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Where do these guys get a 2% withdrawal rate?


Where do these guys get a 2% safe
withdrawal rate?

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This article was posted on January 1, 2005.

Most readers are familiar with the Retire Early Study on Safe Withdrawal Rates and the fact that 130 years of historical stock market returns show that a 4% inflation-adjusted withdrawal rate would have survived even the worst of times. Yet, there are still ways to calculate an even more pessimistic outcome. Let's look at a couple of alternative approaches.

Monte Carlo Method

The Monte Carlo method uses random sampling of the data and a large number of trials to converge on a solution. For example, random sampling might select the S&P500 return for 1954, the inflation rate for 1981, and the short term interest rate for 1992 for the beginning year of the first 30-year pay out period examined. The fact that one would be unlikely to see the 4% short term interest rate of 1992 during a period when inflation was running at 12% per annum (as it was in 1981) is typically ignored in this type of sampling. It's not surprising that this method would yield results much worse than any in the historical record.

One advantage of the Monte Carlo method is that allows the use of limited data sets. Few asset classes have the 130 years of historical data for the S&P 500 and three-month commercial paper that are contained in Shiller's database. If you're willing to assume that 30 years of REIT or small cap value stock data can be projected well into the future, Monte Carlo analysis allows you to measure survivability for portfolios containing asset classes with limited historical data.

A typical analysis would run anywhere from 1,000 to 10,000 of these imaginary 30-year pay out periods and the percentage of failures would be determined. The greater the number of periods examined, the greater the chance of converging on a solution.

One very accessible Monte Carlo calculator can be downloaded for free from Prof. Peter Ponzo's web site - "Gummy's stuff". You'll need Microsoft Excel to run it.

Actuarial Method

The Society of Actuaries published a very interesting retirement planning calculator in Summer 2004 that's available for free on their web site. The Retirement Probability Analyzer uses a series of partial differential equations in an attempt to overcome some of the shortcomings of the Monte Carlo method.

The Retirement Probability Analyzer can be downloaded at this link: click here.

One useful feature of the Retirement Probability Analyzer is that it allows the user to measure portfolio survivability over both one's actuarial life span as well as the fixed pay out period common in other calculators. For example, a 55-year old stands at least some chance of living longer than age 85, but an even better chance of expiring before that age. The 30-year survivability for a 60% stock/40% cash portfolio and a 4% withdrawal rate is 80.7%, the survivability over the 55-year-old's expected lifespan rises to 85.9%. Running the same numbers for a 75-year-old yields a 99.2% survivability over their lifetime.

Comparison of Retirement Withdrawal Calculators
0.00% expense ratio, inflation indexed to CPI-U, January start date, $1,000 initial balance,
Asset allocation of 60% S&P500, 40% short-term fixed income securities.
. .
Survivability for a
----30-Year Pay Out Period-----
Inflation-adjusted withdrawal rate 2% 3% 4% 5%
Retire Early Home Page
Safe Withdrawal Calculator
(Note 1)
100% 100% 100% 76%
Gummy's Monte Carlo
Safe Withdrawal Calculator
(Note 2)
99.6% 96.3% 89.1% 72.5%
Society of Actuaries
Retirement Probability Analyzer
99.6% 95.1% 80.7% 58.9%
Note (1): Version 1.61 of the REHP spreadsheet was used for this analysis click here.

Note (2): You'll find a copy of Gummy's Monte Carlo calculator with the settings used in this example at this link click here.


Asset Allocation

Modern Portfolio Theory (MPT) maintains that combining several non-correlated asset classes in an investment portfolio reduces volatility, thus improving the survivability of a given retirement withdrawal rate. You can see the effect of this with either the Monte Carlo or Retirement Probability Analyzer calculators. The following table shows the survivability for several different asset allocations using the Retirement Probability Analyzer.

Comparison of Various Asset Allocations using the
Society of Actuaries Retirement Probability Analyzer

0.00% expense ratio, inflation indexed to CPI-U.
. .
Survivability for a
----30-Year Pay Out Period-----
Inflation-adjusted withdrawal rate 2% 3% 4% 5%
100% Stock 99.4% 89.3% 77.6% 64.3%
100% Cash 100% 99.3% 5.9% 0%
100% Nominal Return Bonds 99.6% 92.6% 69.8% 40.7%
100% Real Return Bonds (TIPS) 99.9% 94.8% 68.5% 32.7%
60% Stocks/40% Cash 99.6% 95.1% 80.7% 58.9%
60% Stocks/40% Nominal Bonds 99.8% 97.1% 87.5% 70.3%
60% Stocks/40% Real Bonds 99.8% 96.9% 86.6% 68.6%
40% Stocks/20% REITs/40% Cash 100% 98.6% 86.4% 57.6%
40% Stocks/20% REITs/20% Real Bonds/
10% Nominal Bonds/10% Cash
100% 99.3% 91.7% 69.3%

One surprising result in the table above is that the SOA calculator shows little difference in the performance between Real Bonds and Nominal Bonds. Many researchers see Real Bonds (e.g., TIPS) as being clearly superior for a retirement portfolio.

Should I be using a 2% retirement withdrawal?

Probably not. You'll find few reputable analysts suggesting that a retiree limit his or her withdrawals to 2% from an adequately diversifed retirement portfolio. Indeed, few Americans could amass enough capital to support a 2% withdrawal even if they worked well into their 70's.

William J. Bernstein (author of The Efficient Asset Allocator and The Four Pillars) points out that aiming for a portfolio survivablity of more than 80% (based on Monte Carlo analysis) really doesn't improve your overall safety. In his article The Retirement Calculator from Hell, Part III: Eat, Drink, and Be Merry Bernstein says this:

"The historically naÔve investor (or academic) might consider reducing his monthly withdrawals to a very low level to maximize his chances of success. But history teaches us that depriving ourselves to boost our 40-year success probability much beyond 80% is a foolís errand, since all you are doing is increasing the probability of failure for political, economic, and military reasons relative to the failure of banal financial planning."

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Copyright © 2005 John P. Greaney, All rights reserved.

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