The 4% Safe Withdrawal Rate – Validation with Monte Carlo Simulations for Our Scenario

In the FI/RE circles, the 4% Safe Withdrawal Rate (SWR) is often used as a “golden rule” but is really a rule of thumb and various factors will determine what safe withdrawal rate you will be comfortable with.  The SWR is key to help define your “Number”, where your financial capital (savings and non-work income) is significant enough to provide your income for the rest of your life without work. 

When starting out a SWR of 4% is a good place to start.  By planning for the worst case, we can have a ~96% change of our savings not just outlasting us but having a balance greater than the starting balance.  The focus on the worst case does make sense, since the negative impact of running out of money far outweighs the impact of having too much money in the end. 

We should understand that, though we can’t control the markets, we do have a lot of control of our plans and each year we have options to adjust and tweak.  We should not pick a number and then run on auto pilot for 30+ years.

This article covers a little of the history of the 4% rule and then introduces an Excel based Monte Carlo simulation tool that we developed to test our preferred SWR. 

Note: Links to the references used in this article are included in the reference section at the end of the article.

The 4% Rule Background

This is not meant to be an entire treatise on the 4% rule, but I want to provide a little background.   

Back in 1994, William Bengen wrote the article “Determining Withdrawal Rates Using Historical Data.” 1 This was ground breaking at the time. Prior to this research investor advisors would use things like average returns to provide guidance to their clients with recommendations of withdrawal rates of 6% or higher.  He introduced the term “SAFEMAX”, or the highest withdrawal rate possible in the worst-case scenario based on his back tested study.  This study showed the SAFEMAX at a 4.15% withdrawal rate based on a portfolio of the S&P 500 and intermediate-term government bond returns.

This initial work did not get as much traction as the next study.  In 1998, Philip L. Cooley, Carl M. Hubbard and Daniel T. Walz published the article “Retirement Savings: Choosing a Withdrawal Rate That Is Sustainable” 2.  This became known as the “Trinity Study” since all the authors were professors at Trinity University in Texas.  They used the same methodoly as Bengen but changed the focus from SAFEMAX to the idea of a “portfolio success rate”.   They swapped the intermediate-term government bond returns with long-term high-grade corporate bond returns so their performance was a little different and showed the 4% withdrawal rate had a 95% chance of success.  Again, both studies are based on historical data.

Recent Updates to the 4% Rule

A recent Forbes article by Wade Pfau3 revised the work of the Trinity Study and applied the government bond yield instead of corporate bonds and showed the decreased volatility increased the chance for success for the 4% withdrawal rate to 100% (30 year period, 50/50 stock and bonds).

In a recent AMA Reddit4 post by Mr. Bengen, he recommends that his SAFEMAX rate is really 4.5%, in his own words:

“The “4% rule” is actually the “4.5% rule”- I modified it some years ago on the basis of new research. The 4.5% is the percentage you could “safely” withdraw from a tax-advantaged portfolio (like an IRA, Roth IRA, or 401(k)) the first year of retirement, with the expectation you would live for 30 years in retirement. “

Mr. Bengen also added for longer time Horizons

” As your “time horizon” increases beyond 30 years, as you might expect, the safe withdrawal rate decreases. For example, for 35 years, I calculated 4.3%; for 40 years, 4.2%; and for 45 years, 4.1%. … If you plan to live forever, 4% should do it.”

There have been many other articles and studies written since the original 1994 publication but they all come down to similar basis of 4% as a Safe Withdrawal Rate. If you want to be more conservative over a longer period consider something less than 4%. 

This provides a good foundation of determining your own Safe Withdrawal Rate based on your personal situation, but can we simulate our own situation?  In researching our own plans for Financial Independence, we asked, instead of back testing prior history why not apply a Monte Carlo simulation to review 1000’s of life cycles of a portfolio performance?

Simulation Requirements

Since I am an Excel geek and did not find any simple tools online that gave the details I wanted, I decided to create my own simulation tool.  It is not meant to be exhaustive or to be the final answer on the ideal SWR but provides some validation with our own data what the future could look like.

