### Can Retirees Still Use a 4% Withdrawal Rate? Practical Applications of Monte Carlo Analysis

Some advisors remain critical of Monte Carlo simulations, instead preferring to use analysis based on rolling historical periods or specific pre-defined scenarios. We believe Monte Carlo is a superior tool for measuring the uncertainties in long-term financial planning.

Lynn Hopewell implored the financial advisory profession to adopt Monte Carlo simulation tools in his seminal 1997 article^{1} in the *Journal of Financial Planning*. He argued forcefully against merely developing spreadsheets for financial plans based on average input assumptions, or by testing the robustness of plans with worst-case scenarios. Those approaches do not provide probabilities for outcomes, and one must struggle to figure out how to save, spend and develop a financial plan using such limited analysis.

In the past 17 years, the widespread use of Monte Carlo simulations has led to much progress. In our previous article, we provided a brief refresher about Monte Carlo to help ensure that readers are up to speed. In this column, we extend our analysis to illustrate what Monte Carlo simulations show relative to other methodologies when developing a retirement-income plan.

As an example, we use Monte Carlo simulations to predict the likelihood of a successful 4% withdrawal rate under today’s market conditions.

### Comparing Monte Carlo simulations to rolling historical periods

The 1998 “Trinity” study, by Cooley, Hubbard, and Walz, is one of the classics in the field of retirement income planning. The authors concluded that the 4% rule (that is, withdraw 4% of retirement-date assets and adjust this amount for inflation in subsequent years) has a 95% chance for success over 30 years based n investing in a portfolio with 50% large-capitalization U.S. stocks and 50% long-term corporate bonds (i.e., a 50/50 portfolio).

The phrase “95% chance for success” might lead one to conclude that the Trinity Study is based on Monte Carlo simulations. It wasn’t. It was based on rolling historical returns.

With data from 1926 through 2013, we used Monte Carlo simulations to calculate sustainable withdrawal rates for hypothetical 30-year retirements starting between 1926 and 1984. (We don’t yet know how matters will work out for post-1984 retirees.) This represents 59 retirement periods, each lasting 30 years. Our results are shown in Figure 1, for stock allocations ranging from 0% to 100%.

Figure 1 compares the historical portfolio success rates based on the Trinity study’s rolling-period analysis to our success rates using Monte Carlo simulations. We parameterized our analysis to the same annual historical data as was used with historical simulations, the *Stocks, Bonds, Bills, and Inflation* dataset from Ibbotson and Morningstar.

To calculate the probability of success for the 4% rule, the Trinity approach adds up the percentage of these historical retirement periods where the target withdrawal amount was achieved. When using the long-term corporate bond series, retirements beginning in 1965 and 1966 would have just missed being sustainable over 30 years with a 4% initial withdrawal rate. William Bengen’s initial research from 1994 used less-volatile intermediate-term government bonds, and he found that 4% would have always worked for a 50/50 portfolio (100% success rate).

Monte Carlo simulations have a number of advantages over their historical-simulation counterparts. First, Monte Carlo allows for a wider variety of scenarios than the rather limited scenarios that historical data can provide. In this case, we simulated 10,000 retirements, compared to the 59 available with the historical data. (Those 59 are not even independent of each other, because they share data points.) This provides an opportunity to observe a much wider variety of return sequences that support a deeper perspective about possible retirement outcomes.

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