	3.13%

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