I wanted a simulation tool that would do the following:

  • Provide a Monte Carlo based simulation of performance over many different “life time” cycles to test different savings and retirement income plans
  • Use my current age and savings and forecast my potential nest egg at my defined retirement age
  • Use that as the starting point to simulate my retirement performance for my estimate lifetime.
  • Estimate the remaining balance (or age I would run out of money) at the end of each life cycle.
  • Be simple enough to use to allow testing of many different scenarios
  • Include ability to change investment approach pre and post retirement.
  • Account for inflation on future income needs
  • Allow for future expansion to include testing for retirement age sensitivity, investment amounts variations, and add in future income streams such as Social Security. These were not designed into the initial model but wanted to make sure I could expand the model to support this.

The Monte Carlo Simulation Tool

Based on the above criteria, an Excel tool was created to simulate 1000’s of life time cycles to estimate the growth and survival rate of our retirement savings.

The simulation can be used in two ways, 

  1. Those close to retirement can simulate retirement performance to validate things like a Safe Withdrawal Rate (SWR).
  2. Those with a longer time before retirement, with at least a few years of growth, can simulate pre-retirement performance from the current age to the retirement age and then simulate the retirement performance. This provides ability to use your real current savings and do studies around your savings rate, retirement age, and income needs.

The basic simulation allows includes inputs for the following personal data:

  1. Current Age
    • For looking at retirement performance to investigate SWR, set Current Age to the Planned Retirement Age
  2. Planned Retirement Age
  3. Life Expectancy (or, “How long do you need this money to last?”)
  4. Projected Income
    • Set to today’s dollars if using your real current age and simulating pre-retirement savings and performance. It will adjust income need for inflation as well as investment performance.
    • If looking only at a future retirement forecast (setting Current Age to Planned Retirement Age) adjust for inflation at the expected retirement age.  It does not simulate the pre-retirement inflation in this case.
    • The income need will be adjusted each year based on inflation simulated.
  5. Current Savings
    • Today’s dollars if using real current age and will simulate performance up to your retirement age based on the Pre-Retirement Investment settings.
    • Adjust for estimate retirement need if just simulating retirement.
  6. Your annual savings amount
    • Set to zero for retirement performance, simulations assumes no savings from income in retirement.

Note: A  bug was found in the Simulation Tool where the average investment performance was fixed to 9.5% with a standard deviation of 8.9% for both pre and post retirement simulations.  This was roughly about 50/50 stock/bond performance using 50 years of historic data.  Results are still valid, just note the portfolio ratio is not as shown below.

Monte Carlo Simulator Input Data

Our Test Case – Validating Our Initial 4% Safe Withdrawal Rate

Using the data from our earlier post on “Our Number” we came out with a rough income need of $72.5k with an estimated retirement savings of $1.8M based on the 4% rule.   We will continue to use this date for our example.  We want to understand the risk of how long this savings will last for our projected need of at least 45 years if we retired at 50.

We used a 2% inflation rate with a 0.5% deviation, historically this has been much higher with an average of 3.18% (since 1913) but for the last 20 years it has been closer to 2%.6   

Entering the numbers into the simulation tool and running 1,000 “Life Times” of data (comment from Mrs. FoF: did we mention Mr. FoF is an Excel geek? Who else would do 1,000 years of simulations!).  We came up with some interesting results.

Our initial 4% withdrawal rate is shown to have a 98.6% probability for success for a period of 45 years.   Note: This aligned well with Mr. Bengen updated analysis mentioned above for extended time periods, where he recommended 4.1% SWR for 45 years.

The output of the simulation results includes the Average, Minimum, and Maximum results over all the simulated life times. In addition, it includes histogram graphs for the Final Investment Values and the selected End of Life as well as the age distribution where funds are exhausted.   The example output is shown below:

Our Test Case Monte Carlo Simulation Results

We feel comfortable with the success rate of 98.6% since this is not a passive one-time effort.  We have control over how we manage our situation.  If we find the market has done poorly our first few years of retirement and we have higher sequence risk, Mrs. FoF and I are good with adjusting our spending or even considering some part time supplemental work.  We had already planning for some side income during our first few years which may be through our hobbies or maybe some part time consulting.

The data also shows we have 100% chance of our money surviving to age 68.  By this time, we would also have access to Social Security which could provide another safety net we can start accessing at age 62.  We are close enough to see some benefit from Social Security but planning only about 75% benefit right now.  A future simulation upgrade will add this in for consideration to see how our SWR can be increased when considering Social Security.  

Probability of Fund Survival By Age

Based on this simulation and the rest of the research we have done, we are very happy with a 4% Safe Withdrawal Rate (SWR).  The numbers give us great confidence if we build our nest egg to $1.8 million, we can achieve a sustainable income of $72k.  Our final numbers will likely adjust as we continue to get closer to our target date.  We will keep an eye on the market. We are entering a phase of the market where sequence risk has a higher likelihood of being a concern. There are several studies on sequence risk we will discuss in the future articles.

On the positive side of the graphs, there is a 97.8% probability our final balance will be greater than our starting balance.  Also a 95.5% chance we could have over $10 million dollars (Mrs. FoF comment: !!!).  That would be crazy, and we are not counting on this.  We spend so much time worried about the worst case and running out of money, we sometime lose sight of the positive side of the distribution curves.

Distribution of Final Investment Values at End of Life

We are just getting started with this tool and one of our future articles will look at several test scenarios for different case studies.  Can we improve our probability with different investment options?  How does this tool work for a younger person who has a longer time before retirement?  How do we use the tool for couples of different ages (like the FoFs!).

If you subscribe to the blog, we are planning to send out a limited number of copies of the Monte Carlo simulation spreadsheet for Beta testing.  If interested in Beta testing the spreadsheet, just subscribe below.  We will send out an invite email for the Beta testing to get some feedback on the tool.

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Notes on Random Market Data Generation in the Monte Carlo Simulation

Note: A  bug was found in the Simulation Tool where the average investment performance was fixed to 9.5% with a standard deviation of 8.9% for both pre and post retirement simulations.  This was roughly about 50/50 stock/bond performance using 50 years of historic data. 

Tool is now corrected (Version 8D1) so you can select the returns for pre and post retirement.

As with all investment data, past performance is not an indication of future performance.  Using 90-year historic data provides a decent basis covering many periods of good and bad performance, but there could be a case in the future that does not align to the historic returns and variation.

For market performance, the 90-year performance data for return and volatility (standard deviation) for the risk adjusted portfolios from Index Fund Advisors5 was used.   

Index Fund Advisors Portfolios with 90 Year Market Data

Investment Risk Portfolio is the rough weighting of stocks to bonds, a 10 would be roughly 10% stocks to 90% bonds.   The higher the stock ratio, the higher the average return but also the variation.   

The Monte Carlo simulation uses the inverse cumulative normal distribution function.  This simulates the annual inflation and market return for each year in the investment cycle based on the average historic return and volatility (standard deviation) of the investment or selected inflation.   Inflation is not allowed to be negative so limited to zero if simulation comes up with a random negative value.

It does not predict trending or future performance based on prior performance or mean reversion seen in the real markets.   Recent research also shows that using a normal distribution with a Monte Carlo simulation may overstate the risk of the portfolio.  A simulated 93.5% success rate may be equivalent to 100% success rate in the real world.7Derek Tharp wrote in his 2017 article “Does Monte Carlo Analysis Actually Overstate Tail Risk In Retirement Projections?”7

“… despite the common criticism that Monte Carlo analysis and normal distributions understate “fat tails”, when it comes to long-term retirement projections, typical Monte Carlo assumptions actually overstate extreme outcomes relative to historical returns due to the failure to account for mean reversion – yielding a material number of projections that are worse (or better) than any sequence that has actually occurred in history.”


References and Links

  1. Determining Withdrawal Rates Using Historical Data William Bengen, 1994
  2. Retirement Savings: Choosing a Withdrawal Rate That Is Sustainable   aka The Trinity Study,  Philip L. Cooley, Carl M. Hubbard and Daniel T. Walz  ,  1998 
  3. I’m Bill Bengen, and I first proposed the 4% safe withdrawal rate in 1994. Ask me anything! Reddit AMA Post from William Bengen, 2017, 
  4. The Trinity Study And Portfolio Success Rates (Updated To 2018) Wade Pfau, 2018 
  5. Portfolio Performance Data from Index Fund Advisor Portfolios 
  6. Historic Inflation Data 
  7. Does Monte Carlo Analysis Actually Overstate Tail Risk In Retirement Projections? , Derek Tharp, 2017 

If you subscribe to the blog, we are planning to send out a limited number of copies of the Monte Carlo simulation spreadsheet for Beta testing.  If interested in Beta testing the spreadsheet, just subscribe below.  We will send out an invite email for the Beta testing to get some feedback on the tool.

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